UNIT Plan SPH4U - WordPress.com

UNIT Plan SPH4U Wednesday, January 20, 2010 12:40 PM

Energy and Momentum SPh4U Overall Expectations By the end of this course, students will: C1. analyse, and propose ways to improve, technologies or procedures that apply principles related to energy and momentum, and assess the social and environmental impact of these technologies or procedures; C2. investigate, in qualitative and quantitative terms, through laboratory inquiry or computer simulation, the relationship between the laws of conservation of energy and conservation of momentum, and solve related problems; C3. demonstrate an understanding of work, energy, momentum, and the laws of conservation of energy and conservation of momentum, in one and two dimensions. Specific Expectations 201 Physics SPH4U C2.2 analyse, in qualitative and quantitative terms, the relationship between work and energy, using the work–energy theorem and the law of conservation of energy, and solve related problems in one and two dimensions [PR, AI] C2.3 use an inquiry process to analyse, in qualitative and quantitative terms, situations involving work, gravitational potential energy, kinetic energy, thermal energy, and elastic potential energy, in one and two dimensions (e.g., a block sliding along an inclined plane with friction; a cart rising and falling on a roller coaster track; an object, such as a mass attached to a spring pendulum, that undergoes simple harmonic motion), and use the law of conservation of energy to solve related problems [PR, AI] C2.4 conduct a laboratory inquiry or computer simulation to test the law of conservation of energy during energy transformations that involve gravitational potential energy, kinetic energy, thermal energy, and elastic potential energy (e.g., using a bouncing ball, a simple pendulum, a computer simulation of a bungee jump) [PR, AI] C2.5 analyse, in qualitative and quantitative terms, the relationships between mass, velocity, kinetic energy, momentum, and impulse for a system of objects moving in one and two dimensions (e.g., an off-centre collision of two masses on an air table, two carts recoiling from opposite ends of a released spring), and solve problems involving these concepts [PR, AI] C2.6 analyse, in qualitative and quantitative terms, elastic and inelastic collisions in one and two dimensions, using the laws of conservation of momentum and conservation of energy, and solve related problems [PR, AI] C2.7 conduct laboratory inquiries or computer D1.2 assess, on the basis of research, how simulations involving collisions and explosions technologies in one and two dimensions (e.g., interactions related to nuclear, thermal, or geothermal between masses on an air track, the collision of energy affect society and the environment two pucks on an air table, collisions between spheres of similar and different masses) to test D2.2 analyse, and solve problems relating the laws of conservation of momentum and to, conservation of energy [PR, AI] Newton’s law of universal gravitation and C3. Understanding Basic Concepts circular motion By the end of this course, students will: C3.1 describe and explain Hooke’s law, and explain the relationships between that law, work, and elastic potential energy in a system of objects C3.2 describe and explain the simple harmonic motion (SHM) of an object, and explain the relationship between SHM, Hooke’s law, and uniform circular motion C3.3 distinguish between elastic and inelastic collisions C3.4 explain the implications of the laws of

Physics II 4131U Page 1

Ref:

University of Colorado Cognitive dissonances

C3.4 explain the implications of the laws of conservation of energy and conservation of momentum with reference to mechanical systems (e.g., damped harmonic motion in shock absorbers, the impossibility of developing a perpetual motion machine) C3.5 explain how the laws of conservation of energy and conservation of momentum were used to predict the existence and properties of the neutrino


Unit 2 Grade 12

http://www.dsbn.edu.on.ca/Schools/eLearning/courses/sph4u/

Thursday, March 11, 2010 2:09 PM

Unit 2: Energy and Momentum Time: 20 hours

Unit Description This unit develops students’ understanding of work, energy, momentum, and conservation of energy and momentum. Through laboratory investigations and simulations, students analyse and solve problems involving energy and momentum using vectors, graphs, and free-body diagrams. Students analyse and describe the design and development of collision and impact-absorbing devices with respect to energy and momentum changes.

Unit Overview Chart

Unit 2: Energy and Momentum Chapter 4: Work and Energy

Section

Practice

Questions

4.1

1, 2, 3, 4, 5, 6.

5, 6, 7.

4.2

2, 4, 5, 6, 7.

2, 4, 6, 7, 8.

4.3

2, 3, 4, 5.

3, 4, 5.

4.4

2, 6, 4, 5, 11, 13, 14.

2, 3, 5, 6, 7, 10.

4.5

1, 3, 8, 9, 10, 11, 12, 17, 18, 24, 25.

5, 6, 7, 9, 10, 13, 15.

Review

10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25.

Chapter 5: Momentum and Collisions

Section

Practice

Questions

5.1

1, 2, 3, 7, 8, 10.

3, 5, 6, 7, 9, 10.

5.2

3, 4, 5, 6, 7.

5, 6, 7, 8, 10.

5.3

2, 10, 11, 12, 13, 14.

4, 5, 6.

5.4

3, 4, 5.

2, 3, 4.

Review

9, 10, 11, 12, 16, 17, 19, 20, 21.

Chapter 6: Gravitation and Celestial Mechanics Section

Practice

Questions

6.1

4, 6.

1, 2, 4, 6.

6.2

1, 2, 3, 4, 9.

4, 5, 7.

6.3

1, 2, 8, 9, 11.

4, 5, 6.

Review

4, 5, 7, 8, 10, 12, 15, 19.

Unit Review

9, 10, 12, 13, 14, 18, 21, 22, 23, 24, 25, 26, 27, 36, 38.


Discussion 2 Sunday, March 14, 2010 10:33 PM

Unit 2 Energy and Momentum Discussion 2

Introduction There are many practical applications of gravitational potential energy. For example, hydroelectric generating stations take advantage of the gravitational potential energy of water as it flows or falls from one level to a lower level. At many stations, huge dams store the water, allowing engineers to control the flow of water through pipes into turbines connected to the generators. One of the major problems with building large dams is that the local ecology is drastically and permanently affected. Large artificial lakes created by dams flood previously dry areas, destroying plant life and animal habitat. Bhutan, located east of Nepal and north of India (see Map), has found a method of generating hydroelectricity without large dams. This small country, with a land area only about 85% that of Nova Scotia, is located in the Himalayan Mountain region. It has very strict environmental laws to protect its great forests, which cover more than 70% of its land. Careful environmental policy is evident in the design of the Chukha electrical generating station, which generates power at a rate of 360 MW. (By comparison, the two huge Robert Beck generating stations and the adjacent pumping-generating station at Niagara Falls generate 1800 MW.) The design of this generating station along the Wong Chu River is called a "run-of-the-river scheme," as shown in Tunnel Diagram. In this design, a small dam diverts some of the river’s water flow into a large entrance tunnel, or head race, that is 6.0 km long. This tunnel, drilled through solid granite, is angled downward to the top of the generating station and takes advantage of the drop in elevation to convert the gravitational potential energy of the water into kinetic energy.

After the water falls through the turbines at the generating station, it flows through an exit tunnel, or tail race, rejoining the river 1.0 km downstream. Only about 5% of the electrical energy generated at the Chukha plant is used in Bhutan. The remainder is exported to India along 220-V transmission lines.


Instructions 1. On your own a. Starting with energy from the Sun, list all the energy transformations that occur in the production of electrical energy at the Chukha plant. b. What is a run-of-the-river generating station? 2. Research more about Bhutan’s generation of electrical energy, from the Internet or other appropriate publications, and report your findings to the Discussion 2 on course moodle . a. What are the sources of water in Bhutan? b. Describe how Bhutan is trying to preserve its environment while adapting to growing energy needs. 3. In Disscussion 2 Debate on course moodle: "That Canada should place more emphasis on developing environmentally friendly ways of generating electrical energy." 4. Submit your report on the discussion to the course moodle. The report should include a summary of the discussion, your views, and a conclusion to the debate.


Unit Assignment Sunday, March 14, 2010 10:30 PM

Unit 2 Energy and Momentum Assignment 1. A driver carelessly ignores the reduced speed limit of 40.0 km/h in a school zone and continues at 65 km/h. Assuming a good reaction time of 0.80 s, how many more metres will it take him to stop than if he had reduced his speed? Assume a constant emergency braking acceleration of –7.8 m/s 2 . 2. A robin of mass 110 g speeds up from 12.3 m/s to 15.4 m/s in level flight. Calculate how much work is done by the robin. 3. As you travel faster, more work is required to increase your speed by 15 m/s. (a) Use an example to compare two different speed increases of 15 m/s to demonstrate this. (b) How does this affect someone who is trying to set a new speed record for a land vehicle? 4. Two boxes each of mass 12 kg are raised 1.8 m to a shelf. The first one is lifted and the second is pushed up a smooth ramp. If the applied force on the second box is 48 N, calculate the angle between the ramp and the ground. 5. Two boxes are connected over a pulley and held at rest as shown below. Box A has a mass of 15 kg and box B has a mass of 12 kg. If the bottom of box A is originally 85 cm above the floor, with what speed will it contact the floor when the system is released? Use conservation of energy and assume that friction is negligible. 6. Two common and identical carts are used to perform an experiment. Cart A is pushed toward the stationary cart B with a velocity of 2.6 m/s. After the collision, cart A bounces back with a speed of 0.8 m/s and cart B moves of with a speed of 3.4 m/s. Why is this not possible? 7. During a free dance program in figure skating, Victor (m = 71 kg) glides at 2.1 m/s to a stationary Shae-Lynn (52 kg) and hangs on. How far will the pair slide after the “collision” if coefficient of kinetic friction mK between their skates and the ice is 0.052? 8. A spring with a force constant of 89 N/m is compressed 8.7 cm and placed between two stationary dynamics carts of mass 1.0 kg and 1.5 kg. If friction is negligible, determine the final speed of the more massive cart when the spring is released. 9. A dog named Pinky throws a pan of lasagna (m = 2.3 kg) at his friend Flowers. The pan hits and sticks to Flowers (m = 6.7 kg), who then slides a total of 2.2 m in 1.4 s. How fast was the lasagna moving before the impact? 10. A 1.8-kg block, initially at rest, slides down a frictionless ramp that is angled at 35º to the horizontal. At a point 0.45 m down the slope it collides with and sticks to a stationary block of mass 1.1 kg. The blocks then continue another 0.88 m down the ramp. How long does the whole event take? (For those of you wondering how a block is stationary on a frictionless ramp, it was projected up the ramp from below so it had no speed at the time of impact.) 11. Given that Fc = Fg for a satellite, show that the radius of orbit for an Earth satellite is 12. How much work is done against gravity to fire a 7.2 ´ 102 -kg weather monitor 120 km into the air? (rE = 6.38 ´ 10 6 m, ME = 5.98 ´ 10 24 kg) 13. How far above the surface of Earth does an object need to be so that it weighs half as much as it would normally? 14. The average radius of orbit for Jupiter is 7.78 × 10 11 m. Using CS = 3.355 × 10 18 m3 /s 2 , calculate the number of Earth years it will take for Jupiter to complete one orbit. 15. The International Space Station is in orbit about 420 km above the surface of Earth. Calculate how many minutes it would take for the ISS to complete one orbit. (rE = 6.38 ´ 10 6 m, ME = 5.98 ´ 10 24 kg)


Gizmos resources Thursday, March 18, 2010 11:43 AM

C: Energy and Momentum C.2: investigate, in qualitative and quantitative terms, through laboratory inquiry or computer simulation, the relationship between the laws of conservation of energy and conservation of momentum, and solve related problems; C.2.1: use appropriate terminology related to energy and momentum, including, but not limited to: work, work?energy theorem, kinetic energy, gravitational potential energy, elastic potential energy, thermal energy, impulse, change in momentum?impulse theorem, elastic collision, and inelastic collision 2D Collisions Air Track Ants on a Slant (Inclined Plane) Energy of a Pendulum Inclined Plane - Simple Machine Potential Energy on Shelves C.2.2: analyse, in qualitative and quantitative terms, the relationship between work and energy, using the work?energy theorem and the law of conservation of energy, and solve related problems in one and two dimensions Ants on a Slant (Inclined Plane) Inclined Plane - Simple Machine C.2.3: use an inquiry process to analyse, in qualitative and quantitative terms, situations involving work, gravitational potential energy, kinetic energy, thermal energy, and elastic potential energy, in one and two dimensions (e.g., a block sliding along an inclined plane with friction; a cart rising and falling on a roller coaster track; an object, such as a mass attached to a spring pendulum, that undergoes simple harmonic motion), and use the law of conservation of energy to solve related problems Inclined Plane - Simple Machine Inclined Plane - Sliding Objects Period of Mass on a Spring Period of a Pendulum Roller Coaster Physics C.2.5: analyse, in qualitative and quantitative terms, the relationships between mass, velocity, kinetic energy, momentum, and impulse for a system of objects moving in one and two dimensions (e.g., an offcentre collision of two masses on an air table, two carts recoiling from opposite ends of a released spring), and solve problems involving these concepts 2D Collisions Air Track C.2.6: analyse, in qualitative and quantitative terms, elastic and inelastic collisions in one and two dimensions, using the laws of conservation of momentum and conservation of energy, and solve related problems 2D Collisions Air Track C.2.7: conduct laboratory inquiries or computer simulations involving collisions and explosions in one and two dimensions (e.g., interactions between masses on an air track, the collision of two pucks on an air table, collisions between spheres of similar and different masses) to test the laws of conservation of momentum and conservation of energy 2D Collisions Air Track

C.3: demonstrate an understanding of work, energy, momentum, and the laws of conservation of energy and conservation of momentum, in one and two dimensions. C.3.1: describe and explain Hooke?s law, and explain the relationships between that law, work, and elastic potential energy in a system of objects Determining a Spring Constant C.3.3: distinguish between elastic and inelastic collisions 2D Collisions

D: Gravitational, Electric, and Magnetic Fields D.2: investigate, in qualitative and quantitative terms, gravitational, electric, and magnetic fields, and solve related problems; D.2.1: use appropriate terminology related to fields, including, but not limited to: forces, potential Physics II 4131U Page 7

D.2.1: use appropriate terminology related to fields, including, but not limited to: forces, potential energies, potential, and exchange particles Coulomb Force (Static) Energy of a Pendulum Potential Energy on Shelves D.2.3: analyse, and solve problems involving, electric force, field strength, potential energy, and potential as they apply to uniform and non-uniform electric fields (e.g., the fields produced by a parallel plate and by point charges) Coulomb Force (Static) D.2.5: conduct a laboratory inquiry or computer simulation to examine the behaviour of a particle in a field (e.g., test Coulomb?s law; replicate Millikan?s experiment or Rutherford?s scattering experiment; use a bubble or cloud chamber) Charge Launcher

D.3: demonstrate an understanding of the concepts, properties, principles, and laws related to gravitational, electric, and magnetic fields and their interactions with matter. D.3.2: compare and contrast the corresponding properties of gravitational, electric, and magnetic fields (e.g., the strength of each field; the relationship between charge in electric fields and mass in gravitational fields) Pith Ball Lab Pasted from


Ch 6 Sunday, March 14, 2010

Overview

Unit 2: Energy and Momentum Chapter 6: Gravitation and Celestial Mechanics Time: 20 hours Chapter 6: Gravitation and Celestial Mechanics Section

Practice

Questions

6.1

4, 6.

1, 2, 4, 6.

6.2

1, 2, 3, 4, 9.

4, 5, 7.

6.3

1, 2, 8, 9, 11.

4, 5, 6.

Review

4, 5, 7, 8, 10, 12, 15, 19.


Sec 6.1 Sunday, March 14, 2010 10:15 PM

Unit 2

Energy and Momentum

Chapter 6 Gravitation and Celestial Mechanics Section 1

Gravitational Fields

Overview Copy the following terms into your notebook. Define and give examples for each. gravitational field up

What's up? A direction opposite to the center of the earth or a comparable gravitational center.

Equations Add the following equations to your Physics Toolbox. You should be able to rearrange the equations to solve for the unknown. From the law of universal gravitation

From Newton's Second Law

simplified

Gravitational Fields Surface Gravity Planet

Actual

Earth = 1.00

Mercury

3.68

0.375

Venus

8.80

0.898

Earth

9.80

1.00

Mars

3.68

0.375

Jupiter

24.8

2.53

Saturn

10.4

1.06

Uranus

8.96

0.914

Neptune

11.2

1.14

Pluto

0.66

0.067

Try these Practice Problems from the Text (Nelson, Physics 12)

Practice Questions Chapter

Section

Questions

6

1

4, 6.

Section Questions Physics II 4131U Page 10

Section Questions Chapter

Section

Questions

6

1

1, 2, 4, 6.


Sec 6.1 Quick Quiz Sunday, March 14, 2010 10:16 PM

Chapter 6 Quick Quiz 1

Completion Complete each sentence or statement. 1.

The force of attraction between all objects with mass is called ____________________.

2.

A _________________________ exists in the space surrounding an object in which the force of gravity is exerted on objects.

3.

Using Earth as the centre of celestial objects is called the ____________________ model of the universe.

4.

The model which suggests that the planets revolve around the Sun is called the ____________________ model of the solar system.

5.

Earth traces out the shape of a conic as it orbits the sun. The Sun is located at one ____________________ of this shape.

6.

How can we say that g is constant near Earth’s surface when it actually depends on the distance from the centre of Earth?

7.

If the gravitational field strength at the surface of Venus is g, at what distance from the surface of Venus will it be 0.25g? State your answer in terms of the radius of Venus.

8.

If humans wish to colonize a planet with a larger gravitational field strength than Earth’s, what could they do to prepare for this venture?

Short Answer



Unit 2

Energy and Momentum


Orbits and Kepler's Laws

Overview Copy the following terms into your notebook. Define and give examples for each. Kepler's First Law of Planetary Motion Kepler's SecondLaw of Planetary Motion Kepler's Third Law of Planetary Motion

Equations Add the following equations to your Physics Toolbox. You should be able to rearrange the equations to solve for the unknown. This relationship was found through observation by Kepler. See Kepler's Third Law

A constant of proportionality is added, CS. Where S, is for Sun. Re-arranging.

we know this for an object moving in a circular path.

Since , then

, solving we find v. Substituting for v, where MS is mass of the sun.

Squaring

simplifying

re-arranging

substitution,

, for the sun


, for the sun in general, for any planet with a satellite.



Section

Questions

6

2

1, 2, 3, 4, 9.


Section

Questions

6

2

4, 5, 7.


Sec 6.2 Quick Test Sunday, March 14, 2010 10:20 PM



The _________________________ is the average distance from the planet to an orbiting satellite.

2.

Using Earth as the centre of celestial objects is called the ____________________ model of the universe.

3.

The model which suggests that the planets revolve around the Sun is called the ____________________ model of the solar system.

4.

Earth traces out the shape of a conic as it orbits the sun. The Sun is located at one ____________________ of this shape.

5.

Why is Jupiter sometimes referred to as a “meteor magnet”?

6.

What mathematical shape do satellites trace out as they orbit?

7.

A comet orbiting the Sun changes speed as it moves through its orbit. Sketch a diagram of the orbit and indicate where the comet is moving the fastest (label this F) and the slowest (label this S).

8.

Any comet that passes Earth is usually only visible for a short time (a few weeks). Why does it take so long (decades or centuries) before we see them again?

9.

Scientists have placed the Hubble Space Telescope (HST) in orbit around Earth. Why?

10.

Why can we not have a satellite in orbit 15 km above Earth’s surface?

11.

Why are most satellites equipped with small rockets that are controlled from Earth?

Short Answer



Unit 2

Energy and Momentum


Gravitational Potential Energy in General

Overview apo peri geo helio escape speed escape energy binding energy black hole event horizon singularity Schwartzschild radius

Many students have difficulty with this next section. To help you out, read this introduction carefully. To this point in time we have talked about the increase in gravitational potential energy as a change in height. Eg =mg h. That is, an increase in height is an increase in Eg.We set the zero Eg at an arbitrary height... the top of a table, the ground, etc. But what if an object is far into space where gravity decreases, by the inverse square law? At some point in space (infinity) there will be no Eg. We will now need to define define Eg = 0 at infinity. Hence as you approach an object from infinity you gain Eg. A graph of the Force required to hold an object r metres away from the Earth surface would look like this:

Recall that the area under a Force vs. displacement graph yields the work done. So for the following graph the work done is:

Note that the derivation of this equation requires calculus beyond the scope of this course.


Note that the derivation of this equation requires calculus beyond the scope of this course.

If r2 is at infinity then the first term become zero and we get:

or

That is,

As you can see, if r → ∞ then Eg → 0. The graph below shows Eg is in the fourth quadrant.

Equations Add the following equations to your Physics Toolbox. You should be able to rearrange the equations to solve for the unknown. Eg = mg h

gravitational energy, at infinity this is 0 (zero).


kinetic energy of a rocket

at infinity all the kinetic energy has become gravitational

substitution

solving for vesc, escape velocity. vesc = 2.98 × 104 m/s for all objects (notice that mass has been removed from the equation.)

Animations 1. Escape Speed (right click on movie and save target as...)



Section

Questions

6

3

1, 2, 8, 9, 11.


Section

Questions

6

3

4, 5, 6.





The minimum speed needed by an object on the surface of Earth to escape from Earth’s gravitational force is called the ____________________.

2.

The minimum kinetic energy needed by an object on the surface of Earth to escape from Earth’s gravitational force is called the ____________________.

3.

The additional kinetic energy needed by an object orbiting Earth to escape from Earth’s gravitational force is called the _________________________.

4.

A ____________________ is a small, very dense body with a gravitational field so strong that nothing can escape from it.

5.

The dense centre of a black hole is called a ____________________.

6.

The _________________________ is the surface of a black hole.

7.

The Schwartzschild radius is the distance from the centre of the singularity to the _________________________.


Ch 6 Review Sunday, March 14, 2010 10:26 PM

Unit 2

Energy and Momentum

Chapter 6 Gravitation and Celestial Mechanics Review

Summary This is a summary of concepts in a diagrammatic form.

Equation Development For each equation below you should be able to show it is defined or how it was derived. Also, you must be able to solve for any one variable given the remaining. Number

Equation

1 2

3 4

5 6

7

8

9

Key Terms • gravitational field

• Kepler's Laws

• escape speed

• escape energy

• binding energy

• black hole

• event horizon

• singularity

• Schartzschild Radius

•



Section

6

Review

Page

Questions 4, 5, 7, 8, 10, 12, 15, 19.


6

Review

4, 5, 7, 8, 10, 12, 15, 19.


Ch 6 PT1 Sunday, March 14, 2010 10:28 PM

Chapter 6 Practice Test 1

Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1.

2.

3.

4.

5.

6.

How far from the centre of Earth do you need to go for g to be reduced to 0.5 of its value on the surface of Earth? a.

0.41rE

d.

1.4rE

b.

0.50rE

e.

2.0rE

c.

0.71rE

A planet has twice Earth’s radius and twice Earth’s mass. The value of g on this planet would be a.

0.25g

d.

2g

b.

0.5g

e.

4g

c.

6g

The value of g on Saturn is 10.9 N/kg. The weight of a 2.5-kg mass on Saturn is a.

2.5 kg

d.

4.4 kg

b.

4.4 N

e.

27 N

c.

11 N

A 722-kg satellite is in circular orbit 7380 km above the surface of Earth (ME = 5.98 1024 kg). The gravitational force acting on the satellite is a. 7.33 N 1.52 103 N d. b.

5.29

109 N e.

c.

5.29

103 N

7.08

103 N

The mass of Neptune is 1.03 1026 kg. If g = 13.80 N/kg on the surface of Neptune, the radius of Neptune is a.

5.38

106 m d.

2.65 107 m

b.

6.38

106 m e.

not enough information

c.

2.23

107 m

The radius of Mercury is 2.57 106 m. If g = 3.52 N/kg on the surface of Mercury, the mass of Mercury is a.

3.49

1023 t


d.

3.49

1022 kg

7.

8.

9.

10.

11.

12.

13.

a.

3.49

1023 t

d.

3.49

1022 kg

b.

9.70

1023 t

e.

none of the above

c.

9.70

1023 kg

The Sun has a mass of 1.99 1030 kg. Jupiter has a mass of 1.90 1027 kg and a mean radius of orbit around the Sun of 7.78 108 km. The speed that Jupiter travels in its orbit around the Sun is a. 1.31 104 km/s d. 4.04 102 m/s b.

4.70

104 km/h

c.

4.13

105 m/s

1.28 104 m/s

e.

The Kepler’s third-law constant of proportionality for the Sun, CS, is 3.4 1018 m3/s2 . If Earth’s radius of orbit is doubled, then CS would become a. 4.2 1017 m3 /s2 d. 1.4 1019 m3/s2 b.

8.5

1017 m3 /s2

c.

3.4

1018 m3 /s2

e.

2.7

1019 m3 /s2

Kepler’s constant for the Sun is CS = 3.4 1018 m3 /s2 . The average period of orbit for Earth is 365.26 d. The average radius of Earth’s orbit is a. 7.7 107 km d. 1.5 1011 m b.

3.4

109 m

c.

1.8

1010 m

5.8 1016 m

e.

The average radius of orbit for Jupiter is 7.78 1011 m. Using CS = 3.355 1018 m3 /s2 , the period of orbit for Jupiter is a.

4.25

102 s

d.

4.25

1012 s

b.

3.75

108 s

e.

1.80

105 s

c.

1.43

1021 s

If the average radius of orbit for a satellite is doubled, the period will increase by a factor of a.

0.35

d.

2.0

b.

0.50

e.

2.8

c.

1.0

If the mass of Earth is 5.98 1024 kg and the radius is 6.38 106 m, the gravitational potential energy of a 2.2 103 -kg vehicle located on the surface of Earth is a. –1.4 104 J d. –2.2 1012 J b.

–2.2

104 J

c.

–1.4

1011 J

e.

If the mass of Earth is 5.98


0J

1024 kg and the radius is 6.38

106

m, the gravitational potential energy of a 1.2 103 -kg satellite located in an orbit 230 km above the surface of Earth is a. –1.1 104 J d. –9.0 1012 J

14.

15.

16.

17.

18.

b.

–7.2

1010 J e.

c.

–2.1

1012 J

–2.1

1015 J

Looking at the diagram above, which part of the orbit corresponds to the aphelion? a.

A

d.

D

b.

B

e.

none of the above

c.

C

Looking at the diagram above, in which part of the orbit does the planet have maximum kinetic energy? a.

A

d.

D

b.

B

e.

none of the above

c.

C

Looking at the diagram below, in which part of the orbit does the planet have zero kinetic energy? a.

A

d.

D

b.

B

e.

none of the above

c.

C

Looking at the diagram below, which part of the orbit corresponds to the perihelion? a.

A

d.

D

b.

B

e.

none of the above

c.

C

A satellite of mass m is in orbit around a planet of mass M at an altitude a above the planet’s surface. The radius of the planet is r. The speed of the satellite is a. d.


b.

e.

c.

19.

A satellite of mass m is in orbit around a planet of mass M at an altitude a above the planet’s surface. The radius of the planet is r. The total energy of the satellite is a. d.

b.

e.

c.

20.

The altitude of a geosynchronous satellite is a. 6.4 106 m d. 3.6 107 m b.

4.2

106 km e.

c.

3.6

106 m


4.2 107 m

Ch 6 PT2 Sunday, March 14, 2010 10:28 PM

Chapter 6 Practice Test 2

Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1.

2.

3.

4.

5.

6.

The force of gravity between two 4.0-kg objects that are 10.0 cm apart is a.

1.1

10–11 N d.

2.7 10–11 N

b.

1.1

10–7 N

2.7 10–8 N

c.

1.1

10–8 N

e.

How far above the surface of Earth do you need to go for g to be reduced to 0.5 of its value on the surface of Earth? a.

0.41rE

d.

1.4rE

b.

0.50rE

e.

2.0rE

c.

0.71rE

How far from the centre of Earth do you need to go for g to be reduced to 0.5 of its value on the surface of Earth? a.

0.41rE

d.

1.4rE

b.

0.50rE

e.

2.0rE

c.

0.71rE

The value of g on Saturn is 10.9 N/kg. The weight of a 2.5-kg mass on Saturn is a.

2.5 kg

d.

4.4 kg

b.

4.4 N

e.

27 N

c.

11 N

Earth’s mass is 5.98 1024 kg. Calculate the value of g at a point 4.8 105 km from the centre of Earth. a.

9.8

10–2 N/kg d.

1.7 103 N/kg

b.

8.3

105 N/kg

9.8

c.

1.7

10–3 N/kg

e.

10–5 N/kg

A 722-kg satellite is in circular orbit 7380 km above the surface of Earth (ME = 5.98 1024 kg). The gravitational force acting on the satellite is a. 7.33 N 1.52 103 N d. b.

5.29

109 N e.


7.08 103 N

7.

8.

9.

10.

11.

12.

b.

5.29

109 N e.

c.

5.29

103 N

7.08 103 N

The mass of Neptune is 1.03 1026 kg. If g = 13.80 N/kg on the surface of Neptune, the radius of Neptune is a. 5.38 106 m d. 2.65 107 m b.

6.38

106 m e.

c.

2.23

107 m


Kepler’s constant for the Sun is CS = 3.4 1018 m3/s2 . The average period of orbit for Earth is 365.26 d. The average radius of Earth’s orbit is a. 7.7 107 km d. 1.5 1011 m b.

3.4

109 m

c.

1.8

1010 m

e.

5.8

1016 m

The average radius of orbit for Jupiter is 7.78 1011 m. Using CS = 3.355 1018 m3 /s2 , the period of orbit for Jupiter is a.

4.25

102 s

d.

4.25

1012 s

b.

3.75

108 s

e.

1.80

105 s

c.

1.43

1021 s

If the average radius of orbit for a satellite is doubled, the period will increase by a factor of a.

0.35

d.

2.0

b.

0.50

e.

2.8

c.

1.0

If the period of orbit for a satellite increases by a factor of 2, the average radius of orbit will increase by a factor of a.

0.50

d.

1.6

b.

0.63

e.

2.0

c.

1.0

If the mass of Earth is 5.98 1024 kg and the radius is 6.38 106 m, the gravitational potential energy of a 1.2 103 -kg satellite located in an orbit 230 km above the surface of Earth is a. –1.1 104 J d. –9.0 1012 J b.

–7.2

1010 J e.

c.

–2.1

1012 J


–2.1

1015 J

13.

14.

15.

16.

17.

18.

Looking at the diagram above, in which part of the orbit is the planet moving the slowest? a.

A

d.

D

b.

B

e.

none of the above

c.

C

Looking at the diagram above, in which part of the orbit does the planet have maximum kinetic energy? a.

A

d.

D

b.

B

e.

none of the above

c.

C

Looking at the diagram above, in which part of the orbit does the planet have minimum kinetic energy? a.

A

d.

D

b.

B

e.

none of the above

c.

C

If an orbiting satellite has a total energy of –1.4 the binding energy is

1012 J, then

a.

–1.4

1012 J d.

–7.0

b.

+1.4

1012 J e.


c.

–2.8

1012 J

1011 J

The total energy of a 257-kg satellite in orbit at an altitude of 5.9 106 m above Earth’s surface (rE = 6.38 106 m, ME = 5.98 1024 kg) is a. –4.2 109 J d. –2.7 1010 J b.

–1.2

1010 J e.

c.

–1.6

1010 J

–5.4

The speed of a satellite in orbit 7.4 Earth is

1010 J

106 m from the centre of

a.

2.0 103 km/h

d.

5.4 107 km/h

b.

7.3 103 km/h

e.

dependent on the mass of the satellite

c.

2.6 104 km/h


km/h 19.

A satellite of mass m is in orbit around a planet of mass M at an altitude a above the planet’s surface. The radius of the planet is r. The speed of the satellite is a. d.

b.

e.

c.

20.

A satellite of mass m is in orbit around a planet of mass M at an altitude a above the planet’s surface. The radius of the planet is r. The total energy of the satellite is a. d.

b.

c.


e.

Ch 5 Thursday, March 11, 2010 3:25 PM

Unit 2: Energy and Momentum Chapter 5: Momentum and Collisions Time: 20 hours

Chapter 5: Momentum and Collisions Section

Practice

Questions

5.1

1, 2, 3, 7, 8, 10.

3, 5, 6, 7, 9, 10.

5.2

3, 4, 5, 6, 7.

5, 6, 7, 8, 10.

5.3

2, 10, 11, 12, 13, 14.

4, 5, 6.

5.4

3, 4, 5.

2, 3, 4.

Review

9, 10, 11, 12, 16, 17, 19, 20, 21.


Section 5.1 Thursday, March 11, 2010 3:29 PM

Unit 2

Energy and Momentum

Chapter 5 Momentum and Collisions Section 1

Momentum and Impulse

Overview Copy the following terms into your notebook. Define and give examples for each. linear momentum impulse

Equations Add the following equations to your Physics Toolbox. You should be able to rearrange the equations to solve for the unknown. linear momentum = mass x velocity linear momentum in the x-direction linear momentum in the y-direction the change in momentum (over a period of time) is due to an applied force... if you apply a force then the velocity will change and hence the the momentum changes. This can be determined by finding the area under a Force time graph.

Animations 1. momentum Introduction (right click on movie and save target as...) 2. Momenta of Objects in Collision (right click on movie and save target as...) 3. Impulse Basic Concepts (right click on movie and save target as...) 4. Impulse Basic Concepts (right click on movie and save target as...)




Section

Questions

5

1

1, 2, 3, 7, 8, 10.


Section

Questions

5

1

3, 5, 6, 7, 9, 10.


Section 5.1 Quick quiz Sunday, March 14, 2010

Chapter 5 Section 1 Quick Quiz Completion Complete each sentence or statement. 1.

Linear momentum depends on both the ____________________ and the velocity of an object.

2.

A rotating object possesses ____________________ momentum.

3.

The change in momentum of an object is called the ____________________.

4.

The proper unit for momentum is ____________________ and the proper unit for impulse is ____________________.

5.

If the net force acting on a system of interacting objects is zero, then linear momentum is ____________________.

6.

Momentum is conserved in a system unless a(n) ____________________ net force acts on the system.

7.

Why is “follow-through” so important for maximizing speeds in sporting activities?

8.

A 57-g tennis ball travelling at 28 m/s is hit straight back with the same velocity. Determine the average force on the tennis ball if the racket is in contact with the ball for 4.9 ms.

9.

A blazing spike of a 0.290-kg volleyball is blocked at the net. It is originally travelling at 18.3 m/s and bounces straight back at 14.9 m/s after being in contact with the blockers arms for a total of 18.2 ms. What average force did the blocker exert on the ball?

10.

A raw egg dropped from a height of 1.0 m will break if it lands on a concrete floor, but not if it lands on a thin sponge, even though it experiences the same impulse from each type of drop. Explain why.

Short Answer



Sect 5.2 Sunday, March 14, 2010

Unit 2

Energy and Momentum


Conservation of Momentum in One Dimension

Overview Copy the following terms into your notebook. Define and give examples for each. Law of Conservation of Momentum

Elastic Collision in One Dimension In the diagrams below... (a) shows two gliders moving towards each other on a "frictionless" track. (b) shows the glides at the moment they collide. (c) shows the gliders moving apart after the collision

(a)

(b)

(c)

Equations Add the following equations to your Physics Toolbox. You should be able to rearrange the equations to solve for the unknown. total momentum before is equal to the total momentum after (note: p' is referred to as "p prime" and means "momentum after") as above when two objects have a elastic collision the change in momentum of the first object is equal and opposite to the change momentum of the second object. as above

Animations 1. Conservation of Momentum Basic Concepts (right click on movie and save target as...) 2. Collision between Moving Mass and Equal Stationary Mass (right click on movie and save target as...) 3. Collision between Moving Mass and Stationary Smaller Mass (right click on movie and save target as...) 4. Conservation Momentum Newton's Third Law (right click on movie and save target as...) 5. Conservation Momentum Application (right click on movie and save target as...)


Practice Questions



Section

Questions

5

2

3, 4, 5, 6, 7.


Section

Questions

5

2

5, 6, 7, 8, 10.




If the net force acting on a system of interacting objects is zero, then linear momentum is ____________________.

2.


3.

If a person is standing in a stationary canoe, the total momentum of the person–canoe system is zero. If he walks forward and then stops, both the canoe and person are moving. (a) Is momentum conserved? (b) What force is acting on the system?

4.

The captain of a small barge notices the front corner of the boat is on a collision course with a edge of a small pier. What could he ask the passengers to do to help him avoid a collision?

5.

As a car coasts down a hill, it gains momentum. State the system that contains the car and where momentum is conserved. Where does the momentum gained by the car come from?

6.

A 25-kg bag of cement thrown at 2.5 m/s [E] is caught by a person sliding 1.8 m/s [E] on a frictionless surface. If the velocity after the catch is 2.0 m/s, calculate the mass of the person.

7.

Why do you feel the “kick back” of a gun?

8.

At a shooting range for hand guns, you often observe the shooters bend their elbows and allow the gun to move up. Why?

9.

What advice could be useful to a person who drives a car and habitually cuts in front of large trucks on the highway? Use your knowledge or physics and collisions in your answer.

Short Answer


Section 5.3 Sunday, March 14, 2010 9:54 PM

Unit 2

Energy and Momentum


Elastic and Inelastic Collisions

Overview Copy the following terms into your notebook. Define and give examples for each. elastic collision inelastic collision

Solving Collision Problems Elastic Collisions (superballs colliding... objects collide and no energy is lost... objects bounce off "perfectly intact")

In this case energy and momentum are conserved. That is,

and

Use these two equations to solve the problems:

and Inelastic Collisions

In this case only momentum are conserved. That is,

(tennis balls colliding...objects collide and objects "spring" back into shape but slowly) Use this equation to solve the problems:

Completely Inelastic Collisions

(putty balls colliding.. objects collide and stick together)

In this case only momentum are conserved. And the kinetic energy before is greater than the kinetic energy after. That is,

but

Use this equation to solve the problems:

Bounce Chart


Exactly what happens to these balls as they stretch and squeeze depends on what the ball is made of. Suppose you drop a ball of putty. Rather than bouncing, it hits the floor and flattens. All of the organized motion of the falling ball becomes the random motion of jiggling molecules. The random motion of jiggling molecules is a measure of "thermal energy." The putty gets warmer, but it doesn't bounce. Putty is completely inelastic -- it doesn't return to its original shape. The steel ball returns to its original shape almost a quickly at it was deformed. It is 98% elastic. This chart shows how much of the original height is re-gained by various types of balls.

Equations Add the following equations to your Physics Toolbox. You should be able to rearrange the equations to solve for the unknown.

Animations/Simulations 1. This applet: Elastic and Inelastic Collisions allows you to "play" with colliding balls of various elasticities. Try it out.



Section

Questions

5

3

2, 10, 11, 12, 13, 14.


Section

Questions

5

3

4, 5, 6.



Name: Chapter 5 Section 3 Quick Quiz



2.

A ball is dropped and bounces back to its original height. The collision between the ball and the ground was ____________________.

3.

A ball is dropped and bounces back to 90% of its original height. The collision between the ball and the ground was ____________________.

4.

If you squeeze a rubber ball and it springs back slowly, a collision involving that ball will most likely be ____________________.

5.

If you squeeze a rubber ball and it springs back quickly, a collision involving that ball will most likely be ____________________.

6.

Give two observations that would enable you to conclude that the bounce of a superball is not a completely elastic collision.

7.

Why are perfectly elastic collisions so unlikely?

8.

A 0.25-kg snowball moving at 15 m/s [E] collides and sticks with a 1.9-kg toy truck travelling at 2.8 m/s [W]. Neglecting friction, calculate the velocity of the snowball–truck system after the collision.

9.

A 25-kg bag of cement thrown at 2.5 m/s [E] is caught by a person sliding 1.8 m/s [E] on a frictionless surface. If the velocity after the catch is 2.0 m/s, calculate the mass of the person.

10.

Describe two features of a hockey helmet that help minimize head injury from a slapshot that hits the helmet.

11.

A common novelty sold at many stores consists of five steel balls suspended in a row as shown below. When one is pulled back and released, what happens and why? The collisions between the balls are nearly elastic.

Short Answer


nearly elastic.

12.

How is an inelastic collision different than a completely inelastic collision?


Collision Applet Sunday, March 14, 2010 10:01 PM

Unit 2

Energy and Momentum


Elastic and Inelastic Collisions

Conservation of Momentum (1D) See below for Controlling the Motion Elastic Collisions (superballs colliding... objects collide and no energy is lost... objects bounce off "perfectly intact")

Set the Java Applet with following initial conditions: • m1 = 5 kg • m2 = 5 kg • v1 = 40 m/s • v2 = -40 m/s • restitution = 1

Inelastic Collisions (tennis balls colliding...objects collide and objects "spring" back into shape slowly)

• • • • •

m1 = 5 kg m2 = 5 kg v1 = 40 m/s v2 = -40 m/s restitution = 0.5

Completely Inelastic Collisions (putty balls colliding.. objects collide and stick together)

• • • • •

m1 = 5 kg m2 = 5 kg v1 = 40 m/s v2 = -40 m/s restitution = 0

Now experiment with the setting... What happens to the Centre of Mass is you change the value of one mass?

Can you predict the velocity of the centre of mass given: • m1 = 10 kg • m2 = 5 kg • v1 = 20 m/s • v2 = -40 m/s • restitution = 1 What happens when you change the Frame of Reference?

Introduction to Applet Newton's law of motion look the same to all observers in inertial frames of reference. It is equally true that if momentum is conserved in one inertial reference frame, it is conserved in all inertial frames. This java applet apply the above concept to one dimensional collision problem.

Objects Two circular objects are confined to move in one dimension (between two gray blocks). Their relative velocities are shown immediately above. The Centre of Mass (CM) of the system is represented by an X. The relative velocity of the CM is shown immediately above.

Controls The properties the objects and actions can be control using mouse controls. Click the start button to run the animation. Click the mouse button in the grey area to pause. Click it again to resume the animation. While the animation is suspended: Click near the yellow arrow of the velocity vector and drag it left/right to change the initial velocity. Click and drag at the center of the circle to move it : drag the object left ←→ right. Click right mouse button within a circle to increase mass by one unit. Physics II 4131U Page 42

Click and drag at the center of the circle to move it : drag the object left ←→ right. Click right mouse button within a circle to increase mass by one unit. Click left mouse button within a circle to decrease mass one unit. Click Reset to reset most parameters to default values.

Restitution - Elasticity restitution is the coefficient of restitution

For elastic collision restitution =1., for perfectly inelastic collision restitution =0.

Frames of Reference (advanced) You can select different frame of reference to view the relative motion of all the objects. lab is a laboratory inertial frame. mass1 (m1), mass2 (m2) and Centre of Mass (CM) are frame of reference with respect to

Pasted from



Unit 2

Energy and Momentum


Conservation of Momentum in Two Dimensions

Animations 1. Elastic Collision Between Masses in 2D Try these Practice Problems from the Text (Nelson, Physics 12)


Section

Questions

5

4

3, 4, 5.


Section

Questions

5

4

2, 3, 4.


Sec 5 Review Sunday, March 14, 2010 10:08 PM

Unit 2

Energy and Momentum

Chapter 5 Momentum and Collisions Review

Summary This is a summary of concepts in a diagrammatic form.

Equation Development For each equation below you should be able to show it is defined or how it was derived. Also, you must be able to solve for any one variable given the remaining.

Number

Equation

1 2 3

4 5 6 7

8 9

10

Key Terms • linear momentum • impulse • Law of Conservation of Momentum

• elastic collision • inelastic collision



Section

5

Review

Page

Questions 9, 10, 11, 12, 16, 17, 19, 20, 21.


Summary of concepts Sunday, March 14, 2010 10:12 PM

Elastic Collision in One Dimension In the diagrams below... (a) shows two gliders moving towards each other on a "frictionless" track. (b) shows the glides at the moment they collide. (c) shows the gliders moving apart after the collision

(a)

(b)

(c)

Inelastic Collision in One Dimension In the diagram below....

Initially the football players are moving towards each other. When they collide they may: 1. bounce off each other... but energy is lost through the movement of bones, muscles, legs and the denting of equipment. This is called an inelastic collision 2. "stick" together via the grasping of hands. This is a completely inelastic collision.

Elastic Collision in Two Dimensions Before

After



Chap 5 PT1 Sunday, March 14, 2010 10:09 PM

Chapter 5 Practice Test 1 Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1.

2.

3.

4.

5.

A net force of 12 N changes the momentum of a 250-g ball by 3.7 kg m/s. The force acts for a.

0.31 s

d.

3.2 s

b.

0.81 s

e.

44 s

c.

1.2 s

A 2200 kg car starts from rest and speeds up to 12 m/s in 5.2 s. The net force acting on the car is 102 N d.

a.

1.8

b.

4.2 102 N e.

c.

1.1

103 N

5.1

1.4 105 N

104 N

A car with a mass of 1800 kg slows from 42 km/h [E] to 28 km/h [E]. The impulse from the brakes is a.

2.5

104 N s [E]

d.

2.1

104 N s [W]

b.

2.5

104 N s [W] e.

7.0

103 N s [W]

c.

2.1 104 N s [E]

A 1.5-kg bird is flying at a velocity of 18 m/s [22º above the horizontal]. The vertical component of its momentum is a. 10 m/s [up] (2 d. 17 m/s [up] significant digits) b.

6.7 kg m/s [up]

c.

25 kg m/s [up]

e.

none of the above

A 1.5-kg bird is flying west at a velocity of 18 m/s [22º above the horizontal]. The horizontal component of its momentum is a. 10 m/s [W] (2 d. 17 m/s [W] significant digits) b.

6.7 kg m/s [W]

c.

25 kg m/s [W]


e.

17 kg m/s [E]

6.

7.

8.

9.

10.

A person jumps from an airplane and reaches terminal speed. a.

The momentum of the jumper is constant because there is no external net force.

b.

The momentum of the person–Earth system is not conserved because of air friction.

c.

When the chute is opened, the force disrupts the conservation of momentum of the person– Earth system.

d.

two of A, B, and C are correct

e.

all of A, B, and C are correct

An arrow slows down from 43 m/s to 28 m/s as it passes through an apple. If the 493-g apple was originally at rest and sped up to 0.44 m/s, the mass of the arrow is a. 5.0 g d. 29 g b.

7.7 g

c.

14 g

e.

7.7 kg

A boy throws a 15-kg ball at 4.7 m/s to a 65-kg girl who is stationary and standing on a skateboard. After catching the ball, the girl is travelling at a. 0 m/s d. 3.2 m/s

b.

0.88 m/s e.

c.

1.1 m/s

4.7 m/s

A 55-kg person carrying a 5.0-kg ball slides along a horizontal frictionless surface. He tosses the ball forward. a. His path will not change. b.

The ball will have a smaller angle from the original path than he will.

c.

His speed does not change.

d.

He speeds up.

e.

He will most likely stop moving forward.

A moving curling stone, A, collides head on with a stationary stone, B. Both stones are of identical mass. If friction is negligible during this linear elastic collision, a. stone A will slow down b.

after the collision, the momentum of stone B will be less than that of stone A

c.

both stones will come to rest shortly after the collision

d.

after the collision, the kinetic energy of the stone B will be less than that of stone A

e.

after the collision, stone A will have a speed of zero


e. of zero 11.

12.

13.

14.

15.

16.

If an arrow’s mass is doubled and the speed is halved, the momentum is changed by a factor of a.

0.25

d.

2

b.

0.5

e.

4

c.

1

A car (of constant mass) doubles its kinetic energy while driving down a hill sloped at 45º. The factor by which its momentum changes is a. 1 d. 2.8 b.

1.4

c.

2

e.

4

A ball rolling down a hill doubles its speed but reduces its gravitational energy to one-fifth its starting value. The factor by which its momentum changes is a. 0.4 d. 2 b.

1

c.

1.4

e.

10

A ball rolling down a hill doubles its momentum but reduces its gravitational energy to one-third its starting value. The factor by which its kinetic energy changes is a. 0.66 d. 4 b.

1

c.

2

e.

6

A 72-kg girl on a skateboard doubles her kinetic energy coasting down a hill. a.

Momentum is conserved.

b.

The increase in kinetic energy is offset by a decrease in momentum.

c.

The momentum will also double.

d.

Her momentum does not change.

e.

none of the above

A two-dimensional collision occurs as shown below.


16.

Which vector below most closely represents the new velocity of P?

17.

18.

19.

a.

A

d.

D

b.

B

e.

E

c.

C

To compare the kinetic energies of two objects, you must know a.

their masses

d.

the forces acting on them

b.

their velocities

e.

the work done to stop each of them

c.

their momenta

When you catch a fast-moving baseball, your hand hurts less if you move it in the direction of the ball because a.

the ball changes momentum more slowly

b.

the force applied is smaller

c.

you decrease the impulse required to stop the ball

d.

two of A, B, and C

e.

all of A, B, and C

When a baseball bounces on the ground a. momentum is conserved in the Earth–ball system b.

the impulse is the same as if the baseball landed without bouncing

c.

it leaves the surface with the same speed that it impacted the surface with

d.

kinetic energy is imparted to the ground

e.

the force applied by the surface is smaller than if it didn't bounce


20.

Without knowing any other information than is given in the diagram below, which deductions could be true? a.

The eastbound car was travelling faster.

b.

The northbound car was lighter.

c.

Both cars had the same speed.

d.

two of A, B, and C

e.

all of A, B, and C


Chap5 PT2 Sunday, March 14, 2010 10:10 PM

Chapter 5 Practice Test 2 Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1.

2.

3.

4.

5.

A 5.0-kg cat travelling at 1.3 m/s [E] has a momentum of a. 6.5 m/s [E] d. 3.8 m/s [W] b.

6.5 m/s [W] e.

c.

3.8 m/s [E]

none of the above

During collisions, it is often acceptable to ignore the force of gravity on an object. This is because a.

the time the other forces act is so short that we can ignore the force of gravity

b.

the force of gravity is always acting on the object and we only consider change

c.

the object may be in space and the gravitational force does not exist

d.

the collision is often perpendicular to the force of gravity, so Fg does not play a role

e.

the force of gravity is insignificant compared to the other forces acting on the object

A 2200 kg car starts from rest and speeds up to 12 m/s in 5.2 s. The net force acting on the car is a.

1.8

102 N d.

5.1

103 N

b.

4.2

102 N e.

1.4

105 N

c.

1.1

104 N

A 1.5-kg bird is flying at a velocity of 18 m/s [22º above the horizontal]. The vertical component of its momentum is a.

10 m/s [up] (2 significant digits)

d.

17 m/s [up]

b.

6.7 kg m/s [up]

e.

none of the above

c.

25 kg m/s [up]

A shell is fired from a gun mounted on a battleship. Which of the following statement is NOT true? a.

There will be a force to push the boat in the opposite


6.

7.

8.

9.

10.

a.

There will be a force to push the boat in the opposite direction of the shell.

b.

The recoil spring on the barrel is to minimize the force on the deck of the ship.

c.

Neglecting fluid friction, the momentum of the boat and shell have the same magnitude.

d.

To calculate the speed of the boat we would need to know the recoil length of the gun.

e.

A larger mass of shell will increase the recoil force felt by the ship.

An arrow slows down from 43 m/s to 28 m/s as it passes through an apple. If the 493-g apple was originally at rest and sped up to 0.44 m/s, the mass of the arrow is a. 5.0 g d. 29 g b.

7.7 g

c.

14 g

e.

7.7 kg

A boy throws a 15-kg ball at 4.7 m/s to a 65-kg girl who is stationary and standing on a skateboard. After catching the ball, the girl is travelling at a. 0 m/s d. 3.2 m/s b.

0.88 m/s e.

c.

1.1 m/s

4.7 m/s

A goalie standing on a frictionless surface catches a 270.0-g puck travelling at 95.0 km/h. After catching the puck, the goalie is moving at 8.90 cm/s. The mass of the goalie (including equipment) is a. 75.2 kg d. 84.2 kg

b.

79.8 kg e.

c.

80.1 kg

91.7 kg

A 55-kg person carrying a 5.0-kg ball slides along a horizontal frictionless surface. He tosses the ball forward. a.

His path will not change.

b.

The ball will have a smaller angle from the original path than he will.

c.

His speed does not change.

d.

He speeds up.

e.

He will most likely stop moving forward.

A moving curling stone, A, collides head on with a stationary stone, B. Both stones are of identical mass. If friction is negligible during this linear elastic collision, a. stone A will slow down b.

after the collision, the momentum of stone B will be less than that of stone A

c.



11.

12.

13.

14.

15.

16.

c.


d.

after the collision, the kinetic energy of the stone B will be less than that of stone A

e.

after the collision, stone A will have a speed of zero

If an arrow’s mass is doubled and the speed is halved, the momentum is changed by a factor of a.

0.25

d.

2

b.

0.5

e.

4

c.

1

A car (of constant mass) doubles its speed while driving up a hill sloped at 45º. The factor by which its momentum changes is a.

0

d.

3

b.

1

e.

4

c.

2

A ball rolling down a hill doubles its speed but reduces its gravitational energy to one-fifth its starting value. The factor by which its momentum changes is a. 0.4 d. 2 b.

1

c.

1.4

e.

10

A 72-kg girl on a skateboard doubles her kinetic energy coasting down a hill. a.

Momentum is conserved.

b.

The increase in kinetic energy is offset by a decrease in momentum.

c.

The momentum will also double.

d.

Her momentum does not change.

e.

none of the above

A sabotaged curling stone explodes into three pieces as it travels across the ice. Neglecting the force of friction, a.

all three pieces will travel at the same speed

b.

the magnitudes of the momenta for each piece will be the same

c.

an external net force had to act on the stone to accelerate the three pieces

d.

the components perpendicular to the original motion must add up to zero

e.

momentum is not conserved because of the small explosive charge

To compare the kinetic energies of two objects, you must know a. their masses d. the forces acting on them

b.

their


e.

the work done to stop each of

17.

18.

19.

20.

b.

their velocities

c.

their momenta

e.

the work done to stop each of them

When you catch a fast-moving baseball, your hand hurts less if you move it in the direction of the ball because a.

the ball changes momentum more slowly

b.

the force applied is smaller

c.

you decrease the impulse required to stop the ball

d.

two of A, B, and C

e.

all of A, B, and C

A gun is mounted on a wooden plank. The plank is stationary and is mounted on frictionless wheels. A heavy wooden block is set in front of the gun, and the gun is fired into the wooden block, which then slows to a stop due to friction between the block and the plank. a. The plank does not move. b.

Momentum is not conserved because of the frictional force.

c.

The speed of the plank is zero immediately after the collision between the bullet and block.

d.

The plank will have shifted position relative to its starting point.

e.

Kinetic energy is conserved because the speed of the system is zero before and after the collision.

The collision time between a bullet and a block of wood is best measured in a.

nanoseconds

d.

seconds

b.

microseconds

e.

hours

c.

milliseconds

Without knowing any other information than is given in the diagram below, which deductions could be true? a.

The eastbound car was travelling faster.

b.

The northbound car was lighter.

c.

Both cars had the same speed.

d.

two of A, B, and C


e.

all of A, B, and C


Ch 4 Thursday, March 11, 2010 3:22 PM

Chapter 4: Work and Energy Time: 20 hours Chapter 4: Work and Energy Section

Practice

Questions

4.1

1, 2, 3, 4, 5, 6.

5, 6, 7.

4.2

2, 4, 5, 6, 7.

2, 4, 6, 7, 8.

4.3

2, 3, 4, 5.

3, 4, 5.

4.4

2, 6, 4, 5, 11, 13, 14.

2, 3, 5, 6, 7, 10.

4.5

1, 3, 8, 9, 10, 11, 12, 17, 18, 24, 25.

5, 6, 7, 9, 10, 13, 15.

Review

10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25.


Prac. Test 4.2 Thursday, March 11, 2010 3:27 PM

Name:

Modified True/False Indicate whether the sentence or statement is true or false. If false, change the identified word or phrase to make the sentence or statement true. 1.

More work is done to lift a 2.00-kg object a distance of 1.00 m at a constant velocity than to push a 1.00-kg block a distance of 1.00 m with a force of 19.6 N. ______________________________

2.

The maximum work a force can do on an object occurs when the force is parallel to the direction of motion. _________________________

3.

To raise a 2.3-kg mass from its resting place on a table, more work is done by lifting it diagonally than lifting it straight up. ___________________________________

4.

A car speeds up as it descends a hill, gaining gravitational potential energy. _________________________

5.

Hooke’s law is true for all possible values of x for a real spring. _________________________

6.

In which situation is work not done? a. a frozen turkey is carried upstairs

Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.

7.

8.

b.

a frozen turkey is carried on level ground

c.

a frozen turkey is dropped

d.

a frozen turkey is carried downstairs

e.

a frozen turkey is fired from a cannon

Which of the following is NOT a unit of energy? a. J d. Nm b.

W/s

c.

kg m2 /s2

e.

kW h

The kinetic energy of a 24-kg dog running at 22 km/h is


8.

9.

10.

11.

12.

13.

14.

The kinetic energy of a 24-kg dog running at 22 km/h is a. 4.5 102 J d. 2.6 102 J b.

5.8 103 J e.

c.

1.2 104 J

73 J

A car slows down as it descends a hill. Which of the following is true? a.

the gravitational potential energy decreases

b.

the kinetic energy increases

c.

heat is produced by friction

d.

two of A, B, and C are correct

e.

all of A, B, and C are correct

A student has 474 J of gravitational energy while standing on a stool 0.84 m above the ground. The mass of the student is a. d. 40 kg (to two significant 5.8 102 digits) kg b.

48 kg

c.

58 kg

e.

60 kg (to two significant digits)

A 0.25-kg apple is gently hung from a spring that stretches 4.6 cm. The force constant of the spring is a.

0.054 N/m d.

53 N/m

b.

6.1 N/m

180 N/m

c.

18 N/m

e.

A spring with force constant 87 N/m is set into simple harmonic motion when a 350-g mass is attached to it. The period is a. 0.40 s d. 25 s

b.

3.1 s

c.

13 s

e.

99 s

A spring-powered SHM oscillator vibrates with a period of 0.29 s. If the force constant of the spring is 180 N/m, the mass used is a. 0.38 kg d. 2.4 kg b.

0.77 kg e.

c.

1.3 kg

2.6 kg

If the period of vibration of a SHM oscillator increases a. the mass might have decreased b.

the spring constant might have decreased

c.

the frequency also increases

d.

two of A, B, and C

e.

all of A, B, and C


e. 15.

16.

17.

18.

19.

20.

all of A, B, and C

If the mass of a car is doubled and its speed is cut in half, then the kinetic energy changes by a factor of

a.

0.25

d.

2

b.

0.5

e.

4

c.

1

A bird flying at a height of 12 m doubles its speed as it descends to a height of 6.0 m. The kinetic energy has changed by a factor of a. 0.25 d. 2

b.

0.5

c.

1

e.

4

A person running in a race has to pick up a mass equal to her own mass. Assuming she can still do the same amount of work, her speed will be changed by a factor of a. 0.25 d. 1 b.

0.50

c.

0.71

e.

2

A person runs at a constant speed up a slope that is angled at 12 to the horizontal. At one point, he is 3.2 m vertically above the bottom of the hill. To double the gravitational energy compared to the bottom of the hill, the runner must run an additional

a.

0.66 m up the slope

d.

6.4 m up the slope

b.

1.6 m up the slope

e.

15 m up the slope

c.

3.2 m up the slope

You want to ride a bicycle to the house shown below. Neglecting friction, at which point should you start in order to use the least amount of work to get there? a. A d. D b.

B

c.

C

e.

E

You want to ride a bicycle to the house shown below. Neglecting friction, at which point should you start in order to use the most amount of work to get there?


order to use the most amount of work to get there? a. A d. D b.

B

c.

C


e.

E

Prac. Test 4.1 Thursday, March 11, 2010 3:26 PM

Name:

Modified True/False Indicate whether the sentence or statement is true or false. If false, change the identified word or phrase to make the sentence or statement true. 1.

Work is done when the force and the displacement are in the same direction. _________________________

2.

Kinetic energy is a vector quantity. _________________________

3.

If you raise an object above your head and then set it on a table, you do the same work as if you only lifted the object onto the table. ______________________________

4.

All of the waste energy of a lawn mower is sound. _________________________

5.

Hooke’s law is true for all possible values of x for a real spring. _________________________

6.

Which of the following is not a unit of energy? a. J d. Ws

Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.

b. c. 7.

8.

e. Nm

A person picks up a 1.00-kg box of macaroni from off the shelf and lowers it 0.77 m into a shopping cart. The work done on the macaroni by Earth is a. 0J d. 7.5 J b.

0.77 J

c.

–0.77 J

e.

–7.5 J

Which of the following is NOT a unit of energy? a. J d. Nm b.

W/s

c.

kg m2 /s2


e.

kW h

c. 9.

10.

11.

12.

13.

14.

kg m2 /s2

A 75-kg parachutist jumps from a plane at a height of 1.2 km. At the instant he leaves the plane, his gravitational potential energy compared to the plane is a. 8.8 102 J d. –8.8 105 J b.

–8.8

c.

8.8

103 J e.

0J

105 J

A student has 474 J of gravitational energy while standing on a stool 0.84 m above the ground. The mass of the student is a. d. 40 kg (to two significant 5.8 102 digits) kg b.

48 kg

c.

58 kg

e.

60 kg (to two significant digits)

In the picture of a roller coaster track shown below, the point where the roller coaster car would be travelling the fastest, under negligible friction is a. A d. D b.

B

c.

C

e.

E

A 19.1-kg curling stone travels 28.8 m against a frictional force of 8.22 N. The thermal energy produced is a.

184 J

d.

237 J

b.

237 N

e.


c.

362 J

Rubbing your hands together can quickly produce 45 J of thermal energy. If it is done with an average frictional force of 8.4 N, the distance your hands have slid past each other is a. 49 m d. 3.7 m b.

5.4 m

c.

4.5 m

e.

1.2 m

A 0.25-kg apple is gently hung from a spring that stretches


14.

15.

16.

17.

18.

19.

A 0.25-kg apple is gently hung from a spring that stretches 4.6 cm. The force constant of the spring is a.

0.054 N/m d.

53 N/m

b.

6.1 N/m

180 N/m

c.

18 N/m

e.

A spring-powered SHM oscillator vibrates with a period of 0.29 s. If the force constant of the spring is 180 N/m, the mass used is a. 0.38 kg d. 2.4 kg b.

0.77 kg e.

c.

1.3 kg

2.6 kg

As the mass of a SHM oscillator increases a. the period of vibration increases b.

a larger spring constant would be required to prevent a change in the period

c.

the frequency is inversely proportional to the mass

d.

two of A, B, and C

e.

all of A, B, and C

If the period of vibration of a SHM oscillator increases a. the mass might have decreased b.

the spring constant might have decreased

c.

the frequency also increases

d.

two of A, B, and C

e.

all of A, B, and C

If the mass of a car is doubled and its speed is cut in half, then the kinetic energy changes by a factor of a.

0.25

d.

2

b.

0.5

e.

4

c.

1

A race is set up with five balls placed at the top of the five ramps shown below and released at the same instant. Each


19.

ramps shown below and released at the same instant. Each ramp drops the same vertical height. The ramp that will allow the ball to arrive at the bottom first is a. A d. D

20.

b.

B

c.

C

e.

E

You want to ride a bicycle to the house shown below. Neglecting friction, at which point should you start in order to use the least amount of work to get there? a. A d. D b.

B

c.

C


e.

E

Review 4 Thursday, March 11, 2010 3:26 PM

Unit 2

Energy and Momentum

Chapter 4 Work and Energy Review Summary of concepts in diagrammatic form Equation Development For each equation below you should be able to show it is defined or how it was derived (if done in class). Also, you must be able to solve for any one variable given the remaining.

Number

Equation

Key Terms

1

• • • • • • •

2

3 4

5

work joule kinetic energy work-energy theorem gravitational potential energy law of conservation of energy isolated system

• • • • • •

Hooke's Law ideal spring force constant elastic potential energy simple harmonic energy damped harmonic motion


Practice Questions

6 7

Chapter

Section

1

Review

Page

8 (pendulum)

9 10 11

12

13

14

(pendulum)


Questions 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25.


Unit 2

Energy and Momentum

Chapter 4 Work and Energy Section 5

Elastic Potential Energy and Simple Harmonic Motion

Overview Copy the following terms into your notebook. Define and give examples for each. Hooke's Law ideal spring force constant elastic potential energy simple harmonic motion (SHM) damped harmonic motion

Hooke's Law For a spring shown at right the force exerted can be show, experimentally, to be .

If you can obtain access to a spring and a Newton Scale try make a graph of F vs. x to show this is true.

Elastic Potential Energy To determine the equation for elastic potential energy we must consider the work done on spring as it is stretched (or compressed). The area under a F vs. d graph yields work. We can see from the diagram (at right) that the area is triangular and hence the area under the graph is A = ½bh. This then is

(1)

. From equation (1) above we substitute kx for F.

Simplifying we get.

Remember that the total energy before (ET) = the total energy after (ET') (Read ET' as ET prime)


energy after (ET') (Read ET' as ET prime) Therefore the elastic energy in the spring (Ee) is found

Simple Harmonic Motion (SHM) (Constant repetitive motion)

Simple harmonic motion has two basic equations associated with it. Here is the development of those equations.

SHM Equation 1 From the previous unit we found that the acceleration of an object moving in a circle was

Solving for T we get

(SHM Equation 1)

SHM Equation 2 From Newton's Second Law we know From the previous section we found

Equating these we get Solving for a we get

Substituting into Equation 1 above we get

Simplifying we get

(SHM Equation 2)

Equations Add the following equations to your Physics Toolbox. You should be able to rearrange the equations to solve for the unknown. 1

determined experimentally

2

definition of work

3

Work required to compress a spring x metres.

4

elastic energy in the spring

5

6


7

For Pendulums, a special case of equation (5)

Animations There are a number of animations, right click on the link to each animation and save target as... 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

SimpleHarmonicOscillators.mov HarmonicMotionandAmplitude.mov SHMIntroduction1.mov SHMIntroduction2.mov SHMandHookesLaw.mov SHMandNewtonsFirstLaw.mov SHMandNewtonsSecondLaw.mov SHMVelocity-timegraph.mov SHMForce-AccelerationGraph.mov SHMPeriodofaWave.mov SHMPhaseAngle.mov SHMPositionVelocityandAcceleration.mov SHMWaveFunction1.mov SHMWaveFunction2.mov AmplitudeofaWave.mov SpeedofaWave.mov UniversalWaveEquation.mov PhaseofaWave.mov WavelengthofaWave.mov WaveNumber.mov



Section

Questions

4

4

1, 3, 8, 9, 10, 11, 12, 17, 18, 24, 25.


Section

Questions

4

4

5, 6, 7, 9, 10, 13, 15.



Unit 2

Energy and Momentum


Law of Conservation of Energy

Overview Copy the following terms into your notebook. Define and give examples for each. Law of Conservation of Energy

isolated system thermal energy

electromagnetic energy electrical energy

electrical potential energy gravitational potential energy chemical potential energy

nuclear potential energy sound energy

elastic energy

Complete this Table The following is a table for a ball being dropped from a height of 10 m. Fill in this table a submit it to the Conservation of Energy Dropbox - Bonus Marks. Time (s)

Height (m) (d=½at 2)

Eg (J) (Eg=mgh)

EK (J) (EK=mg d)

0.00

11.00

540

0.0

0.10

10.95

537

2.4

0.20

10.80

530

9.6

ET (J) (ET=Eg+EK)

0.30

0.40 0.50 0.60 0.70 0.80

0.90 1.00 1.10 1.20

1.30 1.40 1.50

Equations Add the following equations to your Physics Toolbox. You should be able to rearrange the equations to Physics II 4131U Page 71

Add the following equations to your Physics Toolbox. You should be able to rearrange the equations to solve for the unknown. 1

ET = Eg + EK

Conservation of Energy.

2

ET1 = ET2

Total Energy for system is the same before and after an event.

3

from equation (2) above.

4

the kinetic energy gained by the bob of a pendulum is equal to the potential energy lost.

5

Substituting

for

6

Hence for a pendulum we can solve for v.

Animations 1. 2. 3. 4. 5.

PotentialintoKineticEnergy.mov (right click on movie and save target as...) KineticintoPotentialEnergy.mov (right click on movie and save target as...) ConservationofEnergyBasic.mov (right click on movie and save target as...) ConservationofEnergyPendulum.mov (right click on movie and save target as...) FormsofEnergy.mov (right click on movie and save target as...) Note: this is the basics of how a rocket is moved.



Section

Questions

4

4

2, 6, 4, 5, 11, 13, 14.


Section

Questions

4

4

2, 3, 5, 6, 7, 10.


Section_4.4 Quick Quiz Thursday, March 11, 2010 3:14 PM


The law of conservation of energy applies to a(n) ____________________ system.

2.

Friction causes kinetic energy to transform into ____________________ energy.

3.

Thermal energy occurs when the ____________________ inside an object begin to speed up.

4.

____________________ law states that the magnitude of the force exerted by an ideal spring is directly proportional to the distance the spring moves from equilibrium.

Matching

Match the type of energy to the correct description. a. electromagnetic f. nuclear potential b.

electrical

g.

sound

c.

electric potential

h.

elastic potential

d.

gravitational potential

i.

thermal

e.

chemical potential

5.

includes radio waves and microwaves

6.

electrons flowing in a wire

7.

energy that causes static cling

8.

stored in raised objects

9.

stored in sugar molecules

10.

released in a nuclear reactor


11.

a longitudinal wave

12.

propels an arrow from a bow

13.

easily produced by friction

14.

A wrecking ball is commonly used to destroy old buildings. The energy comes from a motor pulling a large pendulum back, which then allows it to swing against a wall. Why not just use the motor to do the same work on the wall?

15.

When a car travels down a highway, only about 25% of the chemical potential energy from the gasoline is converted to kinetic energy. Name two other forms of energy that are produced.

Short Answer


Sec 4.3 gizmo activity Thursday, March 18, 2010 4:09 PM

Name: ______________________________________

Date: ________________________

Student Exploration: Roller Coaster Physics Vocabulary: friction, gravitational potential energy, kinetic energy, momentum, speed Prior Knowledge Questions (Do these BEFORE using the Gizmo.) An object’s momentum reflects how easy it is to stop. Objects with greater momentum are harder to stop and can also inflict more damage when they collide with other objects.

1. Which do you think has more momentum, a moving car or a moving train? ____________ 2. The speed of an object is how fast it is moving. Which has more momentum, a car with a speed of 20 km/h (kilometers per hour) or a car moving at 100 km/h? __________________

3. What are the two factors that affect an object’s momentum? _________________________

Gizmo Warm-up The Roller Coaster Physics Gizmo™ shows a toy car on a track that leads to an egg. You can change the track or the car. For the first experiment, use the default settings (Hill 1 = 70 cm, Hill 2 = 0 cm, Hill 3 = 0 cm, 35-g car).

1. Press Play () to roll the 35-gram toy car down the track. Does the car break the egg? _________

2. Click Reset (). Raise Hill 1 to 100 cm, and click Play again. Does the car break the egg? _________

3. Click Reset. Lower Hill 1 back to 70 cm and select the 50-gram toy car. Click Play. Does the 50-gram car break the egg? _________

4. What factors determine whether the car will break the egg? __________________________ _________________________________________________________________________ _________________________________________________________________________ Activity A:

Get the Gizmo ready: Physics II 4131U Page 75

Activity A:

Get the Gizmo ready: Click Reset. Momentum

Question: What determines whether the egg will break?

1. A. B. C.

Form hypothesis: Which factor(s) determine whether the car breaks the egg? (Circle one.) The mass of the car only. The speed of the car only. The mass and speed of the car.

2. Collect data: Use the Gizmo to find five situations in which the car breaks the egg, and five in which the car does not break the egg. In each situation, record the mass of the car and the speed of the car when it hits the egg. Include units. Leave the last column blank for now.

Egg breaks

Mass

Speed

Egg does not break

Mass

Speed

3. Calculate: Momentum (p) is calculated by multiplying mass (m) by speed (v): p = m • v. Label the third column in each table Momentum, and calculate the momentum in each situation. Because mass is measured in grams and speed is measured in centimeters per second, the units of momentum here are grams centimeters per second, or g•cm/s.

4. Analyze: Carefully analyze and compare the data in each table.

A. Does the car’s mass alone determine whether the egg breaks? _________________ B. Does the car’s speed alone determine whether the egg breaks? ________________ C. Does the car’s momentum determine whether the egg breaks? _________________ Explain: ____________________________________________________________

5. Draw conclusions: What is the minimum momentum required to break the egg? __________ Use the Gizmo to test and refine your answer. Activity B:

Get the Gizmo ready:


The speed of a roller coaster

Click Reset. Select the 35-g toy car.

Question: What factors determine the speed of a roller coaster?

1. Observe: Set Hill 1 to 100 cm, Hill 2 to 0 cm, and Hill 3 to 0 cm. Be sure the Coefficient of friction is set to 0.00. (This means that there is no friction, or resistance to motion.)

A. Click Play. What is the final speed of the toy car? _______________

B. Try the other cars. Does the mass of the car affect its final speed? ______________ 2. Collect data: Find the final speed of a toy car in each situation. Leave the last column blank. Hill 1

Hill 2

Hill 3

40 cm

0 cm

0 cm

40 cm

30 cm

0 cm

60 cm

50 cm

20 cm

60 cm

0 cm

0 cm

60 cm

45 cm

0 cm

90 cm

75 cm

30 cm

Final speed

3. Analyze: Look at the data carefully. Notice that it is organized into two sets of three trials.

A. What did each set of trials have in common? _______________________________ B. Did hill 2 have any effect on the final speed? _______________________________ C. Label the last column of the table Total height lost. Fill in this column by subtracting the height of hill 3 from the height of hill 1.

D. What do you notice about the Total height lost in each set of trials? ____________ ___________________________________________________________________

4. Draw conclusions: When there is no friction, what is the only factor that affects the final speed of a roller coaster? ____________________________________________________ What factors do not affect the final speed of a roller coaster? ________________________ _________________________________________________________________________ Activity C: Get the Gizmo ready: Click Reset. Energy on a roller Set Hill 1 to 100 cm, and Hill 2 and 3 to 0 coaster cm. Select the 50-g car. Question: How is energy expressed in a moving roller coaster?

1. Observe: Turn on Show graph and select E vs t to see a graph of energy (E) versus time. Click Play and observe the graph as the car goes down the track. Does the total energy of the car change as it goes down the hill? _____________________

2. Experiment: The gravitational potential energy (U) of a car describes its energy of position. Click Reset. Set Hill 3 to 99 cm. Select the U vs t graph, and click Play. Physics II 4131U Page 77

Click Reset. Set Hill 3 to 99 cm. Select the U vs t graph, and click Play.

A. What happens to potential energy as the car goes down the hill? _______________

B. What happens to potential energy as the car goes up the hill? __________________

3. Experiment: The kinetic energy (K) of a car describes its energy of motion. Click Reset. Select the K vs t (kinetic energy vs. time) graph, and click Play.

A. What happens to kinetic energy as the car goes down the hill? _________________ B. What happens to kinetic energy as the car goes up the hill? ___________________ 4. Compare: Click Reset. Set Hill 1 to 80 cm, Hill 2 to 60 cm, and Hill 3 to 79 cm. Be sure the 50g toy car is selected, and press Play. Sketch the U vs t, K vs t, and E vs t graphs below.

5. Draw conclusions: Based on the graphs, how are potential energy, kinetic energy, and total energy related to one another? _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ Pasted from



Unit 2

Energy and Momentum


Kinetic Energy and the Work Theorem

Overview Copy the following terms into your notebook. Define and give examples for each. kinetic energy (EK) work-energy theorem

Development of the Kinetic Energy Equation #

Statement

Explanation

1

the definition of work

2

Newton's Second Law

3

equation of uniformly accelerated motion ( )

4

combining (2) and (3)

5


6

simplifying (5)

7

if vi = 0

8

simplifying (7)

9

The work done has been converted into Kinetic Energy (EK).

10

substitution of EK for W total into equation (8)

The Work Energy Theorem The total work done on an object equals the change in the object's kinetic energy. So into equation (6) above we can write:

or

Equations Physics II 4131U Page 79


Animations 1. KineticEnergyBasics.mov (right click on movie and save target as...) Note: In the animation v 2 = vf and v1 = vi 2. FrictionandWorkEnergyTheorem.mov (right click on movie and save target as...) Note: The animation uses n to represent the normal force (FN) and uses s to represent displacement (d).



Section

Questions

4

2

2, 4, 5, 6, 7.


Section

Questions

4

2

2, 4, 6, 7, 8.



Unit 2

Energy and Momentum


Kinetic Energy and the Work Theorem

Overview Copy the following terms into your notebook. Define and give examples for each. kinetic energy (EK) work-energy theorem

Development of the Kinetic Energy Equation #

Statement

Explanation

1

the definition of work

2

Newton's Second Law

3

equation of uniformly accelerated motion ( )

4


5


6

simplifying (5)

7

if vi = 0

8

simplifying (7)

9

The work done has been converted into Kinetic Energy (EK).

10

substitution of EK for W total into equation (8)

The Work Energy Theorem The total work done on an object equals the change in the object's kinetic energy. So into equation (6) above we can write:

or

Equations Add the following equations to your Physics Toolbox. You should be able to rearrange the equations to Physics II 4131U Page 81

Add the following equations to your Physics Toolbox. You should be able to rearrange the equations to solve for the unknown.

Animations 1. KineticEnergyBasics.mov (right click on movie and save target as...) Note: In the animation v 2 = vf and v1 = vi 2. FrictionandWorkEnergyTheorem.mov (right click on movie and save target as...) Note: The animation uses n to represent the normal force (FN) and uses s to represent displacement (d).



Section

Questions

4

2

2, 4, 5, 6, 7.


Section

Questions

4

2

2, 4, 6, 7, 8.



Unit 2

Energy and Momentum


Work Done by a Constant Force

Play Energy & Work Introduction Movie EnergyWorkIntro.mov (right click on movie and save target as...)

Overview Copy the following terms into your notebook. Define and give examples for each. work joule


direction Work done by the force (F) at angle ( ) to the displacement is (Fcos

d

The x-component of a force (F) is Fcos The y-component of a force (F) is Fsin Work done in the x plane equals the x component of F times the displacement.

Animations 1. WorkBasicConcepts.mov (right click on movie and save target as...) Note: the animation uses for displacement and show the equation as rather than 2. WorkbyaConstantForce.mov (right click on movie and save target as...) Note: this animation mentions calculus. For us, it is only necessary to know the the Work done is equal to the area under the curve for Force Displacement graph, as shown below. The work done in the first 2.0 m is


then 2 m × 8 N = 16 J, the work in the next 4 m is 4 m × -2 N = -8 J 3. PositiveNegativeWork.mov (right click on movie and save target as...) 4. WorkDoneLiftingBarbell.mov (right click on movie and save target as...) Note: the Woman weightlifter does no work when she hold the barbell high above her head... however, she does do work while she lifts the barbell. 5. WorkDoneCompressingSpring.mov (right click on movie and save target as...) Note: This topic is covered in detail in section 4.5 Try these Practice Problems from the Text (Nelson, Physics 12)


Section

Questions

4

1

1, 2, 3, 4, 5, 6.


Section

Questions

4

1

5, 6, 7.


Ch 4 Overview Sunday, March 14, 2010 10:35 PM

Chapter 4

Energy, Work, Heat, & Power Overview Chapter 4 Date

Section Practice Exercises

Questions

Supplementary Chapter Review Questions 3, 4, 5, 7, 8, 10, 11, 12, 16, 18, 19, 20, 21, 22, 23, 25, 26, 30.

1

2

2

2

1, 4, 5, 6, 8, 9, 10, 11, 12, 14.

1, 2, 4, 6.

3

1, 4, 5, 6, 8, 11, 12.

2, 3, 4, 5, 6, 7.

4

2, 3, 4, 5. Do Investigation 4.4.1 (Lab 3)

1, 2, 4, 7.

5

1, 4, 5, 7, 8, 9, 10, 11, 13, 15, 16.

2, 3, 6.

6

1, 4, 5. Submit Investigation 4.4.1

1, 2.

add Formulae to "My Physics Toolbox" Chapter 4 Test


Practice Test 4.1 Practice Test 4.2