# Kinetic energy of inelastic collision problem

1. Jan 21, 2008

### physicspupil

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

A particle of mass m1 and velocity u1 collides with a particle of mass m2 at rest. The two particles stick together. What fraction of the original kinetic energy is lost in the collision?

2. Relevant equations

Conservation of momentum law

3. The attempt at a solution

I think this one is right but was hoping somebody could check for me... It seemed too easy, so I just wanted to make sure I'm understanding it correctly.

m1u1 = (m1 + m2)u by conservation of momentum, so u = m1u1/(m1+m2)

Ti = ½ m u1^2 and Tf = ½ (m1+m2)u^2 = m1^2 u1^2/2(m1+m2) in terms of u1

Then I found Ti – Tf = (m1m2 u1^2)/2(m1 + m2) and then found ratio of this with Ti

I got m2/(m1 + m2). Is this correct? Thanks!!! :)

2. Jan 21, 2008

### rock.freak667

I got $\frac{m_1}{m_1+ m_2}$ and worked it the same basic way you did.

3. Jan 21, 2008

### D H

Staff Emeritus
At least one of you two is obviously wrong. How much energy is lost when you throw a 1 gram spitball at a 75 kg man? What happens when a 75 kg man runs into a 1 gram spitball suspended from the ceiling?

4. Jan 24, 2008

### physicspupil

Hi, rock.freak667, isn't your answer the amount of the original remaining (not lost)? I'm not sure, I'll check my work again. Man's kinetic energy isn't effected much but spitball's is - I think that's what makes me uncomfortable about these problem w/o numbers - harder to get an intuitive feel for them but making up concrete examples helps. Thanks to both of you.