Torque about P (Cross Product?)

[Reefy]

Homework Statement

Homework Equations

The book says that

Torque = the length of the moment arm X the magnitude of the vertical component of F
= r X F

The Attempt at a Solution

My problem is that I don't have any vectors to do a cross product. Instead I tried to just multiply what I know:

50lbs x 9in x sin60° ≈ 389.71ft-lb

which is far from the correct answer, 32.5ft-lb. The problem seemed simple enough so am I making some small mistake or going about this completely wrong?

 

[SteamKing]

Just because you aren't given any explicit vectors doesn't mean you can't formulate your own.

Looking at the problem, suppose that we set up an x-axis along the wrench.
In this case, vector r is (9,0) inches, with the emphasis on inches

The force vector F is going to be (50 cos (-60), 50 sin (-60)) lbs.

You can then evaluate r x F in the usual manner

Remember: in x lbs is not equal to ft-lbs

 

[Reefy]

Ah, you're right! Thank you, that makes perfect sense.