Ladder vs Wall Homework - Force Calculation

[Dante5454]

Homework Statement

A 10m ladder whose weight is 180N is placed against a smooth vertical wall. A person whose weight is 652N stands on the ladder a distance of 3.2m up the ladder. The foot of the ladder rests on the floor 5.7m from the wall. What is the force exerted by the wall? What is the force exerted by the floor? (Answers in N)

Homework Equations

Static Equilibrium, so Sum of Torques=0, Sum of Forces in the y-direction=0, and Sum of forces in the x-direction=0

I think the two answers should be the same, because they are the only two forces acting in the x-direction.

The Attempt at a Solution

I first solved for the height of the ladder off the ground using pythagorean's theorem. Then, with trig, got both the angle of the ladder to the floor and the ladder to the wall. I placed the pivot point at the floor and calculated each torque, one for the man, using (distance up ladder)*(weight of man)*(cos of angle between ladder and floor) and one for the ladder using (half the length of ladder)*(weight of ladder)*(cos of angle between ladder and wall). Dividing that answer by (height of ladder off ground)*(cos of angle between ladder and floor) SHOULD have given me the force of the floor against the ladder, which would have been the same as the force of the wall against the ladder, but it was incorrect when I submitted it. Thanks!

 

[Doc Al]

I think the two answers should be the same, because they are the only two forces acting in the x-direction.

Careful! The force exerted by the floor has both a vertical and a horizontal component.