# How do you calculate the coefficient of restitution?

This law states that: "in a system of colliding bodies(usually 2 bodies) the relative velocity of separation is directly proportional to the relative velocity of approach".

Thus, all you need to calculate e are the respective initial and final velocities of the two bodies involved in collision.

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The coefficient of restitution (( e )) is calculated using the formula:

[ e = \frac{{\text{Relative velocity of separation}}}{{\text{Relative velocity of approach}}} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- In a game of pool, the cue ball strikes another ball of the same mass and initially at rest. After the collision, the cue ball moves at 1.10 m/s along a line making an angle of 29.0° with its original direction of motion, and the second ball has a speed ?
- A ball with a mass of #3 kg # and velocity of #7 m/s# collides with a second ball with a mass of #5 kg# and velocity of #- 4 m/s#. If #10%# of the kinetic energy is lost, what are the final velocities of the balls?
- A ball with a mass of #4 kg# moving at #7 m/s# hits a still ball with a mass of #32 kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?
- A ball with a mass of # 5 kg# is rolling at #2 m/s# and elastically collides with a resting ball with a mass of #2 kg#. What are the post-collision velocities of the balls?

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