Where does a car’s energy go when it comes to a stop? Is it possible to capture this energy?

You have been tasked by an electric vehicle manufacturer to design a computational model that will be part of a visual display for an electric vehicle that shows the energy captured using regenerative braking. The model will need to consider the mass of the vehicle, its speed, and its regenerative braking efficiency.

In order to design the visual display, an engineer starts by identifying the elements of the system and how they are related. An engineer may also simplify the problem by selecting the most important features of the situation and removing unnecessary complexity. An engineer will also create representations of the system to help visualize and think about the system.

Today you are going to:

(1) Analyze a system involving an electric car coming to a stop.

(2) Create a visual representation of the system and solve a problem.

(3) Generalize the problem solving process into a series of steps.

Let’s get started!

Background Information

An object in motion possesses kinetic energy and to bring the object to a stop this kinetic energy must be removed. Removing the kinetic energy can be accomplished by dissipating the energy to the atmosphere through friction or by converting it into another form of energy.

The most common type of braking is a mechanical brake which inhibits motion through friction brake pads. A mechanical brake applies a friction force to convert the kinetic energy of the vehicle into thermal energy which then dissipates into the atmosphere.

As with any system, the process of braking must follow the principle of conservation of energy. Energy cannot be created or destroyed but only converted from one form to another.

The energy present in an object in motion is given by the following equation:

where,

• is the mass of the object in kilograms (kg).

• is the velocity of the object in meters per second (m/s).

• is the kinetic energy in joules (J)

Friction braking is the most commonly used braking method in modern vehicles. It involves the conversion of kinetic energy to thermal energy by applying friction to the moving parts of a system. The friction force resists motion and in turn generates heat, eventually bringing the velocity to zero. The energy taken from the system is given by the following equation:

where,

• is the force of friction in newtons (N).

• is the stopping distance in meters (m).

• is the thermal energy produced by the brakes in Joules.

Applying conservation of energy, the thermal energy produced must equal the kinetic energy dissipated.

Regenerative Braking explained by Greg Solberg of Tesla Motors
“In a battery-powered electric vehicle, regenerative braking is the conversion of the vehicle’s kinetic energy into chemical energy stored in the battery, where it can be used later to drive the vehicle. It is braking because it also serves to slow the vehicle. It is regenerative because the energy is recaptured in the battery where it can be used again.

The kinetic energy stored in a moving vehicle is related to the mass and speed of the vehicle by the equation E = ½mv². All else being equal, if your car is twice as heavy it has twice the kinetic energy and if it is moving twice as fast it has four times the kinetic energy. Any time your car slows down the kinetic energy stored in the vehicle has to go somewhere. Let’s take a look at where this energy goes. There is always some kinetic energy consumed by the rolling resistance, mechanical friction, and aerodynamics of your car. These bits of energy go into heating the road, the surrounding air, and various spinning parts in your car. But the vast majority of the kinetic energy is converted into heat by your brake pads when you stomp on the brakes. In the Tesla Roadster, regenerative braking recovers some energy [estimated at around 64%] that would otherwise have been wasted in the brakes.”

References

http://energyeducation.ca/encyclopedia/Braking

https://en.wikipedia.org/wiki/Regenerative_brake

https://www.tesla.com/blog/magic-tesla-roadster-regenerative-braking