Why Does W(sub ab) = 0 and W(sub bc) = 4 in Dynamics?

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The discussion centers on the dynamics problem involving the equations W(sub ab) = 0 and W(sub bc) = 4, where W represents work done in a mechanical system. The stationary nature of point A and the movement of block C along the x-axis are critical to understanding the system's behavior. The horizontal bar (ab) remains stationary, indicating no work is done on it, while the vertical bar (bc) experiences work due to the movement of block C. The key takeaway is that while the horizontal bar does not move, it can still have acceleration, which affects the overall dynamics of the system.

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My professor has given us the problem and solution here; http://mielsvr1.ecs.umass.edu/mie310/13-176.JPG however, he has left out steps. I want to figure out as much on my own as possible, but don't really understand this one.

One of the equations written is W (sub ab) = 0, W (sub bc) = 4. However, if the top bar (ab) isn't moving, but the vertical bar (bc) is moving, the block C would just spin in circles. It appears to be going in the X direction only, confined in a track.

Any help would be greatly appreciated, especially if you could just translate some equations into words. When I look at them I come up with things like the problem above where they don't seem physically possible or equal.

Thanks a bunch in advance.
 
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The block is pulling on the vertical bar which pulls the horizontal bar. At that instant the horizontal bar is not moving, but it does not mean it doesn't have an acceleration. At the very next instant the bar will be moving.
Point A is pinned therefore stationary, meaning velocity=0 at A. The block at C is confined to the x-axis so a velocity component in the y axis=0 at C.
The first equation written there means the velocity at one point is equal to the velocity at a second point plus the velocity of the first point as seen from the second point.
Use what is known when you apply the equations for velocity and acceleration to solve for the unknowns
 

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