# Statics Problem - finding angle

1. Sep 16, 2010

### btbam91

Hey guys I'm having trouble with this simple statics problem.

[PLAIN]http://img443.imageshack.us/img443/7218/37statics.png [Broken]

[PLAIN]http://img841.imageshack.us/img841/6734/372.png [Broken]

My set up.

[PLAIN]http://img543.imageshack.us/img543/9349/ya1x.jpg [Broken]

I'm confused on where I'm supposed to take it from here. The solutions are: 6.12, 33.8 degrees.

Thanks!

Last edited by a moderator: May 4, 2017
2. Sep 16, 2010

### btbam91

Can a moderator delete this thread please? I'm going to post it in the physics section.

3. Sep 16, 2010

### PhanthomJay

I'm not a moderator, but if you post to the Physics section, they'll probably kick it back to this section, as it is apparently a homework problem. Your equation appears correct, but I think you need a trig identity to solve it, and you get 2 solutions. You might want to try the alternate definition for torque: Torque = r X F = rFsintheta, and see what you get.

Edit: To clarify, I mean to say that T = r X F is the vector cross product, where r is the position vector from the pivot to the point of application of the force, and F is the applied force. The magnitude of the torque (moment) about the pivot is T=(r)*(F)*(sin theta), where theta is the interior angle between the force and position vectors. You need a bit of geometry/trig to find theta as a function of alpha. You will get 2 solutions for alpha.

Last edited: Sep 16, 2010
4. Sep 16, 2010

### Staff: Mentor

Yes, this post belongs here and not in the general technical forums. Thanks for the help, PhantomJay.

5. Sep 16, 2010

### btbam91

Thanks for the responses!

I'm confused as to why taking the inverse sin of something results in two angles.

Here's a solution to an extremely similar kind of problem.

[PLAIN]http://img178.imageshack.us/img178/959/statiscs11.png [Broken]

I don't understand how taking the inverse sin of .99658 results in 85 degrees and 95 degrees, two angles that are only about 10 degrees apart. Is there a trig identity that I'm missing?

Thanks!

Thanks!

Last edited by a moderator: May 4, 2017
6. Sep 16, 2010

### PhanthomJay

The sin function is positive in both the first and 2nd quadrants. When you plug the inverse into your calculator, it only gives you the first quadrant result. For example, in your first posted problem, you find, approximately, that sin (70 + alpha) = .97 , therefore, 70 + alpha = 76, and alpha =6 degreees. But arc sin 0.97 is also 103 degrees, therefore 70 + alpha = 103, and alpha = 33 degrees. Draw a sketch to confirm this.