# Worksheet: Impulse and Momentum

In this worksheet, we will practice relating the impulse on a body to the change of momentum of the body.

**Q1: **

A constant force acted on a body of mass 6 kg. As a result, its speed changed from 37 km/h to 49 km/h. Calculate the magnitude of the impulse of this force on this body.

**Q2: **

Three forces, , , and , where , , and are three mutually perpendicular unit vectors, acted on a body for 3 seconds. Find the magnitude of their combined impulse on the body.

- A27 N⋅s
- B N⋅s
- C N⋅s
- D9 N⋅s

**Q3: **

A constant force acted on a body of mass changing its speed from 9 m/s to 54 km/h. Given that the impulse of the force was 5.82 N⋅s, determine the value of .

**Q5: **

A sphere of mass 125 g was moving along a section of horizontal ground at 165 cm/s when it hit a vertical wall. Given that the wall applied an impulse of magnitude 0.214 N⋅s to the sphere, find the speed of the sphere as it bounced off the wall.

**Q6: **

A railway carriage of mass 23 t
was moving at 14 m/s
before it crashed into a barrier.
Given that it took 4 s
for the carriage to come to rest,
determine the magnitude of the impulse and the average force to the nearest kilogram weight.
Consider the acceleration due to gravity to be 9.8 m/s^{2}.

- A ,
- B ,
- C ,
- D ,

**Q7: **

A sphere of mass 83 g fell vertically from a height of
8.1 m onto a section of horizontal ground. It
rebounded and reached a height of 3.6 m. Given that the duration of the
impact was 0.42 seconds, and the acceleration due to gravity
is 9.8 m/s^{2},
find the average impact force to the nearest two decimal places.

**Q8: **

A ball of mass 560 g fell 3.6 m onto a section of horizontal ground. It rebounded to a height of 1.6 m. Given that the ball and the ground were in contact for 0.08 seconds, determine the average impact force between the ball and the ground. Take .

- A180.488 N
- B98 N
- C103.488 N
- D960.4 N

**Q9: **

A ball of mass 5 kg fell from a height of 6.4 m onto a section of horizontal ground. It rebounded to a height of 2.5 m. Given that the duration of the impact was 0.5 seconds, determine the magnitude of the average force the ground exerted on the ball. Take .

**Q10: **

A smooth ball of mass 240 g was projected vertically upward at 16 m/s toward a horizontal ceiling 390 cm above the ground. The ball collided with the ceiling and rebounded vertically downward. The magnitude of the impact force acting on the ceiling from the ball was 960 g-wt, and they were in contact for of a second. Determine the ball’s speed when it rebounded from the ceiling. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

**Q11: **

A body of mass 349 g was projected vertically upward at 539 m/s from a
point which was 78 cm below the ceiling of a room. When it hit the ceiling,
it rebounded and, 0.6 seconds later, it hit the floor. Given that the height of the
ceiling was 390 cm, and the duration of the impact was seconds, find the
impact force to the nearest newton. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

**Q12: **

The given figure shows a force-time graph for a force acting in a constant direction on a body moving along a smooth horizontal plane. Using the information provided, calculate the magnitude of the force’s impulse.

**Q13: **

The given figure shows a force-time graph. At time seconds, where , the force is given by . Find the impulse over the first four seconds.

- A4 N⋅s
- B8 N⋅s
- C N⋅s
- D N⋅s

**Q14: **

The given figure shows a force-time graph. At time seconds, where , the force is given by . Find its impulse during the sixth second.

- A2 N⋅s
- B N⋅s
- C N⋅s
- D8 N⋅s

**Q15: **

Two forces and act on a body of unit mass for 19 seconds. Given that and , find the magnitude of the impulse.

- A N⋅s
- B N⋅s
- C N⋅s
- D N⋅s

**Q16: **

The forces , , and acted on a body for 3 seconds. If their combined impulse on the body was , find the values of and .

- A ,
- B ,
- C ,
- D ,

**Q17: **

A stone was thrown into a well at 4.5 m/s and reached the bottom 4 seconds later. Given that , determine the stone’s velocity when it reached the bottom of the well.

**Q18: **

A bullet of mass 24 g was shot horizontally at 496 m/s towards a wooden body of mass 1 kg which was resting on a rough horizontal table. The bullet lodged into the wooden block, and they started to move together as one body across the table. After sliding across the table for 70 cm, this body collided with a perpendicular barrier fixed to the table. It rebounded at 66 cm/s. Given that the resistance of the table to the movement of the block was 39.7 N, find the impulse of the barrier on the body.

**Q19: **

A ball of mass 400 g moves in a straight line along a smooth horizontal surface towards a vertical wall with a constant speed of 16 m/s. Given that the direction of the ball’s motion is perpendicular to the wall, and that the wall exerts an impulse of 11 N⋅s on the ball during the impact, find the rebound speed of the ball.

- A5.75 m/s
- B27.5 m/s
- C11.5 m/s
- D19.5 m/s

**Q20: **

A sphere of mass 163 g hit a vertical wall as it was moving horizontally at 67 cm/s. Given that it rebounded in the opposite direction and the change in its momentum was 11,899 g⋅cm/s, determine its speed after it struck the wall.

**Q21: **

A rubber ball of mass 41 g was moving horizontally along a smooth surface. It struck a barrier at 62 cm/s and rebounded in the opposite direction at 45 cm/s. Find the magnitude of the change in its momentum as a result of the impact.

**Q22: **

From a point that lies 225 cm
below the ceiling of a room, a ball of mass 51 g
was projected vertically upward with a speed of 885 cm/s.
If the change in the ball’s momentum when it hit the ceiling was 36,720 g⋅cm/s,
determine the ball’s speed after the collision. Consider the acceleration due to gravity to be 9.8 m/s^{2}.

**Q23: **

A rubber ball of mass 10 g fell from a height of 8.1 m onto a section of horizontal ground. It struck the ground and rebounded to a height of 4.9 m. Calculate the magnitude of the change in momentum that resulted from the impact. Take .

- A224 g⋅cm/s
- B112 g⋅cm/s
- C 11,200 g⋅cm/s
- D 22,400 g⋅cm/s

**Q24: **

A rubber ball fell vertically from a height 6.4 m above the ground. It then rebounded to a height of 1.6 m. If the change in the ball’s momentum due to impact is 1,113 kg⋅cm/s, determine the ball’s mass. Take .

**Q25: **

A rubber ball of mass 54 g fell on a section of horizontal ground. Its speed just before hitting the ground was 41 m/s. After striking the ground, it rebounded to a height of 250 cm before it momentarily came to rest. Taking , determine the magnitude of the change in momentum which resulted from the impact.