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# A different scaffold that weighs 400 N supports two ISBN: 9780321909107 29

## Solution for problem 4P Chapter 2

Conceptual Physics | 12th Edition

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Problem 4P

A different scaffold that weighs 400 N supports two painters, one 500 N and the other 400 N. The reading in the left scale is 800 N. What is the reading in the right-hand scale?

Step-by-Step Solution:
Step 1 of 3

First of all in the question the particular condition is not given that whether the whole system is balanced or not. So, let’s solve it. STEP 1:- At point “A” the person with 500 n is standing and at point “B” the person with 400 N is standing. Point “O” represents the centre point where the whole mass is concentrated and weighs 400 N. From the figure it is clearly visible that the distance of two persons from the centre “O” is different. And if we use the formula for the centre of mass where R is the coordinate of centre of mass, m R +m R R = m +m 2 2----------------(1) 1 2 So, intuitively we can say that this is an unbalanced system, because According to the centre of mass condition, m 1 =1m R -2-2---------(2) Here, R 1 R an2 m > m a1 the 2wo painters have different weights and they weigh different. So, the system cannot remain in a balanced state. STEP 2:- To find the distances R & R we will use equation (2). 1 2 m R = m R 1 1 2 2 9.8 × R1= 9.8 × R2 R 1 = 4/5--------------------(3) R2 STEP 3:- The left side reading is 800 N and we know the ratio of R & R1. so 2gain let’s use the centre of mass relation, 800 × R 1 x × R 2 Where x is our required reading at the right hand side. R 1 800 × R 2= x x = 800 × (4/5) = 640 N . CONCLUSION: So, the reading at the right side will be 640 N which is very intuitive. As the right side will accelerate upwards because less mass is there, then the weight which is the normal reaction will decrease. And it’s very obvious that the left side 640 N is less than right side 800 N.

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321909107

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A different scaffold that weighs 400 N supports two