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## Homework Statement

a 1500 kg car is moving up a 25 degree incline at a constant speed of 30 mph. the tires and road have an effective friction coefficient of u = 0.25 . determine the power output the engine must provide to keep the car moving at this speed. express your final answer in units of watts and horse-power. if an answer cannot be found then briefly explain why this is so.

## Homework Equations

Wnet = E_final - E_initial

Power = Work / Time

Power = Force (dot) Velocity

KineticE= 1/2 * Mass * Velocity^2

F_friction= u * F_normal

## The Attempt at a Solution

I assumed the answer can be found...

__step 1:__

I initially drew a Free Body Diagram:

Normal - perpendicular to the incline pointing above it

Push - parallel to the incline pointing up it

Friction - parallel to the incline pointing down it

MG - straight down

__Step 2:__

This is where I am stuck. What I believe I am trying to find is the energy consumed per time unit overcoming friction PLUS the energy consumed per time unit to keep the car moving at 30mph. If this is correct I still am struggling with how to use the equations to find power.(mostly how to go from Force to Work to Power)

__my attempt to set up the equation:__

30mph = 13.4112m/s

F_f = .25 * sin(65) * 1500 * 9.8 = 3330.68 N

W_f = 3330.68 * delta X

Above where would I even get (delta X)

KE= (1/2) * 1500 * 13.4112^2 = 134895 J

W_f + KE = Total Energy

after this I don't have a time defined to turn work to power