Moment of Force about specified axis

[jonnburton]

Hi,

I have been working on the following problem and havign done it several times have failed to come to the solution provided by the book. I was wondering whether anybody could point out what I am doing wrong?



\(\displaystyle F_1\) components

tex] (80cos120)i + (80cos60)j+(80cos45)k[/tex]

\(\displaystyle -40i+40j+56.6k\)

\(\displaystyle F_2\) Components


As this goes straight up the z axis it's 50k


\(\displaystyle r_B = 2i + 3.5j +6k\)

\(\displaystyle r_{F_2} = -2.5j\)


Getting unit vector for \(\displaystyle Oa\)


\(\displaystyle Oa = 4.33i-2.5j\)

\(\displaystyle U_{Oa} = 0.866i-0.5j\)



Finding moments around \(\displaystyle Oa\)


For \(\displaystyle F_1\)

i	j	k
0.866	-0.5	0
2	3.5	6
-40	40	56.6

\(\displaystyle 0.866(198.1-240)i+0.5(113.2+240)j\)

For \(\displaystyle F_2\):

i	j	k
0.866	-0.5	0
0	-2.5	0
0	0	50

\(\displaystyle 0.866(-125)i\)


Adding the components:

-144.5 i +176.6j


Whereas the correct answer should be 26.1i-15.1j


I've been throught the worked examples on this topic again, and understand those (although they only involve one force, rather than two as is the case here). So I have a feeling the mistake might be in adding the two moments. Any information would be much appreciated, as ever.

 

[Deleted member 4993]

Hi,

I have been working on the following problem and havign done it several times have failed to come to the solution provided by the book. I was wondering whether anybody could point out what I am doing wrong?

View attachment 3098

\(\displaystyle F_1\) components

tex] (80cos120)i + (80cos60)j+(80cos45)k[/tex]

\(\displaystyle -40i+40j+56.6k\)

\(\displaystyle F_2\) Components


As this goes straight up the z axis it's 50k


\(\displaystyle r_B = 2i + 3.5j +6k\)

\(\displaystyle r_{F_2} = -2.5j\)


Getting unit vector for \(\displaystyle Oa\)


\(\displaystyle Oa = 4.33i-2.5j\)

\(\displaystyle U_{Oa} = 0.866i-0.5j\)



Finding moments around \(\displaystyle Oa\)


For \(\displaystyle F_1\)

i	j	k
0.866	-0.5	0
2	3.5	6
-40	40	56.6

\(\displaystyle 0.866(198.1-240)i+0.5(113.2+240)j\)

Assuming your arithmetic is correct upto this point, the detrminant of the matrix above is the magnitude of the moment. So it does not have any i or j or k associated with it.

M₁ = 0.866(3.5*56.6) - (-0.5)*[2*56.6 - 6*(-40)] + 0*[..] ......................... this is the magnitude of the moment of F₁ around line OA


Similarly

For \(\displaystyle F_2\):

i	j	k
0.866	-0.5	0
0	-2.5	0
0	0	50

\(\displaystyle 0.866(-125)i\)

Similarly

M₂ = 0.866[(-2.5)*50]......................... this again is the magnitude of the moment of F₂ around line OA

So the moment vector would be:

M = [M₁ + M₂]U_OA

Adding the components:

-144.5 i +176.6j


Whereas the correct answer should be 26.1i-15.1j


I've been throught the worked examples on this topic again, and understand those (although they only involve one force, rather than two as is the case here). So I have a feeling the mistake might be in adding the two moments. Any information would be much appreciated, as ever.

Try it again - with corrections indicated above.

 

[jonnburton]

Try it again - with corrections indicated above.

Thank you Subhotosh; I will give it another go.