What would happen if there was no air resistance during rain?

[Arkronus]

My teacher gave us these extra credit problems and I couldn't really solve them. Here they are:

"If air resistance did not exist, would rain be dangerous? Why?"

"On the imaginary planet Zelth, a 100 kg mass weighs 15.8N. What is the acceleration due to gravity on Zelth? How does it compare to gravity on Earth? What is your weight on Zelth?"

Also don't just give me the answers, show me how to do them.

 

[Arkronus]

I found that the average height of rain clouds are above 1000 meters and the formula: Vf^2=Vi^2+2AD would find the final velocity of over 140 m/s but I'm not sure if water could hurt people.

 

[berkeman]

We neither give you the answers nor show you exactly how to do the problems. We try to help guide you into solving the problems yourself. You wouldn't learn much if we just solved the problems for you.

So, what would be different for the rain if there were no air resistance? What does air resistance do as the raindrops fall?

What equation do you use to relate a force F to the acceleration a of a mass m? What is the similar equation that gives your weight in terms of your mass and the acceleration due to gravity "g"?

 

[berkeman]

I found that the average height of rain clouds are above 1000 meters and the formula: Vf^2=Vi^2+2AD would find the final velocity of over 140 m/s but I'm not sure if water could hurt people.

That's a good start. I don't think the drops would kill anybody, but they sure would sting!

 

[Arkronus]

I found that 1 Newton is equal to about .102 kilograms, so If I weigh about 50 kg, my weight in Newton on Earth would be 500N, and if I converted it from N to kg on the planet Zelth, I would weigh over 3000 kg. Is this right?

 

[Arkronus]

Also, I know that the acceleration due to gravity on Earth is 9.8m/s^2, but how can I use F=ma to find the mass of the Earth?

 

[berkeman]

Let's be a little clearer here. You don't need to know the mass of the Earth. That is what creates the acceleration of gravity, $$9.8 \frac{m}{s^2}$$

So you are correct that if your mass is 50kg, then your weight (the force down due to the acceleration of gravity) is 50*9.8 = 490N.

But on Zelth, 100kg has a pretty light weight, right? What is the acceleration due to Zelth's gravity? Call it z. Then calculate your weight on Zelth as F=mz, where m is your mass.

 

[Arkronus]

oh, i get it now, you're the coolest berkeman!

 

[Arkronus]

so is the acceleration on Zelth .16m/s^2 and my weight on Zelth is 7.9N?

 

[berkeman]

so is the acceleration on Zelth .16m/s^2 and my weight on Zelth is 7.9N?

If you weigh 50N on Earth, then yes. Good work.

BTW, I thought more about the "dangerous rain" question, and although it won't kill any people outright, it would sure make it harder for planes to fly and other activities. Birds would have to "run" for cover as well. Maybe put some creative thought into your final answer to that part of the question. It is an extra credit question, after all, and you'll be expected to put in some extra thought into your answers.

Welcome to PF, BTW.