Comprehensive Review. Part-1 ... work, momentum, energy, power, conservation
laws; ... Newton's Second Law. ◇ Fundamental equation of dynamics: F = m a.
Physics 1010
Comprehensive Review Part-1
Extra Credit Grades Will be posted on website by Tuesday for the current EC assignment EC credits for the surveys will be posted after all surveys have been completed, probably next Thursday Last EC assignment will post tonight, due next Thursday
General Test Information Final is worth 80 points, as much as all your mid-terms put together Equivalent to ~16% of your final grade; that’s more than a letter grade Will do comprehensive reviews from now on Most review questions will be graded for clicker credit, BUT last week of reviews will NOT be graded
General Test Information All material is eligible for the final That includes Extra Credit Assignments (eg. aeropllanes, greenhouse effect, friction) Bring questions to class
Skill and Concept Overview Concepts – velocity, acceleration, force, Newton’s laws, gravity, springs; work, momentum, energy, power, conservation laws; pressure; oscillators, waves (sound and EM); black bady radiation, temperature scales; electric charge, magnetic dipoles, Coulomb force; voltage, current, resitance, circuits Skills – read and interpret graphs, linear equations, quadratic equations (squares or square roots).
Velocity Velocity is the change of an object’s position with respect to time. x is position, v is velocity.
!x v= !t
Velocity is the slope!
Acceleration Acceleration is the change of an object’s velocity with respect to time. v is velocity, a is acceleration.
!v a= !t
Acceleration is the slope!
Kinematic Equations of Motion Rearranging equation from previous slide:
v = vi + at Similarly for position:
x = xi + vit + (1/2) at2
Newton’s First Law An object that is not subject to any outside forces moves at a constant velocity. When an object is not accelerating, it can still be subject to external forces, but the net force is zero.
Newton’s Second Law Fundamental equation of dynamics:
F=ma Acceleration is in the same direction as net force.
Newton’s Third Law For every force that one objects exerts on a second object, there is an equal and opposite force that the second object exerts on the first. This does not apply to two forces acting on the same object.
Gravity Objects of different masses fall at the same rate. The gravitational force on an object must be proportional to its mass.
Fgravity = mg g ! 9.8 m / s
2
Friction Frictional forces oppose motion. Two types: static and sliding. Sliding friction force is generally smaller than normal force. Friction force is related to the force that is normal to the contact surface.
Springs Hooke’s law:
Fspring = !kx The spring force is a restoring force proportional to the displacement of the object. Spring constant k depends on the type of spring.
Momentum & Impluse Momentum is a body-specific quantity that is conserved during collisions. Its unit is kg m/s. Impulse is the change in an object’s momentum over some time interval, and is equal to the force applied to the object times the duration of that force. Its unit is kg m/s = N s
p ! mv
I " F!t = !p
Work Work is defined as the displacement of an object multiplied by the force on that object in the direction of the displacement. Its unit is N m = J. Net work is the net force on the object in the direction of the displacement multiplied by the displacement.
W " F!x
Power Power is the work done per unit time. Its unit is J/s = W.
W #" !t
Pressure and Density Pressure is defined as the force applied to a surface divided by the area of that surface. Its unit is N/m2 = Pa. Mass density is defined as the mass of an object divided by the volume of the object. Its unit is kg/m3.
F P= A
m ! = V
Energy Energy comes in a variety of forms: kinetic, thermal, spring potential, gravitational potential, etc. Energy always has the unit J. The forms we discussed in class:
1 2 Ek = mv 2
E g = mgh
1 2 Esp = kx 2
Conservation of Momentum As previously mentioned, momentum is conserved during collisions. This is not the momentum of the individual objects – only the total momentum of the system is conserved.
m1vi + m2 vi = m1v f + m2 v f
Conservation of Energy The total mechanical energy of a system is constant in time. This allows us to compare the energy quantities at different times.
E = Ek + E g + Esp + Eth + K 1 1 2 2 E = mvi + mghi = mv f + mgh f 2 2
The Work-Energy Relation If net work is done on an object, energy is transferred to that object. That energy is equal to the work done (notice the same units for each). The energy can be in any form whatsoever.
Wnet = !E
The energy change can be kinetic, potential, spring, or thermal.
Bouyancy Forces Archimedes’ Principle: The buoyancy force on an object is equal to the weight of the fluid displaced by the object. Fb = W f = ρ V g Where ρ is the density of the displaced fluid
Oscillators A harmonic oscillator is something that exhibits periodic motion where the period is independent of the amplitude of the motion. m Tsp = 2! k
Tpendulum
l = 2! g
The frequency of an oscillator is the inverse of the period. 1 f =
T
Sound waves Sound waves are compression (longitudinal) waves that travel through the air (or water, or other fluids or solids). The pitch of a sound is directly related to its frequency. The speed, frequency, and wavelength of a sound wave exhibit a simple relationship:
v s = f!
Useful Formulae Kinematics: v=v0+at, x=x0+v0t+(1/2)at2 Newton’s II: F = ma Gravity: Fw= mg (g=9.8 m/s2) Friction: Ff = µFN (µ ~0.3 if not otherwise given) Hook’s Law: Fs= -kx Momentum: p = mv
Useful Formulae Work: W=F L (L is length along which F is applied) Torque: T=F d (d is perpendicular distance to the line of force) Rotational Newton’s II: T=Iα (I=moment of inertia, α=angual acceleration)
Useful Formulae Power: P=E/t Pressure: P=F/A (careful, confusing notation) Density: ρ=m/V Bernoulli: P+ρgh+(1/2)ρv2=const. Energy: Ek=(1/2)mv2, Eg=mgh, Es=(1/2)kx2 Buoyancy: Fb = Ffluid weight = ρfluidVfluidg
Useful Formulae Spring oscillator: Pendulum:
m Tsp = 2! k
Tpendulum
l = 2! g
Period-Frequency: f=1/T Waves: v= λ /T=λf
Useful Formulae Black Body Radiation: P=σT4 Coulomb Force: F = k (q1 q2)/R2 Ohm’s Law: V=IR EPE = qV Circuits: P=IV; parallel: same voltage, currents add up series: same current, voltages add up
Useful Formulae Transformers:
North pole
Right hand rule: current
Unit Conversions k (kilo) = 1000 (1km=1000m) M (mega) = 1,000,000 (1MW=1,000,000W) c (centi) = 1/100 (1m=100cm) m (milli) = 1/1000 (1m=1000mm) µ (mirco) =1/1,000,000 (1m=1,000,000µm) n (nano)=1/1,000,000,000 (1m=1,000,000,000nm)
Practice Questions; Acceleration v start
The car is subjected to a constant force in the direction away from the motion detector. Sketch your predictions for the velocity and acceleration of the cart moving toward the motion detector, slowing down at a steady rate, and then reversing direction and speeding up. (Start your graph after the push that gets the cart moving; + is to the right)
+ 0
time
+ 0
time
+ 0 -
#1 time
time
+ 0
time
-
C #1
B
0
Velocity
Velocity
Sketch your predictions for the velocity and acceleration of the cart moving toward the motion detector, slowing down at a steady rate, and then reversing direction and speeding up. + is to the right
Acceleration
-
+
Velocity
time
Acceleration
0
Acceleration
Velocity
+
A
+ 0
D #1 time
+ 0 -
#1 time
+ 0
time
+ 0
time
+ 0 -
#1 time
time
+ 0
time
-
C #1
B
0
Velocity
Velocity
Answer is D Acceleration is constant, and positive
Acceleration
-
+
Velocity
time
Acceleration
0
Acceleration
Velocity
+
A
+ 0
D #1 time
+ 0 -
#1 time
Practice Questions; Waves You hook up a speaker to an amplifier that generates a tone of frequency f=2.0kHz What is the period of the wave A) 10ms B) 5ms C) 0.5ms D) 1ms E) 2ms
Practice Questions; Waves You hook up a speaker to an amplifier that generates a tone of frequency f=2.0kHz What is the period of the wave A)10ms B) 5ms C) 0.5ms D) 1ms E) 2ms Answer is C: T=1/f=1/2000 s = 0.5 ms
Practice Questions; Waves You hook up a speaker to an amplifier that generates a tone of frequency f=2.0kHz What is the wavelength of the wave in air A) 16.5cm B) 33cm C) 2.0cm D) 1.65cm E) 6.6cm
Practice Questions; Waves You hook up a speaker to an amplifier that generates a tone of frequency f=2.0kHz What is the wavelength of the wave in air A) 16.5cm B) 33cm C) 2.0cm D) 1.65cm E) 6.6cm
Answer is A: v=λ/T, λ =vT=330m/s*0.5ms= =0.165m=16.5cm
Practice Questions; Waves You place the speaker in water, where the speed of sound is four times that in air The period of the wave in water is A) twice B) four times C) half D) one quarter E) the same
as that in air
Practice Questions; Waves You place the speaker in water, where the speed of sound is four times that in air The period of the wave in water is A) twice B) four times C) half D) one quarter E) the same
as that in air Anwer is E: T=1/f (does not depend on speed)
Practice Questions; Waves You place the speaker in water, where the speed of sound is four times that in air The wavelength of the wave in water is A) twice B) four times C) half D) one quarter E) the same
as that in air
Practice Questions; Waves You place the speaker in water, where the speed of sound is four times that in air The wavelength of the wave in water is A) twice B) four times C) half D) one quarter E) the same
as that in air Anwer is B: v=λ/T, λ =vT=v/f; wavelength is proportional to wave velocity
Practice Questions; Waves A LED laser in your new BlueRay DVD produces blue light with a wavelength of 450nm in air What is the period of the wave A) 1.0 *10-15s B) 1.5*10-15s C) 0.5 *10-15s D) 2 *10-15s
Practice Questions; Waves A LED laser in your new BlueRay DVD produces blue light with a wavelength of 450nm in air What is the period of the wave A) 1.0 *10-15s B) 1.5*10-15s C) 0.5 *10-15s D) 2 *10-15s c = λ/T = 450nm / 3*108 m/s = 1.5*10-15s
Practice Questions; Waves You place the LED in water, where the speed of light is 1.2 times slower that in air The period of the laser in water is A) 1.2 times B) 2.4 times C) 1/1.2 times D) 1/2.4 times E) the same
as that in air
Practice Questions; Waves You place the LED in water, where the speed of light is 1.2 times slower that in air The period of the laser in water is A) 1.2 times B) 2.4 times C) 1/1.2 times D) 1/2.4 times E) the same
as that in air Anwer is E: (Period does not depend on speed)
Practice Questions; Buoyancy A brick has a density of about 3000 kg/m3. What is magnitude of the boyancy force on a brick of volume 0.001 m3 immersed in water? A) 10N B) 20N C) 1N D) 2N E) 200N
Practice Questions; Buoyancy A brick has a density of about 3000 kg/m3. What is the magnitude of the boyancy force on a brick of volume 0.001 m3 immersed in water? A) 10N B) 20N C) 1N D) 2N E) 200N
Anwer is A: Fb=Fwater weight=ρVg= =1000kg/m3*0.001m3*9.8m/s2=9.8N
Practice Questions; Buoyancy A brick has a density of about 3000 kg/m3. What is the magnitude of the net force on a brick of volume 0.001 m3 immersed in water? A) 10N B) 20N C) 1N D) 2N E) 200N
Practice Questions; Buoyancy A brick has a density of about 3000 kg/m3. What is the magnitude of the net force on a brick of volume 0.001 m3 immersed in water? A) 10N B) 20N C) 1N D) 2N E) 200N
Anwer is B: Fn=Fbrick weight-Fwater weight= ρbrickVg-ρwaterVg= (ρbrick- ρwater)Vg= =(3000kg/m3-1000kg/m3)*0.001m3*9.8m/s2=19.6N
Practice Questions; Work You are using a frictionless ramp to move a 200kg filing cabinet onto a truck. The bed of the truck is 2m above the ground, and the ramp is 8m long. How much work will you do moving the cabinet onto the truck A) 4000N B) 2000N C) 4000J D) 2000J E) 200N
Practice Questions; Work You are using a frictionless ramp to move a 200kg filing cabinet onto a truck. The bed of the truck is 2m above the ground, and the ramp is 8m long. How much work will you do moving the cabinet onto the truck A) 4000N B) 2000N C) 4000J D) 2000J E) 200N
Anwer is C: W=mgh=200kg*9.8m/s2*2m=3920J
Practice Questions; Work You are using a frictionless ramp to move a 200kg filing cabinet onto a truck. The bed of the truck is 2m above the ground, and the ramp is 8m long. Once you get the cabinet moving at a constant speed, how much force will you exert to move the cabinet onto the truck A) 200N B) 200kg C) 500N D) 25kg E) 25N
Practice Questions; Work You are using a frictionless ramp to move a 200kg filing cabinet onto a truck. The bed of the truck is 2m above the ground, and the ramp is 8m long. Once you get the cabinet moving at a constant speed, how much force will you exert to move the cabinet onto the truck A) 200N B) 200kg C) 500N D) 25kg E) 25N
Anwer is C: mgh=FL, L=mg(h/L)= 200kg*9.8m/s2*(2m/8m)=490N
Practice Questions; Oscillators A mass of 10kg is hooked to a spring with spring constant k=100N/m. What is the period of the oscillator A) 20s B) 1s C) 5s D) 10s E) 2s
Practice Questions; Oscillators A mass of 10kg is hooked to a spring with spring constant k=100N/m. What is the period of the oscillator A) 20s B) 1s C) 5s D) 10s E) 2s
Anwer is E: T=2π sqrt(m/k)= =2 π sqrt(10kg/100N/m)=1.99 s
Practice Questions; Oscillators A mass of 10kg is hooked to a horizontal spring with spring constant k=100N/m. If I stretch the spring horizontally by 0.2m and let it go, how fast will the mass be moving as it crosses the equilibrium point? A) 0.6m/s B) 6m/s C) 20m/s D) 1.3m/s E) 13m/s
Practice Questions; Oscillators A mass of 10kg is hooked to a horizontal spring with spring constant k=100N/m. If I stretch the spring horizontally by 0.2m and let it go, how fast will the mass be moving as it crosses the equilibrium point? A) 0.6m/s B) 6m/s C) 20m/s D) 1.3m/s E) 13m/s
Anwer is A: (1/2)mv2=(1/2)kx2 so v=x*sqrt(k/m) v= 0.2m sqrt(100N/m / 10kg)=0.63 m/s
