# Find the factor by which the KE of the ball increases

• nolee52738
In summary, the conversation is about a physics question involving a collision between a ball and a bat with the same speed of 1.30 m/s. The question asks for the speed of the ball after the collision and the factor by which its kinetic energy increases. The responder suggests solving the problem from a frame in which the bat is at rest, making it easier to find the velocity of the ball. The conversation also includes equations for conservation of momentum and energy and a hint to consider the relative velocities before and after the collision. The final summary is focused on solving the problem more efficiently by considering the frame of reference and using simplified equations.
nolee52738
Hi,
Can anyone help me in this question?
1) A ball and bat, approach one another each with the same speed of 1.30 m/s, collide. Find the speed of the ball after the collision. (Assume the mass of the bat is much much larger than the mass of the ball and that this is an elastic collision with no rotational motion).
(in m/s)
2)Find the factor by which the KE of the ball increases due to the collision.

I have tried to solve it but I did not know how to continue.

Sorry for my broken english & thanks in advance.

Show what you have tried.

Hint: View things from a frame in which the bat is at rest.

*mass of the ball= m
mass of the bat= M
*speed of the ball after the collision= u1
speed of the bat after the collision= u2
*speed of the ball before the collision= v1= 1.30m/s
speed of the bat before the collision=v2= 1.30 m/s

*mv1 + Mv2 = mu1 + Mu2
1.30m + 1.30M = mu1 + Mu2

*0.5m*(1.30)^2 +0.5M*(1.30)^2 = 0.5m*(u1)^2 +0.5M*(u2)^2
1.69m + 1.69M = m*(u1)^2 + M*(u2)^2

And then I did not know how to continue.

I have tried this now:

(1)m(1.30-u1) = M(u2-1.30)
(2)m(1.69-u1^2) = M(u2^2 - 1.69)

(2)/(1) --> (1.69-u1^2)/(1.30-u1) = (u2^2 -1.69)/(u2-1.30)

(1.30-u1)(1.30+u1)/(1.30-u1)= (u2-1.30)(u2+1.30)/(u2-1.30)
1.30+u1 = u2 +1.30
u1=u2

??

I think the responder tried to make it easier for you by assuming the bat was at rest. To make the problem the same for this situation what would the velocity of the ball be?

Makes it a whole lot easier.

You can certainly solve the problem from the 'ground' frame, it's just harder. To do that, first combine the equations for conservation of momentum and energy to deduce a relationship about relative velocities before and after the collision.

Hint: Since the ball is assumed to be much heavier than the ball, M >> m, what can you say about the final speed of the bat to a good approximation?

My point was that it might be easier to solve this from a frame in which the bat is at rest. In that frame, the bat is like a wall. If you bounce a ball elastically off a wall, what is its final velocity? Get the answer in that frame, then transform back to the original frame.

nolee52738 said:
*mass of the ball= m
mass of the bat= M
*speed of the ball after the collision= u1
speed of the bat after the collision= u2
*speed of the ball before the collision= v1= 1.30m/s
speed of the bat before the collision=v2= 1.30 m/s

*mv1 + Mv2 = mu1 + Mu2
1.30m + 1.30M = mu1 + Mu2
Careful. While the speed of ball and bat is the same, their direction of motion is not. They move in opposite directions, so they have different velocities.

## 1. What is the equation for finding the kinetic energy (KE) of a ball?

The equation for finding the KE of a ball is KE = 1/2 * m * v^2, where m is the mass of the ball and v is the velocity of the ball.

## 2. How can I calculate the increase in KE of a ball?

To calculate the increase in KE of a ball, you will need to know the initial KE and the final KE. The increase in KE can be found by subtracting the initial KE from the final KE.

## 3. Can the factor by which the KE of a ball increases be greater than 1?

Yes, the factor by which the KE of a ball increases can be greater than 1. This indicates that the ball's final KE is greater than its initial KE, resulting in an increase in energy.

## 4. How does the mass of the ball affect the increase in KE?

The mass of the ball directly affects the increase in KE. The greater the mass of the ball, the greater the increase in KE will be, assuming the velocity remains constant.

## 5. What factors can cause the KE of a ball to increase?

The KE of a ball can increase due to an increase in velocity, an increase in mass, or a combination of both. Other factors such as air resistance and friction may also play a role in the increase of KE.

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