An object with a mass of #12 kg# is on a surface with a kinetic friction coefficient of # 2 #. How much force is necessary to accelerate the object horizontally at # 14 m/s^2#?
1 Answer
Answer:
Explanation:
We're asked to find the necessary applied force that must act on an object to make the object accelerate at
There will be two forces acting on the object:

an applied force (directed in the positive
#x# direction, although this is arbitrary) 
the kinetic friction force
#f_k# (directed in the negative direction, because it will oppose motion)
The net force equation is therefore
#ul(sumF_x = ma_x = overbrace(F_"applied")^"positive"  overbrace(f_k)^"negative"#
We're given that the mass
#sumF_x = ma_x = (12color(white)(l)"kg")(14color(white)(l)"m/s"^2) = color(red)(ul(168color(white)(l)"N"#
Updating our equation:
#sumF_x = F_"applied"  f_k = color(red)(168color(white)(l)"N"#
The frictional force
#ul(f_k = mu_kn#
The normal force magnitude
#f_k = mu_kmg = (2)(12color(white)(l)"kg")(9.81color(white)(l)"m/s"^2) = color(green)(ul(235color(white)(l)"N"#
Plugging this in for
#F_"applied"  color(green)(235color(white)(l)"N") = color(red)(168color(white)(l)"N"#
Therefore,
#color(blue)(ulbar(stackrel(" ")(" "F_"applied" = 403color(white)(l)"N"" "))#
The necessary force is thus