Statics - I get a different angle than the solution manual who's wrong?

[Femme_physics]

The X axis in the first diagram is in line with the surface, but when you isolate BC it doesn't have to be. Notice how when we isolate BC our angles our different. Who's correct?

Homework Statement

http://img192.imageshack.us/img192/236/objectthingy.jpg

The object is in static equilibrium.
Static Coeffecient between the box and surface: 0.3
Weight of box: 500 [N]
Measurements in mm
Joints are smooth pin.
Do the calculations as the box about to descend down the surface
Ignore the weight of lever ACCalculate:

Force at AB
The moment around C, acting on the arm BC

The Attempt at a Solution

I got Fab correct (in the solution manual they call it "S"). However, we have our differences at beam BC about the angle, which I'd like you to help me resolve. The manual thinks it's 20 degrees, I think it's 50 degrees. Attached my attempt and the solution manual's.

 

[Hurkyl]

Precisely what angle are you referring to?

 

[I like Serena]

Hi FP, :)

I'm afraid the angle of BC is unknown.
It seems to me that the problem statement is incomplete.
What you'd actually would need to do, is define a generic angle phi that BC makes, and calculate the moment as a function of phi, but it seems to me that it's as yet too early to do that.

In the drawing BC seems to be parallel to the ground, making the angle in your calculations correct! :)
The solution manual's "choice" makes BC parallel to the slope.

I'd recommend putting a note in your solution that you have "chosen" to take BC parallel to the ground in order to find a numeric solution.

 

[Femme_physics]

Precisely what angle are you referring to?

http://img838.imageshack.us/img838/8595/anglez.jpg

I'm afraid the angle of BC is unknown.
It seems to me that the problem statement is incomplete.

Really? Are you sure? We're told the surface is 30 degrees from the ground, and that AB is 20 degrees from it. It appears clear to me it's 50 degrees! (20+30)

http://img171.imageshack.us/img171/7159/angle2p.jpg

In the drawing BC seems to be parallel to the ground, making the angle in your calculations correct! :)
The solution manual's "choice" makes BC parallel to the slope.

Hmm, it's drawn and calculated though as though it's parallel to the ground!

I'd recommend putting a note in your solution that you have "chosen" to take BC parallel to the ground in order to find a numeric solution.

But we have different numeric solutions, so someone must be wrong!

 

[I like Serena]

Hmm, it's drawn and calculated though as though it's parallel to the ground!

Yes, but there might be tiny angle of say 3 degrees and it would throw all your calculations off!

Really? Are you sure? We're told the surface is 30 degrees from the ground, and that AB is 20 degrees from it. It appears clear to me it's 50 degrees! (20+30)

I find no fault in your trigonometry.

But we have different numeric solutions, so someone must be wrong!

If you ask 2 people to slice a pie into 2 pieces, is it wrong if they come out with different sized pieces? :)
As long as they get the job done...

On a scientific note, it is good practice to write down any assumptions and choices you make!

 

[Femme_physics]

Yes, but there might be tiny angle of say 3 degrees and it would throw all your calculations off!

But all the measurements are given to me, that's the exercise. It doesn't say anything about hidden degrees, and I never heard they exist. Have anyone ever seen those 3 degrees? I keep hearing stories about them, but where are they? Frankly I'm a 3 degrees atheist. Call me a sinner!

If you ask 2 people to slice a pie into 2 pieces, is it wrong if they come out with different sized pieces? :)
As long as they get the job done...

On a scientific note, it is good practice to write down any assumptions and choices you make!

Wait wait wait, so far in all my calculations of static exercises (and I've solved tons, you've participated in some) I never had that you can get a different numerical result for using a different plane. Fab is the combined vector of its y and x components. But the combined vector must have a certain defined angle from the horizontal plane. Look at the solution manual, it draws a STRAIGHT LINE and still defines it at 20 degrees. But we agreed it's 50! I'm totally baffled.

 

[I like Serena]

But all the measurements are given to me, that's the exercise. It doesn't say anything about hidden degrees, and I never heard they exist. Have anyone ever seen those 3 degrees? I keep hearing stories about them, but where are they? Frankly I'm a 3 degrees atheist. Call me a sinner!

I seem to remember a mechanics problem a little while ago, where you had neglected a *tiny* angle.
At the time thou claimeth that thou hath not seen it and did not know it existed.
I was pleased that you mended your ways, and became a firm believer in tiny angles (bringing you to the righteous answer of course).
Have your beliefs become so weak yet again?

[edit]In my job I had to revise the entire model being used once to take care of an angle of about 0.1 degrees.
However, the accuracy of the machine increased dramatically. :)[/edit]

Wait wait wait, so far in all my calculations of static exercises (and I've solved tons, you've participated in some) I never had that you can get a different numerical result for using a different plane. Fab is the combined vector of its y and x components. But the combined vector must have a certain defined angle from the horizontal plane. Look at the solution manual, it draws a STRAIGHT LINE and still defines it at 20 degrees. But we agreed it's 50! I'm totally baffled.

I give in!

You are *right*.
The angle is 50 degrees and the solution manual is *wrong*.
I give it my *stamp of dogma approval*.

 

[Femme_physics]

I seem to remember a mechanics problem a little while ago, where you had neglected a *tiny* angle.
At the time thou claimeth that thou hath not seen it and did not know it existed.
I was pleased that you mended your ways, and became a firm believer in tiny angles (bringing you to the righteous answer of course).
Have your beliefs become so weak yet again?

Haha, well 3 degrees atheist does mean 357 degrees believer. ;) I'd say I'm pretty righteous and deserve to get to math heaven where I'll have fun with 72 sexy mechanic problems ;)--------------

Are you referring to this exercise?https://www.physicsforums.com/showthread.php?t=470087

I give in!

You are *right*.
The angle is 50 degrees and the solution manual is *wrong*.
I give it my *stamp of dogma approval*.

LOL

Wait wait, you can't just give in! So I was right all along? What about your previous arguments about 2 possible solutions depending on how you look at it? Were they false too?

 

[I like Serena]

Haha, well 3 degrees atheist does mean 357 degrees believer. ;) I'd say I'm pretty righteous and deserve to get to math heaven where I'll have fun with 72 sexy mechanic problems ;)
--------------
Are you referring to this exercise?

LOL

I say, that's a very sexy mechanic problem ;)
But no, that was before my time.
I see you had other help at the time. :grumpy:
And what's this, are you a dwarf from Tolkien?

The one I meant is this one: https://www.physicsforums.com/showthread.php?t=490836
And now that you mention it, it's kind of sexy too
They would combine perfectly! ;)

Wait wait, you can't just give in! So I was right all along? What about your previous arguments about 2 possible solutions depending on how you look at it? Were they false too?

Nah, I am right! I'm always right!
(Aherm, ... unless of course I'm ... *cough* wrong *cough*)

 

[Femme_physics]

And what's this, are you a dwarf from Tolkien?

Hehe... my nickname before this was "Dory"... I changed it, but I now regret having changed it :P Oh well.

And now that you mention it, it's kind of sexy too
They would combine perfectly! ;)

Judging by the fact they're both hangers, I'd say it'll be kinda gay if they combine lol

But I remember that exercise well. Good call :)

Nah, I am right! I'm always right!
(Aherm, ... unless of course I'm ... *cough* wrong *cough*)

AHA :D So wait, can I submit it as an official mistake the solution manual made?
I do have your coveted stamp of approval on the page it appears^^

 

[I like Serena]

Hehe... my nickname before this was "Dory"... I changed it, but I now regret having changed it :P Oh well.

Why the regret?

Judging by the fact they're both hangers, I'd say it'll be kinda gay if they combine lol

But I remember that exercise well. Good call :)

Good call :)
I think we need yet another mechanics problem!

AHA :D So wait, can I submit it as an official mistake the solution manual made?
I do have your coveted stamp of approval on the page it appears^^

Let me put it this way.
It's obvious to me that they made a mistake in the solution manual. They misjudged the angle and thought it was 20 degrees. I give my stamp of approval for saying that.

But if you would make that "mistake" yourself on an exam, I expect you could convince the teacher to allow it^^

 

[Femme_physics]

Why the regret?

Because then I had an actual nickname, like an identity. Now the nick more general. Nevermind, I was just led to believe after a while that "Dory" is more of a male name, or a male dwarf name, so I went radically opposite. Oh well.

Plus, it hints that I know very well physics, while I'm more of a beginner. Well, beginner+, let's make it :)

I think we need yet another mechanics problem!

One is never too far off :D

Let me put it this way.
It's obvious to me that they made a mistake in the solution manual. They misjudged the angle and thought it was 20 degrees. I give my stamp of approval for saying that.

But if you would make that "mistake" yourself on an exam, I expect you could convince the teacher to allow it^^

Gotcha!

 

[Femme_physics]

Speaking of tiny wrong angles... my alpha in this question (11.537) IMO is more accurate than the solution manual's alpha (11.31). Can you confirm that?

 

[I like Serena]

Speaking of tiny wrong angles... my alpha in this question (11.537) IMO is more accurate than the solution manual's alpha (11.31). Can you confirm that?

Sorry, no.

Alpha is part of a triangle where the hypothenusa is as yet unknown.
The fraction of the other 2 sides corresponds to the tangens.
So alpha = arctan(0.2 / 4) which is what the solution manual says (as opposed to your alpha = arcsin(0.2 / 4) which is not true).

In your drawing the right angle on top is drawn like a little bit less than a right angle (just a tiny bit) making it easy to think that the other angle near the center of the sphere is a right angle.

 

[Femme_physics]

Alpha is part of a triangle where the hypothenusa is as yet unknown.

But the hypotenuse is 2! I think.

So alpha = arctan(0.2 / 4) which is what the solution manual says (as opposed to your alpha = arcsin(0.2 / 4) which is not true).

I didn't do arcsin (0.2/4)
I did arcsin (0.4/2)!

In your drawing the right angle on top is drawn like a little bit less than a right angle (just a tiny bit) making it easy to think that the other angle near the center of the sphere is a right angle.

Are you telling me that the hypotenuse is actually the length from A to the center of the circle? Hmm.. I now see in the manual's drawing that it is indeed not 90 degrees angle...

 

[I like Serena]

Because then I had an actual nickname, like an identity. Now the nick more general. Nevermind, I was just led to believe after a while that "Dory" is more of a male name, or a male dwarf name, so I went radically opposite. Oh well.

Plus, it hints that I know very well physics, while I'm more of a beginner. Well, beginner+, let's make it :)

I'm not aware of any dwarf with the name Dory, the closest I know of is Torin.
And Dory appears to be a strictly female name.

You have shown yourself to be a true physics lover!
So that fits! :)

My own nick is a carry over from an old forum.
Every now and then I feel I should have picked a more physics like nick, but that's too late now.

 

[I like Serena]

Are you telling me that the hypotenuse is actually the length from A to the center of the circle? Hmm.. I now see in the manual's drawing that it is indeed not 90 degrees angle...

Yes.

I didn't do arcsin (0.2/4)
I did arcsin (0.4/2)!

My mistake. I mixed the numbers up.
I meant arctan(0.4 / 2) which is arctan(0.2).

 

[Femme_physics]

Yes.
My mistake. I mixed the numbers up.
I meant arctan(0.4 / 2) which is arctan(0.2).

I think I see it now, thanks :)

As long as I have you genius here, I'd like to milk it for as much as I can!

I know this is getting back to trigonometry but I seem to have an issue with angles in mechanics questions and I already started this thread so I'm just continuing it here.How are my calculations wrong in determining angle ADC equals 90? Visually it doesn't look like 90, but according to the numbers it does turn out 90!

http://img832.imageshack.us/img832/9943/trap1.jpg

http://img848.imageshack.us/img848/8400/trap2g.jpg

I'm not aware of any dwarf with the name Dory, the closest I know of is Torin.
And Dory appears to be a strictly female name.

Not sure, I once played a paladin character in a fantasy role-playing online called "Dory" and someone sent me a PM thinking I'm a dwarf. Ugh.

You have shown yourself to be a true physics lover!
So that fits! :)

Guess so! :)

My own nick is a carry over from an old forum.
Every now and then I feel I should have picked a more physics like nick, but that's too late now.

Menne physics? :D

 

[I like Serena]

How are my calculations wrong in determining angle ADC equals 90? Visually it doesn't look like 90, but according to the numbers it does turn out 90!

Always trust your visual queues!
And in case of doubt, make a drawing that is on scale and measure up what you want to know (that will also give you an acceptable answer!). And again: trust your visual queues!

In this case you have found AC=38.01 while AB=35.717
So the numbers say AC is longer than AB, but if you look to your drawing you'll find that AC is visually shorter than AB. The numbers must be wrong! How?

Not sure, I once played a paladin character in a fantasy role-playing online called "Dory" and someone sent me a PM thinking I'm a dwarf. Ugh.

I think it's the first letter "D".
In fantasy games it's not uncommon to characterize your name with the first letter of the race. "Elory" would have been an elf! :)
Makes it easier to remember what kind of character you're playing this time.

Menne physics? :D

:rofl:

*TOOOOOOOOOOOT* (blowing the golden horn)

 

[Femme_physics]

Always trust your visual queues!
And in case of doubt, make a drawing that is on scale and measure up what you want to know (that will also give you an acceptable answer!). And again: trust your visual queues!

In this case you have found AC=38.01 while AB=35.717
So the numbers say AC is longer than AB, but if you look to your drawing you'll find that AC is visually shorter than AB. The numbers must be wrong! How?

Cuz I'm stupid and I didn't see where's the hypotenuse. Thanks!
I just jumped on the diagonal one instead of looking for the length opposite to the 90 degrees. *smacks forehead 38.01 times*

I think it's the first letter "D".
In fantasy games it's not common to characterize your name with the first letter of the race. "Elory" would have been an elf! :)
Makes it easier to remember what kind of character you're playing this time.

This is great, trigonometric, mechanic, and role-playing advice all in one thread. This must what cyber-heaven feels like. No, no... it IS cyber-heaven! :D

*TOOOOOOOOOOOT* (blowing the golden horn)

LOL