Kinetic energy (tough algebra problem)

[captainsmith1]

Homework Statement

Derive an algebraic statement for the fractional loss of kinetic energy in terms of symbols only and show that loss of kinetic energy/inital kinetic energy=M/(M+m)

this is for a ballistics pendulum lab, and M is the weight of the holder and m is the weight of the metal ball. The task is to prove that the ratio of the kinetic energy lost to the inital kinetic energy equals the ratio of the mass of the holder (M) to the mass of the holder and the ball together (M+m)

Homework Equations

kinetic energy (.5mv^2)

The Attempt at a Solution

i set the two ratios equal to each other, giving something that looks like this-

.5mv(initial)^2-.5(m+M)v(final)^2 = M/(m+M)
.5mv(initial)^2

but i can't figure out the algebra to prove that the two in fact do equal each other (and they do, earlier calculations in the lab prove it)
ps, sorry if the equation looks really bad, its kind of hard to type it using a keyboard

 

[Delphi51]

You need more than algebra! You need some relationship between those velocities - another equation. You haven't made the problem clear, but perhaps you also have a momentum equation?

 

[tiny-tim]

Hi captainsmith1! Welcome back!

Yes, you nearly always need two equations for this sort of problem …

if it's a collision, one of them will be conservation of momentum (it applies to all collisions), and the other will be conservation of energy (if it is conserved), otherwise some geometric constraint.