# How do I calculate the work due to air drag when throwing a ball in the air?

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In summary, the conversation discusses how to find the work done due to gravity and drag on a ball thrown into the air with some velocity V. It is mentioned that the force is not constant, so it is not just a matter of finding d. Instead, it is the integral of the force with respect to the distance. The conversation also suggests using a method like Runge Kutta (RK4) with differential equations to calculate the result.

## Homework Statement

There isn't really a "problem statement", but more so a conceptual prompt.

Say you throw a ball in the air with some velocity V. The work done due to gravity and drag is Mgh + Fdragd. What I don't know how to do (and there is no additional information, the prompt is very open ended) is how to find that "d", or if that "d" is relevant at all. Perhaps I'm taking the wrong approach to this.

Know that this data needs to be graphed as a function of time through coding, but that part I can do just fine. It's simply the conceptual part of the equation that I'm not getting.

To make it clear, I'm not sure how to find the work due to gravity and drag on a ball thrown into the air with some velocity V.

## Homework Equations

F = kv2, F = 1/2ρ*V2A

As you can see from your equations, the force is not constant, so it is not just a matter of finding d. The work done against drag is therefore not just the product of the two. Instead, it is the integral of the force with respect to the distance.
You need to write down the differential equation of motion, starting with Fnet=ma. At some instant, at speed v upwards, what is the net force?

There's a solution if the ball is dropped vertically, I'm not sure if this could be used for a ball thrown upwards vertically:

http://en.wikipedia.org/wiki/Free_fall#Uniform_gravitational_field_with_air_resistance

Otherwise, you'll need to use a method like Runge Kutta (RK4) with differential equations to calculate the result.

To keep the sense of the direction of drag force correct, use F = - 1/2 ρ V |V| Cd A .

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## What is air drag?

Air drag, also known as air resistance, is a force that opposes the motion of an object as it moves through the air. It is caused by the collision of air molecules with the surface of the object.

## How does air drag affect objects?

Air drag can slow down the speed of an object, change its direction, and eventually cause it to come to a stop. It can also cause objects to lose energy and momentum as they move through the air.

## What factors affect the amount of air drag an object experiences?

The amount of air drag an object experiences depends on its size, shape, speed, and the density of the air it is moving through. Objects with larger surface areas and higher speeds experience more air drag.

## Can air drag be beneficial?

Yes, air drag can be beneficial in certain situations. For example, air resistance can help slow down objects like parachutes and gliders, allowing them to land safely. In sports such as skiing and cycling, air drag can also be used to improve performance by reducing the amount of force needed to move through the air.

## How do scientists study and calculate air drag?

Scientists study air drag through experiments and mathematical calculations. They use wind tunnels to simulate different air conditions and measure the forces acting on objects. They also use mathematical equations, such as the drag equation, to calculate the amount of air drag an object will experience based on its characteristics and the air conditions.