How Do You Solve an Elastic Collision Problem with Different Masses?

[harkkam]

Elastic Collision...Problem

The problem states. The collison is elastic and head on. One ball has a mass of m1=.250kg and initial velocity of 5.00m/s. The other has a mass of m2=.800kg and is initially at rest. No external forces act on the ball. What are the velocities after collision.

So far I got up to a certain point and I get stuck.

I deduced that

(Vf1)^2 = (Vo1)^2 - (M2/M1)(Vf2)^2
Vf2 = (M1/M2)(Vo1-Vf1)


Now when I substitute Vf2 into the first equation I get

(Vf1)^2 = (Vo1)^2 - (M2/M1)[(M1/M2)(Vo1-Vf1)]^2

This is where I get stuck. I can't solve for Vf1. I have the answer but I want to learn the steps to get to.

Vf1= (M1-M2/M1+M2)Vo1

Thnks

 

[Doc Al]

Now when I substitute Vf2 into the first equation I get

(Vf1)^2 = (Vo1)^2 - (M2/M1)[(M1/M2)(Vo1-Vf1)]^2

This is where I get stuck. I can't solve for Vf1.

Expand the right hand term, then rearrange so that you end up with a quadratic equation for Vf1.

 

[thomate1]

Hello, it seems like you are on the right track with your equations. In order to solve for Vf1, you will need to use the conservation of momentum and the conservation of kinetic energy equations.

The conservation of momentum equation states that the total momentum before the collision is equal to the total momentum after the collision. In this problem, since there are no external forces acting on the balls, the total momentum before the collision is equal to the total momentum after the collision. This can be written as:

m1*Vo1 + m2*Vo2 = m1*Vf1 + m2*Vf2

The conservation of kinetic energy equation states that the total kinetic energy before the collision is equal to the total kinetic energy after the collision. This can be written as:

1/2*m1*Vo1^2 + 1/2*m2*Vo2^2 = 1/2*m1*Vf1^2 + 1/2*m2*Vf2^2

Now, you can substitute the expression for Vf2 that you found in the first equation into the second equation. This will give you an equation with only one unknown, Vf1. You can then solve for Vf1 using algebraic manipulation.

Once you have solved for Vf1, you can use the equation you found earlier to solve for Vf2.

I hope this helps and good luck with your problem solving!