Dynamics：練習題

An object of mass \(4.0 \text{ kg}\) is acted upon by a constant resultant force of \(12 \text{ N}\). Starting from rest, what is the momentum of the object after a time of \(3.0 \text{ s}\)?

Two objects, P and Q, have masses \(m\) and \(3m\) respectively. They are moving towards each other in a straight line with speeds \(2v\) and \(v\). After a perfectly elastic collision, what is the relative speed of separation of the two objects?

A steel ball of mass \(0.50 \text{ kg}\) is moving at a speed of \(4.0 \text{ m s}^{-1}\) when it hits a flat plate at an angle of \(60^\circ\) to the normal. It rebounds with the same speed and at the same angle to the normal. What is the magnitude of the change in momentum of the ball during the collision?

A ball of mass \(m\) moving with velocity \(u\) makes a head-on elastic collision with a stationary ball of mass \(2m\). After the collision, the first ball moves backwards with velocity \(v_1\) and the second ball moves forwards with velocity \(v_2\).
Which equation correctly relates the relative speed of approach to the relative speed of separation?

Sand falls vertically at a constant rate of \(5.0 \text{ kg s}^{-1}\) onto a horizontal conveyor belt moving at a constant speed of \(2.0 \text{ m s}^{-1}\). What is the additional horizontal force required to keep the belt moving at this constant speed?

A conveyor belt moves at a constant speed \(v\). Sand falls vertically onto the belt at a constant rate of \(M\) kg per second. Explain why a constant force \(F = Mv\) is required to keep the belt moving at speed \(v\).

A particle of mass \(m\) moving with velocity \(u\) collides with an identical stationary particle. After the collision, the particles move at equal angles \(\alpha\) to the original direction of motion. Explain why the total momentum of the system in the direction perpendicular to the initial velocity must be zero after the collision.

A trolley of mass \(2.5\text{ kg}\) is moving with a constant momentum of \(15\text{ kg m s}^{-1}\). Calculate the magnitude of the average force required to stop this trolley in a time interval of \(0.60\text{ s}\).

(a) Define linear momentum.
(b) State the principle of conservation of momentum.
(c) A ball of mass \(0.15 \text{ kg}\) is dropped from rest at a height of \(1.2 \text{ m}\) onto a horizontal floor. It rebounds to a height of \(0.85 \text{ m}\). Calculate the magnitude of the change in momentum of the ball during its collision with the floor. (Take \(g = 9.81 \text{ m s}^{-2}\)).

(a) Explain the difference between an elastic collision and an inelastic collision.
(b) A truck of mass \(2500 \text{ kg}\) travelling at \(12 \text{ m s}^{-1}\) collides with a stationary car of mass \(800 \text{ kg}\). The two vehicles stick together and move off immediately after the collision.
(i) Calculate the common velocity of the vehicles after the collision.
(ii) Calculate the total kinetic energy lost during the collision.
(iii) Explain what happens to this lost kinetic energy.