# Suppose Justin, with a mass of 55 kg, is going down an 8.0-m-high water slide. He starts at rest,...

## Question:

Suppose Justin, with a mass of 55 kg, is going down an 8.0-m-high water slide. He starts at rest, and his speed at the bottom is 12 m/s. How much thermal energy is created by friction during his descent?

## Conservation Law of Energy:

Imagine a perfectly isolated system that contains a collective amount of energy (E). As per the conservation law of energy, this energy will be unchanged or remain constant. Although, the forms of this energy can be changed.

Given data:

• Mass of Justin, {eq}m = 55 \ kg {/eq}
• Vertical height of the water slide, {eq}h = 8.0 \ m {/eq}
• Initial speed, {eq}u = 0 {/eq}
• Final speed, {eq}v = 12 \ m/s {/eq}

Let the magnitude of the thermal energy released in the process be Q.

From the conservation law of energy,

{eq}U_{i} + K_{i} = U_{f} + K_{f} + Q\\ mgh + \frac{1}{2}mu^{2} = mgh' + \frac{1}{2}mv^{2} + Q\\ 55 \times 9.80 \times 8.0 + \frac{1}{2} \times 55 \times (0)^{2} = 55 \times 9.80 \times 0 + \frac{1}{2} \times 55 \times (12)^{2} + Q\\ \Rightarrow \ Q = 352 \ \rm J.\\ {/eq} 