# Coefficient of restitution problem

• Samtheguy
In summary, the problem involves two identical steel balls, A and B, colliding with initial velocities VA = 6 m/s and VB = 8 m/s respectively. The coefficient of restitution is given as 0.7 and the goal is to determine the magnitude and direction of the velocity of each ball after impact. The solution involves calculating the y-component of VA, using the equation for coefficient of restitution, and solving for the relative velocity of separation. The questioner is unsure if their method is correct and is seeking assistance.
Samtheguy

## Homework Statement

The two identical steel balls A and B moving with initial velocities VA = 6 m/s and VB = 8 m/s collide, as shown in figure Q4. If the coefficient of restitution is e = 0.7, determine the magnitude and direction of the velocity of each ball just after impact.
(See Attachment, Question 4)

## The Attempt at a Solution

Calculate the y-component of VA.
VA(y) = 6*cos(30) = -5.196 m/s (Since it is traveling in the -y direction)

e = (VB' - VA')/(VA - VB)

Where:

(VB' - VA') is the relative velocity of separation after impact (m/s)
(VA - VB) is the relative velocity of approach (m/s)
e is the coefficient of restitution

0.7 = (VB' - VA')/(-5.196 - 8)

0.7*(-5.196 - 8) = (VB' - VA')

-9.2372 = (VB' - VA')

Is this method correct so far? If so, I don't know where to go from here.

#### Attachments

• 06mmb140_exam.pdf
165.3 KB · Views: 1,263
Any help on this question would be great as I got this same question on an exam and I am wondering if I got the beginning right or not.

## 1. What is the coefficient of restitution?

The coefficient of restitution (COR) is a measure of the elasticity of a collision between two objects. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach between the two objects.

## 2. How is the coefficient of restitution calculated?

The COR is calculated by dividing the velocity of the object after the collision by the velocity of the object before the collision. This value is typically between 0 and 1, with 0 representing a completely inelastic collision and 1 representing a perfectly elastic collision.

## 3. What factors can affect the coefficient of restitution?

The COR can be affected by several factors, including the material properties of the objects involved, the angle of collision, and the surface conditions. In addition, the COR may also change if the objects experience deformation or rotation during the collision.

## 4. Why is the coefficient of restitution important in physics?

The COR is important in physics because it helps us understand how energy is conserved in collisions. In an elastic collision, the COR is equal to 1, indicating that no kinetic energy is lost. In an inelastic collision, the COR is less than 1, indicating that some kinetic energy is lost and converted into other forms of energy.

## 5. How is the coefficient of restitution used in sports?

In sports, the COR is used to measure the bounciness or liveliness of balls and other equipment. It can also be used to compare the performance of different types of balls or to determine if a ball is within the acceptable range of COR for a particular sport. In some cases, the COR may also be regulated to ensure fairness and consistency in competition.

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