If the raindrops hit at 8.3 m/s , estimate the magnitude of the force on the bottom of a 1.0-m2 pan due to the impacting rain which we assume does not rebound.

F = 0.1153 N

Explanation:

Given:

- Rain fall rate = 5 cm/hr

- Velocity before impact vi = 8.3 m/s

- The Area of the pan A = 1.0 m^2

- The density of water ρ = 1000 kg/m^3

Find:

Estimate the magnitude of the force

Solution:

- Consider rain drops impacting a surface  looses all its momentum. So the change in its momentum is just the momentum with which it impacted.

- We do not know the size of each drop. But the rain fall rate allows us to calculate the rate of change of momentum.

- Total Force: The total force experience by the surface due to the momentum transfer from the impacting rain drops is:

                         F = m(Δv) / t = ρ*v*A*Δh/Δt

Where  

                         Δh/Δt = rain-fall rate.

                         F = 1000*8.3*1*0.05 / 3600

                         F = 0.1153 N