A Table for Momentum Conservation Problems

Solving collision and explosion problems does not involve complicated math, just multiplying, dividing, adding and subtracting. What is hard is keeping track of lots of numbers. Here is a table that is meant to help.

Example: 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.

  • Put the known quantities into the table.
  • Calculate the original momentum (p0 = m v) of each person.
  • Get totals where you can (notice that there is no total v0, because Grandpa and Beatrice are separate).
  • Here’s the important connection between before and after: p0 = p1.
  • In this case, we know they travel together afterward. We can find their speed because we know the system’s total momentum and total mass
    (v = p / m).

At this point, the problem has been solved. The task was to find the final velocity, and we have it now. However, we can take a couple more steps:

  • We know the individual speeds because they are the same as the system’s speed.
  • Now find the momentum of each character individually (p1 = m v1).

We can now describe the momentum transfer, saying, “100. kg m/s of momentum transferred from Grandpa to Beatrice.

Before / After
Object / Mass / v0 / po / v1 / p1
A Grandpa / 100. kg / 5 m/s / 500. kg m/s / 4 m/s / 400. kg m/s
B Beatrice / 25 kg / 0 m/s / 0 kg m/s / 4 m/s / 100. kg m/s

System AB

/ 125 kg / If together:

X

/ 500 kg m/s / If together:
4 m/s / 500 kg m/s

A Table for Momentum Conservation Problems

This worksheet accompanies a presentation about solving momentum problems. After seeing the example, there are some other examples to try.

Example 1: 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.

Fill in the table below according to the directions in the presentation.

Before / After
Object / Mass / v0 / po / v1 / p1
A
B

System AB

/ If together: / If together:

Example 2: What is the recoil velocity of a 3 kg gun that fires a bullet of mass 0.06 kg at a velocity of 200. m/s?

Before / After
Object / Mass / v0 / po / v1 / p1
A
B

System AB

/ If together: / If together:

Example 3: An 80. kg hockey player moving at 10. m/s collides with a 50. kg figure skater who is originally standing still. If the hockey player's velocity after the collision is 3.0 m/s in the same direction, what is the figure skater's final velocity?

Before / After
Object / Mass / v0 / po / v1 / p1
A
B

System AB

/ If together: / If together:

Example 4: A boy shoots a 0.25 kg rock out of his sling shot and hits a stationary 2.0 kg board. The rock is traveling 28 m/s before the collision. After the elastic collision, the board flies straight off at a speed of 2 m/s.

For this problem, make your own table.