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 𝑒 when it collided with a smooth vertical wall. The motion direction of the sphere at the instant of collision formed an angle of 60∘ with the wall. Its speed immediately after the collision was 1314𝑒. Determine the coefficient of restitution between the sphere and the wall.

  • A 2 √ 1 0 7
  • B 2 2 4 9
  • C √ 2 2 7
  • D 4 0 4 9
  • E √ 3 0 7

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 60∘. Given that the coefficient of restitution between the ball and the cushion is 310, find the ball’s speed and the angle its path makes with the cushion after the impact, rounding the answer to one decimal point.

  • A 4.5 m/s, 2 7 . 5 ∘
  • B 7.9 m/s, 7 . 4 ∘
  • C 4.5 m/s, 6 2 . 5 ∘
  • D 19.8 m/s, 2 7 . 5 ∘
  • E 7.9 m/s, 2 7 . 5 ∘

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 60∘ with the line of centers of the spheres. Given that the coefficient of restitution between the spheres is 18, find the velocity of the first sphere after the collision. Express the magnitude of this velocity 𝑣 in meters per second and the direction of the velocity πœƒ as the angle made with the line of centers of the spheres. Give both values correct to one decimal place.

  • A 𝑣 = 3 . 2 / m s , πœƒ = 7 1 . 2 ∘
  • B 𝑣 = 3 . 1 / m s , πœƒ = 8 3 . 5 ∘
  • C 𝑣 = 5 . 2 / m s , πœƒ = 8 3 . 5 ∘
  • D 𝑣 = 5 . 2 / m s , πœƒ = 7 8 . 9 ∘
  • E 𝑣 = 5 . 3 / m s , πœƒ = 7 8 . 9 ∘

Q4:

A small smooth sphere was moving in the horizontal π‘₯𝑦-plane at (17βˆ’7)ij m/s when it collided with a vertical wall whose base is the 𝑦-axis. Given that the coefficient of restitution between the sphere and the wall is 12, find the velocity of the sphere after the collision.

  • A ( βˆ’ 8 . 5 βˆ’ 7 ) i j m/s
  • B ( βˆ’ 7 βˆ’ 8 . 5 ) i j m/s
  • C ( 8 . 5 + 7 ) i j m/s
  • D ( 1 7 βˆ’ 7 ) i j m/s
  • E ( 8 . 5 βˆ’ 7 ) i j m/s

Q5:

A smooth ball hit a smooth wall at an angle of tan138 to the wall and rebounded at an angle of tan32 to the wall. What proportion of the ball’s kinetic energy was lost due to the impact?

  • A 2 0 8 2 3 3
  • B 2 5 2 3 3
  • C 2 5 2 0 8
  • D 3 9 1 6
  • E 4 4 1 2 3 3

Q6:

A smooth ball vertically fell, striking a smooth plane inclined at 𝛼 to the horizontal such that tan𝛼=34. Given that the ball’s speed just before impact was 9.6 m/s and that its speed after impact was 8.1/ms, 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 tanοŠ±οŠ§ο€Ό157 to the wall and rebounded at an angle of tanοŠ±οŠ§ο€Ό34 to the wall. Determine the coefficient of restitution between the ball and the wall.

  • A 2 5 1 6
  • B 2 0 7
  • C 1 6 2 5
  • D 7 2 0
  • E 1 9 6 8

Q8:

A smooth ball hit a smooth wall at 62∘ 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.

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