How Much Work is Needed to Push a Car Up an Incline?

[Interception]

Homework Statement

What is the minimum work needed to push a 950-kg car 810m up along a 9.0 degree incline? (a) Ignore friction. (b) Assume the effective coefficient of friction working against the car is 0.25.

Homework Equations

I know that W=F x displacement x cos. In the second part of the problem, Friction= effective coefficient x Normal Force. Since this is an incline problem, I believe that the Normal Force is F=m x g(9.8 m/s^2) x cos (angle of inclination).



3. The attempt at a solution For the first part of the problem, I used the height of the the hill as the displacement since the work was being done by the vertical component (I assume, could be wrong) and found the height to be around 127m. I plugged that into the equation for Work and got 1.18x10^6 J, the F I used in the equation being the weight (mass x gravity).
For the second part, I found the normal force to be around 9195 N, and for the force applied by friction, I got 2.3x10^3. I then found the work performed by friction to be around -1.86x10^6 J (negative since it is going along the negative x-axis).
To try and find the work needed to move the car against friction, I added the work value from the first, disregarding friction, and the work performed by the friction thinking that an extra amount of work equivalent to the work done by the friction was needed to counterbalance.
The final answer I got was 3.04x10^ J. I feel like this answer is waaaay off and I can't check in the back of my book as it is an even number.

 

[ehild]

The final answer I got was 3.04x10^? J. I feel like this answer is waaaay off and I can't check in the back of my book as it is an even number.

Your method is correct, the numerical values too, but the exponent is missing from the final result.

ehild