Minimum Force to Move 6kg Object on Friction Surface

[uchicago2012]

Homework Statement

A 6 kg object sits on a horizontal surface with coefficient of friction = .8. What is the minimum force (not necessarily horizontal) necessary to make the object slide?

Homework Equations

f_r = u * N
where f_r = the friction force
u = coefficient of friction
N = the normal force

The Attempt at a Solution

I knew there was something more to this problem- In lecture, my prof talked about a "magic" angle theta in the positive x and positive y direction that would take the least amount of force to move an object is one was pulling on the object at said "magic" angle. Since no value was mentioned, I assume the angle varies with the mass and the force being applied to the object.

As usual for me, I have an apparently sound free body diagram, apparently sound equations, and too many unknowns. I have normal force N, force of gravity mg, friction force f_r, and the force on the object F.

F_net,x = F cos theta - f_r = ma
(my prof doesn't believe in the difference between F_k and F_s (static and kinetic friction) so when a = 0 is when the minimum force is being exerted to make the block move)
F_net,x = F cos theta = f_r
F_net,y = N - mg + F sin theta = ma
acceleration is zero in the y direction so:
F sin theta = mg - N

I can sub in u * N for f_r and set tan theta equal to (mg - N) / (u * N), but I don't know N or theta and I'm trying to get to F.

Am I approaching these problems wrong or do I just keep getting lost along the way? I feel like I keep getting stuck in the same places.

 

[Doc Al]

F_net,x = F cos theta - f_r = ma
(my prof doesn't believe in the difference between F_k and F_s (static and kinetic friction) so when a = 0 is when the minimum force is being exerted to make the block move)
F_net,x = F cos theta = f_r
F_net,y = N - mg + F sin theta = ma
acceleration is zero in the y direction so:
F sin theta = mg - N

Looks good to me, so far.

I can sub in u * N for f_r

Definitely.

and set tan theta equal to (mg - N) / (u * N), but I don't know N or theta and I'm trying to get to F.

Eliminate N. Solve for F in terms of theta.

Am I approaching these problems wrong or do I just keep getting lost along the way? I feel like I keep getting stuck in the same places.

These are tricky. You're doing fine. Keep playing with it.