Sisyphus was famed as the craftiest of men. He was nasty, deceitful and greedy. As a punishment from the gods for his trickery, Sisyphus was made to push a huge rock up a steep hill, but before he could reach the top of the hill, the rock would always roll back down, forcing him to begin again – an endless cycle of energy conservation. The gravitational potential energy gained by pushing the rock up the hill was converted to kinetic energy as the rock rolled down again.
Notice that Sisyphus had to push the stone up a hill. The VERTICAL height of the hill is used to calculate the gain in gravitational potential energy, not the length of the slope of the hill.
Next: conserving E, cancelling m gives the expression to show how fast the stone would be
going if it was allowed to fall freely (forget about rolling)
You might think about how much higher the hill would have to be to cause the stone to be going twice as fast at the bottom – this kind of thing crops up in MC all the time.
My ‘hill’ in the diagram is a straight line. In terms of energy conservation, would the shape of the hill matter? The answer is ‘no’, but can you explain why?
The original track to the hilltop fortress of Masada in Israel is shaped like this.
You might like to reflect on this…
Work done = energy transformed (against gravity) = applied force x distance moved in the direction of the force.