What Is the Normal Force on a Sliding Ladder?

[Quantum1990]

Homework Statement

A ladder of length l and mass m leans against the side of a house, making an angle θ with the vertical. Assume that the ladder is free to slide at the point where it touches the side of the house (there is no significant friction). Find an expression for the normal force that the side of the house exerts on that end of the ladder in terms of m,g,l,θ

Homework Equations

Ʃτ = Iα
ƩF = ma

The Attempt at a Solution

First, I thought the problem was static(it is in a statics chapter), but with no friction force, I don't think the ladder can be static. Calling the desired normal force N1, and the normal force at the ground N2, I set up the following equations:

max = N1
may = mg-N2
ax = -tanθ ay

I arrived at the third equation using the constraint of a fixed length of the ladder. My problem is using torque( which I think I need). If I sum the torques about the CM, how do I relate angular acceleration(and what angle would I even be measuring) to ax and ay? I believe with this step, I can complete the problem.

 

[Basic_Physics]

There will be static friction at the bottom end of the ladder. Try setting up the torques/moments acting on the ladder about the bottom end.

 

[Quantum1990]

Are we allowed to assume that there is friction at the ground (or is this required for the problem to make sense)? And will mu not be required?

 

[Basic_Physics]

Yes, there must be friction, otherwise the ladder would slip, but it won't have a moment if you take torques about this end.

 

[Quantum1990]

But can I set the torques to zero, or am I solving for angular acceleration? Maybe my physical picture is off, but I imagine both ends of the ladder moving(how can only one end move?), so there is a net torque and force. This would make the problem much more complicated.

 

[Quantum1990]

I just got it. Thanks for your patience. I thought the problem said the ladder was sliding, rather than having the potential to slide.