Question

What is the reading on each of the scales?
On the right scale. Express your answer using two significant figures.

Answer 1

we have touse vertical and rotational equilibrium to solve this problem.

LetL be the force exerted by the left support (and this will also be the reading on the left scale), and R bethe force exerted by theright support

these two supports must balance the weight of the person and the board, so

L+R=(54+10) g = 627.2N

the board is also in rotational equilibrium, so all the torques sum to zero; let's sum torques around the left support, this means the lever arm of theforce at L is zero so its torque is zero

torque due to weight of board = 10 kg x g x 1 m = 98Nm (cw=clockwise)
torque due to weight of person=54 kg x g x 1.5m=793.8Nm (cw)
torque due to force at R= R x 2m (counterclockwise)

so the torque at R equals the sum of the other two torques:

2R=793.8+98=>R=445.9

therefore since L+R=627.2, L=181.3