Which Force Application Minimizes Effort When Moving a Box?

[21385]

Homework Statement

You want to apply a force on a box so that it moves with constant speed across a horizontal floor. The coefficient of kinetic friction between the box and the floor is u. Of the four following cases, the force you apply on the box will be smallest when you

a) Push on it with a force applied at an angle 0<X<90 downward from the horizontal;
b) pull on it with a force applied at the same angle X as in (a), upward from the horizontal;
c)do either (a) or (b) since the applied force is the same;
d)pull or push with a force applied horizontally

Homework Equations

Ff=Fa, to keep at a constant speed

The Attempt at a Solution

The correct answer is b but I have no idea why.
I chose c as my answer seeing that a and b would both result in the same thing, only that the weight of the box would concentrate in the front in situation (a) and that the weight would concentrate in the back in situation (b). I felt that this difference would not change the amount of force needed. Are there any other factors I have not considered? Thanks

 

[cristo]

The friction can be calculated by F=uR, where R is the normal reaction force. Do you know how to find the normal reaction force? More specifically, how will it be different when the force applied is a pull compared to when it is a push?

 

[21385]

The friction equation is Ff=u(mg-FasinX).
I actually have no idea why the force would be different pushing from one side or pulling from the another.

 

[cristo]

The friction equation is Ff=u(mg-FasinX).

That's for a pull. If you are pushing the box with a force downwards from the horizontal, you will be adding to the normal force, and thus the correct equation will be Ff=u(mg+FasinX).

 

[denverdoc]

Cristo, interesting. You're adding ergonomics to the eqn. But i see the wisdom, at arms length to pull relieves N force while pushing adds to it.
Cheers.

 

[21385]

thanks, cristo
omg, i am so stupid, i thought choice a) was pushing from the angle below the horizontal