You and a friend are playing tennis. (a) What is the...

You and a friend are playing tennis. (a) What is the magnitude of the momentum of the $0.057-\mathrm{kg}$ tennis ball when it travels at a speed of $30 \mathrm{m} / \mathrm{s} ?$ (b) At what speed must your 0.32-kg tennis racket move to have the same magnitude momentum as the ball? (c) If you run toward the ball at a speed of $5.0 \mathrm{m} / \mathrm{s},$ and the ball is flying directly at you at a speed of $30 \mathrm{m} / \mathrm{s},$ what is the magnitude of the total momentum of the system (you and the ball)? Assume your mass is $60 \mathrm{kg} .$ In every case specify the object of reference.

Key Concepts

Linear Momentum

Linear momentum is a fundamental concept in mechanics defined as the product of an object's mass and its velocity. It represents the quantity of motion an object has and indicates how challenging it is to bring the object to a stop.

Momentum as a Vector

Momentum is a vector quantity, which means it possesses both magnitude and direction. Understanding momentum as a vector is crucial when dealing with problems that involve objects moving in different directions, as the direction of each momentum must be taken into account, especially when summing them.

Reference Frame

A reference frame is the point of view or coordinate system relative to which measurements such as velocity and momentum are made. Specifying the object of reference is important to ensure consistency in analyzing the motion and correctly assigning directions to vector quantities.

Momentum Addition in a System

When analyzing systems comprised of multiple objects, the total momentum is determined by vectorially adding the individual momenta. This process takes into account both the magnitudes and directions of the momentum contributions from each object, making it essential for problems where objects move in opposite directions or at different speeds.

Transcript

00:01 In the first part of this question, we have a bull, which is moving with a velocity of 30 meters per second.

00:12 Here we assume the velocity of the ball is to the left.

00:17 The mass of the ball is 0 .057 kilograms.

00:23 And we are asked to calculate the magnitude of the momentum of the ball.

00:27 So we're not interested in its direction right now.

00:31 Remember momentum is a vector so it has both magnitude and direction we are only interested in its magnitude now which we calculate using the equation p equals m times b where p is momentum m is mass and b is velocity so to calculate it we just times 0 .057 the mass of the ball by 30 the velocity of the ball and this gives us about 1 .7 kilograms meters per second.

01:04 So this is the magnitude of the momentum of the ball.

01:09 We're not interested in its direction right now.

01:13 The second part of the question, there is a racket with a mass of 0 .32 kilograms.

01:22 And this racket is moving with a certain velocity which we need to calculate.

01:30 We don't know the velocity yet.

01:33 We know the mass, 0 .32 kilograms.

01:39 And we are told that the momentum of the racket should be the same as the momentum of the ball, which we have just calculated in part a.

01:51 So 1 .7 kilograms meters per second.

01:54 At this point, we can calculate the velocity of the racket by just rearranging the equation for momentum.

02:02 So velocity is equal to p over m, where p is momentum and m is mass of the racket.

02:11 So the velocity of the racket will be 1 .7, its momentum, divided by 0 .3 to its mass.

02:20 And this gives us the value of the magnitude of the velocity of the racket, which is 5 .3 meters per second...

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