GERAK MELINGKAR dan HUKUM NEWTON - filetosi

Newton's Laws Work and Energy Department of Physics Faculty of Mathematics and Natural Sciences Bogor Agricultural University

PART I Newton's Laws

Exercise 1. A 2-kg block sits on a 4-kg block that is on a frictionless table (Figure 1.1). The coefficients of friction between the blocks are μs = 0.3 and μk = 0.2. (a) What is the maximum horizontal force F that can be applied to the 4-kg block if the 2-kg block is not to slip? (b) If F has half this value, find the acceleration of each block and the force of friction acting on each block. (c) If F is twice the value found in (a), find the acceleration of each block 2 kg

Fig. 1.1

4 kg

F

2. In Figure 1.2, the mass m2 = 10 kg slides on a frictionless table. The coefficients of static and kinetic friction between m2 and m1 = 5 kg are μs = 0.6 and μk = 0.4. (a) What is the maximum acceleration of ml? (b) What is the maximum value of m3 if m1 moves with m2 without slipping? (c) If m3 = 30 kg, find the acceleration of each body and the tension in the string m1 m2

Fig. 1.2

m3

3. A 20-kg block with a pulley attached slides along a frictionless ledge, It is connecected by a massless string to a 5-kg block via the arrangement shown in Figure 1.3, (a) Find the horizontal distance the 20-kg block moves when the 5-kg block descends a distance of 10 cm, (b) Find the acceleration of each block and the tension in the connecting string, 20 kg

Fig. 1.3 5 kg

4. A 10-kg block rests on a 5-kg bracket shown in Figure 1.4. The 5-kg bracket sits on a frictionless surface. The coefficients of friction between the 10-kg block and the bracket on which it rests are μs = 0.40 and μk = 0.30. (a) What is the maximum force F that can be applied if the 10-kg block is not to slide on the bracket? (b) What is the corresponding acceleration of the 5-kg bracket? Fig. 1.4 5 kg

F 10 kg

5. Suppose you ride a bicycle on a horizontal surface in a circle with a radius of 20 m. The resultant force exerted by the road on the bicycle (normal force plus frictional force) makes an angle of 15° with the vertical. (a) What is your speed? (b) If the frictional force is half its maximum possible value, what is the coefficient of static friction? 6. A curve of radius 30 m is banked so that a car traveling at 40 km/h can round it even if the road is so icy that the coefficient of static friction is approximately zero. Find the range of speeds at which a car can travel around this curve without skidding if the coefficient of static friction between the road and the tires is 0.3.

PART II Work and Energy

Exercise 1. A roller coaster car of mass m=1500 kg starts at a distance H = 23 m above the bottom of a loop 15 m in diameter (Figure 2.1). If friction is negligible, the downward force of the rails on the car when it is upside down at the top of the loop is (a) 4.6 x 104 N (b) 3.1 x 104 N (c) 1.7 x 104 N (d) 980 N (e) 1.6 x103 N

Fig. 2.1

2. A theoretical formula for the potential energy associated with the nuclear force between two protons, two neutrons, or a neutron and a proton is the Yukawa potential  a  xa U  U 0  e  x

where U0 and a are constants. (a) make a graph of U versus x (Using a spreadsheet program such as Microsoft Exce), using U0 = 4 pJ (a picojoule, pJ, is 1x10-12 J) and a = 2.5 fm (a femtometer, fm, is 1x 10-15 m). (b) Find the force F(x) (c) Compare the magnitude of the force at the separation x = 2a to that at x = a. (d) Compare the magnitude of the force at the separation x = 5a to that at x = a.