# 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/s2 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 ballβs 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 ballβs 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 ballβs 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,