Find angle given tension and friction?

[theintarnets]

Help Please! Find angle given tension and friction?

Homework Statement

An initially stationary box of sand is to be pulled across a floor by means of a cable in which the tension should not exceed 1100 N. The coefficient of static friction between the box and the floor is 0.35. (a) What should be the angle between the cable and the horizontal in order to pull the greatest possible amount of sand, and (b) what is the weight of the sand and box in that situation?

Homework Equations

Tcosθ = μF_n
mg = F_n + Tsinθ

The Attempt at a Solution

I know there's an easy way to do this using derivatives, but my professor didn't teach us that method and expects us to solve it some other way. I'm not sure what to do, I can't seem to eliminate the variables. Help please? I know the answer is just the arctan of .35, I just don't know how to get there...

 

[tiny-tim]

hi theintarnets!

Tcosθ = μF_n
mg = F_n + Tsinθ

that's right! …

now put T = 1100, eliminate θ, and solve for F_n ​

 

[theintarnets]

Erm, how do I eliminate theta?

 

[tiny-tim]

square

 

[BruceW]

Your professor is right, you don't need to do any derivatives. You have enough information in your two equations. Only rearranging the two equations is required. You can eliminate theta or Fn, whichever you prefer.

Edit: sorry for stepping your toes tiny-tim.

 

[theintarnets]

I tried squaring... But I'm still left with the unknowns m and theta. I can't seem to figure out how to eliminate Fn either. I'm really confused.

 

[tiny-tim]

I tried squaring... But I'm still left with the unknowns m and theta.

how do you get left with a θ ?

show us what you did ​

 

[BruceW]

Fn is probably a bit easier to eliminate, so maybe try that. You've got two equations, each containing Fn once. I'm guessing you've done similar problems where you have two simultaneous equations? So try to think of how you solve simultaneous equations.