Biomechanics. The mass of a regulation tennis ball is 57.0 g (although it can vary slightly), a

step 1 Momentum and impulse are all about collisions. So in this question, we are looking at a collisio

Biomechanics. The mass of a regulation tennis ball is 57.0...

Biomechanics. The mass of a regulation tennis ball is $57.0 \mathrm{~g}$ (although it can vary slightly), and tests have shown that the ball is in contact with the tennis racket for $30 \mathrm{~ms}$. (This number can also vary, depending on the racket and swing.) We assume a $30.0 \mathrm{~ms}$ contact time in this problem. In the 2011 Davis Cup competition, Ivo Karlovic made one of the fastest recorded serves in history, which was clocked at $156 \mathrm{mph}(70 \mathrm{~m} / \mathrm{s}) .$ (a) What impulse and what average force did Karlovic exert on the tennis ball in his record serve? (b) If his opponent returned this serve with a speed of $55.0 \mathrm{~m} / \mathrm{s},$ what impulse and what average force did his opponent exert on the ball, assuming purely horizontal motion?

Key Concepts

Impulse

Impulse is the product of force and the time interval over which it is applied, and it is equivalent to the change in an object's momentum. It is a central concept in analyzing collisions and force interactions in dynamics.

Momentum

Momentum is a measure of the quantity of motion an object has, calculated as the product of its mass and velocity. This concept is critical in understanding how forces, when applied, alter an object's speed or direction.

Impulse-Momentum Theorem

The Impulse-Momentum Theorem connects impulse to momentum by stating that the impulse acting on an object equals the change in its momentum. This theorem provides a framework for solving problems that involve forces acting over time intervals.

Average Force

Average force refers to the constant force that, if applied over the same time interval, would produce the same impulse as that from a variable force. It is useful in simplifying analyses of collisions and interactions where force may not be constant.

Transcript

00:01 Momentum and impulse are all about collisions.

00:05 So in this question, we are looking at a collision between a tennis racket and a tennis ball.

00:11 So let's look at some of the data that we have.

00:14 So we have the mass of the tennis ball, which i'm going to convert to kilograms, so it's 57 grams, which is 057 kilograms.

00:29 We also know that the tennis ball on average is in contact with the racket.

00:35 For 30 milliseconds, which we're going to use 0 .0 .30 seconds.

00:48 So in the first part, so part a, let's do this part in red.

00:53 We want to know how much impulse and how much force karlovick needed to be exerted on a tennis ball to record a serve at 156 miles per hour or 70 meters per second.

01:04 So the way that we're going to do this is with the following equation, j equals ft, equals, equals delta p.

01:14 So the way that we do this, this is impulse, which is j equals force times time, which also equals the change in momentum.

01:23 So for this first question, we're trying to figure out what's the impulse.

01:26 So we're going to utilize just the j equals delta p.

01:33 Now momentum is also mass time velocity.

01:37 So we can make this mass times final velocity minus, and this.

01:46 Initial velocity.

01:50 So mass times change in velocity gives us the change in momentum.

01:53 Normally mass doesn't change.

01:55 And that's true in this scenario as well.

01:59 So our impulse here, we have j equals 0 .057 kilograms times 70 meters per second minus zero meters per second.

02:20 The tennis ball isn't moving when he first hits it, at least not horizontally.

02:24 So we plug in and calculate, we get impulse is equal to 3 .99 kilograms times meters per second...

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