This is another problem involving Dr Wang and his electric s

This is another problem involving Dr. Wang and his electric skateboard. Dr. Wang rides is skateboard up the hill behind the HREL building at a constant speed of 7 m/s. The hill behind the HREL building has a constant inclination of 3degree and the combined mass of Dr. Wang and the skateboard is 80 kg. Drag forces come from both rolling resistance and aerodynamic drag. The coefficient of rolling resistance (Crr) between the skateboard wheels and the ground is 0.02 (unitless). Just like sliding friction, the rolling friction is a function of the normal force: The aerodynamic drag force is a strong function of velocity: where the drag coefficient, a, is equal to 0.2 Ns^2/m^2 Given this information, what is the average power output of Dr. Wang\'s electric skateboard?

Solution

To maintain a constant speed, say V, the skateboard must produce a force equal to the the sum of the forces acting against the direction of motion. Lets call that as F.

Now, for a constant force of F acting on a body to maintain a constant speed of V, the power is given as:

P = F x V

Now, the skateboard is moving at 7 m/s at an inclination of 3 degrees.

So the net frictional force = 80 x 9.81 x 0.02 x Cos3 = 15.67449 N

Net force due to the gravitational pull = 80 x 9.81 x Sin3 = 41.07326 N

Also, the net drag force = av^2 = 0.2 x 49 = 9.8 N

So the net force = 66.54775 N

Therefore, the net power being generated = P = F x V = 66.54775 x 7 = 465.83425 Watts