# Statics

In the movie The Fast and the Furious (2001) there is a car race between the film’s two main characters Brian and Dominic. During the race the front of Dominic’s car comes off the ground like a motorcycle popping a wheelie.

This is similar to a case of dynamical equilibrium. In truth the cars should be accelerating in the x direction, but we can clearly see that there is no acceleration is y direction and no net torque. Dominic’s car in the film is a 1970 Dodge Charger. We can look up that cars properties. The mass of the car is 1650kg, the wheelbase (distance between the wheels) is 3.0m and the wheel diameter is 0.33m. The forces on the car are gravity which acts at the car’s center of mass, the normal force which acts on at the wheel and the friction force between the tire and the road which accelerates the car. The forces in the y-direction therefore give us $\sum F_y = F_N - mg = 0$

So $F_N = mg$. If the car is raised to an angle of θ to the road then the torques around the axis of the back wheel would be $\sum \tau = mg(1.5m)\sin \theta - F_{fr}(0.165m) = 0$

So we get that $F_{fr} = 9mg\sin \theta$. If θ = 30 then $F_{fr} = 4.5mg = 72,765 N$.  The acceleration in the x direction would be 4.5g or 44.1m/s².  This is why you don’t see this happen to often, most cars can not accelerate this quickly.

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