Deriving EOM to Describe Wheelie Motion of a Car

In summary, the conversation discusses the need to derive equations of motion for a car in order to determine the force required for it to perform a wheelie. The problem is simplified by assuming the car is a rectangle sliding on a horizontal surface with a horizontal force acting at the point of contact. The derived equations include the force equation, the vertical force equation, and the equation for rotation. There is a struggle in applying the equations of motion for a rigid body to the problem.
  • #1
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Homework Statement



Equations of motion are to be derived to describe the motion of a car(rear wheel drive) at rest which then accelerates to perform a wheelie.

Basically, I need equations of motion that would help me determine the force that the rear wheels exert on the car in order to cause a wheelie.

Homework Equations





The Attempt at a Solution



I have simplified the problem by assuming the car is a rectangle sliding on a horizontal surface with a horizontal force acting where the rectangle meets the surface.

This leads to the EOMs that I THINK are correct

[tex]\[F = m \ddot{x}\][/tex]
[tex]\[N - mg = m \ddot{y}\][/tex]
[tex]\[-mgLcos(\theta ) + NLcos(\theta ) = I \ddot{\theta }\][/tex]

I made a guess that I should sum moments about the edge where the force is applied.

The problem that I am having is that the equation for rotation contains 0 x-direction force terms, but it is obviously the x acceleration which causes the rotation.
 
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  • #2
I think that I need to use the equations of motion for a rigid body, but I am having trouble applying them to this problem. Any help would be greatly appreciated.
 

Related to Deriving EOM to Describe Wheelie Motion of a Car

1. How do you derive the equations of motion (EOM) for describing wheelie motion of a car?

To derive the EOM for wheelie motion, we use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. We also take into account the moments of inertia of the car's body and wheels, as well as the torque applied by the engine and the friction forces acting on the wheels. By analyzing the forces and moments acting on the car, we can derive the EOM for wheelie motion.

2. What is the significance of deriving EOM for describing wheelie motion of a car?

The EOM for wheelie motion allows us to mathematically model and predict the behavior of a car performing a wheelie, which is a common maneuver in motorsports and stunt driving. This information is useful for understanding the forces and energy involved in wheelie motion, as well as for optimizing the design and performance of vehicles.

3. What factors affect the EOM for describing wheelie motion of a car?

The EOM for wheelie motion is affected by various factors such as the mass and distribution of weight of the car, the engine power and torque, the surface and traction of the wheels, and any external forces acting on the car, such as wind or drag. The shape and dimensions of the car's body and wheels also play a role in determining the EOM.

4. Can the EOM for describing wheelie motion be applied to different types of cars?

Yes, the EOM for wheelie motion can be applied to any type of car, as long as the relevant parameters and variables are taken into account. However, the equations may need to be adjusted for different types of vehicles, such as cars with different weight distributions, engine placements, or wheel sizes.

5. Are there any limitations to the EOM for describing wheelie motion of a car?

Like any mathematical model, the EOM for wheelie motion may have limitations in accurately predicting the behavior of a car in real-world situations. Factors such as driver skill, road conditions, and mechanical failures can affect the actual motion of a car performing a wheelie. Additionally, the model may not take into account all possible forces and factors, so its predictions may not be entirely accurate.

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