# Conservation of energy/momentum in a pendulum?

## Homework Statement

http://www.phy-astr.gsu.edu/Hsiao-Ling/quiz2211-F10.ppt" [Broken]

You have a pendulum:
The bob's mass is 200g.
The string length is 1m.
The angle the bob is raised to is 45 degrees.

You also have a block that is at rest at the bottom of the pendulum's swing:
The block's mass is 1kg.
The block is at rest.
No friction.

What is the speed of the bob right before it makes impact with the block?
What is the velocity of the bob and block right after impact?
What is the maximum rebound angle of the bob after impact?

## Homework Equations

Total energy of system = U + K
Initial momentum of the system = Final momentum of the system
Total initial energy = total final energy

## The Attempt at a Solution

I think I have solved the first question:
By calculating the change in height of the bob, to be .293m, I found the potential energy to be .574 joules. The kinetic energy right before impact should also equal .574, therefore velocity = 2.4 m/s. So right before impact the bob's speed is 2.4 m/s, is this right?

For the second questions:
Initial momentum = final momentum
.48 = .2Vf(bob) + Vf(block)

This is as far as I can get. How can I solve these velocities individually, and how to I go about finding the rebound angle?

Last edited by a moderator:

I think I may have answered the second part too.

Vf(block)=.8 m/s
Vf(bob)= -1.6 m/s

Does this look right?

Redbelly98
Staff Emeritus
Homework Helper
Welcome to Physics Forums ## The Attempt at a Solution

I think I have solved the first question:
By calculating the change in height of the bob, to be .293m, I found the potential energy to be .574 joules. The kinetic energy right before impact should also equal .574, therefore velocity = 2.4 m/s. So right before impact the bob's speed is 2.4 m/s, is this right?
Yes.
For the second questions:
Initial momentum = final momentum
.48 = .2Vf(bob) + Vf(block)

This is as far as I can get. How can I solve these velocities individually, and how to I go about finding the rebound angle?
Looks like you got the correct velocities below.

For rebound angle, you now have the "reverse" problem from before: when you knew the initial height of the bob, you were able to calculate it's velocity at the bottom of the swing. Now you know it's velocity at the bottom, so how high will it go in its upward swing?
I think I may have answered the second part too.

Vf(block)=.8 m/s
Vf(bob)= -1.6 m/s

Does this look right?
Yes.

Got it, thank you much.