A box is sliding on a rough patch of ice, and the only horizontal force acting on it is friction. You observe that it slides to a stop in 600 seconds over a distance of 20 meters. What magnitude is coefficient of static friction between the box and the ice?

The coefficient of static friction is 1.13x10⁻⁵.      

Explanation:

We can find the coefficient of static friction as follows:

   (1)

Where:

: 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:

     (2)

Where:

is the final speed of the box = 0

is the initial speed of the box

t is the time = 600 s

   (3)

Where:

X: is the distance traveled by the box = 20 m

By solving equation (2) for and by entering into equation (3) we have:

Now, we can calculate the coefficient of static friction by entering the above value into equation (1) :

Therefore, the coefficient of static friction is 1.13x10⁻⁵.              

I hope it helps you!                                                                                  

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