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Chapter 7: Q.54 (page 180)

In FIGURECP7.54, find an expression for the acceleration of m1. The pulleys are massless and frictionless.

Hint: Think carefully about the acceleration constraint.

Short Answer

Expert verified

The acceleration of blockm1is given bya1=2m2g(2m1+m2)

Step by step solution

01

Given information

Mass of the block 1is m1

mass of the block 2is m2

The pulleys are massless and frictionless

The acceleration of the block 1is localid="1649864857767" a1

The acceleration of the block2isa2

02

Explanation

Consider the Forces of two masses given in thefigureCP7.54

For block of massm1

For block of massm2

m2g-T2=m2a2

Considering the pulley is massless,鈭�T1=T2

Let a2=a鈭�T=2m1a

鈭�a1=2aacceleration constraint

On substituting the above equations on block equation, we get

m2g-2m1a=m2a(2m1+m2)a=m2ga=m2g(2m1+m2)

Therefore, the acceleration for m1is given by,

a1=2m2g(2m1+m2)

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