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Ch 08: Momentum, Impulse, and Collisions
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 08: Momentum, Impulse, and CollisionsProblema 20a
Capitolo 8, Problema 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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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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Conservation Of Momentum

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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Intro to Momentum

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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Adding Mass to a Moving System
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