Collisions：練習問題

A ball of mass \( m \) travelling with velocity \( u \) hits a vertical wall and rebounds elastically in the opposite direction. What is the magnitude of the impulse exerted by the wall on the ball?

A particle of mass \( m \) moving with velocity \( u \) undergoes a perfectly elastic collision with a stationary particle of mass \( 2m \). After the collision, the first particle moves backwards with speed \( v_1 \) and the second particle moves forwards with speed \( v_2 \). Which of the following equations represents the conservation of kinetic energy for this system?

A ball of mass \( 0.20 \text{ kg} \) strikes a horizontal floor vertically with a speed of \( 5.0 \text{ m s}^{-1} \) and rebounds vertically with a speed of \( 3.0 \text{ m s}^{-1} \). The ball is in contact with the floor for \( 0.040 \text{ s} \). What is the magnitude of the average net force exerted on the ball during the collision?

A perfectly elastic collision occurs between two spheres, P and Q. Sphere P of mass \( m \) travels at velocity \( u \) and hits sphere Q of mass \( 3m \) which is initially at rest. After the collision, P moves in the opposite direction with velocity \( v_P \) and Q moves forward with velocity \( v_Q \). Using the principle of conservation of momentum and the fact that the relative velocity of approach equals the relative velocity of separation, determine the magnitude of \( v_Q \).

A trolley of mass \( 2.0 \text{ kg} \) moving at \( 6.0 \text{ m s}^{-1} \) collides with a stationary trolley of mass \( 4.0 \text{ kg} \). After the collision, the two trolleys stick together and move with a common velocity \( v \). Calculate the value of \( v \).

An object of mass \( 0.50 \text{ kg} \) is moving at \( 4.0 \text{ m s}^{-1} \) and collides with a stationary object of mass \( 1.5 \text{ kg} \). If the collision is perfectly elastic, determine the total kinetic energy of the system after the collision.

In a perfectly elastic collision between two spheres of equal mass, where sphere A is moving with velocity \( u \) and sphere B is initially stationary, use the conservation of kinetic energy and momentum to explain why the two spheres must exchange velocities completely.

A truck of mass \( 1.5 \times 10^4 \text{ kg} \) moving at a constant velocity of \( 12 \text{ m s}^{-1} \) collides with a stationary car of mass \( 1200 \text{ kg} \). Immediately after the collision, the car moves forward with a velocity of \( 18 \text{ m s}^{-1} \) in the same direction as the truck's initial motion.

(a) Calculate the velocity of the truck immediately after the collision.

(b) Determine whether the collision is elastic or inelastic by calculating the total kinetic energy before and after the interaction.

(c) The car's brakes are applied after the collision, providing a constant braking force of \( 4500 \text{ N} \). Use Newton’s second law to calculate the time it takes for the car to come to rest.

In a safety experiment, a test vehicle of mass \( m_1 = 800 \text{ kg} \) moving at \( 15 \text{ m s}^{-1} \) collides with a stationary barrier of mass \( m_2 = 2400 \text{ kg} \) which is free to slide on a low-friction track. After the collision, the vehicle rebounds in the opposite direction at \( 2.0 \text{ m s}^{-1} \).

(a) Show that the velocity of the barrier immediately after the collision is approximately \( 5.7 \text{ m s}^{-1} \).

(b) Determine, by calculation of kinetic energies, whether this collision is perfectly elastic or inelastic.

(c) During the collision, the barrier exerts a force on the vehicle that varies with time. If the contact time was \( 0.25 \text{ s} \), calculate the average force exerted by the barrier on the vehicle and explain, using Newton's third law, the force the vehicle exerts on the barrier.