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Okay, so the problem. Say we have a bar fixed to a horizontal surface by a hinge, at the end of the bar is a weight, which is fixed so that it cannot move. The bar is lifted to some angle [tex]\theta[/tex] and let go of. I'm ignoring air resistance and the weight of the bar.

I'm trying to calculate the velocity of the weight at the end of the bar by finding the resultant force on it and then using a = F/m, then v = u + at.

This is all happening in something I've programmed, so at set intervals I'll be recalculating the forces acting, then the acceleration and hence the velocity. The weight is then moved by the velocity (x and y components) and I draw a line from the weight to the hinge to indicate the bar.

I've said that the weight has weight W. Parallel to the slope the component of the weight is W*sin([tex]\theta[/tex]) will cancel with the compression of the bar pushing back up (as these will be equal, assuming the bar does not change length).

This leaves W*cos([tex]\theta[/tex]), the perpendicular component of W, as the force moving the system.

I then say that, in x and y components, this comes out to be:

F_{x}= W*cos([tex]\theta[/tex])*sin([tex]\theta[/tex])

F_{y}= W*cos^{2}([tex]\theta[/tex])

This almost works: the motion is in the correct direction and looks great for some situations. However, the bar ends up changing length - and quite substantially in some situations.

So, what have I done wrong? What are the actual x and y components of the force moving the system?

Thanks in advance for any help!

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# Forces Acting on a Moving Hinged Bar

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