(a) Calculate the momentum of a 110-kg football player running at 8.00 m/s. (b) Compare the player’s momentum with the momentum of a hardthrown 0.410-kg football that has a speed of 25.0 m/s.

Question

Strategy
No information is given regarding direction, and so we can calculate only the magnitude of the momentum, p . (As usual, a symbol that is in italics is a magnitude, whereas one that is italicized, boldfaced, and has an arrow is a vector.) In both parts of this example, the magnitude of momentum can be calculated directly from the definition of momentum given in the equation, which becomes

p = mv (8.3)

when only magnitudes are considered.

Accepted Answer

Solution for (a)
To determine the momentum of the player, substitute the known values for the player’s mass and speed into the equation.

[latex]p_{player} = (110 kg)(8.00 m/s) = 880 kg · m/s [/latex] (8.4)

Solution for (b)
To determine the momentum of the ball, substitute the known values for the ball’s mass and speed into the equation.

[latex]p_{ball} = (0.410 kg)(25.0 m/s) = 10.3 kg · m/s [/latex] (8.5)

The ratio of the player’s momentum to that of the ball is

[latex] \frac{p_{player}}{p_{ball}} = \frac{880}{10.3} = 85.9. [/latex] (8.6)

Discussion
Although the ball has greater velocity, the player has a much greater mass. Thus the momentum of the player is much greater than the momentum of the football, as you might guess. As a result, the player’s motion is only slightly affected if he catches the ball. We shall quantify what happens in such collisions in terms of momentum in later ections.

Question 8.1: (a) Calculate the momentum of a 110-kg football player runni...

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