A very simple kinetic energy problem

[Todd88]

Homework Statement

Okay for some reason I guess I don't understand this problem. Here is the question:

A 7.50kg shell at rest explodes into two fragments, one with a mass of 1.50kg and the other with a mass of 6.00kg.

If the heavier fragment gains 100J of kinetic energy from the explosion, how much kinetic energy does the lighter one gain?

Homework Equations

K = 1/2mv^2

The Attempt at a Solution

I calculated the velocity with the above equation and then tried to find the kinetic energy of the smaller particle and got 25J. This is not correct and I have no idea why...any help is appreciated. Thanks.

 

[LowlyPion]

Homework Statement

Okay for some reason I guess I don't understand this problem. Here is the question:

A 7.50kg shell at rest explodes into two fragments, one with a mass of 1.50kg and the other with a mass of 6.00kg.

If the heavier fragment gains 100J of kinetic energy from the explosion, how much kinetic energy does the lighter one gain?

Homework Equations

K = 1/2mv^2

The Attempt at a Solution

I calculated the velocity with the above equation and then tried to find the kinetic energy of the smaller particle and got 25J. This is not correct and I have no idea why...any help is appreciated. Thanks.

Maybe you flipped something?

m1V1 = m2V2

with m1 = 4m2 => v2 = 4V1

So if (1/2*m1V1²) = 100

then ...

1/2m2V2² = 1/2(m1/4)(4V1)² = 4*(1/2*m1V1²)

 

[Mzachman]

You are trying to say that the velocities are conserved, which isn't correct, but almost. The momentum is conserved. The momentums of the two parts must be equal after the explosion, since the momentum of the whole shell was 0 before the explosion.

m1v1 - m2v2 = 0

So your kinetic of 100J for the larger particle gives a velocity of 5.774 (through the normal 1/2*mv^2). Multiply that by mass to get a momentum of 34.64 kg*m/s (P = mv).

Now divide that 34.64 kg*m/s by the mass of the smaller, 1.5 kg, to get a velocity of 23.09 m/s (because m1v1 = m2v2, so v2 = m1v1/m2).

Now put this into the 1/2*mv^2 to get 400 Joules for the smaller piece. That should be your answer. Hope that helps :)

 

[Todd88]

Ah of course. Thanks a lot guys you really helped!