The boy at D has a mass of 50 kg, a center of mass at G, and stands on a plank at the position shown. The plank is pin-supported at A and rests on a post at B. Neglecting the weight of the plank and post, determine the magnitude of force P his friend (?) at E must exert in order to pull out the post. Take B = 0.3 and C = 0.8.

The boy at D has a mass of 50 kg, a center of mass at G, and stands on a plank at the position shown. The plank is pin-supported at A and rests on a post at B. Neglecting the weight of the plank and post, determine the magnitude of force P his friend (?) at E must exert in order to pull out the post. Take _B = 0.3 and _C = 0.8.

 

Solution

Take vertical forces equal to zero, Ay + Ny = 490.5.
Take moment at A, then Ny*3=mg*2, By solving we get N=327.

Friction force = static friction coefficient * normal force.
f = 0.3 * 327 = 98.1;

Now take moment at c(post bottom),we get 

f(0.3+0.4) = Fcos30 * 0.3
By solving the above equation we get ;

F = 264.115 Newtons.