Finding smallest forces required to produce a given moment

[sanddrag]

I've been at this problem for a good while now and I'm still not coming up with the correct answer. I got the correct answer for part (a) but I'm not sure if I achieved it by proper means. Part (b) and (c) I'm not able to come up with the correct answer and I know I'm doing something wrong, I'm just not sure what. The correct answers are (a) 12 lb (b) 10.29 lb (c) 6.36 lb

I'm assuming it wants you to find what forces would make a couple (equal magnitude and opposite direction) so that the resulatant force is zero so the object does not translate, but it rotates. Is this correct?

Yes this is a homework problem but I'm looking more to gain an understanding of how to do it more than the points for doing it. I could just move on to the next problem but I'd rather get an understanding of it so I am sure that I'm attacking the next problems the right way. Please understand I'm not trying to freeload an answer off the wise people on these forums. I'm trying to correct my problem solving methods so one day when I design the car you're driving in, its suspension arm doesn't snap and cause the car to crash and injure you. So please, help me solve this correctly so I don't make a future mistake where it really matters.

This seems like something that should be very simple and I think I'm just missing one little something in solving this problem.

Any help is appreciated and as always sooner is better than later. Thanks in advance.

EDIT: Yes, this is statics.

[Greg Needel]

i was going to go to bed but now you have be thinking about this...give me a few mins and i should have something forward. My initial thoughts are about the fact that Fa and Fd are equal and act in the same direction so using Sum of the moments= 0 you can get your required force....let me play with this a bit.


edit: sorry dude my brain isn't working this second but i will look at it in the morning for ya. I hope it isn't due at 8 am

[sanddrag]

edit: sorry dude my brain isn't working this second but i will look at it in the morning for ya. I hope it isn't due at 8 amDon't worry. Thanks for coming back to tell me so instead of just disappearing. Actually, it is due in the morning but I don't care about getting points for it. I only want to understand.

Now, can you honestly sleep at night with this problem lingering on your mind? I know I can't. Which is why hopefully someone will come along soon with an explanation. :)

[Leo M]

The Given Moment at P is Mp = 10 lb-ft.

a) Corners A and D are 10” apart = 0.833 ft.

The equivalent moment is Force X Distance = Fad X 0.833 ft = 10 lb-ft.

So, smallest F = 10 lb-ft/0.833 ft. = 12 lb, applied perpendicularly to side AD.

b) Corners B and C are 11.66 inches apart = 0.97 ft.

The equivalent moment is Fbc X 0.97 ft = 10 lb-ft

So, smallest Fbc = 10/0.97 = 10.3 lb., applied perpendicularly to side BC.

c) The greatest distance between two points on the block is from A to C, 18.867 inches = 1.572 ft.

The equivalent moment is Fac X 1.572 ft = 10 lb-ft

So smallest Fac = 10/1.572 = 6.36 lb, applied perpendicularly to the line AC.

Hope this helps and is in time for you - dashed it off quickly this AM - have to run.

Good luck.

[Leo M]

I have a diagram in the attached Word file that may help some. Just remember that a moment is a moment wherever on the object it is applied, as long as the equivalent forces are coplanar and the plane is the same as for the original moment applied to the object.

[sanddrag]

You are magnificent! Thanks so much. I totally understand now. I knew it was something simple I was missing. For parts (b) and (c) I wasn't applying the forces perpendicular to the longest distance between the points. I knew this wasn't a hard problem but I couldn't understand why I wasn't getting it, but now I understand it no problem and I took a look at the rest of my problems and I don't think they will be any problem for me. (I've already done 3D moment and force equilibrium problems successfully, but this simple 2d one got me).Anyway, thanks again for the help! It is greatly appreciated. :)

[Leo M]

Glad I could help. Let me know when you get to trusses - those are tricky. And, it's really fun when you get to virtual work and strength of materials - the statics stuff gets boring real fast!