# An ice skater moving at 10.0 m/s coasts to a halt in 100 m on a smooth ice surface. What is the coefficient of friction between the ice and the skates?

Mar 9, 2018

let,the combined mass of the ice skater and the skate is $M$

So,if the coefficient of frictional force is $\mu$,then frictional force acting is $\mu N = \mu M g$

so,deceleration due to friction is $\mu M \frac{g}{M} = \mu g$

So,we can apply ${v}^{2} = {u}^{2} - 2 a s$ here for constant deceleration,

Here, $v = 0 , u = 10 , s = 100$ and $a = \mu g$

So, we get, ${0}^{2} = {10}^{2} - 2 \mu g \cdot 100$

so, $\mu = \frac{100}{200 \cdot 9.8} = 0.051$