How Do You Calculate the Coefficient of Kinetic Friction on an Incline?

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SUMMARY

The discussion focuses on calculating the coefficient of kinetic friction for a 3kg block sliding down a 30-degree incline. The acceleration of the block was determined to be 1.778 m/s² using the equation x = v₀ + 1/2at². Two methods were employed to find the coefficient of kinetic friction (u), yielding different results: u = 0.577 from the first method and u = 0.372 from the second. The conclusion drawn is that the first method is incorrect, as it assumes the force of friction equals mgsin(θ), which is not valid when ΣF ≠ 0.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Familiarity with trigonometric functions in physics
  • Knowledge of kinematic equations
  • Basic concepts of friction and forces on inclined planes
NEXT STEPS
  • Study the derivation of the coefficient of friction using free body diagrams
  • Learn about the implications of ΣF = 0 in static versus kinetic friction scenarios
  • Explore advanced kinematic equations for varying acceleration
  • Investigate the effects of different incline angles on friction coefficients
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Physics students, educators, and engineers interested in mechanics, particularly those studying motion on inclined planes and frictional forces.

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A 3kg block starts at the top of a 30 degree incline and slides 2m down the incline in 1.5 seconds.
a) Find acceleration of the block.
b) Find the coefficient of kinetic friction between the blcok and the incline.

For a) x = volt + 1/2at^2 --> a = 1.778m/s^2
For b) *here's where I'm having some problems*
I tried doing it two different ways and i get two different answers.

Way 1:
Ff = uFn
Ff/Fn = u
mgsinx/mgcosx=u
tanx=u
u = .577

Way 2:
ΣF=ma
mgsinx - umgcosx = ma
gsinx - ugcosx =a
a-gsinx/-gcosx = u
(1.778m/s^2 - 5m/s^2)/-(10*cos30) = u
u = .372

which way is wrong?
 
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So after reviewing what i typed in, i think that you can only use u = tanx when ΣF=0, is my assumption correct?
 
Way 1 is wrong, since the force of friction does not equal mgsinx.
 

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