- #1

Elias Waranoi

- 45

- 2

## Homework Statement

Two ladders, 4.00 m and 3.00 m long, are hinged at point A and tied together by a horizontal rope 0.90 m above the floor (Fig. P11.89). The ladders weigh 480 N and 360 N, respectively, and the center of gravity of each is at its center. Assume that the floor is freshly waxed and frictionless. (a) Find the upward force at the bottom of each ladder. (b) Find the tension in the rope. (c) Find the magnitude of the force one ladder exerts on the other at point A

## Homework Equations

τ = F×L

## The Attempt at a Solution

So with the help of my textbook I was able to solve (c) by taking the sum of vertical forces of the right ladder F

_{normal}- F

_{gravity}= F

_{y}and sum of horizontal forces F

_{tension}= F

_{x}and correctly got the magnitude of the force one ladder exerts on the other at point A to be 335 Newton.

This got me thinking though, since the ladder is in static equilibrium and we have all the forces acting on the right ladder then the sum of torque τ on that ladder should be zero right? I did the maths and got F

_{gravity}*cos(53.13)*1.5 + F

_{tension}*0.9 - F

_{x}*sin(53.13)*3 = -160 where 53.13 is the angle in degrees between the floor and right ladder, 1.5 is half the length of the ladder and 3 is the length of the ladder. This is not zero, why not? Is my math wrong? Are there other forces affecting the torque about the point between the right ladder and the floor that I did not account for?