Question

Justin, with a mass of $30$ kg, is going down an $8.0$-m-high water slide. He starts at rest, and his speed at the bottom is $11$ m/s. How much thermal energy is created by friction during his descent?

Short answer

${\mu }_k=0.037$

Step-by-step solution

Step 1. Given Information

We have,

a mass of $30$kg, is going down an$8.0$-m-high water slide. He starts at rest, and his speed at the bottom is $11$ m/s.

Step 2. Find the friction

We know that,

$$\begin{gathered} W=K_f-K_i \\ -{\mu }_{k}n∆s=\frac{1}{2}m{v^2}_f-\frac{1}{2}m{v^2}_i \\ {\mu }_{k}n∆s=\frac{1}{2}m{v^2}_i \\ {\mu }_k=\frac{m{v_i}^2}{2n∆s} \end{gathered}$$

Then, ${\mu }_k=\frac{m{v_i}^2}{2mg∆s}=\frac{{v_i}^2}{2g∆s}$

Now, we put the values

$$\begin{gathered} {\mu }_k=\frac{{v_i}^2}{2g∆s} \\ =\frac{{(1.2m/s)}^2}{2(9.8m/s^2)(2m)} \\ =0.037 \end{gathered}$$