Power Required to Climb 10% Grade at 35 m/s with 600N Force

[spj1]

Car travels up 10% grade at constant speed of 35 m/s. The car is 2000 kg and requires a total force of 600N on a regular, flat incline. What is the power required to get up the grade?




P=FxV




%10 percent incline = arctan(.1)... theta = 5.7, so the displacement would be about 10.1 (depending how you treat the grade). Then I plugged into the equation P = Fcos(theta)(displacement)(velocity)... This does not yield the correct answer! It's got to be how I'm dealing with the grade. I'm not sure what to do with it. Any hints?

 

[PhanthomJay]

I'm guessing from the problem that a 'flat incline' is one with no slope, and that it requires 600N force to keep the car moving at 35m/s on a horizontal surface (apparently to overcome friction and air drag, etc.). So when it moves up the incline, it must provide 600N PLUS an additional component to overcome the gravity component acting down the plane. No need to look at displacements, just calculate the required 'F' and multiply it by V. Your angle theta is correct.