Explanation Given data: Refer to the Figure P10.84 in the textbook for the two-box pulley system. Mass of the box A ( m A ) is 12.0 kg. Mass of the box B ( m B ) is 4.0 kg. The two boxes release from rest. The box B is fallen a distance of 0.50 m. Formula used: Write the expression for energy conservation equation for the given system as follows. Δ K + Δ U g = 0 (1) Here, Δ K is the change in the kinetic energy, and Δ U g is the change in the gravitational potential energy. Write the expression for change in the gravitational potential energy. Δ U g = m g Δ y (2) Here, m is the mass of the object, g is the acceleration due to the gravity, which is 9.8 m s 2 , and Δ y is the change in the height. Write the expression for change in the kinetic energy for the given system as follows. Δ K = K A + K B (3) Here, K A is the kinetic energy of box A, and K B is the kinetic energy of box B. Write the expression for kinetic energy. K = 1 2 m v 2 (4) Here, m is the mass of the object, and v is the velocity (speed) of the object. Explanation: Consider the speed of the boxes (together with pulley) as v , which is to be determined. Calculation of kinetic energy of box A: Modify the expression in equation (4) to find the kinetic energy of box A as follows. K A = 1 2 m A ( v A ) 2 Substitute 12.0 kg for m A , and v for v A , K A = 1 2 ( 12.0 kg ) ( v ) 2 = 6 v 2 kg Calculation of kinetic energy of box B: Modify the expression in equation (4) to find the kinetic energy of box B as follows. K B = 1 2 m B ( v B ) 2 Substitute 4.0 kg for m , and v for v B , K B = 1 2 ( 4.0 kg ) ( v ) 2 = 2 v 2 kg Calculation of change in the kinetic energy: Substitute 6 v 2 kg for K A , and 2 v 2 kg for K B in equation (3), Δ K = 6 v 2 kg + 2 v 2 kg =8 v 2 kg Calculation of change in the gravitational potential energy: As the ball B is fallen, find the change in the gravitational potential energy with respect to the box B as follows

College Physics: A Strategic Approach Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition) (What's New in Astronomy & Physics)

4th Edition

ISBN: 9780134641492

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Question

Chapter 10, Problem 84GP

To determine

To find: The speed of the boxes when box B fallen a distance of 0.50 m.

Expert Solution & Answer

Chapter 10 Solutions

College Physics: A Strategic Approach Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition) (What's New in Astronomy & Physics)

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