University of California, San DiegoPHYS 2AS08P2AChap11Sol Chapter 11 SolutionsProblem1. What is the impulse associated with a 650-N force acting for 80 ms? Problem6. A proton moving in the positive x direction at 4.3 Mm/s collides with a nucleus. The collision lasts 0.12 fs, and the average impulsive force is 42î + 17ˆ j µN. (a) Find the velocity of the proton after the collision. (b) Thro
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S08P2AChap11Sol
Chapter 11 Solutions
Problem
1. What is the impulse associated with a 650-N force acting for 80 ms?
Problem
6. A proton moving in the positive x direction at 4.3 Mm/s collides with a nucleus. The collision lasts 0.12 fs, and the
average impulsive force is 42î + 17ˆ j µN. (a) Find the velocity of the proton after the collision. (b) Through what angle
has the proton’s motion been deflected?
Problem
11. (a) Estimate the impulse imparted by the force shown in Fig. 11-18. (b) What is the average impulsive force?
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Problem
16. A 340-g ball moving at 7.40 m/s collides with a 230-g ball initially at rest. After the collision the first ball is moving at
1.60 m/s and the second at 8.57 m/s, both in the initial direction of the first ball. (a) Calculate the momenta before and
after the collision and show that, to three significant figures, momentum is conserved. (b) Is the collision elastic, totally
inelastic, or somewhere in between? Justify your answer.
Problem
17. In a railroad switchyard, a 56-ton freight car is sent at 7.0 mi/h toward a 31-ton car that is moving in the same direction
at 2.6 mi/h. (a) What is the speed of the pair after they couple together? (b) What fraction of the initial kinetic energy
was lost in the collision?
Problem
18. In a totally inelastic collision between two equal masses, one of which is initially at rest, show that half the initial kinetic
energy is lost.
Problem
25. A neutron (mass 1 u) strikes a deuteron (mass 2 u), and the two combine to form a tritium nucleus. If the neutron’s initial
velocity was 28î + 17ˆ j Mm/s and if the tritium nucleus leaves the reaction with velocity 12î + 20ˆ j Mm/s , what was the
velocity of the deuteron?
Problem
27. Two identical pendulum bobs are suspended from strings of equal length, and one is released from a height h as shown
in Fig. 11-19. When the first bob hits the second, the two stick together. Show that the maximum height to which the
combination rises is 1
4 h.
Problem
30. A 1300-kg car moving at 10 km/h collides with a 1600-kg car moving in the same direction at 6.6 km/h. The first car is
equipped with spring-loaded bumpers to prevent damage. If the spring constant is 28,000 N/m, find the maximum
compression of the spring.
Problem
33. While playing ball in the street, a child accidentally tosses a ball at 18 m/s toward the front of a car moving
toward him at 14 m/s. What is the speed of the ball after it rebounds elastically from the car?
Problem
34. A block of mass m undergoes a one-dimensional elastic collision with a block of mass M initially at rest. If both blocks
have the same speed after the collision, how are their masses related?
Problem
38. A 59.1-g tennis ball is moving at 14.5 m/s when it collides elastically and head-on with a basketball moving in the
opposite direction at 9.63 m/s. If the tennis ball rebounds at twice its initial speed, find the mass and final velocity of the
basketball.
39. Blocks B and C have masses 2m and m, respectively, and are at rest on a frictionless surface. Block A, also of mass m, is
heading at speed v toward block B as shown in Fig. 11-20. If all subsequent collisions are elastic, determine the final
velocity of each block.
FIGURE 11-20 Problem 39.
Problem
51. Two identical billiard balls are initially at rest when they are struck symmetrically by a third identical ball moving with
velocity v0 = v 0î , as shown in Fig. 11-24. Find the velocities of all three balls after they undergo an elastic collision.
FIGURE 11-24 Problem 51 Solution.
Problem
53. A 590-g basketball is moving at 9.2 m/s when it hits a backboard at 45° . It bounces off at a 45° angle, still moving at
9.2 m/s. If the ball is in contact with the backboard for 22 ms, find the average impulsive force on the ball.
Problem
62. A proton (mass 1.0 u) collides elastically with a deuteron (mass 2.0 u) initially at rest. After collision the proton is
moving at 6.2 ! 105 m/s at 31° clockwise from its initial direction of motion. Find the initial speed of the proton, the
final speed of the deuteron, and the direction of the deuteron’s motion.
Problem
70. A 200-g block is released from rest 25 cm high on a frictionless 30° incline. It slides down the incline, then along a
frictionless surface until it collides elastically with an 800-g block at rest 1.4 m from the bottom of the incline
(Fig. 11-27). How much later do the two blocks collide again?
The larger block moves with constant speed to the right; its position, relative to the bottom of the incline, is
x2(t) = 1.4 m + 2 5 v0t .
The smaller block takes time t1 = (1.4 m)=(3 5v0 ) to get back to the incline, and t2 = 2( 3 5=v 0 )=a to go up and down the
incline, where a = gsin30° = 1 2 g . (Use Equation 2-7, with initial speed ! 3 5v0 up the incline and final speed + 3 5v0 down
the incline, to calculate t2 .) It then proceeds with constant speed in pursuit of the larger block, its position being
x1(t) = 3 5v0 (t ! t1 ! t2) , for t ! t1 + t2 .
The blocks collide for the second time when x1(t) = x2(t), or 3 5 v0 (t ! t1 ! t2) = 1.4 m+ 2 5v0t . Solving for t, we find
t = 5[1.4 m + 3 5 v 0(t1 + t2)]=v0 = (7 m=v0 ) + 3(t1 + t2).
Numerically, v0 = 2(9.8 m/s2)(0.25 m) = 2.21 m/s , t1 = 1.4 m=(0.6 ! 2.21 m/s) = 1.05 s, and t2 = 12v0=5g =
2.4(2.21 m/s)=(9.8 m/s2) = 0.542 s. Thus, t = 7.95s (we did not use intermediate rounded-off values).
FIGURE 11-27 Problem 70 Solution.
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