Solving Friction up a Slope: Coefficient of Friction

[Intrusionv2]

Homework Statement

Lindsey's car is driving up a hill when her book bag, which she forgot on the roof, falls off. The bag has a mass of 19kg and slides up the hill 60 meters from its initial speed of 20m/s to rest. If the hill climbs at an angle of 30 degrees then what was the coefficient of friction?

Homework Equations

Fn = mgcosx
Ff = $$\mu$$cosx
F = ma
Vf² = Vi² + 2ad
Fp = mgsinx (?)

The Attempt at a Solution

Fn = 19*9.8cos30 = 161N


Vf² = Vi² + 2ad
0 = 20² + 2a(60)
-400 = 120a
a = -3.33 m/s²

F = ma
F = 19 * -3.33 = 63.27N

Ff = $$\mu$$mgcosx
63.27 = $$\mu$$19*9.8*cos30
$$\mu$$ = .393

Is this correct? Is the parallel component required in this case? In what cases is it required?

 

[selter01]

you mean it slides down a hill?

 

[lanedance]

I would draw an FBD (Free Body Diagram) before attempting this one

Looks close...
Acceleration & net force on the book look correct...

however the book also has a gravity component along the slope, which i don't think has been taken into account - this will also act to slow down the book