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

The thermal energy generated is$537$ J

Step-by-step solution

Step 1. Given Information

Mass of Justin $m=30$Kg

Height of water fall $h=8$m

Initial speed $v_i=0$m/s

Final speed$v_f=11$m/s

Step 2. Find the amount of thermal

For that, we need to calculate the change in kinetic energy as well as the work done by gravity on it. If work done by gravity and change in kinetic energy is equal then is no work done by friction. But if there is a difference then that difference will be equal to the thermal energy generated

Let's do the calculation based on the above concept

$$\begin{gathered} ∆K=\frac{1}{2}m{v_f}^2-\frac{1}{2}m{v_i}^2 \\ ∆K=\frac{1}{2}\times 30\times {11}^2-0=1815J \\ W=mgh=30\times 9.8\times 8=2352J \\ ∆E=W-∆K \\ =2352-1815 \\ =537J \end{gathered}$$