Calculating the Minimum Force for Box to Move at Constant Velocity

[Watney]

Homework Statement

A force F is applied to a box of mass M at an angle θ below the horizontal (see figure). The coefficient of static friction between the box and the floor is μs, and the coefficient of kinetic friction between the two surfaces is μk.

a) What is the minimum value of F to get the box to start moving from rest?
b) What is the minimum value of F so that the box will move with constant velocity? (Assuming it's already moving.)
c) If θ is greater than some critical angle θcrit, it is impossible to have the scenario described in part b. What is θcrit ?

Homework Equations

I figured out part a which is μs*mg/cosθ-μssinθ. Then part b which is the same equation except with μk instead of μs.

The Attempt at a Solution

Honestly, I don't even know where to start. My professor has never gone over problems with critical angles. Is there a formula I can use to solve this?

 

[haruspex]

Honestly, I don't even know where to start

Look at your answer to part b. Part c is saying that if theta is too large then no F is large enough. At what value of theta does F get impossibly large?

 

[BvU]

Hi Watney,
You start with a drawing (probably you did that already).
The formula you are looking for is called Newton's law. Constant velocity requires a zero sum of forces.

[edit] Ha! Haru was quicker and brought you even closer to your solution. Lucky you !