How much power does a 1500 kg car need to go up a 4 degree incline highway with a constant speed of 80km/hr? The surface of the highway is rough and the coefficient of kinetic friction is approximately 0.2.

I think I should use P = Fv(cosΘ).
I just wanna know what would be my Force?

Question

How much power does a 1500 kg car need to go up a 4 degree incline highway with a constant speed of 80km/hr? The surface of the highway is rough and the coefficient of kinetic friction is approximately 0.2.

I think I should use P = Fv(cosΘ).
I just wanna know what would be my Force?

anonymous · Answer

I find that drawing a free body diagram, or force diagram helps for these problems. Remember the car needs to work against the force of gravity and friction, and Newton's first law would dictate that for constant speed the force from the car would equal that of gravity and friction if it is to go at a constant speed.

Be careful using $$P=Fv(\cos \theta)$$ as that would only work if there was no friction.  I prefer to find the component of gravity acting down the ramp.

anonymous · Answer

Here is the free body diagram and the equivalent diagram where the gravitational force is broken into it's components.

anonymous · Answer

Then which equation should I use? Sorry, but I don't know much about this free body diagram. Can you kindly teach me? Thanks so much

anonymous · Answer

Sure, a free body diagram illustrates all the forces acting on a object.  As this car tries to travel up the incline (ramp) it has the following forces acting on it: Normal force directed away from the road, Gravitational force directed straight down, a frictional force from the road in the direction opposite the car's motion, and the force from the car's engine propelling it forward.

All we are concerned with in this problem is the forces in the direction of motion.  For us that means the force from the car, the friction, and the part of gravity acting down the ramp.  At a constant speed, Newton's first law tells us that the net force would be zero, so the friction and gravitational component down the ramp have to equal the force from the car up the ramp.  If we find that force we can solve using P=Fv.

So the first thing to do is calculate the friction $$Ff=muN$$ and then calculate the gravitational component down the ramp.  Both calculations will rely on dividing the gravitational force into it's components (because the normal force N is equal to the component of gravity against the ramp).

anonymous · Answer

Is the frictional force 2940N? Am I right?

anonymous · Answer

Yes, that's right.