If a #8 kg# object moving at #18 m/s# slows to a halt after moving #180 m#, what is the coefficient of kinetic friction of the surface that the object was moving over?

Question

Adrian Ayala · Accepted Answer

k=0.0917

#m:# mass of object
#g=9,81#
#G=m.g=8 . 9,81=78,48 N# "Gravity of object"
#N=-G=-78,48 N# "reaction to object by surface"
#F=k.N=-k.78,48 N#" friction force between surface and object"

#step 1:#

Object have lost the kinetic energy between the Point A and B.
#Delta E_k=1/2 m(0^2-18^2)#
#Delta E_k=1/2 8 (0+324)#
#Delta E_k=4* 324=1296 # Joule

#step 2:#
#W:# work doing by friction force
#Delta E_k=W#
#1296=F * Deltax#
#Delta x=180 meters#
#1296=k*78,48*180#
#1296=k*14126,4#
#k=0.0917# "has no unit"

Axel Acevedo · Answer

undefined To find the coefficient of kinetic friction (μk), you can use the formula:

μk = (force of friction) / (normal force)

First, calculate the force of friction using Newton's second law:

Force of friction = mass × acceleration

Acceleration = (final velocity^2 - initial velocity^2) / (2 × distance)

Then, calculate the normal force:

Normal force = mass × gravity

Finally, plug the values into the formula for the coefficient of kinetic friction:

μk = (force of friction) / (normal force)