Work-Kinetic Energy Theorem problem

[anne921]

Homework Statement

A 2.1 X 10^3 kg car starts from rest at the top of a driveway that is sloped at an angle of 20.0 degrees with the horizontal. An average friction force of 4.0 X 10^3 N impedes the car's motion so that the car's speed at the bottom of the driveway is 3.8 m/s. What is the length of the driveway?

Homework Equations

Wnet - ΔKE = KEf - KEi
Wnet = Fd cos θ
Fnet = mgsinθ - Fk

The Attempt at a Solution

I understand the basic idea of how to solve this problem. I think I would calculate Wnet using 1/2 mvf^2 (vi = 0); solve for Fnet and then substitute these values into solve for d by rearranging Wnet = Fdcosθ. My problem is that the key defines two angles - θ and θ'; with θ=20 degrees and θ' = 0. I don't understand where θ' comes into the picture. I am a Chemistry teacher trying to teach an intro physics course and I need some concrete help!

 

[gneill]

Presumably the θ' represents the angle that the friction force makes with the line of motion of the car (i.e., it acts parallel to the slope). Frictional forces always act to directly oppose the motion.

The other angle, θ, tells you the energy obtained from gravitational PE for a given distance traveled along the slope (since you can calculate the drop in height for the distance traveled).

It boils down to a conservation of energy problem; Energy gained through the drop in height in a gravitational field, energy lost to friction, remainder goes to KE of the car.

 

[anne921]

Thank you - that makes perfect sense. I didn't see that. I am finding that my biggest obstacle seems to be that I have difficulty seeing everything that is there. I appreciate your help!