Frictional forces and the angle for minimum frictional force

1. Feb 26, 2015

Yam

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
Frictional Forces = UkN

3. The attempt at a solution
Frictional Force = Uk(mg)(cosx)

Im stuck.

2. Feb 26, 2015

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 ?

3. Feb 26, 2015

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

4. Feb 26, 2015

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 !

5. Feb 26, 2015

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?

6. Feb 26, 2015

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 ?

7. Feb 26, 2015

Yam

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

8. Feb 26, 2015

BvU

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

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted