Chapter 2, Problem 5TS

Phil Physicer weighs $600\text{ N}\left(132\text{ lb}\right)$ and stands on two bathroom scales. He stands so one scale reads twice as much as the other. What are the scale readings?

To determine

The scale readings.

Answer to Problem 5TS

The scale readings are $200\text{N}$ and $400\text{N}$.

Explanation of Solution

Given Info: Weight of Phil is $600\text{N}$.

The Phil Physicer is in mechanical equilibrium when he is standing on the scale. So, the net force acting on him will be zero.

Write the expression for the equilibrium condition.

$\begin{array}{c}\Sigma F=0\\ \left(N_1+N_2\right)+W=0\\ N_1+N_2=-W\mathrm{......}(\text{I})\end{array}$

Here,

$N_1$ is the reading on onebathroom scale

$N_2$ is the reading on second bathroom scale

The second scale reads twice as much as reading of first scale.

Write the expression for the reading on other scale.

$N_2=2N_1\mathrm{......}(\text{II})$

Substitute ${\mathrm{2N}}_1$ for $N_2$ in equation (I).

$\begin{array}{c}{N}_1+2N_1=-\left(-600\text{N}\right)\\ 3N_1=600\text{N}\\ N_1=200\text{N}\end{array}$

Substitute $200\text{N}$ for $N_1$ in equation (II).

$\begin{array}{l}{N}_2=2\times \left(200\text{N}\right)\\ N_2=400\text{N}\end{array}$

Conclusion:

Therefore, the scale readings are $200\text{N}$ and $400\text{N}$.