Solve Statics w/Friction Homework: P Force for Cabinet Movement

[ME_student]

Homework Statement

A 120lb cabinet is mounted on casters that can be locked to prevent their rotation. The coefficient of static friction between the floor and each caster is 0.30. If h=32in, determine the magnitude of the force P required to move the cabinet to the right (a) if all casters are locked, (b) if the caster at B are locked and the caster at A are free to rotate, (c) if the casters at A are locked and the caster at B are free to rotate.

Homework Equations

For part (a) sum of the forces in x and sum of the forces in y. I solved part (a), though I am stuck on part (b)

The Attempt at a Solution

My attempt solution for (b)
So since I know that the wheel at A is free to move then Fm2 and Fn2 are equal to zero. So the only point I am looking at is point B where there is a normal force called Fn1 and Fm1 (impending force). There is a force P (what I am looking for) acting to the right 32in from the floor. The distance between the wheels are 24in. A little later today I attach a file with my solutions for part (a) and my attempt solution for part (b). I will give you a little summary as to how I solved part (b). So I sum forces in Y to find Fn1, once that was obtained I took the moment about point A assuming that the Fm1 acting at roller B is going right through the location I took moments about, therefore it goes away? After I took moments about point A I got a result of 45lb for P. The answer should be 30lb.

 

[Simon Bridge]

Is there a diagram?

 

[ME_student]

Here is the diagram I drew. For part (b) I was just trying different techniques. If I make the small equations I still get the same results if I solve for individual forces separately. I have a feeling I can't take moments about A because the line of action for Fm1 doesn't go through the point A where I am summing moments?

 

[Simon Bridge]

FN2 + FN1 > 120lbs. ... the front wheels dig into the ground more due to force P.