Frictional forces and the angle for minimum frictional force

[Yam]

Homework Statement

A person is dragging a packing crate of mass 100 kg across a rough floor where the coefficient of kinetic friction is 0.400. He exerts a force F just sufficient to keep the crate moving at a constant velocity. At what angle above the horizontal should his pulling force F be for it to be minimum?

Homework Equations

Frictional Forces = UkN

The Attempt at a Solution

Frictional Force = Uk(mg)(cosx)

Im stuck.

 

[BvU]

I like the "I'm stuck" (you wouldn't post if you weren't). But $F_{fric} = \mu_k mg\cos\theta$ doesn't count as an attempt.

What forces play a role and how can you express the constant speed in an equation ?

 

[Yam]

Forces that play a role:
1) Pulling force F
2) Frictional force

Constant speed means that there is no acceleration.
F = ma = m(0) = 0

 

[BvU]

Frictional force is horizontal, pulling is in some theta direction. What else ? (hint: you already wrote mg -- and there's no vertical acceleration either). So we have a few equations. Magnitude of pulling force might depend on theta. If so, there might be a minimum !

 

[Yam]

Forces that play a role:
1) Pulling force F at an angle
2) Horizontal Frictional force
3) Weight of the block

Yes i understand that the magnitude of the puling force depends on theta, however, how do i relate it to the minimum force?

 

[BvU]

One force missing still.
If |F| depends on theta like, say $2-\cos^2\theta$ then zero degrees would give a nice minimum, wouldn't it ?

 

[Yam]

Is it the upward force generated by the pull at an angle?

 

[BvU]

Wouldn't that mean that if you don't pull, the box drops down like a brick ?