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Ch 08: Momentum, Impulse, and Collisions
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 08: Momentum, Impulse, and CollisionsProblem 20a
Chapter 8, Problem 20a

You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a 0.600-kg ball that is traveling horizontally at 10.0 m/s. Your mass is 70.0 kg. If you catch the ball, with what speed do you and the ball move afterward?

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Step 1: Identify the principle of conservation of momentum, which states that the total momentum of a system remains constant if no external forces act on it. In this case, the system consists of you and the ball, and there is negligible friction.
Step 2: Write the equation for conservation of momentum. The total momentum before catching the ball is equal to the total momentum after catching the ball: m1v1 + m2v2 = (m1 + m2)vf, where m1 is the mass of the ball, v1 is the velocity of the ball, m2 is your mass, v2 is your initial velocity (which is 0), and vf is the final velocity of you and the ball together.
Step 3: Substitute the given values into the equation. The mass of the ball is 0.600 kg, its velocity is 10.0 m/s, your mass is 70.0 kg, and your initial velocity is 0 m/s. The equation becomes: (0.600)(10.0) + (70.0)(0) = (0.600 + 70.0)vf.
Step 4: Simplify the equation. The left-hand side simplifies to 6.0 kg·m/s, and the right-hand side becomes 70.6vf. The equation now reads: 6.0 = 70.6vf.
Step 5: Solve for vf, the final velocity of you and the ball together. Divide both sides of the equation by 70.6 to isolate vf: vf = 6.0 / 70.6. This gives the final velocity in m/s.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Conservation of Momentum

The principle of conservation of momentum states that in a closed system, the total momentum before an event must equal the total momentum after the event, provided no external forces act on it. In this scenario, the momentum of the ball and the person must be conserved when the person catches the ball.
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Momentum Calculation

Momentum is calculated as the product of an object's mass and its velocity (p = mv). For this problem, you will need to calculate the initial momentum of both the ball and the person before the catch, and then use this to find the final velocity after the catch.
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System Mass

The system mass refers to the combined mass of the person and the ball after the catch. In this case, the total mass will be the sum of the person's mass and the ball's mass, which is essential for calculating the final velocity using the conservation of momentum.
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Related Practice
Textbook Question

On a frictionless, horizontal air table, puck A (with mass 0.250 kg) is moving toward puck B (with mass 0.350 kg), which is initially at rest. After the collision, puck A has a velocity of 0.120 m/s to the left, and puck B has a velocity of 0.650 m/s to the right. What was the speed of puck A before the collision?

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Textbook Question

Two vehicles are approaching an intersection. One is a 2500-kg pickup traveling at 14.0 m/s from east to west (the -x-direction), and the other is a 1500-kg sedan going from south to north (the +y-direction) at 23.0 m/s. What are the magnitude and direction of the net momentum?

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Textbook Question

Two vehicles are approaching an intersection. One is a 2500-kg pickup traveling at 14.0 m/s from east to west (the -x-direction), and the other is a 1500-kg sedan going from south to north (the +y-direction) at 23.0 m/s. Find the x- and y-components of the net momentum of this system.

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Textbook Question

You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a 0.600-kg ball that is traveling horizontally at 10.0 m/s. Your mass is 70.0 kg. If the ball hits you and bounces off your chest, so afterward it is moving horizontally at 8.0 m/s in the opposite direction, what is your speed after the collision?

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Textbook Question

On a frictionless, horizontal air table, puck A (with mass 0.250 kg) is moving toward puck B (with mass 0.350 kg), which is initially at rest. After the collision, puck A has a velocity of 0.120 m/s to the left, and puck B has a velocity of 0.650 m/s to the right. Calculate the change in the total kinetic energy of the system that occurs during the collision.

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Textbook Question

To warm up for a match, a tennis player hits the 57.0-g ball vertically with her racket. If the ball is stationary just before it is hit and goes 5.50 m high, what impulse did she impart to it?

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