A mass m1 moving with u collides with mas m2...

[Vriska]

Homework Statement

A mass m1 collides with stationary m2 with velocity u1 u. Find the fraction of energy converted into heat and sound. Show that this energy is equal to the kinetic energy from centre of mass reference frame

Homework Equations

[/B]
let v1 and v2 be velocity of m1 and m2 after collision :

e = v2-v1/u1

m1u1 = m1v1 + m1v1

ke = 1/2 mv^2

The Attempt at a Solution

let k be energy by sound and heat.

m1(u1-v1) = m2v2 (1)

m1u1^2 - m1v1^2 = k + m2v2^2

= m1(u1+v1) (u1-v1)

dividing by 1

u1+v1 = k/m2v2 + v2

u1 = k/m2v2 + v2 - v1

1 = k/(m2v2u1) + e

(1-e)*m2v2u1 = k

annnd stuck. this is the farthest I've gotten and doesn't look like velocity from com reference frame at all : (going further the ratio with initial ke is

(1-e)*m2/m1*v2/u1 which ia nice and symmetric i guess. but i guess it wants me to do stuff and rid off v2 and end up with an ugly expression. I don't think that's right

 

[haruspex]

Show that this energy is equal to the kinetic energy from centre of mass reference frame

Based on that, I presume you were told that the masses stick together?

m1u1^2 - m1v1^2 = k + m2v2^2

Should be 2k?

What is the initial KE in the common mass centre reference frame?

 

[Vriska]

Based on that, I presume you were told that the masses stick together?

Should be 2k?

What is the initial KE in the common mass centre reference frame?

right it's 2k.

initial ke looks to be
: m1m2* u^2/2(m1+m2). The final will be u replaced by ku i guess.

no mention is given about the elasticity of the system : \

 

[haruspex]

no mention is given about the elasticity of the system : \

The result you are asked to prove will not be true if there is any elasticity. There will remain some KE.

 

[Vriska]

The result you are asked to prove will not be true if there is any elasticity. There will remain some KE.

damn i was trying this all day : (

but then shouldn't my answer have m1^2 instead of m1m2?

Anyway here's the question in case I'm misreading something

 

[haruspex]

shouldn't my answer have m1^2 instead of m1m2?

It should not have v₂. Use the equations you have to eliminate that and see what happens.