During a severe storm in Palm Beach, Fla., on January 2, 1999, 31 inches of rain fell in a period of nine hours. Assuming that the raindrops hit the ground with a speed of 14 m/s, estimate the average upward force exerted by one square meter of ground to stop the falling raindrops during the storm. (Note: One cubic meter of water has a mass of 1000 kg.)
So far I have tried using F_av = (P_f - P_i)/(t_f - t_i) but I haven't been able to even figure out exactly what the mass is of the rain...how does 31 inches of rain relate to 1 cubic meter of rain? And also, am I using the correct equation?
To estimate the average upward force exerted by one square meter of ground, we first need to determine the mass of the rain that fell. Given that one cubic meter of water has a mass of 1000 kg, we need to find the volume of rain that fell in order to calculate its mass.
The given information states that during the storm, 31 inches of rain fell in a period of nine hours. To determine the volume of rain in cubic meters, we need to convert the given inches to meters.
1 inch = 0.0254 meters
Therefore, 31 inches is equal to:
31 inches * 0.0254 meters/inch = 0.7874 meters
Now, we can find the volume of rain in cubic meters:
Volume = Area * Height
Assuming a uniform distribution of rain across the area, the area covered is one square meter, and the height is 0.7874 meters.
Now we can calculate the volume:
Volume = 1 square meter * 0.7874 meters = 0.7874 cubic meters
Since the mass of one cubic meter of water is 1000 kg, the mass of the rain is:
Mass = Volume * Density
Mass = 0.7874 cubic meters * 1000 kg/cubic meter = 787.4 kg
Now that we know the mass of rain, we can estimate the average upward force exerted by one square meter of ground.
The formula to calculate force is F = m * a, where F is the force, m is the mass, and a is the acceleration. In this case, the acceleration is due to the raindrops hitting the ground with a speed of 14 m/s.
As the raindrops come to a stop, the deceleration of each raindrop is equal to the acceleration due to gravity (approximately 9.8 m/s^2), as they are slowed down by the upward force exerted by the ground.
Therefore, the average upward force (F_av) exerted by one square meter of ground is given by:
F_av = m * (g + a)
F_av = 787.4 kg * (9.8 m/s^2 + 14 m/s)
Calculating this equation will give you the estimate of the average upward force exerted by one square meter of ground to stop the falling raindrops during the storm.