Approaching the Torque and Ladder Problem

[goonking]

Homework Statement

Homework Equations

F = μ FN

τ = r F

The Attempt at a Solution

how do I approach this problem? Mass isn't given. And If i set the top of the ladder to be the pivot point, the pivot point will move vertically downwards if the ladder slides - is that even allowed?

 

[ehild]

If the ladder does not slip, the pivot point is also in rest. Collect all the forces and all the torques. What is the condition that the ladder does not start to move?

 

[goonking]

If the ladder does not slip, the pivot point is also in rest. Collect all the forces and all the torques. What is the condition that the ladder does not start to move?

does this look correct?

 

[haruspex]

does this look correct?

No.
First, what is "Fg_y"? The horizontal component of the gravitational force?!
Secondly, what force stops the ladder from slipping (until it does)?

 

[goonking]

No.
First, what is "Fg_y"? The horizontal component of the gravitational force?!
Secondly, what force stops the ladder from slipping (until it does)?

Force of the wall should equal force of friction.

 

[ehild]

Is the x-axis horizontal, and the y-axis vertical? I think, you mean Fg the force of gravity. It acts at the centre of mass of the ladder, not at the ends. What is its direction? What are the x and y components?

The normal force at the wall is not the same as the normal force from the ground.

And you completely ignored the force of friction at the ground.

 

[goonking]

Is the x-axis horizontal, and the y-axis vertical? I think, you mean Fg the force of gravity. It acts at the centre of mass of the ladder, not at the ends. What is its direction? What are the x and y components?

The normal force at the wall is not the same as the normal force from the ground.

And you completely ignored the force of friction at the ground.

mg = FN at the bottom of the ladder.

so Force of wall = force of friction since ladder doesn't move.

Fwall = Ffriction = μ FN = μ mg

torques : Torque of wall pushing ladder should equal torque of ladder at the center of mass.
let's pick the bottom of the ladder as the pivot point since the ladder doesn't move.
Fwall⋅ d ⋅sin 55.2 = mg ⋅ d/2 ⋅ cos 55.2

plugging in μ mg for Fwall

μ mg ⋅ d ⋅sin 55.2 = mg ⋅ d/2 ⋅ cos 55.2

canceling out mg and d from both sides, μ should come out to be 0.347

 

[ehild]

It looks correct.