Determine the angle which will cause the greatest torque

In summary, Homework Statement Given F, b, and h, determine the angle θ which will cause the greatest strain. However, the student is having trouble finding the value of θ for which the moment will be maximum. They are also new to engineering, so they may not be able to find the answer without calculus.
  • #1
wannawin
14
0

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 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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  • #2
find the answer keeping it [tex]\theta[/tex] only and then look for the value of [tex]\theta[/tex] 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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  • #3
see, Cos [tex]\theta[/tex] + Sin [tex]\theta[/tex] is to be made maximum
 
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  • #4
snshusat161 said:
see, Cos [tex]\theta[/tex] + Sin [tex]\theta[/tex] is to made maximum

snshusat161 said:
find the answer keeping it [tex]\theta[/tex] only and then look for the value of [tex]\theta[/tex] 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.
 
  • #5
Moment about point A should be maximum to produce maximum strain to the body (okay)

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

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

Now calculate the value of [tex]\theta[/tex] for which the moment will be maximum.
 
  • #6
snshusat161 said:
Moment about point A should be maximum to produce maximum strain to the body (okay)

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

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

Now calculate the value of [tex]\theta[/tex] 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 [tex]\theta[/tex]. 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.
 
  • #7
wannawin: Do you currently use calculus in this course? Or no calculus yet?
 
  • #8
nvn said:
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.
 
  • #9
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.
 
  • #10
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.
 
  • #11
Answer: tan [tex]\theta[/tex] = b/h. If b and h will be equal you'll get [tex]\theta[/tex] = 45 degree but that's not given, I think.
 
  • #12
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.
 
  • #13
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.
 

FAQ: Determine the angle which will cause the greatest torque

1. What is torque and how is it related to angles?

Torque is a measure of the force that causes rotational motion. It is directly proportional to the perpendicular distance between the axis of rotation and the point of application of the force, as well as the magnitude of the force. The angle at which the force is applied also affects the torque, with certain angles resulting in a greater torque than others.

2. How do you determine the angle that will cause the greatest torque?

The angle that will cause the greatest torque depends on the specific situation and the forces involved. Generally, the angle that produces the greatest perpendicular distance between the axis of rotation and the point of application of the force will result in the greatest torque. This can be calculated using trigonometric functions or by graphing the relationship between torque and angle.

3. Can you provide an example of an angle that results in the greatest torque?

One example is when a force is applied perpendicular to a lever arm, with the pivot or axis of rotation at the other end of the lever arm. In this case, the angle between the force and the lever arm is 90 degrees, resulting in the greatest possible perpendicular distance and therefore the greatest torque.

4. What is the importance of determining the angle with the greatest torque?

Determining the angle that will result in the greatest torque is important in many applications, such as engineering, physics, and mechanics. It allows for the optimization of systems and machines by maximizing the force applied and resulting in the most efficient use of energy.

5. How does friction affect the angle that produces the greatest torque?

Friction can reduce the effectiveness of the angle that produces the greatest torque. This is because friction acts in the opposite direction of the applied force, which can decrease the perpendicular distance and therefore the torque. Additionally, friction can cause the angle to change over time, requiring constant adjustments to maintain the maximum torque.

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