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#### Mastermime

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« on: December 01, 2011, 06:52:17 PM »
Hello everyone,

I am in an engineering class at my high school and I am having a difficult time solving this problem.

I am asked to determine the moment in the picture below.  I know moments equal F*D, but here I am only give the magnitude of force along with the angle at which the force is acting upon the moment arm.  How would I go about solving this?  Trigonometry?  Any help is greatly appreciated.

#### NGuggemos

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« Reply #1 on: December 01, 2011, 07:05:26 PM »
I'm working on something similar and need help with something like that too.
« Last Edit: December 01, 2011, 07:08:21 PM by NGuggemos »

#### waltr

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« Reply #2 on: December 01, 2011, 07:56:31 PM »
Hint 1: Use trig to find the force that is perpendicular to the moment arm.
Hint 3: Compare this problem to a similar simpler problem (example problem in the text book).

#### Soeren

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« Reply #3 on: December 01, 2011, 07:58:38 PM »
Hi,

I know moments equal F*D, but here I am only give the magnitude of force along with the angle at which the force is acting upon the moment arm.  How would I go about solving this?  Trigonometry?
Yes, you just need to calculate how much the 5N is reduced due to the angle being 25° from the optimal 90°.
Regards,
Søren

A rather fast and fairly heavy robot with quite large wheels needs what? A lot of power?
Engineering is based on numbers - not adjectives

#### Mastermime

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« Reply #4 on: December 01, 2011, 08:25:59 PM »
Quote
Yes, you just need to calculate how much the 5N is reduced due to the angle being 25° from the optimal 90°.

I am not sure how I would go about doing this.  I understand what you are saying, but I dont not how to execute.

Quote
Hint 1: Use trig to find the force that is perpendicular to the moment arm.
I have only briefly learned about trigonometry when I was in Geometry.  I know about SOHCAHTOA, but this only applies to right triangles.  This is what I got though:  Height= 3  Part of the base is 4.  It was 3-4-5 triangle.  I dont know how to go from there though.

#### richiereynolds

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« Reply #5 on: December 02, 2011, 01:00:02 PM »
Try looking in your textbook (or online) for "resolving forces".

#### Gertlex

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« Reply #6 on: December 02, 2011, 02:50:54 PM »
Surprisingly everyone else trying to help didn't look closely.

You indeed can't solve for what the moment is, without knowing the length of the black line on the green part... Point that out to your teacher is all we can tell you...

You can calculate the force that would be used in F*D=M, though.  This is a basic and common application of trig.

You mentioned that you learned trig with right angle triangles... Do you see the triangle in my modified version of your image?
I

#### Soeren

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« Reply #7 on: December 02, 2011, 05:43:52 PM »
Hi,

Surprisingly everyone else trying to help didn't look closely.
??
Did you see anyone (except OP) mentioning anything about calculating moment here?
Regards,
Søren

A rather fast and fairly heavy robot with quite large wheels needs what? A lot of power?
Engineering is based on numbers - not adjectives

#### Gertlex

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« Reply #8 on: December 02, 2011, 06:09:58 PM »
Hi,

Surprisingly everyone else trying to help didn't look closely.
??
Did you see anyone (except OP) mentioning anything about calculating moment here?

Nope .  Doesn't change the question that the OP asked.
I

• Supreme Robot
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« Reply #9 on: December 02, 2011, 08:52:52 PM »
As I'm a mechanical engineer maybe I should chime in . . .

moment = force * distance

The distance is missing, so you will not be able to get a numerical answer. However, that is ok. Sometimes in engineering you need to determine the optimal length, and so you'd want to find an algebraic equation instead. So in this case, you'd just want to use trig to determine the force and you're done.

Maximum moment is generated when the force is perfectly perpendicular to the moment arm (the handle of the wrench). So if the force that's less then perpendicular is applied, then the moment force is less. Therefore you know the force for the moment is less than 5N.

Now, the angle they give you is 115 degrees. However, you want the angle from an imaginary line that's perpendicular. So the true angle is 115 - 90 degrees.

Using sohcahtoa, you have an angle, you know the hypotenuse (5N), and you want the force that's perpendicular (the adjacent line).

Solving . . .
cos(angle) = perpendicular_force / force
cos(115-90) = perpendicular_force / 5N

and I'll let you figure it out from there . . . oh, and make sure you calculate in degrees, not radians.

ps - This was really hard stuff for me back when I was a noobie engineer. But after a few years it becomes second nature . . .

#### Mastermime

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« Reply #10 on: December 03, 2011, 02:04:09 PM »
Wow!  Thank you everyone for the input!  This really helped me understand it a lot better.  Based off what you guys said, here is what I got;

Moment<5 N

5 N*Cos(25)= 4.96 N= Perpendicular force

#### Gertlex

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« Reply #11 on: December 03, 2011, 04:16:13 PM »
That's, alas, wrong. You're probably are using Cosine (radians) when you mean to use Cosine(degrees).  I don't know where you're doing the calcs so I can't tell you how to fix that, but should be easy enough.
« Last Edit: December 03, 2011, 04:25:54 PM by Gertlex »
I

#### Mastermime

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« Reply #12 on: December 03, 2011, 04:25:39 PM »
Oh I forgot to change my calculator setting back to degrees when I reset the RAM.  Thank you for pointing that out.

Now I get 4.53 N.

Thanks for pointing that out

• Supreme Robot
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« Reply #13 on: December 03, 2011, 09:49:11 PM »
If you want to challenge yourself a bit, and get a bit more practice, solve this:

What is the other force, the one that's pulling the bolt and not contributing to the rotation?

ps - I did say 'make sure you calculate in degrees, not radians'. It's a very common mistake

#### Mastermime

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« Reply #14 on: December 03, 2011, 10:12:49 PM »
Quote
ps - I did say 'make sure you calculate in degrees, not radians'. It's a very common mistake
Yeah I know lol.  After I realized I got it wrong, I asked my brother (civil engineer) and he told me the difference.

Quote
What is the other force, the one that's pulling the bolt and not contributing to the rotation?
Would it be gravity?

I just realized I said thanks for 'pointing that out' twice in my post before this.  Fail.

• Supreme Robot
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« Reply #15 on: December 03, 2011, 10:27:26 PM »
Quote
What is the other force, the one that's pulling the bolt and not contributing to the rotation?
Would it be gravity?
Have a look again at the picture. You have 5N pulling at the wrench at an angle. What you calculated above was the component of the 5N force pulling perpendicular to the wrench (creating a moment). But what is the component of the 5N force pulling parallel to the wrench?

This is called 'breaking a force into component X Y Z forces'. You calculated the X force already, so what is the Y force?

#### waltr

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« Reply #16 on: December 04, 2011, 08:47:32 PM »
Quote
What is the other force, the one that's pulling the bolt and not contributing to the rotation?
Would it be gravity?
Have a look again at the picture. You have 5N pulling at the wrench at an angle. What you calculated above was the component of the 5N force pulling perpendicular to the wrench (creating a moment). But what is the component of the 5N force pulling parallel to the wrench?

This is called 'breaking a force into component X Y Z forces'. You calculated the X force already, so what is the Y force?

Don't guess. Use Hint 2 then Hint 1 I listed above to figure out the answer to Admin's quiz.