If an object is moving at #4 m/s# over a surface with a kinetic friction coefficient of #u_k=80 /g#, how far will the object continue to move?

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Answer 1 · 2017-01-29T17:20:17

The object will travel only #0.10m# (because a kinetic coefficient of #80/g# is very large!)

This problem is most easily done by conservation of energy.
Two energy forms are involved:
A change in kinetic energy: #1/2mv_f^2-1/2mv_i^2#

Frictional heating: #muF_NDelta d#

The equation for conservation of energy is, in this case

#1/2mv_f^2-1/2mv_i^2+mumgDelta d=0#

Notice that we can divide every term by the mass m, (including the right side of the equation)

Also, #v_f=0# , and inserting the values for #mu#, #v_i# and g, we get:

#-1/2(4)^2+(80/g)(g)Delta d=0#

Cancel the two #g#'s

#-1/2(4)^2+(80)Delta d=0#

#-8+80Delatd=0#

#80Deltad=8#

#Deltad=0.1m#