# Work and energy conservation (help me understand!)

1. Jul 10, 2010

### mizzy

1. The problem statement, all variables and given/known data
A 2.1 x 10^3kg car starts from rest at the top of a 5.0m long driveway that is inclined at 20degrees with the horizontal. If an average friction force of 4.0 x 10^3N impedes the motion, find the speed of the car at the bottom of the driveway.

2. Relevant equations
Work-energy theorum: Wnet = delta KE

3. The attempt at a solution
I don't know where to start. Do I need to consider potential energy too? or just kinetic energy?

What I did is to start with this equation: Wnet = KEf - KEi
Since the car started from rest, KEi = 0. Therefore, Wnet = 1/2mvf^2. Solve for vf. Am i right? It's on an incline, do I need to include the x component of gravitational force?

2. Jul 10, 2010

### xcvxcvvc

$$KE_i + U_i = KE_f + U_f + W_{friction}$$
Initial kinetic energy and final potential energy can be set to zero. To find the total force of friction, you must multiply the distance the car moved by that average force (w = fd).
$$U_i = KE_f + F_{friction}D_{driveway}$$

Make sure you use the correct distance for the driveway(the 5 meter hypotenuse) and the correct height for the potential energy (the y-component of that hypotenuse using that 20 degrees)

3. Jul 10, 2010

### mizzy

Why is the Wfriction on the right side of the equation??

4. Jul 10, 2010

### mizzy

I got the answer wrong =(

For Wfriction, I took the Force of friction given x the distance of 5.00m. For the potential energy, I used 5 cos 20.

is that right?

5. Jul 11, 2010

### Staff: Mentor

If you include the work done by all forces (there are only two here) then you don't need to consider potential energy. (You automatically include it by using the force of gravity.)

Perfectly correct.

Definitely. Since the car is moving in the x direction, you must consider all forces in the x direction.

6. Jul 11, 2010

### Staff: Mentor

(I thought I responded to this early this morning, but I must have deleted the post by mistake.)
Good.
5 cos 20 is the horizontal component of the distance. How do you calculate the gravitational PE?

It's perfectly OK to use the conservation of energy equation as suggested by xcvxcvvc, in which case you include gravitational PE. You'll get the same answer as you would using the Work - KE theorem.

7. Jul 11, 2010

### xcvxcvvc

Yeah, you're right. You usually write it in terms of work done. I was thinking of that work quantity as positive. It should be on the initial side, and it should be negative.

Initial energy + work done by friction (which is negative) = final energy