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