Question on tourques and static equilibrium

[sodr2]

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]

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.

 

[sodr2]

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 I am left with the force of the floor [up] and the force of the wall

...​

 

[JaWiB]

from here i am stuck...i could use tourque and put my pivot point on where the rope and gravity intersects, but then I am 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]

from here i am stuck...i could use tourque and put my pivot point on where the rope and gravity intersects, but then I am 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! ​