Question

A 20.0-kg uniform plank is supported by the floor at one end by a vertical rope at the other as shown in the figure. A 50.0-kg mass person stands on the plank a distance three-fourths of the length plank from the end on the floor.

a. What is the tension in the rope?
b. What is the magnitude of the force that the floor exerts on the plank?

Answer 1

I have tried to show the question in a figure

As the System is in equilibrium then

1 Net force will be zero

2 Net torque about every point will be zero

Let the length of rod be 'd' and lets calculate torque about the floor

$N\times0+T\times d=20\times10\times d/2\ +\ 50\times10\times3d/4\\ T=100+375=475 N$

Force will be also zero

$N+T=20\times10+50\times10\\N+T=700 \\N=700-475=225 newtons$