A shell of mass m and speed v explodes into two identical

Question

Question 1- True or false:

(a) The total linear momentum of a system may be conserved even when the mechanical energy of the system is not.

(b) For the total linear momentum of a system to be conserved there must be no external forces acting on the system.

(c) The velocity of the center of mass of a system changes only when there is a net external force on the system.

Question 2- Two identical bowling balls are moving with the same center-of-mass velocity, but one just slides down the alley without rotating, whereas the other rolls down the alley. Which ball has more kinetic energy?

Question 3- A philosopher tells you, "Changing motion of objects is impossible. Forces always come in equal but opposite pairs. Therefore, all forces cancel out. Because forces cancel, the momenta of objects can never be changed." Answer his argument.

Question 4- A 5.0-kg object and a 10-kg object, both resting on a frictionless table, are connected by a mass less compressed spring. The spring is released and the objects fly off in opposite directions. The 5.0-kg object has a velocity of 8.0 m/s to the left. What is the velocity of the 10-kg object?

Question 5- A shell of mass m and speed v explodes into two identical fragments. If the shell was moving horizontally with respect Earth, and one of the fragments is subsequently moving vertically with speed v, find the velocity of the other fragment immediately following the explosion.

Question 6- A proton of mass m is moving with initial speed v₀ directly toward the center of an a particle of mass 4m, which is initially at rest. Both particles carry positive charge, so they repel each other. (The repulsive forces are sufficient to prevent the two particles from coming into direct contact.) Find the speed v_a of the a particle (a) when the distance between the two particles is a minimum, and (b) later when the two particles are far apart.

Question 7- A wedge of mass M is placed on a frictionless, horizontal surface, and a block of mass m is placed on the wedge, which also has a frictionless surface (Figure). The block's center of mass moves downward a distance h as the block slides from its initial position to the horizontal floor. (a) What are the speeds of the block and of the wedge as they separate from each other and go their own ways? (b) Check your calculation plausibility by considering the limiting case when M >> m.

Question 8- A 60-g handball moving with a speed of 5.0 m/s strikes the wall at a 40° angle with the normal, and then bounces off with the same speed at the same angle with the normal. It is in contact with the wall for 2.0 ms. What is the average force exerted by the ball on the wall?

Question 9- A 16-g bullet is fired into the bob of a 1.5-kg ballistic pendulum. When the bob is at its maximum height, the strings make an angle of 60° with the vertical. The pendulum strings are 2.3 m long. Find the speed of the bullet prior to impact.

Question 10- The light isotope, ⁵Li, of lithium is unstable and breaks up spontaneously into a proton and an α particle. In this process, 3.15 x 10^-13 J of energy is released, appearing as the kinetic energy of the two decay products. Determine the velocities of the proton and the α particle that arise from the decay of a ⁵Li nucleus at rest. (Note: The masses of the proton and alpha particle are m_p = 1.67 x 10^-27 kg and m_α = 4 m_p = 6.64 x 10^-27 kg.)

Question 11- In a pool game, the cue ball, which has an initial speed of 5.0 m/s, makes an elastic collision with the eight ball, which is initially at rest. After the collision, the eight ball moves at an angle of 30^o to the right of the original direction of the cue ball. Assume that the balls have equal mass. (a) Find the direction of motion of the cue ball immediately after the collision. (b) Find the speed of each ball immediately after the collision.

Question 12- A 1500-kg car traveling north at 70 km/h collides at an intersection with a 2000-kg car traveling west at 55 km/h. The two cars stick together. (a) What is the total momentum of the system before the collision? (b) What are the magnitude and direction the velocity of the wreckage just after the collision?

Question 13- A 1.0-kg steel ball and a 2.0-m cord of negligible mass make up a simple pendulum that can pivot without friction about the point O, as in Figure. This pendulum is released from rest in horizontal position, and when the ball is at its lowest point it strikes a 1.0-kg block sitting at rest on a shelf. Assume that the collision is perfectly elastic and that the coefficient of kinetic friction between the block and shelf is 0.10. (a) What is the velocity of the block just after impact? (b) How far does the block slide before coming to rest (assuming that the shelf is long enough)?