How Does the Radius of a Raindrop Affect Its Acceleration and Terminal Velocity?

In summary, the conversation discusses a problem involving a falling raindrop with proportional mass and radius and the need to find the acceleration with respect to radius and velocity. The solution involves considering the drag of the drop and using a special substitution for the mass. The conversation also mentions the relationship between acceleration, gravity, and terminal velocity.
  • #1
hollistb
1
0
So i have a problem with a question in which there is a falling raindrop where the mass and the radius are proportional and i have to find the acceleration with respect to radius and velocity.. I figured that bc it was falling its acceleration would be equal to g... but that seems to easy!
 
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  • #2
the thing to be considered may be the drag of the drop as it falls down which depends on the surface area of the rain drop. this drag limits the velocity of the drop to a specific number...
 
  • #3
This is a very old problem. Unfortunately, I remember the answer, g/7, but I don't remember how you get it. It has an unusual solution. There a special substitution that you need to make for the mass, otherwise the problem is insoluble. You might try to research "raindrop problem" with Google.
 
  • #4
hollistb said:
So i have a problem with a question in which there is a falling raindrop where the mass and the radius are proportional and i have to find the acceleration with respect to radius and velocity.. I figured that bc it was falling its acceleration would be equal to g... but that seems to easy!

Sounds right to me, the only force accelerating a rain drop is due to gravity.

The terminal velocity however depends on the mass and radius.

http://en.wikipedia.org/wiki/Terminal_velocity

Maybe you're supposed to show the relationship between g (the rain drop's acceleration) and the terminal velocity of it.
 

1. How does gravity affect the speed of a falling raindrop?

Gravity causes a raindrop to accelerate as it falls towards the ground. The speed of the raindrop will increase until it reaches its terminal velocity, which is the maximum speed at which the drag force of the surrounding air equals the force of gravity.

2. Why do raindrops vary in size?

Raindrops vary in size due to a number of factors, including the temperature and humidity of the air, as well as the strength of updrafts within a cloud. Larger raindrops tend to form in warmer, more humid conditions, while smaller raindrops form in colder, drier conditions.

3. How does air resistance affect the shape of a falling raindrop?

Air resistance, also known as drag, causes a raindrop to flatten as it falls. This is due to the pressure of the air pushing against the bottom of the raindrop, causing it to spread out and become more oblate in shape.

4. What role does surface tension play in the behavior of a falling raindrop?

Surface tension is the force that holds the molecules of a liquid together at its surface. In the case of a falling raindrop, surface tension helps to maintain the spherical shape of the raindrop as it falls through the air, minimizing the effects of air resistance.

5. How does the speed of a falling raindrop affect its impact force?

The impact force of a raindrop is directly related to its speed. The faster a raindrop falls, the greater its impact force will be upon hitting the ground. This is why larger raindrops can cause more damage than smaller ones.

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