# Energy consumed by variable drag force when stopping?

• charlie988
In summary, the conversation discusses the calculation of energy recovered through regenerative braking in a vehicle, taking into account air resistance. The equation for drag force is mentioned, as well as the challenge in integrating it to calculate work. Suggestions are given to express velocity as a function of either position or time to solve this problem.
charlie988
I was trying to roughly calculate the energy that could be recovered by regenerative breaking when bringing a vehicle to a stop, so I calculated to total kinetic energy and then tried to calculate the work done by air resistance that would take away from the energy that could be captured. So I calculated the drag force equation as F = 2.826 x v^2. Therefore, work would equal the the Integral of (2.826 x v^2)dx. But, this can't be integrated, as velocity is a separate variable than distance.

I'm not sure how to get around this to get the work calculation, but any help or suggestions would be greatly appreciated. Thanks.

You need to express velocity as a function of position.

Alternatively, you can express velocity as a function of time and rewrite the integral in terms of time.

That is, you need to get the relation between ##F## and ##x## from ##f=2.826v^2## first, or ##m\frac{dv}{dt}=2.826v^2.##

## What is variable drag force?

Variable drag force is a type of force that opposes the motion of an object through a fluid, such as air or water. It is dependent on the velocity, shape, and size of the object, and can change as these factors change.

## How does variable drag force affect energy consumption?

When an object is moving and experiences variable drag force, it requires energy to overcome this force and maintain its motion. As the drag force increases, more energy is needed to overcome it, resulting in higher energy consumption.

## What factors influence the amount of energy consumed by variable drag force when stopping?

The amount of energy consumed by variable drag force when stopping is influenced by the initial velocity of the object, the shape and size of the object, and the properties of the fluid it is moving through, such as density and viscosity.

## How can we calculate the energy consumed by variable drag force when stopping?

The energy consumed by variable drag force when stopping can be calculated using the equation E = 1/2 mv2, where m is the mass of the object and v is its velocity. This equation takes into account the kinetic energy of the object, which is converted into work to overcome the drag force.

## How can we reduce the amount of energy consumed by variable drag force when stopping?

There are several ways to reduce the amount of energy consumed by variable drag force when stopping. One way is to decrease the initial velocity of the object, as this will result in lower kinetic energy. Another way is to change the shape or size of the object to reduce the drag force. Additionally, using more aerodynamic designs can help reduce drag force and therefore decrease energy consumption.

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