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

In summary: The center of mass of a system is defined by the sum of the products of each particle's mass times its position vector divided by the sum of the masses.In summary, the conversation discusses a physics problem involving determining the acceleration of a plate with a hinged bar attached to it. The solution involves taking the sum of forces and moments, with the key point being that the acceleration of a system is always the acceleration of the center of mass. The center of mass in this problem was found to be located at (2, 6).
  • #1
Northbysouth
249
2

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.

ƩFy = may = Cy - mg

Cy = mg

ƩFx = max = 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

ax = 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.
 

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

Hence:

ƩMG = 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?
 
  • #3
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.
 
  • #4
how did you find the center to be at (2, 6)?
 
  • #5
mgarci88 said:
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?
It must be half way between the mass centres of the two arms taken separately. Where are they?
 
  • #6
I don't know how they got it. It makes sense it would be there, I was looking for a formula possibly.
 
  • #7
mgarci88 said:
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?
 

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

1. What is the definition of acceleration?

Acceleration is the rate of change of an object's velocity over time. It is a vector quantity, meaning it has both magnitude and direction. In simpler terms, it measures how fast an object's velocity is changing.

2. How can acceleration be determined for an object?

Acceleration can be determined by measuring the change in an object's velocity over a specific amount of time. This can be done by using the equation a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. Can an object have acceleration without a force acting on it?

No, according to Newton's Second Law of Motion, an object cannot have acceleration without a net force acting on it. This means that if an object is not experiencing any external forces, it will either remain at rest or continue moving at a constant velocity.

4. How is acceleration related to mass?

Acceleration and mass are inversely proportional, meaning that as mass increases, acceleration decreases, and vice versa. This is because an object with a greater mass requires a greater force to accelerate it.

5. What factors can affect the acceleration of an object?

The acceleration of an object can be affected by factors such as the net force acting on the object, the object's mass, and the surface or medium it is moving through. Other factors, such as air resistance and friction, can also affect an object's acceleration.

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