Suppose The Worker In Exercise 6.3 Pushes Downward At An Angle Of 30 Below The Horizontal. (A) What Magnitude Of Force Must The Worker Apply To Move The Crate At Constant Velocity? (B) How Much Work Is Done On The Crate By This Force When The Crate Is Pushed A Distance Of 4.5 M? (C) How Much Work Is Done On The Crate By Friction During This Displacement? (D)

Suppose the worker in Exercise 6.3 pushes downward at an angle of 30 below the horizontal. (a) What magnitude of force must the worker apply to move the crate at constant velocity? (b) How much work is done on the crate by this force when the crate is pushed a distance of 4.5 m? (c) How much work is done on the crate by friction during this displacement? (d) How much work is done on the crate by the normal force? By gravity? (e) What is the total work done on the crate?

The following question is from University Physics chapter 6 exercise 6.4. I have attempted this problem multiple times but get it wrong because I keep using the wrong angle. The problem specifically mentions that the applied force is at an angle below the horizontal. Which I assume to be -30 degrees. However, the correct solution comes from using positive 30 degrees. Here is the example of the resulting free-body diagram:

Why is the angle positive and not negative? Why can I not use -30 or 330 degrees?

 

 

y n Fcos 30 300 x 30 F Fsin 30 mg