Homework: Part 2 - Momentum-Impulse a. Calculate the impulse delivered to the ball. b. The ball was in contact with the wall for 0.125 s. Find the average force exerted by the ball on the wall. 10. A ball of mass 250 g rolling on a horizontal floor with a speed 4.00 m/s hits a wall and bounces with the same speed, as shown in the diagram. 45° 45° the rocket). Estimate how much fuel must be burnt in that second. 14. A time-varying force varies with time as shown in the graph. The force acts on a body of mass 4.0 kg. a. Find the impulse of the force from t = 0 to t = 15 s. b. Find the speed of the mass at 15 s, assuming the initial velocity was zero. c. State the initial velocity of the body such it is brought to rest at 15 s. F/N 10- a. What is the magnitude and direction of the momentum change of the ball? b. Is momentum conserved here? Why or why not? 8- 6 4 2 0 0 5 10 15 20 t/s 11. Two masses moving in a straight line towards each other collide as shown in the diagram. Find the velocity (magnitude and direction) of the heavier mass after the collision. 4.0 kg before after 12.0 kg 24.0 ms¹ 2.0 ms¹ 3.0 ms¹ v=? 12. Two masses of 2.0 kg and 4.0 kg are held in place, compressing a spring between them. When they are released, the 2.0 kg moves away with a speed of 3.0 m/s. What was the energy stored in the spring? 13. A rocket in space where gravity is negligible has a mass (including fuel) of 5000 kg. It is desired to give the rocket an average acceleration of 15.0 m/s² during the first second of fi ring the engine. The gases leave the rocket at a speed of 1500 m/s (relative to 15. A boy rides on a scooter pushing on the road with one foot with a horizontal force that depends on time, as shown in the graph. While the scooter rolls, a constant force of 25 N opposes the motion. The combined mass of the boy and scooter is 25 kg. a. Find the speed of the boy after 4.0 s, assuming he started from rest. b. Draw a graph to represent the variation of the boy's speed with time. F/N 150 100 50 0 0 0.5 15 11 1.0 1.5 2.0 20 2.5 3.0 3.5 4.0 t/s Homework: Part 2 - Momentum-Impulse 1. A cart moves in a horizontal line with constant speed v. Rain starts to fall and the cart fills with water at a rate of σkg/s. (This means that in one second, σ kg has fallen on the cart.) The cart must keep moving at constant speed. Determine the force that must be applied on the cart. 2. A 0.50 kg ball is dropped from rest above a hard floor. When it reaches the floor, it has a velocity of 4.0 m/s. The ball then bounces vertically upwards. Figure 2.77 is the graph of velocity against time for the ball. The positive direction for velocity is upwards. a. Find the magnitude of the momentum change of the ball during the bounce. b. The ball stayed in contact with the floor for 0.15 s. What average force did the floor exert on the ball? v/ms 4.0 0 -2.0- Figure 2.77 reaction force R weight mg♥ 3. Consider the graph of Figure 2.78c. The force acts on a body of mass 3.0 kg initially at rest. Calculate: a. the initial acceleration of the body b. the speed at 4.0 s c. the speed at 6.0 s. F/N 15 T 10 5 4. A ball of mass 0.20 kg moving at 3.6 m/s on a horizontal floor collides with a vertical wall. The ball rebounds with a speed of 3.2 m/s. The ball was in contact with the wall for 12 ms. Determine the maximum force exerted on the ball, assuming that the force depends on time according to Figure 2.79. 0 Figure 2.79 5. A moving body of mass m collides with a stationary body of double the mass and sticks to it. Calculate the fraction of the original kinetic energy that is lost. 6. A body at rest of mass M explodes into two pieces of masses M/4 and 3M/4. Calculate the ratio of the kinetic energies of the two fragments. 7. The momentum of a ball increased by 12.0 Ns as a result of a force that acted on the ball for 2.00 s. Find the average force on the ball. 8. The bodies in the diagram suffer a head- on collision and stick to each other afterwards. Find their common velocity. 2m 0 -5- m t/s -10 Figure 2.78 c force that varies linearly with time. 9. A 0.150 kg ball moving horizontally at 3.00 m/s collides normally with a vertical wall and bounces back with the same speed.

Homework: Part 2 - Momentum-Impulse a. Calculate the impulse delivered to the ball. b. The ball was in contact with the wall for 0.125 s. Find the average force exerted by the ball on the wall. 10. A ball of mass 250 g rolling on a horizontal floor with a speed 4.00 m/s hits a wall and bounces with the same speed, as shown in the diagram. 45° 45° the rocket). Estimate how much fuel must be burnt in that second. 14. A time-varying force varies with time as shown in the graph. The force acts on a body of mass 4.0 kg. a. Find the impulse of the force from t = 0 to t = 15 s. b. Find the speed of the mass at 15 s, assuming the initial velocity was zero. c. State the initial velocity of the body such it is brought to rest at 15 s. F/N 10- a. What is the magnitude and direction of the momentum change of the ball? b. Is momentum conserved here? Why or why not? 8- 6 4 2 0 0 5 10 15 20 t/s 11. Two masses moving in a straight line towards each other collide as shown in the diagram. Find the velocity (magnitude and direction) of the heavier mass after the collision. 4.0 kg before after 12.0 kg 24.0 ms¹ 2.0 ms¹ 3.0 ms¹ v=? 12. Two masses of 2.0 kg and 4.0 kg are held in place, compressing a spring between them. When they are released, the 2.0 kg moves away with a speed of 3.0 m/s. What was the energy stored in the spring? 13. A rocket in space where gravity is negligible has a mass (including fuel) of 5000 kg. It is desired to give the rocket an average acceleration of 15.0 m/s² during the first second of fi ring the engine. The gases leave the rocket at a speed of 1500 m/s (relative to 15. A boy rides on a scooter pushing on the road with one foot with a horizontal force that depends on time, as shown in the graph. While the scooter rolls, a constant force of 25 N opposes the motion. The combined mass of the boy and scooter is 25 kg. a. Find the speed of the boy after 4.0 s, assuming he started from rest. b. Draw a graph to represent the variation of the boy's speed with time. F/N 150 100 50 0 0 0.5 15 11 1.0 1.5 2.0 20 2.5 3.0 3.5 4.0 t/s Homework: Part 2 - Momentum-Impulse 1. A cart moves in a horizontal line with constant speed v. Rain starts to fall and the cart fills with water at a rate of σkg/s. (This means that in one second, σ kg has fallen on the cart.) The cart must keep moving at constant speed. Determine the force that must be applied on the cart. 2. A 0.50 kg ball is dropped from rest above a hard floor. When it reaches the floor, it has a velocity of 4.0 m/s. The ball then bounces vertically upwards. Figure 2.77 is the graph of velocity against time for the ball. The positive direction for velocity is upwards. a. Find the magnitude of the momentum change of the ball during the bounce. b. The ball stayed in contact with the floor for 0.15 s. What average force did the floor exert on the ball? v/ms 4.0 0 -2.0- Figure 2.77 reaction force R weight mg♥ 3. Consider the graph of Figure 2.78c. The force acts on a body of mass 3.0 kg initially at rest. Calculate: a. the initial acceleration of the body b. the speed at 4.0 s c. the speed at 6.0 s. F/N 15 T 10 5 4. A ball of mass 0.20 kg moving at 3.6 m/s on a horizontal floor collides with a vertical wall. The ball rebounds with a speed of 3.2 m/s. The ball was in contact with the wall for 12 ms. Determine the maximum force exerted on the ball, assuming that the force depends on time according to Figure 2.79. 0 Figure 2.79 5. A moving body of mass m collides with a stationary body of double the mass and sticks to it. Calculate the fraction of the original kinetic energy that is lost. 6. A body at rest of mass M explodes into two pieces of masses M/4 and 3M/4. Calculate the ratio of the kinetic energies of the two fragments. 7. The momentum of a ball increased by 12.0 Ns as a result of a force that acted on the ball for 2.00 s. Find the average force on the ball. 8. The bodies in the diagram suffer a head- on collision and stick to each other afterwards. Find their common velocity. 2m 0 -5- m t/s -10 Figure 2.78 c force that varies linearly with time. 9. A 0.150 kg ball moving horizontally at 3.00 m/s collides normally with a vertical wall and bounces back with the same speed.