Answer:
1.65
Explanation:
The equation of the forces along the horizontal direction is:
[tex]F-F_f = ma[/tex] (1)
where
F = 65 N is the force applied with the push
[tex]F_f[/tex] is the frictional force
m = 4 kg is the mass
[tex]a=0.12 m/s^2[/tex] is the acceleration
The force of friction can be written as [tex]F_f = \mu R[/tex] (2), where
[tex]\mu[/tex] is the coefficient of kinetic friction
R is the normal force exerted by the floor
The equation of forces along the vertical direction is
[tex]R-mg=0[/tex] (3)
since the bookcase is in equilibrium. Substituting (2) and (3) into (1), we find
[tex]F-\mu mg = ma[/tex]
And solving for [tex]\mu[/tex],
[tex]\mu = \frac{F-ma}{mg}=\frac{65-(4)(0.12)}{4(9.8)}=1.65[/tex]
