How Do Weight Distribution and Torque Affect Scale Readings?

[jibjab]

Homework Statement

A 70.7 kg woman stands on a very light, rigid board that rests on a bathroom scale at each end. The total length of the board is L=2.1 m, and the woman's distance from the left of the board is 1.3 m.
What is the reading on the left scale? The right scale?

Homework Equations

n2=d1w/d2

The Attempt at a Solution

I converted the woman's weight to 693.3 N. For d1 I used half the length of the board, 1.05 m, and for d2, I found the distance the woman was away from the right side of the board relevant to the center of gravity on the board, which was 0.25 m. To find n2, I did
(693.3N)(1.05m)/1.3m and got 559.97 N.
I subtracted that amount from the woman's weight and got 133.33 N, which made sense since she was closer to the right side of the board, but the computer says no. Can anyone see what I'm doing wrong? I was following an example in the book.

Thank you!

 

[rl.bhat]

She is standing on a very light board. No neglect its mass.
Let R1 and R2 are the reactions on the scales. Find the moments due to woman and R2 about R1. Hence find the distance of the woman from R1.

 

[tomcue]

Hello,

It seems like you have made a mistake in your calculation for n2. The correct formula to use in this situation is n2 = d1w/d2, where d1 is the distance from the left scale to the center of gravity of the board, and d2 is the distance from the right scale to the center of gravity of the board. In this case, d1 = 1.05 m and d2 = 1.05 m (since the board is symmetric), so the correct calculation would be (693.3N)(1.05m)/1.05m = 693.3N. This means that the reading on both scales should be equal, at 693.3N each.

I hope this helps clarify the calculation for you. Let me know if you have any further questions.

Best,

Scientist