The mass of a regulation tennis ball is 57 g (although it can vary slightly), and tests have sh

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The mass of a regulation tennis ball is 57 g (although it...

The mass of a regulation tennis ball is $57 \mathrm{~g}$ (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 shall assume a $30.0 \mathrm{~ms}$ contact time. One of the fastest-known served tennis balls was served by "Big Bill" Tilden in 1931 , and its speed was measured to be $73 \mathrm{~m} / \mathrm{s}$. (a) What impulse and what total force did Big Bill exert on the tennis ball in his record serve? (b) If Big Bill's opponent returned his serve with a speed of $55 \mathrm{~m} / \mathrm{s}$, what total force and what impulse did he exert on the ball, assuming only horizontal motion?

The mass of a regulation tennis ball is $57 \mathrm{~g}$ (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 shall assume a $30.0 \mathrm{~ms}$ contact time. One of the fastest-known served tennis balls was served by "Big Bill" Tilden in 1931 , and its speed was measured to be $73 \mathrm{~m} / \mathrm{s}$. (a) What impulse and what total force did Big Bill exert on the tennis ball in his record serve?
(b) If Big Bill's opponent returned his serve with a speed of $55 \mathrm{~m} / \mathrm{s}$, what total force and what impulse did he exert on the ball, assuming only horizontal motion?

Key Concepts

Impulse

Impulse is defined as the change in momentum of an object when a force is applied over a period of time. It is mathematically represented as the product of the average force and the time interval during which the force is applied. In many physical contexts, impulse offers a way to connect the applied force with the resulting change in an object's motion.

Momentum

Momentum is a fundamental quantity in mechanics defined as the product of an object’s mass and its velocity. It describes the quantity of motion possessed by an object and plays a crucial role in collision and force analysis, where changes in momentum are central to understanding the impact of applied forces.

Average Force

Average force refers to the constant force that, if applied over the same time interval, would produce the same change in momentum as the actual variable force. This concept is particularly useful in scenarios where a force is exerted over a short contact interval, allowing the relationship between impulse and force (Impulse = Force × Time) to be applied in a simplified manner.

Newton's Second Law of Motion

Newton’s Second Law of Motion establishes the relationship between force, mass, and acceleration, and by extension, the change in momentum of an object. In its impulse-momentum form, the law states that the impulse acting on an object is equal to the change in its momentum, thereby linking the action of forces over time directly to changes in motion.

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