Suppose 560 drops of rain strike each square metre of ground every second. Consider a person stuck out in the rain. The top of their head has a cross-sectional area of 350 cm2.(d) [3 marks]Calculate the force of the rain hitting the person's head, assuming each rain drop comes to a stop?(e) [2 marks]Calculate the resulting pressure.
Question
Suppose 560 drops of rain strike each square metre of ground every second. Consider a person stuck out in the rain. The top of their head has a cross-sectional area of 350 cm2.(d) [3 marks]Calculate the force of the rain hitting the person's head, assuming each rain drop comes to a stop?(e) [2 marks]Calculate the resulting pressure.
Solution
To answer these questions, we need to know the mass and velocity of a raindrop. However, since these values are not provided, I will use some typical values: a mass of 0.05 grams (or 0.05 x 10^-3 kg) and a velocity of 9 m/s.
(d) First, we need to calculate the number of raindrops hitting the person's head per second. The area of the person's head is 350 cm^2, which is 0.035 m^2. So, the number of raindrops hitting the person's head per second is 560 drops/m^2 * 0.035 m^2 = 19.6 drops/second.
The force exerted by each raindrop when it comes to a stop is given by Newton's second law, F = ma, where m is the mass of the raindrop and a is the acceleration. The acceleration is the change in velocity divided by the time it takes for the change to occur. Assuming each raindrop comes to a stop in 0.01 seconds, the acceleration is -9 m/s / 0.01 s = -900 m/s^2. The negative sign indicates that the acceleration is in the opposite direction of the velocity.
So, the force exerted by each raindrop is F = (0.05 x 10^-3 kg)(-900 m/s^2) = -0.045 N. The total force exerted by all the raindrops hitting the person's head per second is -0.045 N/drop * 19.6 drops/second = -0.882 N.
(e) The pressure is the force divided by the area over which the force is distributed. So, the pressure is -0.882 N / 0.035 m^2 = -25.2 Pa. The negative sign indicates that the pressure is directed downwards.
Similar Questions
A raindrop reaching the ground with terminal velocity has momentum P. Another drop of twice the radius, also reaching the ground with terminal velocity, will have momentum.
A rainstorm produces raindrops each with a mass of 7.5 × 10-5 kg and a terminal speed of 25 m/s. Suppose the rain is falling straight down (no wind).(a) [1 mark]What is meant by "terminal speed" and why does it exist?(b) [1 mark]While falling at terminal speed each rain drop is losing gravitational potential energy without gaining kinetic energy. Explain this in the context of conservation of energy.(c) [1 mark]Calculate the magnitude of the momentum of each rain drop. Suppose 560 drops of rain strike each square metre of ground every second. Consider a person stuck out in the rain. The top of their head has a cross-sectional area of 350 cm2.(d) [3 marks]Calculate the force of the rain hitting the person's head, assuming each rain drop comes to a stop?(e) [2 marks]Calculate the resulting pressure. Suppose a horizontal wind springs up giving the raindrops a horizontal velocity of 14 m/s, without changing their vertical velocity.(f) [2 marks]Calculate the momentum of a raindrop now, remembering that momentum is a vector quantity.
A raindrop was 18meters above the ground, falling straight down at a constant velocity. It took the raindrop 3seconds to fall half the distance to the ground. What was the raindrop's velocity?
The rain cloud has an approximate volume of30 km3 and an average height, top to bottom, of 125 m.If a cuboid container collects 58 mm of water after the rainfalls out of the cloud, estimate the total mass of rain that fellfrom the cloud
Two rain drops reach the earth with different terminal velocities having ratio 9 : 4. Then, the ratio of their volumes is :-3 : 24 : 99 : 427 : 8
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.