Answer:
The coefficient of static friction is 1.13x10⁻⁵.
Explanation:
We can find the coefficient of static friction as follows:
[tex] -F_{\mu} = ma [/tex]
[tex] -\mu N = ma [/tex]
[tex] -\mu mg = ma [/tex]
[tex] \mu = -\frac{a}{g} [/tex] (1)
Where:
[tex] F_{\mu}[/tex]: is the friction force
m: is the mass of the box
a: is the acceleration
g: is the gravity = 9.81 m/s²
First, we need to calculate the acceleration:
[tex] v_{f} = v_{0} + at [/tex] (2)
Where:
[tex] v_{f}[/tex] is the final speed of the box = 0
[tex] v_{0}[/tex] is the initial speed of the box
t is the time = 600 s
[tex] v_{f}^{2} = v_{0}^{2} + 2aX [/tex] (3)
Where:
X: is the distance traveled by the box = 20 m
By solving equation (2) for [tex]v_{0}[/tex] and by entering into equation (3) we have:
[tex] 0 = (-at)^{2} + 2aX [/tex]
[tex] a = \frac{-2X}{t^{2}} = \frac{-2*20 m}{(600 s)^{2}} = -1.11 \cdot 10^{-4} m/s^{2} [/tex]
Now, we can calculate the coefficient of static friction by entering the above value into equation (1) :
[tex] \mu = -\frac{a}{g} = -\frac{-1.11 \cdot 10^{-4} m/s^{2}}{9.81 m/s^{2}} = 1.13 \cdot 10^{-5} [/tex]
Therefore, the coefficient of static friction is 1.13x10⁻⁵.
I hope it helps you!
