Worksheet: Elasticity of Collisions

In this worksheet, we will practice distinguishing between the effects of collisions which do and which do not conserve kinetic energy.

Q1:

A ball bounces repeatedly, dissipating 10% of its kinetic energy with each bounce.

Which of the lines plotted on the graph correctly represents the change in the mechanical energy of the ball with time?

  • ALine I
  • BLine ll
  • CLine lll

Q2:

Two objects, I and II, collide. Object I has a mass of 1.2 kg and object II has a mass of 0.75 kg. Object I has a speed of 1.4 m/s before the collision and object II has a speed of 1.8 m/s before the collision. After the collision, object II has a speed of 2.1 m/s.

If the collision is perfectly elastic, what is the speed of object I after the collision?

If the collision is not perfectly elastic, what must the speed of object I after the collision be less than?

If the collision is not perfectly elastic, what is the minimum value of the speed of object I after the collision?

Q3:

Two objects, I and II, collide. Object I has a mass of 0.25 kg and object II has a mass of 0.45 kg. Object I has a speed of 2.8 m/s before the collision and object II has a speed of 3.3 m/s before the collision. The collision is inelastic, dissipating 35% of the kinetic energy of the objects. After the collision, object I has a speed of 1.8 m/s.

What is the speed of object II after the collision?

What is the ratio of the kinetic energy of object I before the collision to its kinetic energy after the collision?

What is the ratio of the kinetic energy of object II before the collision to its kinetic energy after the collision?

Q4:

Two objects, I and II, collide. Object I has a mass of 1.5 kg and object II has a mass of 0.55 kg. Object I has a speed of 1.8 m/s before the collision, and object II has a speed of 1.3 m/s before the collision. The collision is inelastic, dissipating 25% of the kinetic energy of the objects.

If object I is stationary after the collision, what is the speed of object II after the collision?

If object II is stationary after the collision, what is the speed of object I after the collision?

If both objects have the same speed after the collision, what is their speed?

Q5:

The following diagram shows the changes in the positions of two objects from time 𝑡 to their positions at time 𝑡. The objects have the same mass as each other. The arrows above the objects indicate the direction of their velocities, but the magnitudes of the velocities are not known; they may or may not be equal to each other. A point 𝑃 is a distance 𝐷 from both of the objects at 𝑡; but at 𝑡, the objects are at distances 𝑑 and 𝑑 from 𝑃, where 𝑑<𝑑. The directions of the velocities at 𝑡 are shown in the diagram, but the magnitudes are not known and may be zero. No external forces act on either object.

Which of the following is the least distance from the point 𝑃 to the point at which the objects could have come into contact with each other?

  • A𝑑𝑑
  • B𝑑
  • C0
  • D𝑑
  • E𝑑𝑑

Which of the following is the greatest distance from the point 𝑃 to the point at which the objects could have come into contact with each other?

  • A𝑑
  • B𝑑𝑑
  • C𝑑
  • D𝑑𝑑
  • E0

For which of the following quantities is the value the same at 𝑡 and at 𝑡?

  • AThe speed of either object
  • BThe momentum of either object
  • CTotal momentum
  • DThe kinetic energy of either object
  • ETotal kinetic energy

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