Q5.6 Wait for weight (T)

An hourglass is weighed on a sensitive balance. First, when sand is dropping steadily, from the upper to the lower part of the hourglass, and later, after the upper part is empty. Are the two weights the same or not?
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Hint

What happens to the momentum in the steady state? Is it changing?
 

Solution

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Solution

Graphic - No title - fallingsand
In the steady state, with sand falling in a smooth stream, there is no rate of change in the total momentum of the hourglass and sand. Thus the total external force is zero, and the upward force from the balance is equal to the downward gravitational force mg. The balance thus reads the same as it does after all the sand has come to to rest at the bottom.