Solving a 2.1x10^3 kg Car Motion Problem

[princesspriya]

Homework Statement

a 2.1*10^3 kg car starts from rest at the top of a driveway that is sloped at an angle of 20 with the horizontal. An average friction force of 4.0*10^3 N impedes the car's motion so that the car's speed at the bottom of the driveway is 3.8m/s., What is the length of the driveway?

Homework Equations

The Attempt at a Solution

Ff=4000N
2100 Kg
X=20 degrees
Vf=3.8 m/s
Vi=0 m/s

Wnet=1/2MVf^2-1/2MVi^2
Wnet= 1/2*2000*3.8^2
Wnet= 15162 N

Wnet = FfdcosX
15162=4000cos20D
D=4.03m

but the book says 5.1m?
i can't figure out what i did wrong
thx for the help.

 

[Doc Al]

You forgot about gravity. Friction just slows the car; it's gravity which pulls it down the slope.

To find the net work you must consider all the forces: gravity and friction. (Don't forget that they act in different directions.)

 

[princesspriya]

i see so the force applied would be Fgravity*sin20 which would give me 7045.96 and i would subtract the Ff to get the total force. right?

 

[Doc Al]

i see so the force applied would be Fgravity*sin20 which would give me 7045.96 and i would subtract the Ff to get the total force. right?

Right!

 

[princesspriya]

thxxx