Conceptual Physics

Her impulse (change in momentum) is the same, however long it takes her to stop when she hits the ground. In the example, that impulse is í530 kg·m/s. Why does she want to extend the time of her landing? She wants to make this time as long as possible (by landing in the sand, by flexing her knees), since it means the collision lasts longer. Since impulse equals force multiplied by elapsed time, the average force required to produce the change in momentum decreases as the time increases. The reduced average force lessens the chance of injury. Padded mats are another application of this concept: The impulse of landing is the same on a padded or unpadded floor, but a mat increases the duration of a landing and reduces its average force. There are also numerous applications of this principle outside of sports. For example, cars have “crumple zones” designed into them that collapse upon impact, extending the

duration of the impulse during a collision and reducing the average force. The long jumper's speed just

before landing is 7.8 m/s. What is

the impulse of her landing?

J = pfípi

J = mvfímvi

J = 0.0 í (68 kg)(7.8 m/s)

J = í530 kg·m/s

7.4 - Physics at play: hitting a baseball

When a professional baseball player swings a bat and hits a ball square on, he will dramatically change its velocity in a millisecond. A fastball can approach the plate at around 95 miles per hour, and in a line drive shot, the ball can leave the bat in roughly the opposite direction at about 110 miles per hour, a change of about 200 mph in about a millisecond. The bat exerts force on the baseball in the very brief period of time they are in contact. The amount of force varies over this brief interval, as the graph to the right reflects. At the moment of contact, the bat and ball are moving toward each other. The force on the ball increases as they come together and the ball compresses against the bat. The force applied to the ball during the time it is in contact with the bat is responsible for the ball’s change in momentum.

How long the bat stays in contact with the ball is much easier to measure than the average force the bat exerts on the ball, but by applying the concept of impulse, that force can be calculated. Impulse equals both the average force times the elapsed time and the change in momentum. Since the velocities of the baseball can be observed (say, with a radar gun), and the baseball’s mass is known, its change in momentum can be calculated, as we do in Example 1. The time of the collision can be observed using stroboscopic photography and other techniques. This leaves one variable í average force í and we solve for that in the example problem. The average force equals 2.5×10^4 N. A barrier that stops a car moving at 20 miles per hour in half a second exerts a comparable average amount of force.

Baseballs, bats and impulse

Force applied over time changes momentum Impulse = change in momentum Impulse = average force × elapsed time

The ball arrives at 40 m/s and

leaves at 49 m/s in the opposite

direction. The contact time is

5.0×10í^4 s. What is the average

force on the ball?

J = Favgǻt = ǻp = mǻv

Favg = mǻv/ǻt