# Momentum, Impulse, and Collision

## Homework Statement

Two skaters stand in the center of a circular rink of frictionless ice. When the skaters push on one another, they move apart along the same straight line. If the skater of mass m1 = 50 kg reaches the edge of the rink after 12 seconds and the other skater reaches the opposite edge of the rink in 18 seconds, what is the mass m2 of the second skater?

## Homework Equations

M1V1 + M2V1 = M1V2 + M2V2 ???

## The Attempt at a Solution

How do I get the mass if the distance is not given?

ehild
Homework Helper
They travelled the same distance.Find the ratio of the speeds.

ehild

I'm confused >.<

So the equation I'm using is wrong?

no there is no problem with the equation.
let the distance moved be x and then solve. It will get cancelled.

50kg * x/12s+ M2 * x/18s = 50kg * x/12s + M2 * x/18s ?

ehild
Homework Helper
I'm confused >.<

So the equation I'm using is wrong?

It is not wrong, only it does not mean anything. Both sides are identical, so you say that something is equal with itself. What did you want to state with that equation?

ehild

50kg (1/12s) + M2 (1/18s) = 0

M2 = [50kg (1/12s)] / 1/18s

M2 = 75kg

Did I do it right?

ehild
Homework Helper
50kg (1/12s) + M2 (1/18s) = 0

M2 = [50kg (1/12s)] / 1/18s

M2 = 75kg

Did I do it right?

You made two mistakes and they cancelled each other resulting in a correct mass. Your equation would result in a negative mass.

The skaters moved in opposite directions, one velocity is positive, the other is negative. So the correct equation is

m1 x/12 - m2 x/18 =0

Solving the equation correctly,

m1/12 = m2/18 , m2=m1 18/12 = 75 kg.

ehild

do we also have to consider the initial velocity and the amount of force pushed in a given time interval of 6 seconds?

ehild
Homework Helper
I do not get you. There is no question concerning the force between the skaters, setting them to move. It is assumed in such problems that the force acts for a very short time so the skaters are still very near to their original position when they are separated and move with some velocity. The difference between the times reaching the plank (6 s) comes from the different speeds the skaters move.

ehild

I was refering to the fact that Force times Time differenc is equal to the change in momentum. So, maybe you need to find initial velocity through that.

ehild
Homework Helper
I was refering to the fact that Force times Time differenc is equal to the change in momentum. So, maybe you need to find initial velocity through that.

Read the problem: "Two skaters stand in the center of a circular rink" What is the initial velocity?

ehild

Orginially I got 75 kg doing exactly what everyone else is doing, but I tried considering their small force. I know the answer is 75kg but I'm still skeptical about how like a reverse impulse can be tied into. that\s how my mind works though. I try to consider everything, but I still think the answer is 75 kg regaurdless of my skeptics.