University of Wisconsin Green Bay

Estimate the magnitude of the momentum of a runner in a marathon.

  • In this problem, you are asked to estimate momentum in a single situation. Although no information is given, a quick look at the definition of momentum shows that it depends only on mass and velocity—two quantities that you can estimate. So you are not asked to calculate new information in this problem but rather to restate what you can say about motion in a slightly different way.

  • There is no need for a picture in most definition problems, and this is one of them. You can estimate velocity information for a situation and asked for the closely-related momentum information for the same motion. A picture will not provide any additional insight or organization beyond what is already present in the problem.

  • In equation form, momentum is defined as

    p = mv

    This is the only relation you need for this problem.

  • p = mv
    p = mv
    p (55 kg)(4 m/s)
    p 200 kg m/s

    There is no further calculation required in this problem.

  • p = mv
    p = mv
    p ≈ (55 kg)(4 m/s)
    p ≈ 200 kg m/s

    This problem is merely a definition problem. You will use the definition of momentum in Conservation of Momentum problems, much as you use Fg = mg as you solve force problems. Whenever you have information about the speed of an object, you can restate that information as its momentum (or vice versa.)

    Your estimated value of momentum may be higher or lower depending on the values you used for mass and velocity. You should make sure that those values are in a reasonable range.