Chapter 2, Problem 44A

Harry Heavyweight, who weighs 1200 N, stands on a pair of bathroom scales so that one scale reads twice as much as the other. What are the scale readings?

To determine

Reading of both scales.

Answer to Problem 44A

One scale reads 400 N and other reads 800 N.

Explanation of Solution

Given:

Person H weight is 1200 N.

One bathroom scale reads twice the other.

Formula Used:

For mechanical equilibrium, summation of all forces is zero. That is

  $\sum F=0$

Calculation:

Weight of person H will be in downward direction.

Let one scale reads x N,

So, reading of other bathroom scale is 2x N.

Since, person H is in mechanical equilibrium so, $\sum F=0$ or

Upward force = Downward force

  $\begin{array}{l}\Rightarrow x+2x=1200\\ \Rightarrow 3x=1200\text{N}\\ \Rightarrow x=400\text{N}\end{array}$

So, reading of first bathroom scale is 400 N and

Reading of other bathroom scale is $2x=2\times 400=800\text{N}$

Conclusion:

Therefore, one scale reads 400 N and other reads 800 N.