Linear Momentum Algebraic interpretation

[brycenrg]

Homework Statement

A light object and a heavy object have the same kinetic energy. Which has more momentum?

Homework Equations

I am trying to prove this through algebra.
I don't understand how to show this any help?

The Attempt at a Solution

1/2m1v1^2 = 1/2m2v2^2 when m1 > m2

v1 = v2 squareroot(m2/m1)

m1v2 squareroot(m2/m1) = m2v1 squareroot(m1/m2)

 

[ehild]

Homework Statement

A light object and a heavy object have the same kinetic energy. Which has more momentum?

Homework Equations

I am trying to prove this through algebra.
I don't understand how to show this any help?

The Attempt at a Solution

1/2m1v1^2 = 1/2m2v2^2 when m1 > m2

v1 = v2 squareroot(m2/m1)

m1v2 squareroot(m2/m1) = m2v1 squareroot(m1/m2)

I do not see what is the sense of your last line. What are the momenta?

 

[Orodruin]

I suggest you work in the other direction and do not use v as a variable. Instead, solve for v from p = mv and insert this into the expression for kinetic energy.

 

[quantumtimeleap]

Here's a hint. You do have to use algebra here, but this is only a qualitative question where you have to find the relationship

$\frac{KE_1}{KE_2} = constant = \alpha(m_1, m_2) \frac{p_1^2}{p_2^2}$

where $\alpha$ is a function of the two masses. Once you find this relationship, you can answer the question easily.

Goodluck! ;)