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 𝑃 . Another ball of mass 20 g passed point 𝑃 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 𝑃 , 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 π‘₯ 𝑦 -plane at ( 1 7 βˆ’ 7 ) i j 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 1 2 , find the velocity of the sphere after the collision.

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

Q3:

A smooth ball hit a smooth wall at an angle of t a n   1 3 8 to the wall and rebounded at an angle of t a n   3 2 to the wall. What proportion of the ball’s kinetic energy was lost due to the impact?

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

Q4:

A smooth ball vertically fell, striking a smooth plane inclined at 𝛼 to the horizontal such that t a n 𝛼 = 3 4 . Given that the ball’s speed just before impact was 9.6 m/s and that its speed after impact was 8 . 1 / m s , 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 t a n   ο€Ό 1 5 7  to the wall and rebounded at an angle of t a n   ο€Ό 3 4  to the wall. Determine the coefficient of restitution between the ball and the wall.

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

Q6:

A smooth ball hit a smooth wall at 6 2 ∘ 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 𝑒 when it collided with a smooth vertical wall. The motion direction of the sphere at the instant of collision formed an angle of 6 0 ∘ with the wall. Its speed immediately after the collision was 1 3 1 4 𝑒 . Determine the coefficient of restitution between the sphere and the wall.

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

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 6 0 ∘ . Given that the coefficient of restitution between the ball and the cushion is 3 1 0 , 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 7.9 m/s, 7 . 4 ∘
  • B 4.5 m/s, 6 2 . 5 ∘
  • C 7.9 m/s, 2 7 . 5 ∘
  • D 4.5 m/s, 2 7 . 5 ∘
  • E 19.8 m/s, 2 7 . 5 ∘

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