Distance between the force and origin

[goldfish9776]

Homework Statement

In this note , I was told that either vector OD , OC , AD and AC can be used as the distance between the Force and OA axis ... why ? To produce moment , the distance r must be originate from the origin of force ( point C ) , am i right ? So , IMO, only r AC can be used...

Homework Equations

The Attempt at a Solution

 

[Doc Al]

Note the presence of the cross product when calculating the moment. Would any of those choices give a different result?

 

[goldfish9776]

Note the presence of the cross product when calculating the moment. Would any of those choices give a different result?

Sorry, I still don't understand. Can you explain further?

 

[Doc Al]

Realize that when you take the cross product $\vec{r} \times \vec{F}$, where $\vec{r}$ is a vector starting at pt O and extending anywhere along the line of $\vec{F}$, that you get the same answer. Essentially you are finding the perpendicular distance between pt O and the line.

In simpler terms: r X F = r sinθ F. Realize that when r changes, θ also changes so that r sinθ remains the same. Play around with this until you get it.

 

[goldfish9776]

Realize that when you take the cross product $\vec{r} \times \vec{F}$, where $\vec{r}$ is a vector starting at pt O and extending anywhere along the line of $\vec{F}$, that you get the same answer. Essentially you are finding the perpendicular distance between pt O and the line.

In simpler terms: r X F = r sinθ F. Realize that when r changes, θ also changes so that r sinθ remains the same. Play around with this until you get it.

from the figure , it show that the vector r _OD is not along the vector F ...
By saying $\vec{r}$ is a vector starting at pt O and extending anywhere along the line of $\vec{F}$ , do you mean like this ? the r can be any vector ( in different colours ) along the vector F ?

 

[goldfish9776]

Realize that when you take the cross product $\vec{r} \times \vec{F}$, where $\vec{r}$ is a vector starting at pt O and extending anywhere along the line of $\vec{F}$, that you get the same answer. Essentially you are finding the perpendicular distance between pt O and the line.

In simpler terms: r X F = r sinθ F. Realize that when r changes, θ also changes so that r sinθ remains the same. Play around with this until you get it.

Since Force at C is moved towards D , why not Vector r_CD is used ?

 

[Doc Al]

from the figure , it show that the vector r _OD is not along the vector F ...
By saying $\vec{r}$ is a vector starting at pt O and extending anywhere along the line of $\vec{F}$ , do you mean like this ? the r can be any vector ( in different colours ) along the vector F ?

Yes.

 

[Doc Al]

Since Force at C is moved towards D , why not Vector r_CD is used ?

Vector r begins at pt O.

 

[goldfish9776]

Vector r begins at pt O.

sorry, I'm still confused now . IMO, vector r _OD is not along the vector F .

 

[goldfish9776]

sorry, I'm still confused now . IMO, vector r _OD is not along the vector F .

Can you explain further?

 

[Doc Al]

sorry, I'm still confused now . IMO, vector r _OD is not along the vector F .

That's true, it is not. Why would you think it would be?

Are you confusing it with vector CD?

Since Force at C is moved towards D , why not Vector r_CD is used ?

 

[goldfish9776]

That's true, it is not. Why would you think it would be?

Are you confusing it with vector CD?

Becoz I was told that the vector r must originate from anywhere along line of action ( force)

 

[Doc Al]

Becoz I was told that the vector r must originate from anywhere along line of action ( force)

The vector r originates at point O and terminates anywhere along the line of action of the force.

 

[goldfish9776]

The vector r originates at point O and terminates anywhere along the line of action of the force.

the line of action refers to the line along F , right ? Vector CD isn't on this line , so i think vector CD is not suitable ...

 

[Doc Al]

the line of action refers to the line along F , right ?

Right.

Vector CD isn't on this line , so i think vector CD is not suitable ...

Looks to me like F points along the line CD.

 

[goldfish9776]

Right.Looks to me like F points along the line CD.

Ya, it points along cd? Why vector cd is not used? But vector od is used?

 

[Doc Al]

Ya, it points along cd? Why vector cd is not used? But vector od is used?

You seem to be mixing up $\vec{r}$ with $\vec{F}$. The vector r must begin at O and end somewhere on the line of action of F. So r could be OD or OC or anything in between, but not CD!

 

[goldfish9776]

You seem to be mixing up $\vec{r}$ with $\vec{F}$. The vector r must begin at O and end somewhere on the line of action of F. So r could be OD or OC or anything in between, but not CD!

oh , yeah . I forgot that F can be longer . It doesn't necessarily ends at point D. that's why I'm confused.

 

[goldfish9776]

You seem to be mixing up $\vec{r}$ with $\vec{F}$. The vector r must begin at O and end somewhere on the line of action of F. So r could be OD or OC or anything in between, but not CD!

if i use MOA = uOA . (rOC X F) , then my ans = 108 , if i use MOA = uOA . (rOD X F) , then the ans = 100 , is it correct ?

 

[goldfish9776]

sorry , i didnt mean to spam , can someone help me with this ?

 

[Doc Al]

if i use MOA = uOA . (rOC X F) , then my ans = 108 , if i use MOA = uOA . (rOD X F) , then the ans = 100 , is it correct ?

That cannot be correct. The point is that rOC X F = rOD X F.

 

[goldfish9776]

That cannot be correct. The point is that rOC X F = rOD X F.

Which part of my working is wrong?

 

[Doc Al]

Which part of my working is wrong?

Show your work. What are rOC, rOD, and F?

 

[goldfish9776]

OD=0.6i +0.8j

 

[goldfish9776]

 

[Doc Al]

OD=0.6i +0.8j

I believe that's the unit vector uOD, not rOD.

 

[goldfish9776]

I believe that's the unit vector uOD, not rOD.

sorry , i mean rOC= 0.4j + 0.5k ( as shown in the working above )

 

[Doc Al]

sorry , i mean rOC= 0.4j + 0.5k ( as shown in the working above )

What are the others?

 

[goldfish9776]

What are the others?

rOD = 05i +0.5 k , according to transmisbility of forces , the r can be anywhere on the line of action of F ( force ) , am i right ? so , no matter what is the value of r , as long as it has contact with the line of action of F , then the value of MOA should be the same , right ? why the ans for MOA is different if i am using uOA . (rOC x F) ?
to find MOA , i gt my ans = 108 if i am using uOA . (rOC x F)
to find MOA , i gt my ans = 100 if i am using uOA . (rOD x F)
why are they different ?

 

[Doc Al]

sorry , i mean rOC= 0.4j + 0.5k

That doesn't look right. What are the coordinates of C?

rOD = 05i +0.5 k ,

The diagram's a bit hard to read, but that looks right.