Math Is Fun Forum

yonski

Member

Registered: 2005-12-14

Posts: 67

Collisions problem

Hi there,
having a bit of trouble with this question:

Two particles A and B move on a smooth horizontal table. The mass of A is m, and the mass of B is 4m. Initially A is moving with speed u when it collides with B, which is at rest on the table. As a result of the collision, the direction of motion of A is reversed. The coefficient of restitution between the particles is e.

(a) Find an expression for the speed of A and the speed of B immediately after the collision.

In the subsequent motion, B strikes a smooth vertical wall and rebounds. The wall is perpendicular to the direction of motion of B. The coefficient of restitution between the wall and B is 4/5. Given that there is a second collision between A and B,

(b) show that 1/4 < e < 9/16 .

Given that e = 1/2 ,

(c) find the kinetic energy lost in the collision between A and B.

Okay, so that's the question.

I've done part (a) and found that the speeds are

Va = (u/5)(4e-1)
Vb = (u/5)(1+e)

and then done part (b) too.

For part (c) though, I don't see how you can find the total energy lost, since you don't know the initial speed or the speeds after the collision. I found the percentage energy loss to be 60% but that's all I could figure out.

Any help appreciated.

Cheers, Jon.

Last edited by yonski (2007-03-27 08:57:57)

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Student: "What's a corollary?"
Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary."

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Collisions problem

I think you'd just have to write it in terms of m and u.

So, assuming that you're right that it's a 60% loss, that would mean that the energy loss is 0.3mu².

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Why did the vector cross the road?
It wanted to be normal.

jagabandhu

Member

Registered: 2007-03-30

Posts: 6

Re: Collisions problem

Hi, I think you may use the conservation of linear momentum to approach the problem so that you can find out the final velocities of the bodies A and B after collision as you have the initial velocities of A as u and that of B is 0.

This would help you to further solve the problem easily. I hope this works

poop

Guest

Re: Collisions problem

this seems more like a physics problem than a calc problem. you must use the formulas for an elastic collision. do not to consider the restitution. find this using the conservation of momentum. (m1v1+m2v2)i = (m1v1+m2v2)f

for the latter problems, you can use the conservation of energy.

poop

Guest

Re: Collisions problem

same guy as previous post here. use the conservation of momentum which i labeled above. but include the coefficient of restitution also. a perfectly elastic collision has a coeff of 1. the c is determined by dividing the difference of the final velocities by the difference of the initial velocities.
to find the amount of kinetic energy lost, you can find the change in velocities then apply them to the conservation of energy equations.