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.

 

[ogb p]

I would first like to commend you for using a systematic approach to solving this problem. Your understanding of static equilibrium and the use of appropriate equations is commendable. However, I believe the error in your solution lies in the assumption that the force exerted by the floor and the force exerted by the wall are the same.

While it is true that these two forces are the only ones acting in the x-direction, they are acting at different points on the ladder. The force exerted by the floor is at the base of the ladder, while the force exerted by the wall is at the point where the ladder makes contact with the wall. These two points are not at the same height, therefore the forces at these points will not be the same.

To correctly solve for the force exerted by the wall, you can use the equation for torque again, but this time using the distance from the wall to the point of contact on the ladder as the lever arm. You can also use the equation for forces in the y-direction, since the sum of forces in this direction should also be equal to zero in static equilibrium.

I hope this explanation helps and encourages you to continue using a systematic approach to solving physics problems. Good luck!