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An object with a mass of #8 kg# is on a plane with an incline of # - pi/12 #. If it takes #12 N# to start pushing the object down the plane and #9 N# to keep pushing it, what are the coefficients of static and kinetic friction?

Answer 1

Olivia Askew

I assume that the angle of inclination is #pi/12# instead provided ,
we know for that

from the FBD diagram we can conclude that

#f_("static")=mgmucostheta#

#f_("dynamic")=mgmusintheta#

substituting the values you can get your answer (here a in the image is the angle you provided)

#mu_("static")=f_("static")/(mgcostheta)#

#mu_("dynamic")=f_("dynamic")/(mgsintheta)#

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Answer 2

Nicholas Agrusa

The coefficient of static friction is ( \mu_s = \tan(\theta) ), where ( \theta = -\frac{\pi}{12} ). The coefficient of kinetic friction is ( \mu_k = \tan(\phi) ), where ( \tan(\phi) = \frac{9}{mg} ) with ( m = 8 , \text{kg} ) and ( g ) as the acceleration due to gravity.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.