Worksheet: Oblique Impact

In this worksheet, we will practice solving problems about oblique impact of objects in two dimensions involving using conservation of momentum and coefficient of restitution.

Q1:

A body 𝐴 of mass 5 kg, moving with a velocity v i j  = 2 + / m s , collided with another body 𝐡 , of mass 10 kg that was moving with a velocity v i j  = βˆ’ 6 βˆ’ 3 / m s . After the impact, if the velocity of body 𝐴 became v i j   = βˆ’ 6 βˆ’ 3 / m s , determine the speed of body 𝐡 .

  • A 2 √ 5 m/s
  • B βˆ’ 2 βˆ’ i j m/s
  • C √ 5 m/s
  • D βˆ’ 2 + i j m/s

Q2:

Two spheres, 𝐴 and 𝐡 , have equal radii and are moving across a smooth horizontal surface. Sphere 𝐴 has a mass of 3 kg and is moving with velocity ( βˆ’ 4 βˆ’ 4 ) i j m/s. Sphere 𝐡 has a mass of 6 kg and moves with a velocity ( 4 βˆ’ 6 ) i j m/s. The spheres collide when the line of their centres is parallel to j . Sphere 𝐴 has a velocity of 𝑣  immediately after the impact and sphere 𝐡 has a velocity of 𝑣  immediately after the impact. Find the velocities 𝑣  and 𝑣  in vector form, taking the coefficient of restitution between the spheres to be 1 2 .

  • A 𝑣 = ( 4 βˆ’ 6 ) /  i j m s , 𝑣 = ( βˆ’ 4 βˆ’ 6 ) /  i j m s
  • B 𝑣 = ( βˆ’ 4 βˆ’ 6 ) /  i j m s , 𝑣 = ( 4 βˆ’ 5 ) /  i j m s
  • C 𝑣 = ( βˆ’ 4 + 6 ) /  i j m s , 𝑣 = ( 4 βˆ’ 5 ) /  i j m s
  • D 𝑣 = ( βˆ’ 4 βˆ’ 6 ) /  i j m s , 𝑣 = ( 4 βˆ’ 1 0 ) /  i j m s
  • E 𝑣 = ( 4 + 6 ) /  i j m s , 𝑣 = ( βˆ’ 4 βˆ’ 5 ) /  i j m s

Q3:

Two smooth spheres of equal radii and masses π‘š kg and 5 π‘š kg collided while moving on a smooth horizontal surface. Before the collision, the sphere of mass π‘š kg was moving at ( 9 + 5 ) i j m/s and the sphere of mass 5 π‘š kg was moving at ( βˆ’ 5 ) i j m/s. After the collision, the sphere of mass π‘š kg was moving at ( 5 + 7 ) i j m/s. Find the speed of the sphere of mass 5 π‘š kg after the collision.

  • A 9 √ 1 0 m/s
  • B 6 √ 5 5 m/s
  • C 5 √ 5 8 m/s
  • D 9 √ 1 0 5 m/s
  • E 3 √ 7 4 5 m/s

Q4:

A smooth sphere of mass 6 π‘š kg was sliding on a smooth horizontal plane when it collided with another, initially stationary, smooth sphere of the same size and a mass of 9 π‘š kg. The first sphere’s direction of motion after the collision was at right angles to its direction of motion before the collision. Let πœƒ be the angle the first sphere’s direction of motion made with the line of centres of the spheres just before impact. Find an expression for t a n  πœƒ in terms of the coefficient of restitution between the two spheres, 𝑒 .

  • A 2 𝑒 βˆ’ 3 5
  • B 2 𝑒 + 3 5
  • C 3 𝑒 βˆ’ 2 3
  • D 3 𝑒 βˆ’ 2 5
  • E 3 𝑒 + 2 5

Q5:

A small smooth sphere of mass 6 kg was moving in the π‘₯ 𝑦 -plane with a velocity of ( 7 + 3 ) i j m/s. The sphere collided with a smooth vertical wall coincident with the line 𝑦 = π‘₯ . Assuming the coefficient of restitution between the sphere and the wall is 1 3 , find the amount of kinetic energy lost due to the collision. Give your answer correct to the nearest two decimal places.

Q6:

Sphere 𝐴 was moving at a velocity of ( 3 + 7 ) i j m/s on a smooth horizontal plane when it collided with sphere 𝐡 . After the collision its velocity became ( 6 + 4 ) i j m/s. Find a unit vector parallel to the line of centres of the spheres at the instant of collision.

  • A βˆ’ 3 + 3 i j
  • B √ 2 2 ( βˆ’ ) i j
  • C 3 βˆ’ 3 i j
  • D √ 2 2 ( βˆ’ 3 + ) i j
  • E √ 2 2 ( + ) i j

Q7:

A small smooth sphere moving in the π‘₯ 𝑦 -plane collided with a smooth vertical wall, where the 𝑦 -axis is, with a velocity of ( βˆ’ 9 βˆ’ 4 ) i j m/s. The coefficient of restitution between the sphere and the wall is 1 5 . What is the sphere’s speed after impact? Give your answer correct to two decimal places.

Q8:

A smooth ball of mass 730 g fell vertically and struck a smooth plane inclined at an angle of 5 5 ∘ to the horizontal. The ball’s speed just before it hit the plane was 8 m/s and the coefficient of restitution between the ball and the plane is 2 9 . Determine the magnitude of the impulse received by the ball at the moment of impact. Give your answer in newton seconds correct to two decimal places.

Q9:

Two smooth spheres of the same radius are moving on a smooth horizontal surface. One sphere has a mass of 2 kg and moves with velocity ( 2 βˆ’ 3 ) i j m/s. The other sphere has a mass of 4 kg and moves with velocity ( βˆ’ 2 + 4 ) i j m/s. At the moment the spheres collide, the line between their centres is parallel to i . If the coefficient of restitution between the spheres is 1 5 , find the kinetic energy lost in the impact.

Q10:

A small smooth ball of mass 6 kg was moving with velocity ( 3 βˆ’ 7 ) i j m/s when it hit a smooth wall. It rebounded from the wall with velocity ( 8 + 5 ) i j m/s. Find the magnitude of the impulse received by the ball.

Q11:

A small smooth ball of mass 5 kg was moving with velocity ( 9 βˆ’ 6 ) i j m/s when it hit a smooth wall. It rebounded from the wall with velocity ( 3 + 2 ) i j m/s. Find the magnitude of the impulse received by the ball.

Q12:

A smooth sphere moving on a smooth horizontal surface at a velocity of ( βˆ’ 4 βˆ’ ) i j m/s collided with another smooth sphere of the same radius but half the mass, which was moving at ( 4 βˆ’ 2 ) i j m/s. Given that, after the collision, the first sphere’s velocity became ( βˆ’ 2 βˆ’ 2 ) i j m/s, find the coefficient of restitution between the spheres.

  • A 4 1 7
  • B 1 6
  • C 1 2 6
  • D 2 1 7
  • E 2 2 7

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