# How Does Rain Impact the Drag Force on a Moving Car?

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In summary, the problem involves an automobile traveling at 80 km/h through heavy rain, with raindrops falling vertically at 10 m/s. The automobile is shaped like a rectangular box and the question asks about the rate at which raindrops strike the front and top of the car, as well as the momentum and drag force exerted by the raindrops on the car. The equations used include Fdt=d(mv) and mv+m1v'=(m+m1)v'' for inelastic collision. The attempt at a solution involved calculating the volume of air the car passes through in a given time interval and using the mass of raindrops per cubic meter to determine the mass of raindrops hitting the car. However, this approach did not
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## Homework Statement

An automobile is traveling at speed of 80 km/h through heavy rain. The raindrops are falling vertically at 10 m/s and there are 7*10^-4 kg of raindrops in each cubic meter of air. For the following calculations assume that the automobile has the shape of a rectangular box 2m wide, 1.5 high and 4m long.
a) At what rate (kg/s) do the raindrops strike the front and top of the automobile?
b) Assume that when a raindrop hits, it initially sticks to the automobile, although it falls off later. At what rate does the automobile give momentum to the raindrops? What horizontal drag force do the raindrops exert on the automobile?

## Homework Equations

Fdt=d(mv)
mv+m1v'=(m+m1)v'' for inelastic colision

## The Attempt at a Solution

Ok, so for a, I tried the following. The volume of air the upper and front parts of the automobile are going to go through is (w*h+w*l)$$\Delta$$t*vcar, for some interval $$\Delta$$t. If there are 7*10^-4kg of raindrops in a cubic meter, than the mass of raindrops hitting the car in that period is just (w*h+w*l)$$\Delta$$t*vcar*7*10^-4. This is by my textbook not correct. I also tried transforming to the reference frame of the car, but still didn't get the right answer.
I guess for b:
mcarvcar+$$\Delta$$mvrain=(m+$$\Delta$$m)vfinal
$$\Delta$$m=$$\Delta$$t*rate, than take take $$\Delta$$t$$\rightarrow$$0.

FF=mcarvcar-mcarvfinal However, I'm not sure if this makes sense, and I don't know how to take the values for the rate. Could you please help? Thanks!

and assume that rate is constant. However, I am not sure how to calculate v after the collision, because I need to know the mass of the raindrop to use the equation. I am also not sure how to calculate the horizontal drag force.

I appreciate your attempt at solving the problem and your use of equations to approach the problem. However, there are a few things that can be improved in your attempt. First, for part a, you need to take into account the cross-sectional area of the car that the raindrops are hitting. In this case, it would be 2m*1.5m = 3m^2 for the front and 2m*4m = 8m^2 for the top. So the total volume of air that the raindrops are hitting would be (3+8)*Deltat*vcar, and the mass of raindrops hitting the car would be this volume times the density (7*10^-4 kg/m^3). This would give you the rate of raindrops striking the car in kg/s.

For part b, you are correct in using the conservation of momentum equation. However, you need to consider the velocity of the raindrop after the collision, which would depend on the mass of the raindrop and the mass of the car. You can use the given dimensions of the car to calculate its mass, and then use that to calculate the velocity of the raindrop after the collision. As for the horizontal drag force, you can use the equation F = (1/2) * Cd * rho * A * v^2, where Cd is the drag coefficient (which you can look up for a rectangular box shape), rho is the density of air, A is the cross-sectional area of the car, and v is the velocity of the car.

Overall, your approach is on the right track, but make sure to consider all the relevant variables and equations in your calculations.

## 1. What is horizontal drag due to rain?

Horizontal drag due to rain refers to the force that raindrops exert on objects as they fall through the air. This force is caused by the air resistance or drag that the raindrops experience as they move through the atmosphere.

## 2. How does horizontal drag due to rain affect objects?

Horizontal drag due to rain can affect objects in various ways. It can slow down the movement of objects, change their direction, and even cause them to fall to the ground. The magnitude of the effect depends on factors such as the size and shape of the object and the intensity of the rain.

## 3. How is horizontal drag due to rain calculated?

Horizontal drag due to rain is calculated using the drag equation, which takes into account factors such as the density and viscosity of the air, the velocity of the raindrops, and the surface area of the object. It is a complex calculation that is typically done using computer models.

## 4. Can horizontal drag due to rain be reduced?

Yes, horizontal drag due to rain can be reduced by making changes to the shape or surface characteristics of objects. For example, aerodynamic shapes or smooth surfaces can help to minimize the drag force and reduce the impact of rain on objects.

## 5. How does horizontal drag due to rain affect vehicles?

Horizontal drag due to rain can significantly impact the movement and performance of vehicles. It can increase fuel consumption, reduce speed and acceleration, and even cause hydroplaning on wet roads. As such, it is an important consideration for vehicle design and safety.

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