Calculating Momentum: A Football Player and a Football

(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 hard-thrown 0.410-kg football that has a speed of 25.0 m/s.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

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

$p_{player} = (110 kg) (8 . 00 m/s) = 880 kg \cdot m/s$
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.

$p_{ball} = (0.410 kg) (25.0 m/s) = 10.3 kg \cdot m/s$
8.5

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

$\frac{p_{player}}{p_{ball}} = \frac{880}{10.3} = 85 . 9 .$
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 sections.

0 of 4 steps open

How did it go?

Strategy

Solution for (a)

Solution for (b)

Discussion