If an object is moving at #8 m/s# over a surface with a kinetic friction coefficient of #u_k=64 /g#, how far will the object continue to move?

1 Answer
Apr 11, 2018

Answer:

The distance is #=0.5m#

Explanation:

The coefficient of kinetic friction is

#mu_k=F_r/N#

Let the mass of the object be #=mkg#

Then,

The normal force #N=mg#

The acceleration due to gravity is #g=9.8ms^-2#

Therefore,

#F_r=mu_kN=mu_kmg#

But according to Newton's Second Law

#F=ma#

Therefore,

#ma=mu_kmg#

The decelleration is #a=mu_kg#

Apply the equation of motion

#v^2=u^2+2as#

#0=8^2-2mu_kgs#

#mu_k=64/g#

The distance is

#s=64/(2*64/g*g)=1/2=0.5m#