Answer:
0.06683
Explanation:
m = Mass of block = 3.85 kg
g = Acceleration due to gravity = 9.81 m/s²
[tex]\mu[/tex] = Coefficient of kinetic friction
x = Compression of spring = 0.103 m
k = Spring constant = 138 N/m
Work done against friction is given by
[tex]W=m\mu gs\\\Rightarrow W=\mu 3.85\times 9.81\times 0.29\\\Rightarrow W=10.952865\mu[/tex]
The potential energy of the spring is given by
[tex]P=\frac{1}{2}kx^2\\\Rightarrow P=\frac{1}{2}\times 138\times 0.103^2\\\Rightarrow P=0.732021\ J[/tex]
The potential energy and the work done against friction will balance the system
[tex]0.732021=10.952865\mu\\\Rightarrow \mu=\frac{0.732021}{10.952865}\\\Rightarrow \mu=0.06683[/tex]
The coefficient of kinetic friction between the horizontal surface and the block is 0.06683
