How Do You Calculate the Speed of a Car Down an Inclined Driveway with Friction?

[mizzy]

Homework Statement

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.

Homework Equations

Work-energy theorum: Wnet = delta KE

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?

 

[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)

 

[mizzy]

$$KE_i + U_i = KE_f + U_f + W_{friction}$$
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)

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

 

[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?

 

[Doc Al]

I don't know where to start. Do I need to consider potential energy too? or just kinetic energy?

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.)

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?

Perfectly correct.

It's on an incline, do I need to include the x component of gravitational force?

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

 

[Doc Al]

(I thought I responded to this early this morning, but I must have deleted the post by mistake.)

For Wfriction, I took the Force of friction given x the distance of 5.00m.

Good.

For the potential energy, I used 5 cos 20.

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.

 

[xcvxcvvc]

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

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