# Energy and Momentum problem

n1trate

## Homework Statement

Magnetic puck A, with a mass of 0.100 kg, is pushed towards stationary 0.050 kg
magnetic puck B, to cause a head-on collision. You may neglect friction. The initial
velocity of puck A is 12 m/s [E]. Puck B moves with a velocity of 14 m/s [E], after
the collision.
a) Find the velocity of puck A after the collision.

## Homework Equations

p=mv
pinitial=pfinal
Einitial = Efinal
Ek = 1/2mv^2

## The Attempt at a Solution

Basically I understand how to solve the question using the momentum by why is that I get a different velocity when using the energy?
Since friction is neglected, where could this system be losing kinetic energy?
I did Ei=Ef which is Eki=Ekf
1/2(0.100)(12)^2+0=1/2(0.100)v_A^2 + 1/2(0.050)(14)^2
I end up getting 6.8m/s for the final velocity of puck A
But the correct answer is 5.0m/s
I tried to plug that into the equation but I get
7.2J=6.15J which is incorrect. What am I doing wrong here?

## Answers and Replies

Mentor
Hi n1trate, Welcome to Physics Forums.

What's the import of the pucks being magnetic? It's not obvious to me, but perhaps there's some mechanism that's not elaborated upon that is responsible for energy being lost. So we're meant to presume that conservation of energy doesn't hold here.

In fact, if you assume a perfectly elastic collision with the given initial conditions you'll find a different final velocity for puck B than they have provided...

• n1trate
TomHart
Like @gneill said, based on the numbers, it cannot be a perfectly elastic collision, so conservation of energy would not apply. And also like @gneill said, I have no idea what the mention of "magnetic" has to do with the problem. It seems to add no value. What else do you have to work with?

I just realized I ended that last sentence in a preposition, reminding me of a Winston Churchill quote:
"From now on, ending a sentence in a preposition is something up with which I will not put."

n1trate
They didn't give me anything else actually but the first way that came to my mind to solve this problem was using conservation of energy. They didn't put use momentum explicitly, but thanks for the answers now I understand. It was confusing me all night I thought I was wrong but I guess it's just the question. Thank you!

Homework Helper
Dearly Missed

## Homework Statement

Magnetic puck A, with a mass of 0.100 kg, is pushed towards stationary 0.050 kg
magnetic puck B, to cause a head-on collision. You may neglect friction. The initial
velocity of puck A is 12 m/s [E]. Puck B moves with a velocity of 14 m/s [E], after
the collision.
a) Find the velocity of puck A after the collision.

## Homework Equations

p=mv
pinitial=pfinal
Einitial = Efinal
Ek = 1/2mv^2

## The Attempt at a Solution

Basically I understand how to solve the question using the momentum by why is that I get a different velocity when using the energy?
Since friction is neglected, where could this system be losing kinetic energy?
I did Ei=Ef which is Eki=Ekf
1/2(0.100)(12)^2+0=1/2(0.100)v_A^2 + 1/2(0.050)(14)^2
I end up getting 6.8m/s for the final velocity of puck A
But the correct answer is 5.0m/s
I tried to plug that into the equation but I get
7.2J=6.15J which is incorrect. What am I doing wrong here?

If (as the question states) the final speed of B is 14 m/s, then energy cannot be conserved. In the so-called "center-of-momentum" (CM) frame we assume that total kinetic energies before and after the collision are related as
$$\text{K.E.}_{\text{final}} = f\: \text{K.E.}_{\text{initial}}$$
for some factor ##0 \leq f \leq 1##. We have a perfectly elastic collision if ##f=1##, a perfectly inelastic collision if ##f = 0## and something in between if ##0 < f < 1##. Anyway, using momentum conservation and the above KE condition, we can easily determine the final velocities of A and B in the CM frame in terms of ##f##, then transform those back into the original (lab) frame. We find that there is, indeed, a fractional value of ##f## that makes the final lab-frames speed of B equal to 14 m/s and the final lab-frame speed of A equal to 5 m/s, just as your book claims.

Homework Helper
Gold Member
What's the import of the pucks being magnetic?

energy cannot be conserved.

"After the collision" is rather vague. Immediately after the collision some of the energy will be in the form of magnetic potential energy.

Homework Helper
"After the collision" is rather vague. Immediately after the collision some of the energy will be in the form of magnetic potential energy.
It is possible, that the pucks do not touch each other during the "collision", if they repel each other due to interaction between their magnetic moments. In this case, loss of the kinetic energy is not caused by the usual way, that they deform each other and some of the kinetic energy transforms into heat and sound.
As they are magnetic and move, they produce varying magnetic field, and varying magnetic field produces changing electric field, so you have time-dependent electromagnetic field that radiates away. The radiation is strongest when the pucks are close to each other, but "before collision" and "after collision" means the state when the pucks are far away. As electromagnetic fields are involved, the mechanical energy does not conserve.

Homework Helper
Gold Member
First of all, this is a collision problem.
Total-momentum must be conserved.
What happens with energy is secondary.

You can solve for ##v_{1,f}## in terms of ##m_1##, ##m_2##, ##v_{1,i}##, ##v_{2,i}##, and ##v_{2,f}##...
and you are given values for everything.
If, it turns out, there are energy losses, then one can seek reasons** for that.
(If you weren't given enough information, then appealing to the assumption of an elastic collision can be considered.)

In all cases, total-momentum conservation is primary.

**reasons could include other forms of energy not already considered:
rotational kinetic energy? heat?