Determine the angle which will cause the greatest torque

[wannawin]

Homework Statement

Given F, b, and h, determine the angle θ which will cause the greatest strain.
http://img844.imageshack.us/img844/5595/cusersjoshappdatalocalt.th.png

The Attempt at a Solution

I know to break it up into components so that I get M_a = F(bcosθ+hsinθ). But after that I'm at a loss for what to do.
Intuitively I think the answer is 45, but I'm at a loss for how to prove that mathematically.

 

[snshusat161]

find the answer keeping it \theta only and then look for the value of \theta which can give the maximum value to answer. I'm also very new in engineering so can't say for sure but this method should work.

 

[snshusat161]

see, Cos \theta + Sin \theta is to be made maximum

 

[wannawin]

see, Cos \theta + Sin \theta is to made maximum

find the answer keeping it \theta only and then look for the value of \theta which can give the maximum value to answer. I'm also very new in engineering so can't say for sure but this method should work.

I'm not seeing what you're getting at. Maybe its just the wording of your response.

 

[snshusat161]

Moment about point A should be maximum to produce maximum strain to the body (okay)

Now resolve the force F:
1. F Cos \theta along vertically downward direction (-Y)
2. F sin \theta along +X direction

Moment about point A = F Cos \theta. b + F sin \theta. h
(clock wise rotation is taken as positive)

Now calculate the value of \theta for which the moment will be maximum.

 

[wannawin]

Moment about point A should be maximum to produce maximum strain to the body (okay)

Now resolve the force F:
1. F Cos \theta along vertically downward direction (-Y)
2. F sin \theta along +X direction

Moment about point A = F Cos \theta. b + F sin \theta. h
(clock wise rotation is taken as positive)

Now calculate the value of \theta for which the moment will be maximum.

I was able to get that far, but I'm just having trouble with finding that value for \theta. The way it is right now I can't see any way forward other than just factoring out the F...but that doesn't get me any closer.

 

[nvn]

wannawin: Do you currently use calculus in this course? Or no calculus yet?

 

[wannawin]

wannawin: Do you currently use calculus in this course? Or no calculus yet?

We don't use it in the course, but it did cross my mind to take a look at the first derivative and go from there. I guess that's looking more and more like the way to go.

 

[nvn]

wannawin: You might be able to do it without calculus. Perhaps think of it this way (without calculus). Any component of F toward or away from point A causes no harm. Use that concept to figure out what is the worst direction for force F.

 

[snshusat161]

oh there's another way to solve this problem very easily

Resolve the force in such a way that it's one component passes through point A. For that you need to find an angle. Since b and h are given, you can do it easily.

 

[snshusat161]

Answer: tan \theta = b/h. If b and h will be equal you'll get \theta = 45 degree but that's not given, I think.

 

[nvn]

snshusat161: Did you know, we are not allowed to solve the problems for the student. The powers that be only allow us to check math, and occasionally give small hints. Also, your answer is incorrect.

 

[snshusat161]

we don't have to give complete solution. I had only given answer for the problem. I had not solved the whole problem for him. I solved it in my notebook and I myself is in first semester so I'm trying to solve this question along with him sharing my some thoughts and accepting some thoughts from him. It's known as group learning.