Solution: Moment about Y-Axis for Homogenous Plates w/ 10kg Mass

[werson tan]

Homework Statement

the homogenous plates shown in the figure has a mass of 10kg and is subjected to a forec and moments alonf its edges. If it is supported in the horizontal plate by means of a roller at A , a ball and a socket joint at B , and cord at C , determine the components of reaction at the supports .

https://www.physicsforums.com/attachments/3233-png.92686/

Homework Equations

The Attempt at a Solution

I want to ask about the total moment about y ' axis ,
it's -300(1.5) + 981(1.5) -200 +Tc(3) = 0
the 2ooNm is acted along the y-axis , right ? why we should consider it at y 'axis ?

The moment about y given is 300(1.5) +981(1.5) –Bz(3) –Az(3) -200Nm = 0
i can undersatnd for y-axis , but not for y ' axis ...

 

[SteamKing]

Homework Statement

the homogenous plates shown in the figure has a mass of 10kg and is subjected to a forec and moments alonf its edges. If it is supported in the horizontal plate by means of a roller at A , a ball and a socket joint at B , and cord at C , determine the components of reaction at the supports .

Homework Equations

The Attempt at a Solution

I want to ask about the total moment about y ' axis ,
it's -300(1.5) + 981(1.5) -200 +Tc(3) = 0
the 2ooNm is acted along the y-axis , right ? why we should consider it at y 'axis ?

The moment about y given is 300(1.5) +981(1.5) –Bz(3) –Az(3) -200Nm = 0
i can undersatnd for y-axis , but not for y ' axis ...

Thanks for posting the larger image. It makes things much easier to read.

As far as the 200 N-m moment shown on the y-axis in the figure, this is what is known as a couple, or a free moment. A couple can be moved at will, and as long as it is included in the sum of the moments for a particular body, the equilibrium of the body is not disturbed. In other words, it doesn't matter where the couple is located; it will always have the same magnitude and direction.

 

[werson tan]

Thanks for posting the larger image. It makes things much easier to read.

As far as the 200 N-m moment shown on the y-axis in the figure, this is what is known as a couple, or a free moment. A couple can be moved at will, and as long as it is included in the sum of the moments for a particular body, the equilibrium of the body is not disturbed. In other words, it doesn't matter where the couple is located; it will always have the same magnitude and direction.

how do u know that it's a couple ? it's not stated there . If it is , why can't we include the 200Nm in the calculation of moment at x and x' axis ?

 

[SteamKing]

how do u know that it's a couple ? it's not stated there . If it is , why can't we include the 200Nm in the calculation of moment at x and x' axis ?

Well with units of N-m, it's not a force.

The dirty secret about moments and couples is they're also vector quantities, like forces. A couple has a magnitude and a direction.

For this couple, it's shown acting along the y-axis, not the x-axis or the z-axis. When it comes time to sum moments, the magnitude of this couple is supposed to be included with any other moments acting about the y-axis.

 

[werson tan]

Well with units of N-m, it's not a force.

The dirty secret about moments and couples is they're also vector quantities, like forces. A couple has a magnitude and a direction.

For this couple, it's shown acting along the y-axis, not the x-axis or the z-axis. When it comes time to sum moments, the magnitude of this couple is supposed to be included with any other moments acting about the y-axis.

but y and y ' axis are different ? why we have to include the 200Nm which is on y-axis to y' axis ?

 

[SteamKing]

but y and y ' axis are different ? why we have to include the 200Nm which is on y-axis to y' axis ?

Because you can't simply ignore the couple just because you are using a different axis about which to calculate moments.

 

[werson tan]

Because you can't simply ignore the couple just because you are using a different axis about which to calculate moments.

sorry , i still don't gt you , can you explain further ? the question doesn't state the 200Nm is a couple moment , so the 200Nm is just a moment , right ?

 

[SteamKing]

sorry , i still don't gt you , can you explain further ? the question doesn't state the 200Nm is a couple moment , so the 200Nm is just a moment , right ?

Well, it's not the moment of any force which I can see on the diagram, so by the process of elimination, it must be a couple. Whatever you want to call it, a couple, Cyril, or a demiflitchit, you still can't ignore it in your calculations.

 

[werson tan]

Well, it's not the moment of any force which I can see on the diagram, so by the process of elimination, it must be a couple. Whatever you want to call it, a couple, Cyril, or a demiflitchit, you still can't ignore it in your calculations.

a moment must be a couple moment ?

 

[SteamKing]

a moment must be a couple moment ?

It doesn't always have to be. Like I said before, you can have the moment of a force, but you can also have a special moment, which is called a couple, which is produced by equal and opposite forces F which are separated from one another by a distance d = 2s.

https://en.wikipedia.org/wiki/Couple_(mechanics)

The moment produced has a magnitude of M = F * 2s = F * d. There is no net force since the Fs are equal in magnitude but acting in opposite directions.

Statically, the couple created by the two forces acting on the beam above can be located anywhere along the length of the beam without changing the net of the forces and moments acting on the beam.

If there were only one force acting on the beam above, you could move the force F from the end of the beam to the center and add a couple of magnitude F * s. As far as the statics of the beam is concerned, both situations are equivalent.

 

[werson tan]

so , the above one is called special moment ? which is also known as a couple ?

 

[SteamKing]

so , the above one is called special moment ? which is also known as a couple ?

Yes. It's also sometimes referred to as a 'free moment'.

 

[werson tan]

Yes. It's also sometimes referred to as a 'free moment'.

the question just gave the 200Nm acted in negative y direction , how would you know that it's a free vector moment ?

 

[werson tan]

It doesn't always have to be. Like I said before, you can have the moment of a force, but you can also have a special moment, which is called a couple, which is produced by equal and opposite forces F which are separated from one another by a distance d = 2s.

https://en.wikipedia.org/wiki/Couple_(mechanics)

The moment produced has a magnitude of M = F * 2s = F * d. There is no net force since the Fs are equal in magnitude but acting in opposite directions.

Statically, the couple created by the two forces acting on the beam above can be located anywhere along the length of the beam without changing the net of the forces and moments acting on the beam.

If there were only one force acting on the beam above, you could move the force F from the end of the beam to the center and add a couple of magnitude F * s. As far as the statics of the beam is concerned, both situations are equivalent.

so , there are 2 types of moment , namely the moment due to force and free vector moment ( which ia couple moment ) ??

 

[werson tan]

Yes. It's also sometimes referred to as a 'free moment'.

can i explain in this way ? when the -200Nm torque exist at the y-axis , it will turn about the y-axis , when it rotate , it will somehow rotate in the y' direction too...??