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

Recommended explanations on Physics Textbooks

Electrostatics

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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.