# Worksheet: Coefficient of Restitution

In this worksheet, we will practice solving problems on the impact of two particles using conservation of linear momentum and Newton’s law of restitution.

**Q1: **

A smooth sphere was moving on a smooth horizontal surface at a speed of when it collided with a smooth vertical wall. The motion direction of the sphere at the instant of collision formed an angle of with the wall. Its speed immediately after the collision was . Determine the coefficient of restitution between the sphere and the wall.

- A
- B
- C
- D
- E

**Q2: **

A smooth snooker ball is moving at a speed of 7.9 m/s on a smooth snooker table. It strikes one of the smooth cushions of the table at an angle of . Given that the coefficient of restitution between the ball and the cushion is , find the ballβs speed and the angle its path makes with the cushion after the impact, rounding the answer to one decimal point.

- A4.5 m/s,
- B7.9 m/s,
- C4.5 m/s,
- D19.8 m/s,
- E7.9 m/s,

**Q3: **

A smooth sphere of mass 2 kg sliding along a horizontal plane collided with a stationary smooth sphere of mass 5 kg. Just before the collision, the first sphere was moving at 6 m/s and its direction of motion made an angle of with the line of centers of the spheres. Given that the coefficient of restitution between the spheres is , find the velocity of the first sphere after the collision. Express the magnitude of this velocity in meters per second and the direction of the velocity as the angle made with the line of centers of the spheres. Give both values correct to one decimal place.

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

**Q4: **

A small smooth sphere was moving in the horizontal -plane at m/s when it collided with a vertical wall whose base is the -axis. Given that the coefficient of restitution between the sphere and the wall is , find the velocity of the sphere after the collision.

- A m/s
- B m/s
- C m/s
- D m/s
- E m/s

**Q5: **

A smooth ball hit a smooth wall at an angle of to the wall and rebounded at an angle of to the wall. What proportion of the ballβs kinetic energy was lost due to the impact?

- A
- B
- C
- D
- E

**Q6: **

A smooth ball vertically fell, striking a smooth plane inclined at to the horizontal such that . Given that the ballβs speed just before impact was 9.6 m/s and that its speed after impact was , find, correct to two decimal places, the coefficient of restitution between the ball and the plane.

**Q7: **

A smooth ball hit a smooth wall at an angle of to the wall and rebounded at an angle of to the wall. Determine the coefficient of restitution between the ball and the wall.

- A
- B
- C
- D
- E

**Q8: **

A smooth ball hit a smooth wall at to the wall and rebounded at a right angle to its original direction. Find, correct to one decimal place, the coefficient of restitution between the ball and the wall.

**Q9: **

Two spheres, and , collided with each other when was moving with a velocity of 4 m/s and was moving with a velocity of 1 m/s in the opposite direction. After the collision, moved with a velocity of 3 m/s in the same direction. If the coefficient of restitution was , find the velocity of after the collision.

**Q10: **

A smooth sphere was moving on a horizontal table with a velocity of 5 m/s when it collided normally with a vertical wall and rebounded with a velocity of 2 m/s. Calculate the coefficient of restitution between the sphere and the wall.

- A
- B
- C
- D
- E

**Q11: **

A ball at rest falls to collide with the ground surface with a velocity and rebounds with a velocity of 2 m/s. If the coefficient of restitution between the ball and the ground is 0.5, find the velocity of the sphere before the collision.

**Q12: **

A ball at rest falls from a height of 3 m to collide with the ground surface and rebound with a velocity of 2 m/s. Find the coefficient of restitution between the ball and the ground. Approximate your answer to two decimal places.

**Q13: **

A smooth sphere is moving on a horizontal table with a speed of 12 m/s when it collides normally with a vertical wall and rebounds with a speed . Given that the coefficient of restitution between the sphere and the wall is , find the speed of the sphere after the rebound.