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

  • A2√5 m/s
  • Bβˆ’2βˆ’ij m/s
  • C√5 m/s
  • Dβˆ’2+ij 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’4βˆ’4)ij m/s. Sphere 𝐡 has a mass of 6 kg and is moving with a velocity (4βˆ’6)ij m/s. The spheres collide when the line of their centers is parallel to j. Sphere 𝐴 has a velocity of π‘£οŠ§ immediately after the impact and sphere 𝐡 has a velocity of π‘£οŠ¨ immediately after the impact. Find the velocities π‘£οŠ§ and π‘£οŠ¨ in vector form, taking the coefficient of restitution between the spheres to be 12.

  • A𝑣=(4βˆ’6)/ijms, 𝑣=(βˆ’4βˆ’6)/ijms
  • B𝑣=(βˆ’4βˆ’6)/ijms, 𝑣=(4βˆ’5)/ijms
  • C𝑣=(βˆ’4βˆ’6)/ijms, 𝑣=(4βˆ’10)/ijms
  • D𝑣=(4+6)/ijms, 𝑣=(βˆ’4βˆ’5)/ijms
  • E𝑣=(βˆ’4+6)/ijms, 𝑣=(4βˆ’5)/ijms

Q3:

Two smooth spheres of equal radii and masses π‘š kg and 5π‘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)ij m/s and the sphere of mass 5π‘š kg was moving at (βˆ’5)ij m/s. After the collision, the sphere of mass π‘š kg was moving at (5+7)ij m/s. Find the speed of the sphere of mass 5π‘š kg after the collision.

  • A9√105 m/s
  • B6√55 m/s
  • C5√58 m/s
  • D9√10 m/s
  • E3√745 m/s

Q4:

A smooth sphere of mass 6π‘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 9π‘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 centers of the spheres just before impact. Find an expression for tanοŠ¨πœƒ in terms of the coefficient of restitution between the two spheres, 𝑒.

  • A2π‘’βˆ’35
  • B3𝑒+25
  • C3π‘’βˆ’25
  • D3π‘’βˆ’23
  • E2𝑒+35

Q5:

A small smooth sphere of mass 6 kg was moving in the π‘₯𝑦-plane with a velocity of (7+3)ij 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 13, 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)ij m/s on a smooth horizontal plane when it collided with sphere 𝐡. After the collision its velocity became (6+4)ij m/s. Find a unit vector parallel to the line of centers of the spheres at the instant of collision.

  • A√22(+)ij
  • B3βˆ’3ij
  • C√22(βˆ’3+)ij
  • Dβˆ’3+3ij
  • E√22(βˆ’)ij

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’9βˆ’4)ij m/s. The coefficient of restitution between the sphere and the wall is 15. 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 55∘ 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 29. 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 (2βˆ’3)ij m/s. The other sphere has a mass of 4 kg and moves with velocity (βˆ’2+4)ij m/s. At the moment the spheres collide, the line between their centers is parallel to i. If the coefficient of restitution between the spheres is 15, find the kinetic energy lost in the impact.

Q10:

A small smooth ball of mass 6 kg was moving with velocity (3βˆ’7)ij m/s when it hit a smooth wall. It rebounded from the wall with velocity (8+5)ij 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 (9βˆ’6)ij m/s when it hit a smooth wall. It rebounded from the wall with velocity (3+2)ij 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’4βˆ’)ij m/s collided with another smooth sphere of the same radius but half the mass, which was moving at (4βˆ’2)ij m/s. Given that, after the collision, the first sphere’s velocity became (βˆ’2βˆ’2)ij m/s, find the coefficient of restitution between the spheres.

  • A217
  • B227
  • C16
  • D417
  • E126

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