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.

 

[rezeew]

I would first commend the student for their thorough approach to solving the problem and for seeking clarification on the part they are stuck on. It is important to fully understand each step in solving a problem in order to arrive at the correct answer.

For part (b), it appears that the student has correctly identified that the only forces acting on the cabinet are the normal force and the impending force at point B. However, the student's calculation of the moment about point A may not be accurate. Since the caster at A is free to rotate, the force acting at point B may not be directly in line with the distance of 24in from point A. This could result in a different moment calculation and therefore a different value for P.

I would suggest re-evaluating the moment calculation, taking into account the potential direction of the impending force at point B. Additionally, double-checking the values used for the normal force and the coefficient of static friction may also help in arriving at the correct answer.