# Totally elastic and momentum collision equation help! Thanks

## Homework Statement

A 12kg wad of clay is hurled horizontally at a 100g wooden block initially at rest on a horizontal surface. The clay sticks to the block. After impact, the block slides 7.50m before coming to rest. If the coefficient of friction between the bloack and the surface is .650, what is the SPEED of the clay immediately before impact?

## Homework Equations

This is a perfectly inelastic collision correct?

My book tells me in the answer section to use the following formula, but Im not sure where it came from or why to use this. Am I to use this for equations related to inelastic collisions and friction involved?

1/2(m1+m2)V2^2 = friction(m1+m2)gL

How did it come up with that???? I guess I am just having trouble figuring out how I was suppose to come up with that formula.

Any clarification?

## The Attempt at a Solution

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Doc Al
Mentor
This is a perfectly inelastic collision correct?
Yes.

My book tells me in the answer section to use the following formula, but Im not sure where it came from or why to use this. Am I to use this for equations related to inelastic collisions and friction involved?

1/2(m1+m2)V2^2 = friction(m1+m2)gL

How did it come up with that???? I guess I am just having trouble figuring out how I was suppose to come up with that formula.
It's telling you that the kinetic energy the system had after the collision must equal the work done by friction. Note that V2 is the speed of the 'clay+block' after the collision. You'll use that to figure out the speed of the clay before the collision.

1/2(m1+m2)V2^2 = friction(m1+m2)gL
Do you think that above equation is to be used before impact or after impact?

Now i notice that another poster beat me.

Ok great.

When looking at this problem... What is the first and second things I should be trying to figure out. Mainly, when looking at this problem specifically, what would I be looking to do first?

I want to systematically break this equation down from start!

Do you think that above equation is to be used before impact or after impact?

Now i notice that another poster beat me.
I really am not sure... ?

Doc Al
Mentor
When looking at this problem... What is the first and second things I should be trying to figure out. Mainly, when looking at this problem specifically, what would I be looking to do first?

I want to systematically break this equation down from start!
Break the problem into two stages:
(1) The collision itself. What's conserved?
(2) The movement against friction after the collision.

The equation you have deals with part #2.

What equation can you come up with to deal with #1?

I thought for step one, I would use:

Vf = m1V1i + m2V2i / (m1 + m2)

?

Doc Al
Mentor
I thought for step one, I would use:

Vf = m1V1i + m2V2i / (m1 + m2)

?
Good. (Careful with parentheses!)

What does Vf correspond to?

Good. (Careful with parentheses!)

What does Vf correspond to?

Vf would be velocity of the system?

v1i would be for the clay and v2i would be wood ???

Doc Al
Mentor
Vf would be velocity of the system?
Yes, immediately after the collision.

v1i would be for the clay and v2i would be wood ???
Right.

Ok, so first thing I do when looking at this is figure out the Vf of the system after the collision.

With the formula I supplied for the first step Vf = m1V1i + m2V2i / (m1 + m2) , how do I go from there, to here: 1/2(m1+m2)V2^2 = friction(m1+m2)gL

Doc? Can you explain the above reply to me if you can, or anyone else? :)

Doc Al
Mentor
Ok, so first thing I do when looking at this is figure out the Vf of the system after the collision.
Right. You'll do that by solving the second part first, since you have all the needed data. (It's often the case that its best to work a problem 'backwards'.)

With the formula I supplied for the first step Vf = m1V1i + m2V2i / (m1 + m2) , how do I go from there, to here: 1/2(m1+m2)V2^2 = friction(m1+m2)gL
You'll solve the second step first.

How will you relate the two steps? Hint: How does Vf in the first formula relate to V2 in the second? (Generally it's a good idea to use the same symbols for the same quantities. Otherwise things get confusing.)

In your first formula, Vf = (m1V1i + m2V2i) / (m1 + m2), what is V2?

Oh ok Doc, im starting to understand it a little better. Just having trouble coming to a conclusion on what exact formula to use. Like what stpes I take to get the right formula....

You ask what is V2 ? Well, thats the Velocity of the wood, which is zero, correct? What significance is that may I ask?

Again, MUCH thanks for the help!

EDIT: I guess what im missing is how I would come to the formula to get the speed of the system, as detailed here: 1/2(m1+m2)V2^2 = friction(m1+m2)gL

I have never seen that before!

Last edited:
Doc Al
Mentor
You ask what is V2 ? Well, thats the Velocity of the wood, which is zero, correct? What significance is that may I ask?
Yes, in your conservation of momentum equation (which describes the collision), V2 stands for the initial speed of the block, which is zero. You'll need that equation to solve for the initial speed of the bullet. (You'll use this equation last.)

EDIT: I guess what im missing is how I would come to the formula to get the speed of the system, as detailed here: 1/2(m1+m2)V2^2 = friction(m1+m2)gL
That's just an energy equation stating that the change in KE of the system after the collision is equal to the work done by friction. What does V2 stand for here?