# Biophysics Problem 13

A baseball player running with speed  $v = 9\; m/s$  slides into second base through a distance $d = 4\; m.$ Find $\mu,$ the coefficent of friction.

#### First Step

To calculate a coefficient of friction, you need to know a force of friction, and a normal force.

In this question, the player's mass was not given. Don't worry, we'll just represent his/her mass by $'m'.$

The normal force will be equal to the player's weight and will be:

$\text{Normal Force} \;= m \times g$
where $g = 9.8\; m/s^2$

#### Variables

Now in stopping, the player undergoes a negative acceleration.

Calculate this acceleration.

The easiest formula to use is:

$v^2 = u^2 + 2\; a\; d$

where:
$v = \text{final velocity} \\ u = \text{initial velocity} \\ d = \text{distance}$

#### Calculations

$a = \frac{v^2 - u^2}{2 \cdot d}\\ = \frac{0^2 - 9^2}{2\cdot 4}\\ = -10.1\frac{m}{s^2}$

Now ask yourself this question:

What is causing this negative acceleration?

Friction is causing the negative acceleration.

Thus, we must determine the magnitude of the force of friction. Again, we will let the player's mass be  $'m'.$ This gives us, (using Newton's second law):

$\text{Force Friction} = m \times a$

So now we are ready to calculate the friction coefficient.

$F = \mu\; N \\ \mu = \frac{F}{N}\\ = \frac{m\; a}{m\; g}\\ = \frac{a}{g}\\ = \frac{10.1}{9.8}\\ = 1.03$

Note that the mass cancels out.