Optimizing Pulling Force: Solving for Theta and F in Newton's Laws

[Airsteve0]

A large block of mass M is going to be pulled with a constant velocity along a horizontal surface. The coefficient of friction between the surface and block is u.

(1) Find the angle theta=theta_naught that the direction of pull shall make with the direction of motion for the pulling force to be as small as possible.
(2) Find this smallest value of F.


Ok so I know the answers are:
(1) u = tan (thets_naught)
(2) F = (uMg)/sqrt(1 + u^2)

however I have no idea how these answers were arrived at. Could someone please offer some assisstance?

 

[Doc Al]

Why don't you give it a try? Hint: Find the force as a function of theta.

(Five laws?)

 

[Airsteve0]

Solving this system I was able to get to the solution:

tan(theta) = Fy/Fx (forces in x and y-directions)

However, I believe Fx equals the frictional force (uN) so the only way to arrive at the solution posted in the book would be if Fy = u^2N, which seems very strange.

 

[Doc Al]

However, I believe Fx equals the frictional force (uN) so the only way to arrive at the solution posted in the book would be if Fy = u^2N, which seems very strange.

Strange but true. (Not sure why you'd have an opinion about that.)

 

[The legend]

(Five laws?)

I think the five laws would be
3 laws of motion
1 of gravitation
1 of restitution
(though the last 2 arent applied here! )