Shaskolskaya & Eltsin Problem 29

Physics · mechanics · fluid-mechanics

Problem

When the scale-pan with the weight on it is at rest, the spring is extended to such an extent that the spring's elasticity balances the weight of scale-pan plus weight. If the spring is forced out of this position and pulled downwards a little, when it is released it will make oscillations about the position of equilibrium. The spring's extension will then be least when the scale-pan is in its highest position. For the weight to cease to exert pressure on the scale-pan, it is necessary that the pan should begin to move downwards from its highest position with the same acceleration as the weight, i.e, with an acceleration equal to that imparted by the force of gravity, g. This will obviously be the case when the spring is not stretched at all in its highest position. Since the highest position is symmetrically placed to the lowest position relative to the position of equilibrium of weight plus pan, it follows that for the scale-pan to reach a position in which the spring is not extended at all, the spring must first be extended through a distance equal to that through which the scale-pan and weight have stretched it in reaching their position of equilibrium. Consequently the scale-pan and weight must be pulled downwards with a force equal to their combined weight.

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