Free body diagram for a sliding contact

[Racer_Rob]

Homework Statement

Component A is pushed vertically down with a known force F into component B. The angled surface of B is parallel to the angled surface of A. The contact between A and B is rough and so is the contact between B and the ground. The coefficients of friction are known and so is the weight of component B.

Determine the angle at which component B is about to slide.

Homework Equations

See attached image.

The Attempt at a Solution

I've drawn the problem in frame 1. In frame 2 I've drawn a free body diagram of component B. In frame 3 I've resolved these forces into X and Y directions. I assume I then write equations for these two directions and determine the angle which makes the net force in the X direction equal zero.

Could someone please advise if I've identified the forces correctly and if this approach is correct, thanks!

 

[haruspex]

Homework Statement

Component A is pushed vertically down with a known force F into component B. The angled surface of B is parallel to the angled surface of A. The contact between A and B is rough and so is the contact between B and the ground. The coefficients of friction are known and so is the weight of component B.

Determine the angle at which component B is about to slide.

Homework Equations

See attached image.

The Attempt at a Solution

I've drawn the problem in frame 1. In frame 2 I've drawn a free body diagram of component B. In frame 3 I've resolved these forces into X and Y directions. I assume I then write equations for these two directions and determine the angle which makes the net force in the X direction equal zero.

Could someone please advise if I've identified the forces correctly and if this approach is correct, thanks!

What stops component A moving left?

 

[Racer_Rob]

In the system that this is from, component A is constrained such that it's only able to move in the Y axis.

 

[haruspex]

In the system that this is from, component A is constrained such that it's only able to move in the Y axis.

So include a force for that. It is relevant.

 

[Racer_Rob]

So that's going to be a normal force on the left side of A equal to the sum of all the resolved forces that are acting in the -X direction i.e. μ₁Fcosθ sinθ, and I'll need to include this in the force balance?

 

[haruspex]

So that's going to be a normal force on the left side of A equal to the sum of all the resolved forces that are acting in the -X direction i.e. μ₁Fcosθ sinθ, and I'll need to include this in the force balance?

Yes, it will provide the horizontal balance for A, but since it will affect the normal force between A and B do not assume it is equal to μ₁Fcosθ sinθ.

 

[Racer_Rob]

Hm, will there additionally be a Fcosθcosθ term to add to that? I've got this from the X direction reaction force at the interface between A and B.

 

[haruspex]

Hm, will there additionally be a Fcosθcosθ term to add to that? I've got this from the X direction reaction force at the interface between A and B.

I don't know how you are getting that. I don't think it is right.
You can avoid having to worry about the horizontal force on block A if you just look at the balance of the vertical forces on it. What equation do you get for that?

 

[Racer_Rob]

I don't know how you are getting that. I don't think it is right.
You can avoid having to worry about the horizontal force on block A if you just look at the balance of the vertical forces on it. What equation do you get for that?

I've tried doing a force balance for block A first of all. I've written it out in terms of forces normal and parallel to the contact surface (rather than breaking these down into X and Y components.

http://i.imgur.com/TL0g7fr.jpg

If you think this looks somewhat correct I'll go on and do a free body diagram for B.

 

[haruspex]

I've tried doing a force balance for block A first of all. I've written it out in terms of forces normal and parallel to the contact surface (rather than breaking these down into X and Y components.

http://i.imgur.com/TL0g7fr.jpg

If you think this looks somewhat correct I'll go on and do a free body diagram for B.

The free body diagram for A should not know anything about the friction between B and ground.
Trust me, it will be a lot simpler if you just look at the vertical forces on A. Resolving normally and parallel to the surface with B will only add more unknowns and equations.