Momentum：練習問題

Which of the following is equivalent to the rate of change of momentum?

A force-time graph shows the impact of a 0.50 kg ball hitting a wall. The force increases linearly from 0 to 1000 N in 0.05 s, and then decreases linearly back to 0 in another 0.05 s. If the ball was initially at rest, what is its final speed after the impact?

An object of mass \( m \) moving with velocity \( u \) makes a head-on perfectly elastic collision with a stationary object of mass \( 2m \). What is the velocity of the mass \( m \) immediately after the collision?

An object of mass 1.5 kg is moving at a constant velocity of \( 4.0\text{ m s}^{-1} \). What is the linear momentum of this object?

A constant resultant force of 20 N acts on an object of mass 5.0 kg for a duration of 3.0 s. If the object was initially moving at \( 4.0\text{ m s}^{-1} \) in the direction of the force, what is its final velocity?

State the relationship between the resultant force acting on an object and its momentum, expressed in terms of the rate of change.

A rubber ball of mass 0.20 kg hits a floor at a speed of \( 8.0\text{ m s}^{-1} \) and rebounds vertically upwards at a speed of \( 6.0\text{ m s}^{-1} \). Determine the magnitude of the impulse exerted by the floor on the ball.

Water from a hose hits a vertical wall at a rate of \(15 \text{ kg s}^{-1}\) with a horizontal velocity of \(12 \text{ m s}^{-1}\). If the water does not rebound but instead runs down the wall, calculate the magnitude of the force exerted by the water on the wall.

A railway wagon of mass \(8000\text{ kg}\) moving at a velocity of \(3.0\text{ m s}^{-1}\) collides with a stationary wagon of mass \(12000\text{ kg}\). The two wagons couple together and move off with a common velocity \(v\).

(a) Calculate the common velocity \(v\) of the wagons after the collision.
(b) Calculate the total kinetic energy lost during the collision.

A ballistic pendulum consists of a wooden block of mass \(2.5\text{ kg}\) suspended by light strings. A bullet of mass \(15\text{ g}\) is fired horizontally into the block and becomes embedded in it. The block then swings upwards so that its centre of mass rises through a vertical height of \(12\text{ cm}\).

(a) Calculate the velocity of the block and bullet immediately after the collision.
(b) Calculate the initial horizontal velocity of the bullet.