Determine the Acceleration of the plate for which there is no Force

[Northbysouth]

Homework Statement

The right-angle bar with equal legs weighs 6.0 lb and is freely hinged to the vertical plate at C. The bar is prevented from rotating by the two pegs A and B fixed to the plate. Determine the acceleration a of the plate for which no force is exerted on the bar by A either B peg or .

I have attached an image of the question

Homework Equations

The Attempt at a Solution

I'm pretty sure this is a striaghtforward question but I think I'm missing something.

First I summed the forces in the x and y direction.

ƩF_y = ma_y = Cy - mg

Cy = mg

ƩF_x = ma_x = Cx

Then I took the moment about the origin. I assigned the origin as being inbetween A and B.

And I found the center to be (2,6)

ƩM = -1/6*mg -8/12*Cx + 8/12*Cy

Cx = 3/4*mg

a_x = a = Cx/m = [(3/4)mg]/m = (3/4)g

But the answer should be 3g. Where am I making my mistake?

Any help would be appreciated.

 

[Northbysouth]

I looked over the question again and this time I took the moment at the center of mass (2,6)

Hence:

ƩM_G = 0 = -2/12*Cx + 6/12*Cy

Cx = 3mg

a = Cx/m = 3mg/m = 3g

So, I've got the right answer, but why didn't it work when I took the moment about the Origin I assigned? What is the significance of taking the moment about the center of the shape?

 

[PhanthomJay]

Acceleration of a system is always acceleration of the center of mass of the system. Since your force Cx is at the hinge and not at the center of mass, you must choose the center of mass as your rotation point when summing moments. Or use the concept of the pseudo force "-ma" applied at the center of mass, then you can sum moments equal 0 about any point.

 

[mgarci88]

how did you find the center to be at (2, 6)?

 

[haruspex]

how did you find the center to be at (2, 6)?

I agree with that location. Are you asking because you disagree or because you really don't know how to find it?

Spoiler

It must be half way between the mass centres of the two arms taken separately. Where are they?

 

[mgarci88]

I don't know how they got it. It makes sense it would be there, I was looking for a formula possibly.

 

[haruspex]

I don't know how they got it. It makes sense it would be there, I was looking for a formula possibly.

Did you read my spoiler hint?