# Centre of Mass

#### Quantumcom

1. Homework Statement

Two balls with masses m1 and m2 moving on a horizontal table in the same direction but at
different speeds collide elastically.
Obtain expressions for the position and motion of the centre of mass in terms of the
separate positions and motions of the two balls before they collide. Take it that at the
instant of observation they are passing x = x1, x2 respectively with speeds v1 and v2.
How would your expressions simplify if m2 >> m1, while v1 and v2 are not very different.
If m2 >> m1 and v2 << v1, what happens in the collision?

2. Homework Equations

Xcm= M1X1 + M2X2/M1+ M2

3. The Attempt at a Solution

Well, for separate positions the cerntre of mass should be same as above equation. But what about just before the collision?

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#### gneill

Mentor
Write separate equations of motion for the two objects (like x1 = x1o + v1*t). Plug these expressions into your expression for the center of mass. That will give you an equation for the position of the center of mass w.r.t. time.

Given an equation for position with respect to time, how can you find an expression for the velocity?

#### Quantumcom

Write separate equations of motion for the two objects (like x1 = x1o + v1*t). Plug these expressions into your expression for the center of mass. That will give you an equation for the position of the center of mass w.r.t. time.

Given an equation for position with respect to time, how can you find an expression for the velocity?
OH, yeah I got it. Just differentiate it. :D :D Thanks a lot sir!!

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