Power required to move up an incline

[Ut Prosim]

Homework Statement

What power is needed to drive a car at 60 km/h up a 10% grade.

mass=1800kg
v=60km/h
theta=5.7106
g= 9.81 m/s^2

Homework Equations

P = Fv
P_ave= W/T
w=mg
F=ma

The Attempt at a Solution

I drew my diagram and FBD.

Since Fy=mAy=0..

0=N-sin(5.7106)
N=1755.2477

I know that Ax will be 0 since the velocity is constant, and I need to find the frictional constant:

mAx=0=F-uk-mgcos(5.7106)

But I don't have F, since it's what I'm trying to find..and this is where I've been stuck.

 

[LowlyPion]

Welcome to PF.

Maybe consider the rate of change of potential energy?

 

[Ut Prosim]

Problem with that is we haven't learned anything about energy yet so we are supposed to use regular Work, Power, and other Motion formulas.

 

[LowlyPion]

Problem with that is we haven't learned anything about energy yet so we are supposed to use regular Work, Power, and other Motion formulas.

OK. So consider then the force of gravity along the incline.

The car travels at 16.667 m/s, so in 1 second, what force was required to overcome gravity over that distance?

That gives you W per sec = F*d per sec.