Question

Calculate the power output needed for a 950-kg car to climb a 2.00° slope at a constant 30.0 m/s while encountering wind resistance and friction totaling 600 N.

a) 13.4 kW
b) 17.5 kW
c) 20.1 kW
d) 25.8 kW

Answer 1

The power output needed for the car to climb the slope is 13.4 kW.

Step-by-step explanation:

To calculate the power output needed for the car to climb the slope, we need to determine the net force acting on the car and the distance it travels. The net force is the sum of the force due to wind resistance, friction, and the component of the car's weight parallel to the slope.

The force due to wind resistance and friction totals 600N. The component of the car's weight parallel to the slope is given by mg sin(θ), where θ is the slope angle (2.00° in this case).

Using the formula P = Fv, where P is power, F is force, and v is velocity, we can calculate the power output:

P = (600N + (950kg)(9.8m/s^2)sin(2.00°))(30.0m/s) = 13.4 kW