Question

Stopping quickly is very important in roller derby. It’s necessary to avoid going out of bounds, to quickly turn and pursue members of the opposing team, and many other situations. Nova, who studies physics, knows that the coefficient of friction of her toe stops will have an important effect on how quickly she can stop. During a practice, she finds that, if she is skating forward at a speed of 7 m/s, she can turn around and use her skates’ toe stops to come to a complete stop in a distance of 2.5 m. Using this data, Nova wants to determine the coefficient of friction of her toe stops.

Answer 1

Answer:

$\mu_{k} = 0.999$

Explanation:

Changes on gravitational potential energy are neglected. The physical model for the skater is constructed by using the Principle of Energy Conservation and Work-Energy Theorem:

$K = W_{fr}$

$\frac{1}{2}\cdot m \cdot v^{2} = \mu_{k} \cdot m \cdot g \cdot \Delta s\\\frac{1}{2} \cdot v^{2} = \mu_{k} \cdot g \cdot \Delta s$

The kinetic coefficient of friction is:

$\mu_{k} = \frac{1}{2}\cdot \frac{v^{2}}{g \cdot \Delta s}$

$\mu_{k} = \frac{1}{2} \cdot \frac{(7\, \frac{m}{s} )^{2}}{(9.807\,\frac{m}{s^{2}} )\cdot (2.5\,m)}$

$\mu_{k} = 0.999$