Answer:
The value is [tex]\mu_k = 0.102 0[/tex]
Explanation:
From the question we are told that
The initial speed is [tex]u = 10 \ m/s[/tex]
The distance traveled is [tex]d = 50 \ m[/tex]
Generally we can obtain the acceleration using the kinetic equation as follows
[tex]v^2 = u^2 + 2as[/tex]
=> [tex]a = \frac{v^2 - u^2 }{ 2s}[/tex]
=> [tex]a = \frac{0^2 - 10^2 }{ 2 * 50 }[/tex]
=> [tex]a = -1 m/s^2[/tex]
The negative sign shows that the pluck is decelerating
The force driving the pluck is mathematically evaluated as
[tex]F = ma[/tex]
This force is also equivalent to the frictional force acting on the pluck
So
[tex]ma = m * g* \mu_k[/tex]
=> [tex]\mu_k = \frac{a}{g}[/tex]
=> [tex]\mu_k = \frac{1}{9.8 }[/tex]
=> [tex]\mu_k = 0.102 0[/tex]
