# Momentum + Energy

1. Jun 24, 2012

### hybridized

1. The problem statement, all variables and given/known data

A 1.0 Kg cart moving at 4.0 m/s overtakes and collides with a 3.0 kg cart moving in the same direction at 2.0 m/s on the same track. Given that these carts collide elastically due to repelling magnets, determine the maximum energy stored in the magnetic field.

2. Relevant equations
Ke = 1/2mv^2
Ktotal = Ke + Ke

3. The attempt at a solution
Hey guys, I have an exam tomorrow and can't seem to figure this out. I found the total kinetic energy in the system, to be at 14 J. However, I do not know what to do from here on.

2. Jun 25, 2012

### Infinitum

Hi hybridized! Welcome to PF

At the time when the carts collide, their velocities will be same. Do you see why this is true?

3. Jun 25, 2012

### hybridized

So if their velocities are the same, I found the Kinetic energy before cart 1 collides, and after cart 2 gets hit. So in that middle is where the energy is stored or at its max? So how would I go on about to calculate the total energy. Exam in 30 mins!

4. Jun 25, 2012

### Infinitum

Yes. Find the kinetic energy at the instant when both are moving with the same velocity. And you already know the initial kinetic energy(before collision). So now, this initial energy is distributed as the kinetic energy when velocities are equal and the energy stored in the magnetic field.

5. Jun 25, 2012

### hybridized

K so bro, which velocity would I use? Or do I find delta v? to find the kinetic energy when they have the same velocity.

6. Jun 25, 2012

### hybridized

Would you be kind enough to write down the equations i must use to find the total kinetic energy stored? Cause I found the total energy for the two carts, but I'm stuck from there... Which velocity do I use when they are moving at the same speed.

7. Jun 25, 2012

### Infinitum

You cannot use a velocity because you need to find the velocity!!

But, you sure can use the conservation of linear momentum

8. Jun 25, 2012

### hybridized

O so, m1+v1 + m2v2 = mtvt

v1 and v1 cancel as they are the same, solve for vt and then plug into 1/2mv^2 and then add to the Ke i found in the beginning ???

9. Jun 25, 2012

### Infinitum

Noo...

By conservation of momentum you should have...

$$m_1v_1 + m_2v_2 = (m_1+m_2)v$$

and not m1+v1..