203,911 views
5 votes
5 votes
A 62 kg student stands on a very light, rigid board that rests on a bathroom scale at each end as shown in Figure.( i ) What is the reading on left scale?(ii) What is the reading on right scale?

A 62 kg student stands on a very light, rigid board that rests on a bathroom scale-example-1
User Harsha Hulageri
by
2.5k points

1 Answer

20 votes
20 votes

Since the system is at equlibrium this means that the reading on the scales have to add to the weight of the student, this means that:


F_L+F_R=W

or:


F_L=W-F_R

We also know that the moment of the system have to be zero, this means that the momentum for each scale is equal and then we have:


1.5F_L=0.5F_R_{}

Plugin this in the equation for the forces we have:


\begin{gathered} (0.5)/(1.5)F_R=W-F_R \\ F_R+(0.5)/(1.5)F_R=W \\ (1.5+0.5)/(1.5)F_R=W \\ F_R=(1.5W)/(1.5+0.5) \\ F_R=(1.5W)/(2) \\ F_R=(1.5)/(2)(62)(9.8) \\ F_R=455.7 \end{gathered}

Now that we know the reading on the right scale we plug it on the equation for the left scale:


\begin{gathered} F_L=W-F_R \\ F_L=(62)(9.8)-455.7 \\ F_L=151.9 \end{gathered}

Therefore the reading on the left scale is 151.9 N and the reading on the right scale is 455.7 N.

User Eindbaas
by
3.3k points