Solving for Momentum Comparison: Masses and Kinetic Energy in Motion

[mcleodj2]

Homework Statement

I'm given the masses of two objects, m1 and m2. The kinetic energy K is equal in both objects. It wants to know which object has the greater magnitude of momentum.

Homework Equations

K = 1/2mv^2 (Kinetic Energy)
p = mv (Momentum)
K = p^2/2m (K in terms of p)

The Attempt at a Solution

Now, I know that I have two variables to solve for before I can answer the question. I need to find v1 and v2. Finding one of those in terms of the other is easy, but that only leaves me with one equation and two variables. I can't for the life of me remember what relationship I can use to give me a second equation and my book isn't much help at all.

 

[Mindscrape]

Why don't you just equate the two

$$K_1 = K_2$$

$$\frac{p_{1}^2}{2m_1}=\frac{p_{2}^2}{2m_2}$$

Since you know the masses you just solve for one and see which one is greater. If p1^2=2p2^2 then p1 is obviously greater. :) You could take the square root too if you really wanted to get the right scale factor between the momentums.

 

[mcleodj2]

Wow, do I feel stupid. You're right. I don't need an answer at all, just a ratio. I think I was blinded by a collision example done in class where the teacher did some sort of long problem where the solution wasn't immediately obvious. Thanks, Mindscrape.