Chapter 7: Q.54 (page 180)

In $F I G U R E C P 7.54$ , 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 block $m_{1}$ is given by $a_{1} = \frac{2 m_{2} g}{(2 m_{1} + m_{2})}$

Step by step solution

Given information

Mass of the block $1$ is $m_{1}$

mass of the block $2$ is $m_{2}$

The pulleys are massless and frictionless

The acceleration of the block $1$ is localid="1649864857767" $a_{1}$

The acceleration of the block $2$ is $a_{2}$

Explanation

Consider the Forces of two masses given in the $f i g u r e C P 7.54$

For block of mass $m_{1}$

For block of mass $m_{2}$

$m_{2} g - T_{2} = m_{2} a_{2}$

Considering the pulley is massless, $∴ T_{1} = T_{2}$

Let $a_{2} = a$ $∴ T = 2 m_{1} a$

$∵ a_{1} = 2 a$ acceleration constraint

On substituting the above equations on block equation, we get

$m_{2} g - 2 m_{1} a = m_{2} a (2 m_{1} + m_{2}) a = m_{2} g a = \frac{m_{2} g}{(2 m_{1} + m_{2})}$

Therefore, the acceleration for $m_{1}$ is given by,

$a_{1} = \frac{2 m_{2} g}{(2 m_{1} + m_{2})}$

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In $F I G U R E C P 7.54$ , find an expression for the acceleration of m1. The pulleys are massless and frictionless.
Hint: Think carefully about the acceleration constraint.

Short Answer

Step by step solution

Given information

Explanation

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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

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

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Force

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Study anywhere. Anytime. Across all devices.

In $F I G U R E C P 7.54$ , find an expression for the acceleration of m1. The pulleys are massless and frictionless.
Hint: Think carefully about the acceleration constraint.