# Solve Rain Drop VTerminal Homework: Find Drag Force & Time

• cleverfield
In summary, to determine the value of the constant in the drag force equation and the time required for a 3×10−5kg raindrop to reach 63% of its terminal velocity, you must use the equation of motion for a falling object with drag force and integrate it to find the appropriate relationship. Using the incorrect equation of motion will not yield correct results.
cleverfield

## Homework Statement

The terminal velocity of a 3×10−5kg raindrop is about 5m/s . Assuming a drag force , and Drag Force = -bv

1. Assuming a drag force determine the value of the constant .

2. Assuming a drag force determine the time required for such a drop, starting from rest, to reach 63% of terminal velocity.

## The Attempt at a Solution

I solved Q1 with an answer of b=6*10^-5 kg/s

for #2. I used Vfinal = Vinit + at

Equation 1 = V final = 0.63 of Vterm and therefore is 3.15 m/s
V init = 0
a = ?
Time = ?

for a I used the constant b and did FBD and N2

got Fdrag - mg = ma

Work:

-(6E-5kg/s)(3.15m/s) - (3E-5kg)(9.8m/s2) = (3E-5kg)a

but that gives a = -16.1 m/s2 which doesn't make sense to me. And i dropped that number in equation 1 above.

Thanks

Fdrag - mg = ma

Think about the direction of the forces. The raindrop is falling down, thus accelerating downwards. The drag force is slowing the drop down and is working against the direction of motion. Isn't it gravity, on the other hand, that pulls the drop downwards and therefore causes the acceleration?

cleverfield said:

## Homework Statement

The terminal velocity of a 3×10−5kg raindrop is about 5m/s . Assuming a drag force , and Drag Force = -bv

1. Assuming a drag force determine the value of the constant .

2. Assuming a drag force determine the time required for such a drop, starting from rest, to reach 63% of terminal velocity.

## The Attempt at a Solution

I solved Q1 with an answer of b=6*10^-5 kg/s

for #2. I used Vfinal = Vinit + at

Equation 1 = V final = 0.63 of Vterm and therefore is 3.15 m/s
V init = 0
a = ?
Time = ?

for a I used the constant b and did FBD and N2

got Fdrag - mg = ma

Work:

-(6E-5kg/s)(3.15m/s) - (3E-5kg)(9.8m/s2) = (3E-5kg)a

but that gives a = -16.1 m/s2 which doesn't make sense to me. And i dropped that number in equation 1 above.

Thanks

The equation of motion for your situation is $$ma = -mg + F_{drag}$$

This means that you cannot use $$V_{final} = V_{init} + at$$ ! That is the solution for motion without drag. You need to integrate the equation of motion with a drag force and use that, or the appropriate relationship derived from it, to find your answer.

## 1. What is the purpose of solving for drag force and time in a raindrop terminal velocity homework?

The purpose of solving for drag force and time is to calculate the terminal velocity of a raindrop, which is the maximum speed that the raindrop will reach as it falls through the air. This information can help us understand the behavior of raindrops in different weather conditions and make predictions about their trajectories.

## 2. How do you calculate drag force and time for a raindrop?

The drag force on a raindrop can be calculated using the formula Fd = 0.5 * ρ * v^2 * Cd * A, where ρ is the density of air, v is the velocity of the raindrop, Cd is the drag coefficient, and A is the cross-sectional area of the raindrop. The time taken for the raindrop to reach its terminal velocity can be calculated using the formula t = (2 * m * v) / Fd, where m is the mass of the raindrop.

## 3. What factors affect the drag force and time of a raindrop?

The drag force and time of a raindrop are affected by various factors such as the density and viscosity of the air, the velocity and mass of the raindrop, and the shape and size of the raindrop. These factors can also vary depending on the weather conditions and the environment in which the raindrop is falling.

## 4. How does the calculation of drag force and time for a raindrop relate to other scientific concepts?

The calculation of drag force and time for a raindrop is related to various scientific concepts such as fluid dynamics, aerodynamics, and kinematics. It involves the study of the forces acting on objects in motion and their effects on the trajectory and behavior of the object.

## 5. What are some practical applications of understanding drag force and time for a raindrop?

Understanding drag force and time for a raindrop has various practical applications, such as predicting the path of a raindrop during a storm, designing more efficient drainage systems, and improving the accuracy of weather forecasting models. It can also be applied in other fields, such as aviation and engineering, where knowledge of fluid dynamics and aerodynamics is essential.

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