engine of a 2000 kg Mercedes going up
Pike's Peak delivers energy to its drive wheel at the rate 100 kW
Neglecting air resistance, what is the largest speed the car can sustain on the steep Pike's Peak mountain highway, where the road is 30 to the horizontal? The acceleration due to gravity is 10 m/s?
To find the largest speed the car can sustain on the Pike's Peak mountain highway, we need to consider the forces acting on the car. The engine delivers energy to its drive wheels, which we can assume is used to overcome the force of gravity and provide enough force for the car to move up the 30° inclined road.
The force of gravity pulling the car down the inclined road is given by the formula F = mg*sin(θ), where m is the mass of the car (2000 kg), g is the acceleration due to gravity (10 m/s²), and θ is the angle of the road (30°).
F = (2000 kg)(10 m/s²)(sin(30°)) = 10,000 N
The power delivered by the engine to the drive wheels is given as 100 kW. We can convert this to force using the formula P = Fv, where P is power (100,000 W), F is force (10,000 N), and v is velocity.
100,000 = 10,000v
v = 10 m/s
Therefore, the largest speed the car can sustain on the steep Pike's Peak mountain highway without considering air resistance is 10 m/s.