# Homework Help: 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 ?