Work, Power and Energy
© examsnet.com
Question : 13
Total: 30
A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height, it attains its maximum (terminal) speed, and moves with uniform speedthereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey?
What is the work done by the resistive force in the entire journey if its speed on reaching the ground is10 m s – 1
What is the work done by the resistive force in the entire journey if its speed on reaching the ground is
Solution:
Radius of raindrop, r = 2 mm = 2 × 10 – 3 m
Distance covered by drop in each half of the journey
h =
= 250 m
Mass of raindrop = Volume of drop × Density
=
π r 3 ρ ( ρ = 10 3 kg m 3 = density of water )
= 3.35 × 10 − 5 kg
Work done by gravitational force during each half
= m g h = 3.35 × 10 – 5 × 9.8 × 250 = 0.082 J
Whether the rain drop falls with decreasing acceleration or with uniform speed, the work done by the gravitational force on the drop remains same.
If there were no resistive force, energy of drop on reaching the groundE 1 = m g h = 3.35 × 10 – 5 × 9.8 × 500 = 0.164 J
Actual energy,E 2 =
m v 2 =
× 3.35 × 10 − 5 × ( 10 ) 2 = 1.675 × 10 − 3 J
Work done by the resistive force
W = E 2 − E 1 = 1.675 × 10 − 3 − 0.164 = − 0.162 J
Distance covered by drop in each half of the journey
Mass of raindrop = Volume of drop × Density
Work done by gravitational force during each half
Whether the rain drop falls with decreasing acceleration or with uniform speed, the work done by the gravitational force on the drop remains same.
If there were no resistive force, energy of drop on reaching the ground
Actual energy,
Work done by the resistive force
© examsnet.com
Go to Question: