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
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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