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! ;)

 

[HalfLostAndSearching]

Since v1 and v2 are the same, we can cancel them out, leaving m1 squareroot(m2/m1) = m2 squareroot(m1/m2)

Taking the squareroot of both sides, we get m1(m2/m1) = m2(m1/m2)

Simplifying, we get m2 = m1, meaning the heavy object and the light object have the same momentum.

In other words, the mass of an object is directly proportional to its momentum, and since the two objects have the same kinetic energy, their masses cancel out and their momentums are equal.