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## Homework Statement

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.

(A) v = 2P/(mg)

(B) v = 2P/(√3mg)

(C) v = 2P/(µmg)

(D) v = τω/(mg)

(E) v = τω/(µmg)

## Homework Equations

## The Attempt at a Solution

I don't even know how to start on this. I'm supposing that the first step is finding a relationship between the torque, power, and velocity , but I don't know how to do that. Thoughts?