# Determine the angle which will cause the greatest torque

## 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 [Broken]

## The Attempt at a Solution

I know to break it up into components so that I get Ma = 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.

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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.

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

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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.

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.

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

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 thats looking more and more like the way to go.

nvn
Homework Helper
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.

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.

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