# Elastic Collision Problem: Finding Velocities of Two Bodies

• toesockshoe
In summary: One can call the final velociies u and w and substitute for the masses right away.Then conservation of momentum and conservation of KE will give two equations in u and w which can be solved.
toesockshoe

## Homework Statement

A 3 kg body (mass1) moving at 4 m/s makes an elastic collision with a stationary body(mass2) of mass 2 kg. Find the velocity of each body after the collision

pi=pf
w=delta e

## The Attempt at a Solution

so because it is elastic collision, it means that kinetic energy is conserved... we can do the following:
$W=\Delta E$
$0= \Delta KE_1 + \Delta KE_2$
$0= \frac{1}{2}m_1v_{f1}^2-\frac{1}{2}m_1v_{i1}^2+\frac{1}{2}m_2v_{2f}^2-\frac{1}{2}m_2v_{2i}^2$
$v_{f1} = \sqrt{\frac{m_1v_{i1}^2-m_2v_{2f}^2}{m_1}}$
ugh latex won't work:
vf1=((m1(v1f)^2-m2(v2f)^2)/m1)^1/2
now we can use momentum conservation to say

pi=pf
$m_1v_{i1}=-m_1v_{f1}+m_2v_{f2}$
we know vf1 from the energy part so we have the following:
m_1v_{i1}=m_1\sqrt{\frac{m_1v_{i1}^2-m_2v_{f2}^2}{m_1}+m_2v_{f2} [/itex]

so i have one unknown ($v_{f2}$) and one equation, but that seems awfully horrible to eliminate the final velcity of mass 2. am i even doing it correctly?

Last edited:
Your equation should be m_1V_1=m_1V_1'+ m_2V_2

Think about it, why would the second m_1V_1 be negative?

Also I think you are confused on this equation:
"toesockshoe said:
0=12m1v2f1−12m1v2i1+12m2v22f=12m2v22i 0= \frac{1}{2}m_1v_{f1}^2-\frac{1}{2}m_1v_{i1}^2+\frac{1}{2}m_2v_{2f}^2=\frac{1}{2}m_2v_{2i}^2

the second mass initially has a velocity of zero.

Last edited:
RaulTheUCSCSlug said:
Your equation should be m_1V_1=m_1V_1+ m_2V_2

Think about it, why would the second m_1V_1 be negative?

Also I think you are confused on this equation:the second mass initially has a velocity of zero.
i thought it would be negative becasue it is going in the other direction...
i know v2i is 0... that's why i just took it out by the next step (its not in the answer inside my square root).

RaulTheUCSCSlug said:
equation should be m_1V_1=m_1V_1+ m_2V_2
You don't mean that, I hope.
I assume your point is that it is better to keep a constant definition of which direction is positive. I agree.

Last edited:
haruspex said:
You don't mean that, I hope.
I assume your point is that it is better to keep a constant definition of which direction is positive. I agree.
I meant that the second V_1 should be (V_1)' (or V_1 final)

I always thought that both would continue to go in the same direction after collision? Since the first one has no momentum, they will both share a momentum in the same direction won't they?

RaulTheUCSCSlug said:
I meant that the second V_1 should be (V_1)' (or V_1 final)

I always thought that both would continue to go in the same direction after collision? Since the first one has no momentum, they will both share a momentum in the same direction won't they?
actually, yes youre right. because the mass of the object being hit is smaller, they will go in the same direction. i should have changed that to a plus sign.

RaulTheUCSCSlug
A simpler notation may help.

One can call the final velociies u and w and substitute for the masses right away.

Then conservation of momentum and conservation of KE will give two equations in u and w which can be solved.

RaulTheUCSCSlug said:
I meant that the second V_1 should be (V_1)' (or V_1 final)

I always thought that both would continue to go in the same direction after collision? Since the first one has no momentum, they will both share a momentum in the same direction won't they?
Whether they will continue in the same direction depends on the relative masses. In this case, as toesockshoe says, they will

Make terms by the same masses and divide by part. You make a 1st class equation system.

## 1. What is momentum and how is it calculated?

Momentum is a physical quantity that measures the amount of motion an object has. It is calculated by multiplying an object's mass by its velocity.

## 2. What is the formula for momentum?

The formula for momentum is p = m x v, where p is momentum, m is mass, and v is velocity.

## 3. How is momentum conserved in a closed system?

In a closed system, the total momentum before an interaction is equal to the total momentum after the interaction. This is known as the law of conservation of momentum.

## 4. Can momentum be negative?

Yes, momentum can be negative if the direction of an object's velocity is opposite to the direction of its mass. This is known as negative momentum.

## 5. How does an object's mass and velocity affect its momentum?

As an object's mass increases, its momentum also increases. Similarly, as an object's velocity increases, its momentum also increases. This is because momentum is directly proportional to both mass and velocity.

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