Question

A Uniform 80.0 kg that is 10 meters long is at rest supported at its left end and supported by a vertical rope located 3 meters from its right end and a 60 kg woman stands at the right end of the beam.

A- Draw a free body diagram of the beam

B- find the tension of the rope

C- find the force that the column exerts on the left end of the beam.

Answer 1

Given

say uniform beam of mass 80 kg , of length l = 10 m

supported at its left end

vertical rope is supported at 7 m from left end and 3 m from right end

woman of 60 kg stands at right end

from the FBD

the forces along x axis and y axis

so that the system is in equilibrium , the torques acting in x, y directions can be written as  

the torques acting along vertical direction are

T*7 - 5*80*10 - 7*60*10 = 0

T = 1171.43 N

b.

here the Fx = 0 N

and for Fy + T = 800 + 600

Fy = 8200 - 1171.43 = 7028.57 N

the net force is F = 7028.57 N