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Chapter 7: Q.4 (page 177)

Block Ain FIGUREEX7.4is heavier than block Band is sliding down the incline. All surfaces have friction. The rope is massless, and the massless pulley turns on frictionless bearings. The rope and the pulley are among the interacting objects, but you鈥檒l have to decide if they鈥檙e part of the system.

Short Answer

Expert verified

Yes. The rope and the pulley are among the interacting objects and they鈥檙e part of the system.

Step by step solution

01

Given information

mass of block A=mA

mass of block B=mB

acceleration due to gravity g

Tension on the rope is T

friction force between block AandBis f1

friction force between block Bandsurfacef2

Inclination of the blocks are胃

02

Explanation

Newton's Second Law, setting all accelerations to zero, implies the following relationships:

NA=mAgcos(胃)T=mAgsin(胃)+f2NB=mB+mAgcos(胃)T+f1+f2=mBgsin(胃)

The second equation can be substituted into the fourth equation to give

f1+2f2=mB鈭�mAgsin(胃)

Setting the friction forces to their maximum values

f1,max=渭sNB=渭smB+mAgcos鈦�(胃)

f2,max=渭sNA=渭smAgcos鈦�(胃)

Thus the blocks AandBare said to be connected in a system and the friction forces are also in line with the part of the system.

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