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Main Question or Discussion Point
This is from the 2014 F=ma exam:
The maximum torque output from the engine of a new experimental car of mass m is τ. The maximum rotational speed of the engine is ω. The engine is designed to provide a constant power output P. The engine is connected to the wheels via a perfect transmission that can smoothly trade torque for speed with no power loss. The wheels have a radius R, and the coefficient of static friction between the wheels and the road is μ.
What is the maximum sustained speed v the car can drive up a 30 degree incline? Assume no frictional losses and assume μ is large enough so that the tires do not slip.
The solution is as follows:
The fundamental idea is P = Fv where F is the component of the weight parallel to the incline. Then
v = P/mg sin θ Since θ = 30◦, the answer is v = 2P/mg.
Why does the solution ignore the effects of friction when calculating F. Shouldn't F=mgsin(theta)+mu*Fn?
Thanks!
The maximum torque output from the engine of a new experimental car of mass m is τ. The maximum rotational speed of the engine is ω. The engine is designed to provide a constant power output P. The engine is connected to the wheels via a perfect transmission that can smoothly trade torque for speed with no power loss. The wheels have a radius R, and the coefficient of static friction between the wheels and the road is μ.
What is the maximum sustained speed v the car can drive up a 30 degree incline? Assume no frictional losses and assume μ is large enough so that the tires do not slip.
The solution is as follows:
The fundamental idea is P = Fv where F is the component of the weight parallel to the incline. Then
v = P/mg sin θ Since θ = 30◦, the answer is v = 2P/mg.
Why does the solution ignore the effects of friction when calculating F. Shouldn't F=mgsin(theta)+mu*Fn?
Thanks!
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