Calculating Speed in Elastic collision

[connie5828]

Homework Statement

An object of mass 15kg going to the right with a speed of 3 m/s collisdes with a 10kg object at rest. if the collision is ocmpletely elastic, calculate the speed of the 10kg object after collision

Homework Equations

m₁v_li +m₂v_2i=m₁v_lf+m₂v_2f

The Attempt at a Solution

I have tried plugging all the answers in and can't get the answer that is in the book. Also wondering if there is an easier way to get the answer. Also wondering if the # for at rest is 0

 

[hotvette]

You have one equation and two unknowns. A second equation is needed to solve the problem. There are two relevant equations in elastic collision problems. One is the conservation of linear momentum, which you have stated. What is the other?

 

[connie5828]

v_li-V_2i=-(V_lf-V_2f)

is that correct?
Do you have to get the first one to get the speed of the 2nd one?
do you have to do the first equation I posted in order to do the 2nd equation?

 

[hotvette]

Conservation of kinetic energy. Do you know the equation for kinetic energy?

 

[connie5828]

KE=mv²/2

the info my professor gave showed no use of that formula though. I am now officially confused :)thanks for the help.

 

[hotvette]

Hmmm.

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter.

http://en.wikipedia.org/wiki/Elastic_collision

 

[connie5828]

ok, reading that was helpful. To get the 2nd speed would this be the equation?
0(10-15) + 2*15*3/10+15
I put 0 as the 10K object is at rest. Is that correct?

 

[hotvette]

I didn't solve the problem completely, but what you have doesn't offhand look right. You have two equations, the 2nd one containing velocity squared terms:

1. total linear momentum = const

2. total kinetic energy = const

In the end there will be a quadratic equation to solve (only one of the solutions being valid). The beauty of this problem is that it's easy to verify your answer. Once you determine the values of the final velocities of the objects, it's easy to verify that the total linear momentum and kinetic energy is indeed constant.