If an object is moving at #6 m/s# over a surface with a kinetic friction coefficient of #u_k=20 /g#, how far will the object continue to move?

1 Answer
Dec 17, 2015

Answer:

I found #0.9m#

Explanation:

Your object will move under the acton of Friction that wll produe a negative acceleration and eentually stop it.

To find this acceleration we can use Newton's Second law:

#SigmavecF=m veca#

where the only force will be friction (in the opposite direction to the movement so it will need to enter Newton's Law with a minus sign) given as:

#f_k=u_kN#

where:

#N=#normal reaction#=#Weight#=mg# in this case of horizontal movement.

So you have:

#-f_k=ma#
#-u_kN=ma#
#-u_kmg=ma#
#-20/cancel(g)cancel(m)cancel(g)=cancel(m)a#
so that #a=-20m/s^2#
we now use the relationship:
#v_f^2=v_i^2+2ad#
where #v_f=0# (stops)
#0=6^2-2*d*20#
#d=36/40=0.9m#