15. Exercises

Calculate the momentum of

a) a train, of mass 120 tonnes, travelling at 40 \displaystyle \text{m}{{\text{s}}^{-1}},

b) a table tennis ball, of mass 3 grams, travelling at 4 \displaystyle \text{m}{{\text{s}}^{-1}},

c) a car, of mass 1200 kg, travelling at 36 kmph.

A ball, of mass 100 grams, is travelling horizontally at 8 \displaystyle \text{m}{{\text{s}}^{-1}} when it hits a wall and rebounds at 5 \displaystyle \text{m}{{\text{s}}^{-1}}. Assume that all the motion is perpendicular to the wall. Calculate the magnitude of the impulse on the ball.

A van, of mass of 4 tonnes, is travelling at 25 \displaystyle \text{m}{{\text{s}}^{-1}} along a straight road. As it approaches a traffic light it slows down to 8 \displaystyle \text{m}{{\text{s}}^{-1}}. Calculate the magnitude of the impulse on the van.

A ball is released from a height of 2 m and rebounds to a height of 1.4 m. Assume that no air resistance acts on the ball as it moves.

Use constant acceleration equations to find:

a) The speed of the ball when it hits the ground.

b) The rebound speed of the ball.

c) Given that the mass of the ball is 0.08 kg, calculate the magnitude of the impulse on the ball while it is in contact with the ground.

A squash ball, of mass 40 grams, hits a wall travelling horizontally at 9 \displaystyle \text{m}{{\text{s}}^{-1}} and rebounds at 7 \displaystyle \text{m}{{\text{s}}^{-1}}. Assume that the motion is perpendicular to the wall.

a) Calculate the magnitude of the impulse on the ball.

b) Given that the ball is in contact with the wall for 0.2 seconds, find the magnitude of the average force on the ball.

c) Given that the average force on the ball while it is in contact with the wall has magnitude 10 N, find the time for which the ball is in contact with the wall.

A car, of mass 1200 kg, is moving at 8 \displaystyle \text{m}{{\text{s}}^{-1}} along a straight road when the brakes are applied until it comes to rest.

a) Find the magnitude of the impulse on the car.

b) Given that the car takes 3 seconds to come to rest, find the average resultant force on the car.

A particle, of mass 2kg, is sliding at 12 \displaystyle \text{m}{{\text{s}}^{-1}} when it is hits a wall. After hitting the wall, the particle moves at a speed of 6 \displaystyle \text{m}{{\text{s}}^{-1}} at right angles to its original direction of motion.

a) Find the magnitude of the impulse on the particle.

b) Given that the impulse is perpendicular to the wall, find the angle between the wall and the initial direction of motion of the particle..

A car, of mass 1250 kg is moving at 15 \displaystyle \text{m}{{\text{s}}^{-1}}, when it is hit by another vehicle. The other vehicle exerts a force of magnitude 800 N for 3 seconds. This force is perpendicular to the original path of the car.

a) Calculate the magnitude of the impulse on the car.

b) Find the speed of the car after the collision.

c) Find the angle between the initial and final velocities of the car.

A particle, of mass \displaystyle m, is travelling at a of speed \displaystyle 4u. An impulse of magnitude \displaystyle kmu acts on the particle, so that it now moves perpendicular to its original path at a speed \displaystyle 2u.

a) Find \displaystyle k.

b) Find the angle between the impulse and the initial velocity of the particle.