# Determine the Acceleration of point A

1. Apr 28, 2013

### Northbysouth

1. The problem statement, all variables and given/known data
The uniform 22-kg bar is supported on the horizontal surface at A by a small roller of negligible mass. If the coefficient of kinetic friction between end B and the vertical surface is 0.19, calculate the initial acceleration of end A as the bar is released from rest in the position shown. The acceleration is positive if to the left, negative if to the right.

I have attached an image of the question

2. Relevant equations

3. The attempt at a solution

I summed the forces in the x and y directions

ƩFx = max = -NB

ƩFy = may = NA - mg - F

F = ukN

ƩFy = may= NA - mg + ukNB

So, I have 4 unknowns: ax, NB, NA and ay

and two equations. How do I find the other two equations needed to solve this problem?

I considered taking the moment about B, but this then adds in two more unknowns: α and aG. I suspect that I may need to use relative accelerations equations, but is there another way?

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2. Apr 28, 2013

### tiny-tim

Hi Northbysouth!
No, you have 3 independent unknowns.

(and an equation relating ax and ay)
No, they also depend on ax

3. Apr 28, 2013

### Northbysouth

I'm not sure I follow you when you say that I have an equation relating ax and ay. Are you talking about

a = (a2x + a2y)1/2

The questions asks me to find the acceleration of point a which I know is only in the x direction, and point B has an acceleration which only acts in the y direction.

Could you expand a little on what you said, please?

Thank you

4. Apr 28, 2013

### tiny-tim

No, I'm saying a = (x2 + y2)1/2.

(and so y = √(a2 - x2))

5. Apr 28, 2013

### Northbysouth

I'm sorry but I'm still not following you.

When you use x and y, are you referring to the horizontal and vertical distances respectively?

6. Apr 28, 2013

### haruspex

I think tiny-tim is using x for the horizontal position of the roller, y for the vertical position of end B, and a (confusingly) for the length of the bar. The point is that the bar is of constant length, which gives you an equation relating ax to ay.
You will need to take moments too, since the moment of inertia of the bar plays a role. As with ax and ay, there is a direct relationship between these and angular acceleration.