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It is well known that a rain drop falls ...

It is well known that a rain drop falls under the influence of the downward gravitational force and the opposing resistive force. The latter is known to be proportional to the speed of the drop, but is otherwise undetermined. Consider a drop of mass 1.0g falling from a height of 1.00km. It hits the ground with a speed of `50.0ms^(-1)` (a) What is the work done by the gravitational force ? (b) What is the work done by the unknown resistive force ?

Text Solution

Verified by Experts

The change in kinetic energy of the drop is
`triangleK= (1)/(2)mv^(2)-0`
`=(1)/(2)xx10^(-3)xx50xx50 = 1.25 J`
where we have assumed that the drop is initially at rest.
Assuming that g is a constant with a value `10 m"/"s^(2)`, the work done by the gravitational force is,
`W_(g)= mgh`
`=10^(-3)xx10xx10^(3)= 10.0 J`.
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