Momentum (1D and implied 2D)：練習問題

An object of mass \( m \) is moving with an initial speed \( u \). A constant net force \( F \) is applied to the object in the same direction as its motion for a time interval \( \Delta t \). Which of the following expressions represents the magnitude of the final momentum of the object?

A block of mass \( m \) moving with speed \( v \) to the East collides and sticks to another block of mass \( m \) moving with speed \( v \) to the North. What is the magnitude of the total momentum of the combined system immediately after the collision?

An object traveling at \(25\text{ m/s}\) collides head-on with a fixed obstacle and bounces back along the same line at \(15\text{ m/s}\). If the obstacle exerts an average force of \(400\text{ N}\) for \(0.01\text{ s}\), what is the mass of the object?

A block of mass \(2.5 \text{ kg}\) is initially at rest on a smooth horizontal surface. A horizontal force \(F\) is applied to the block. The variation of the force \(F\) with time \(t\) is shown in the graph below. The force increases linearly from \(0\) at \(t = 0\) to \(10 \text{ N}\) at \(t = 2 \text{ s}\), and then remains constant at \(10 \text{ N}\) until \(t = 4 \text{ s}\). What is the speed of the block at \(t = 4 \text{ s}\)?

A \(100\text{ g}\) golf ball approaches a wooden surface at \(20\text{ m/s}\) and leaves the surface directly backward at \(10\text{ m/s}\). If the impact lasted for \(0.02\text{ s}\), what is the magnitude of the average force acting on the ball during impact?

State the principle of conservation of momentum as applied to a system of colliding objects where no external resultant force acts.

A ball of mass \( 0.4 \text{ kg} \) hits a vertical wall horizontally at \( 5 \text{ m s}^{-1} \) and bounces back along the same path at \( 3 \text{ m s}^{-1} \). Calculate the magnitude of the impulse exerted by the wall on the ball.

A golf ball of mass \(45\text{ g}\) hits a rigid vertical wall at an angle of \(30^\circ\) relative to the wall surface with a speed of \(25\text{ m/s}\). It rebounds immediately at the same speed and angle. If the contact time between the ball and the wall is \(0.01\text{ s}\), calculate the magnitude of the average force exerted by the wall on the ball.

A soccer ball of mass \(0.45\text{ kg}\) is initially at rest on a horizontal field. A player kicks the ball, and it leaves the foot with a speed of \(20\text{ m s}^{-1}\). The contact time between the foot and the ball is \(0.1\text{ s}\).

(a) Calculate the magnitude of the change in momentum (impulse) of the ball.
(b) Determine the magnitude of the average force exerted by the player's foot on the ball during the impact.

Trolley \(A\) of mass \(1.5\text{ kg}\) travels at \(4\text{ m s}^{-1}\) on a frictionless horizontal track. It collides head-on with a stationary trolley \(B\) of mass \(2.5\text{ kg}\). Upon collision, the two trolleys stick together and move as a single unit, as shown in the figure.

(a) Using the law of conservation of momentum, calculate the common velocity of the two trolleys after the collision.
(b) Calculate the total kinetic energy of the system before the collision and the total kinetic energy after the collision.
(c) State whether the collision is elastic or inelastic, and justify your answer based on your results in part (b).