Question

Suppose a crate of mass 8.8 kg is placed on the plank in the figure below at a distance x = 6.3 m from the left end. If the plank has a mass of 12 kg, find the forces exerted by the two supports on the plank. (Indicate the direction with the sign of your answer.)

Answer 1

here figure is missing..so solving problem by some assumption

The total length of the plank is 12m, the left support is 3m from the end and the right support is 2m from the end with 7m between the two

The weight of the crate and plank are downward forces. The forces exerted by the supports are upward forces. The sum of the forces exerted by the supports must equal the total weight.
Weight of crate = 8.8 * 9.8 = 86.24 N,

Weight of plank = 12 * 9.8 =117.6 N
F left + F right = 86.24 + 117.6 = 203.84 N

The sum of the clockwise torques must equal the counter clockwise torque. If we let the pivot point be at the left support, we can determine the force at the right support.
Torque = Force * distance from the left support
The weight of the crate will produce a clockwise torque. Weight = 8.8 * 9.8.
The distance from the left support to the weight of the crate is 6.3 – 3 = 3.3 m
Torque = 8.8 * 9.8 * 3.3 = 284.592

The weight of the plank will produce a clockwise torque. Weight = 12 * 9.8.
The distance from the left support to the weight of the plank is 6 – 3 = 3 m
Torque = 12 * 9.8 * 3 = 352.8

Sum of clockwise torque = 284.592 + 352.8 = 637.392

The upward force at right support will produced a counter clockwise torque.
The distance from the left support to the right support = 7 m.
Torque = F right * 7

F right * 7 = 637.39
F right = 457.268 ÷ 7 = 91.05 N

F left + F right = 203.84
F left + 91.05 = 203.84
F left = 203.84 – 91.05 = 112.784 N

I hope this helps you to understand how to solve this type of problem