Momentum：練習問題

A tennis ball with a mass of \(0.06\text{ kg}\) is moving horizontally at \(25\text{ m/s}\) when it hits a wall. It rebounds in the opposite direction at a speed of \(15\text{ m/s}\). If the ball is in contact with the wall for \(0.04\text{ s}\), what is the average force exerted by the wall on the ball?

A trolley of mass \(0.5\text{ kg}\) travels at a velocity of \(4.0\text{ m/s}\) and collides with a stationary trolley of mass \(1.5\text{ kg}\). if the two trolleys stick together during the collision, what is their final common velocity?

An object X of mass \(0.5\text{ kg}\) moving at \(10\text{ m/s}\) to the right makes a head-on collision with object Y of mass \(1.5\text{ kg}\) moving at \(2\text{ m/s}\) to the left. After the collision, the two objects stick together and move as one. What is their final velocity?

A stationary radioactive nucleus of mass \(3.60 \times 10^{-25}\text{ kg}\) emits an alpha particle of mass \(6.64 \times 10^{-27}\text{ kg}\) with a velocity of \(1.50 \times 10^7\text{ m/s}\). Calculate the magnitude of the recoil velocity of the remaining daughter nucleus.

A \(1500\text{ kg}\) car travelling at \(20\text{ m/s}\) stops in \(0.5\text{ s}\) after a collision. Calculate the magnitude of the average resultant force acting on the car during the impact.

A trolley of mass \(2.0\text{ kg}\) moving at \(6.0\text{ m/s}\) collides with a stationary trolley of mass \(4.0\text{ kg}\). If they stick together, calculate their common velocity after the collision.

A trolley A of mass \(0.5\text{ kg}\) travels at a constant velocity of \(4.0\text{ m/s}\) and collides with a stationary trolley B of mass \(1.5\text{ kg}\). After the collision, the two trolleys stick together.
(a) State the principle of conservation of momentum.
(b) Calculate the velocity of the combined trolleys immediately after the collision.
(c) The collision lasts for \(0.25\text{ s}\). Calculate the magnitude of the average force exerted by trolley A on trolley B during the impact.