Inelastic Collisions and ratio of their masses

AI Thread Summary
In a totally inelastic collision where two objects of equal speed collide, half of the initial kinetic energy is lost. The conservation of momentum equation is m1v1 + m2v2 = (m1 + m2)vf, with v1 and v2 being equal in magnitude but opposite in direction. The challenge lies in incorporating the kinetic energy loss into the equations correctly. The approach involves setting up the kinetic energy equation as 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2 = 0.5 * (m1 + m2) * vf^2, factoring in the energy loss. The final goal is to derive the mass ratio m1/m2 accurately through algebraic manipulation.
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Homework Statement



Two objects moving in opposite directions with the same speed undergo a totally inelastic collision, and half the initial kinetic energy is lost. Find the ratio of their masses, m1/m2.

Homework Equations



m1v1+m2v2=(m1+m2)vf
The objects are moving in opposite directions with the same speed, so v1=-v2=v

The Attempt at a Solution



The part that gets me is the part that says half the kinetic energy is lost. Could someone explain how I factor that into the equations? If I just solve for m1/m2, plugging in 1/2v for vf(I don't know if that's right) I get 3, which is not the correct answer.
 
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If the collision were perfectly elastic, kinetic energy is conserved. But it is totally inelastic and 1/2 of the energy is lost. Therefore you can say:

.5 * m1 * v1^2 + .5 * m2 * v2^2 = (.5 * (m1 + m2)* vf^2) * .5

Then start cranking on the algebra to get m1/m2.
 
That makes sense. However, when I solve for m1/m2 I get (.5vf^2 + v^20/(v^2-.5vf^2) when I need an actual ratio.
 

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