Momentum Conservation An Example

A Table to Organize Momentum Problems

Here is the Problem: Grandpa (M = 100. kg) skates along at 5. m/s toward Beatrice (m = 25. kg), who is motionless. Grandpa picks up Beatrice as he passes by, and the two travel together. We’ll find the final velocity of the two of them.

First: Record the Known Quantities Now, what can you calculate from this?

Second: Calculate what you can: p = m v Again, think what you can calculate from this.

Next: Calculate totals Note: They are not traveling together, so there is no “total velocity.” Now, the simple, but crucial point…

Next: Remember that p0 = p1 What can you figure from this?

Finally: Find the final velocity v1 = p1 / (mG + mB) And that’s solves the problem that was posed!

But wait, there’s more… Fill in the rest of the table.

Velocities…

…and the individual momentum of each character. Notice! You can check your work by making sure that the total final momentum (500. kg m/s) is equal to the sum of the separate momenta (400. kg m/s + 100. kg m/s).

Momentum Transfer From this, we can make a statement about momentum transfer : “100. kg m/s of momentum transferred from Grandpa to Beatrice.” Note this includes both the amount and the magnitude of the transfer.