Solve Raindrop Problem: Determine Time to Reach 63% Terminal Velocity

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In summary, the conversation discussed the terminal velocity of a raindrop and how to determine the value of the constant b for a drag force equation. The value of b was found to be 0.0000266 kg/s. The conversation then moved on to determining the time required for the raindrop to reach 63 percent of its terminal velocity, with the solution involving finding the derivative of velocity with respect to time.
  • #1
siwik39
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Homework Statement


The terminal velocity of a 0.000038 kg raindrop is about 14 m/s.

(a) Assuming a drag force FD = -bv, determine the value of the constant b.
correct check mark kg/s

(b) Determine the time required for such a drop, starting from rest, to reach 63 percent of terminal velocity.


2. The attempt at a solution

I got part a by myself, where b= 0.0000266 kg/s

Part b has given me some trouble. I drew a diagram and set the the equation
F=ma=mg - (-bv) Then i tried solving for a, and using that to find t. However, I realized you can't use a=Vf-Vi/t because a is not constant. I have never done an equation like this with t and a non-constant a. I really don't want the answer because I won't learn anything, but any help or hints would be appreciated.
 
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  • #2
Welcome to PF!

siwik39 said:
… Assuming a drag force FD = -bv
…
F=ma=mg - (-bv)

Hi siwik39! Welcome to PF! :wink:

Isn't it ma=mg + (-bv)?

Anyway, just put a = dv/dt, and solve for v. :smile:
 
  • #3
I got part a. I was trying to solve for t. But thanks I got it with the dv/dt.
 

1. What is the raindrop problem and why is it important to solve?

The raindrop problem refers to the calculation of the time it takes for a raindrop to reach 63% of its terminal velocity, which is the maximum speed it can reach due to air resistance. This problem is important to solve because it helps us understand the physics behind raindrop formation and the behavior of falling raindrops, which can have implications for weather forecasting and climate studies.

2. How is the time to reach 63% terminal velocity calculated?

The time to reach 63% terminal velocity can be calculated using the following formula: t = (0.63 * 2m) / (Cd * A * p * g), where t is the time in seconds, m is the mass of the raindrop, Cd is the drag coefficient, A is the cross-sectional area, p is the density of air, and g is the acceleration due to gravity.

3. What factors affect the time to reach 63% terminal velocity?

The time to reach 63% terminal velocity can be affected by several factors, such as the size and shape of the raindrop, the density and viscosity of the air, and the presence of any air currents or turbulence. The drag coefficient, which is dependent on the shape and surface properties of the raindrop, also plays a significant role in determining the time.

4. What is the significance of 63% in the calculation?

The value of 63% is significant in the calculation because it represents the point at which the raindrop has reached over half of its terminal velocity. This is a crucial stage in the raindrop's fall, as it is when the effects of air resistance become more prominent and the raindrop starts to reach a steady speed. As such, determining the time to reach 63% terminal velocity can give us insight into the overall behavior of the raindrop's fall.

5. How accurate is the calculation of the time to reach 63% terminal velocity?

The accuracy of the calculation depends on the accuracy of the input parameters and the assumptions made. In reality, there are many variables that can affect the time and it is difficult to account for all of them. However, the calculation can give a good estimate of the time and can be improved with more precise measurements and calculations.

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