Deriving a differential equation for car motion

He is wondering if there are any other forces, such as gravity, that should be considered. The answer is that weight would affect tire traction, but if the tires are assumed to be rotating freely, it should not be a significant factor. The main force to consider is air drag, as long as it can be accurately represented. In summary, Chetan is looking for guidance on creating a differential equation for a moving car, taking into account initial velocity and forces like air drag and friction. He's questioning the impact of other forces like gravity, but the main focus should be on accurately representing air drag
  • #1
cytochrome
166
3
I'm looking at this scenario where a car is moving and then shifts into neutral. Knowing the initial velocity, how can I derive a differential equation?

I know the air drag and the frictional force... are there any other forces, like gravity, that should be included to make it realistic? I don't understand what a downward gravitational force would do for this problem
 
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  • #2
"Downward gravitational force" (weight) would affect the tire traction. But if you are assuming the tires are rotating freely and not dragging on the ground (no braking or acceleration), that should not be an issue. There will, of course, be friction in the wheel bearings.
 
  • #3
The dominant force is going to be the air drag. That should make things easy for you, if the air drag can be parameterized accurately.

Chet
 

1. What is a differential equation?

A differential equation is a mathematical equation that describes how a quantity changes over time. It involves the derivatives of the quantity with respect to one or more independent variables. In the context of car motion, a differential equation can be used to model the acceleration, velocity, and position of the car as it moves.

2. Why is it important to derive a differential equation for car motion?

Deriving a differential equation for car motion is important because it allows us to mathematically model and predict the behavior of a car as it moves. This can be useful in designing and testing new car designs, as well as understanding the factors that affect a car's motion, such as friction, air resistance, and driver inputs.

3. How do you derive a differential equation for car motion?

To derive a differential equation for car motion, we use the laws of motion, such as Newton's second law, to create a mathematical model of the forces acting on the car. This model can then be translated into a differential equation by taking the derivatives of the car's position, velocity, and acceleration with respect to time.

4. What factors are included in a differential equation for car motion?

A differential equation for car motion can include factors such as the car's mass, air resistance, friction, and the forces applied by the engine and brakes. It can also take into account external factors such as the slope of the road and the conditions of the surface the car is driving on.

5. Can a differential equation accurately predict a car's motion?

While a differential equation can provide a mathematical model of a car's motion, it may not always accurately predict the actual behavior of a car. This is because there are many real-world factors that can affect a car's motion, such as unpredictable weather conditions, human error, and mechanical failures. However, a well-derived differential equation can provide valuable insights and help improve our understanding of car motion.

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