Question on tourques and static equilibrium!

How do you know when to use the sum of all forces acting on a body compared to the sum of all tourques acting on a body when solving for these types of questions involving ladders, hanging signs, etc...

Doc Al
Mentor
It really depends on the specific quantity you are asked to solve for and how many unknowns there are. Sometimes you need both; sometimes one will do. Whenever there's an extended body, be ready to consider torques.

Ill go ahead and give you the question I have been working on:

A ladder which is 4 meters long masses 40 kg and has its centre of gravity 1.5 m up along its length, leans against a frictionless wall and rests on a frictionless floor. To keep it from slipping, it is tied to the wall with a rope which is attached to the ladder at its center of gravity.

and between the ladder and the rope is the center of gravity Fg [ down]

the angle is 53 degrees. Find all forces acting upon the ladder..

from here i am stuck...i could use tourque and put my pivot point on where the rope and gravity intersects, but then im left with the force of the floor [up] and the force of the wall
...​

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from here i am stuck...i could use tourque and put my pivot point on where the rope and gravity intersects, but then im left with the force of the floor [up] and the force of the wall
...

Forces causes linear acceleration, torques cause angular acceleration. In this case, both net torque and net force need to sum to zero.

I'd start by drawing a diagram--in fact, it might help to just draw a regular free body diagram and ignore where the forces act (don't deal with torque). See if you can figure out any of the unknown forces from that.​

Doc Al
Mentor
from here i am stuck...i could use tourque and put my pivot point on where the rope and gravity intersects, but then im left with the force of the floor [up] and the force of the wall
...​

Well, that's just one of the conditions for equilibrium (Net Torque = 0). Sometimes one is enough, but usually it's not. Make use of the the other conditions: Net Force = 0.

Here you have three unknown forces to find, so you need at least three equations. (Hint: Consider vertical and horizontal force components separately.)

Don't be stingy with the equations. No extra charge for using more than one! 