# Worksheet: Newton's Law of Restitution for Collisions of a Particle with a Smooth Plane

In this worksheet, we will practice applying Newton's law of restitution to direct collision of a particle with a smooth surface perpendicular to the direction of motion.

**Q1: **

A ball of mass 84 g
was moving at a constant speed of 90 cm/s
when it passed point .
Another ball of mass 20 g
passed point exactly one minute later,
moving at a speed of 55 cm/s
and accelerating at 5 cm/s^{2} in its direction of movement.
Both balls were moving in the same direction. Some time after passing point ,
the two balls collided and coalesced into one body.
Given that a resistance force of 190 dynes
acted on this compound body, determine the time it took to come to rest.

**Q2: **

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

**Q3: **

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

**Q4: **

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.

**Q5: **

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

**Q6: **

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.

**Q7: **

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

**Q8: **

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.

- A 7.9 m/s,
- B 4.5 m/s,
- C 7.9 m/s,
- D 4.5 m/s,
- E 19.8 m/s,