Elastic collision and kinetic energy problem?

[LarryJ]

Homework Statement

The figure below shows a thin, uniform bar whose length is L and mass is M and a compact hard sphere whose mass is m. The system is supported by a frictionless horizontal surface. The sphere moves to the right with velocity , and strikes the bar at a distance 1/4L from the center of the bar. The collision is elastic, and following the collision the sphere is at rest. The rod is being rotated from its center. Find the value of the ratio m/M.

Homework Equations

1/2mv^2=1/2Iω^2

The Attempt at a Solution

I know the collision is elastic, so kinetic energy is conserved. But I don't know exactly how find which mass ratios will make the collision elastic. I think I know inertia (1/12MR^2). But I'm basically stuck from there.

 

[tiny-tim]

Hi LarryJ!

(try using the X² button just above the Reply box )

I know the collision is elastic, so kinetic energy is conserved. But I don't know exactly how find which mass ratios will make the collision elastic. I think I know inertia (1/12MR^2). But I'm basically stuck from there.

angular momentum is also conserved (in any collision, and about any point)

also, you are told that the bar rotates about its centre

so write out the equations for conservation of energy, and for conservation of angular momentum about the centre …

what do you get? ​

 

[LarryJ]

Kinetic energy: 1/2mv²=1/2Iω²
Angular Momentum: (1/12MR²)(ω)= mv(1/4R)²
So do I set the equations equal to each other and then solve for M and m?

 

[tiny-tim]

So do I set the equations equal to each other and then solve for M and m?

i'm not sure what you mean by "set the equations equal to each other",

but yes, you solve for m/M ​

 

[LarryJ]

How do I set up an equation to solve for M and m?

 

[tiny-tim]

try squaring one equation

 

[LarryJ]

Oh I think I got it. 0.57