Suppose the student in Figure 1 is 58 kg and the board being

Suppose the student in Figure 1 is 58 kg, and the board being stood on has a 12 kg mass. What is the reading on the left scale? Express your answer using two significant figures. What is the reading on the right scale? Express your answer using two significant figures.

Solution

call L the force exerted by the left support (and this will also be the reading on the left scale), and R the force exerted by the right support

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

L+R=(58+12) g = 686N -------------------(1)

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 the force at L is zero so its torque is zero

torque due to weight of board = 12*g*1 =117.6Nm(clockwise)

torque due to weight of person=58*g*1.5=852.6N(clockwise)

torque due to force at R= R x 2m (counterclockwise)

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

2R=117.6Nm+ 852.6Nm

2R=970.2Nm

R=485.1N   (49.5kg)

so L=200.9N (20.4kg)    ( from eq (1)