Explanation Consider the figure given below. Torque due to friction opposes the toque due to the motion of the hanging object. Write the expression for the total torque. ∑ τ = T R − τ f (I) Here, T is the tension, R is the outside radius of the spool, τ f is the torque due to friction. Equate I α for ∑ τ in equation (I) to obtain an expression for τ f . I α = T R − τ f τ f = T R − I α (II) Here, I is the moment of inertia, α is the angular acceleration. Write the expression for the force along y direction. ∑ F y = T − m g = − m a (III) Here, m is the mass of the object, g is the acceleration due to gravity, a is the acceleration. Rearrange equation (III) to obtain an expression for T . T = m ( g − a ) (IV) According to Newton’s laws of motion the change in position of the hanging object is. Δ y = υ i t + a t 2 2 (V) Here, υ i is the initial velocity, t is the time. Since the object was initially at rest the initial velocity will be zero. Substitute, 0 for υ i in equation (V), and rewrite to obtain an expression for a . Δ y = ( 0 ) t + a t 2 2 a = 2 Δ y t 2 (VI) Write the expression for angular acceleration

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN: 9781133104261

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Chapter 10, Problem 70P

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To show that the torque due to friction is.τf=R[m(g−2yt2)−M5y4t2].

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Chapter 10, Problem 69P

Chapter 10, Problem 71P

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To show that the torque due to friction is. τ f = R [ m ( g − 2 y t 2 ) − M 5 y 4 t 2 ] .

Solution Summary: The author illustrates how torque due to friction opposes the toque caused by the motion of the hanging object.

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To show that the torque due to friction is.τf=R[m(g−2yt2)−M5y4t2].

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Chapter 10 Solutions