Solving Friction up a Slope: Coefficient of Friction

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The problem involves calculating the coefficient of friction for a book bag sliding up a hill. Given the mass of the bag, its initial speed, and the hill's angle, the calculations show that the normal force is 161N and the acceleration is -3.33 m/s². The frictional force is determined to be 63.27N, leading to a coefficient of friction of approximately 0.393. However, some participants note that the gravitational component along the slope may not have been fully considered in the calculations. Understanding the role of the parallel gravitational force is crucial for accurate results in similar problems.
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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 = \mucosx
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 = \mumgcosx
63.27 = \mu19*9.8*cos30
\mu = .393

Is this correct? Is the parallel component required in this case? In what cases is it required?
 
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you mean it slides down a hill? O.o
 
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
 

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