# Kinetic Energy

11SCI - Mechanics

2019

# L20: Mahi Tuatahi (2016 Exam)

• Rhiana is riding a horse along New Brighton Beach. Each of the horse’s hooves have a surface area of $$0.0044m^{2}$$ which sink into the sand when the horse stops. The horse exerts a total pressure of $$200155Pa$$.
• Calculate the weight of the horse.
• Equation
• Substitute
• Solve

## Te Whakatika

A horse has four hooves, so the total surface area that the horse is exerting pressure through is $$A = 0.0044 \times 4 = 0.0176m^{2}$$

\begin{aligned} P &= \frac{F}{A} \\ 200155 &= \frac{F}{0.0176} \\ 200155 \times 0.0176 &= F = 3522.728N \end{aligned}

## Ngā Whāinga Ako

1. Give the symbols and units for kinetic energy
2. $$E_{k} = \frac{1}{2}mv^{2}$$

Write the date, the learning outcomes and title “Kinetic Energy” in your books.

# Kinetic Energy

## What is Kinetic Energy?

Kinetic energy is the energy that an object possesses due to its velocity!

## Calculating Kinetic Energy

Kinetic energy depends on the mass and velocity of an object.

\begin{aligned} E_{k} &= \frac{1}{2} \times mass \times \text{velocity squared} \\ E_{k} &= \frac{1}{2} \times m \times v^{2} \end{aligned}

### What does $$v^{2}$$ mean?

• It means $$v \times v$$
• This means we can also write the equation like this, if you find it easier:
\begin{aligned} & E_{k} = \frac{1}{2} \times m \times v \times v \end{aligned}

### Pātai Tahi

Mr LeSueur rides his bike to work at $$32km/h$$ ($$8.89ms^{-1}$$). Both he and his bike have a combined mass of $$80kg$$. Calculate his kinetic energy.

#### Whakatika Tahi

We know $$m=80kg$$ and $$v=8.89ms^{-1}$$, and we are looking for $$E_{k}$$.

\begin{aligned} E_{k} = \frac{1}{2} \times 80 \times 8.89^{2} \\ E_{k} = 3161.284J \end{aligned}

### Pātai Rua

Sophie is skiing down Upper Fascination at Mt Hutt, and is trying to go really fast. Her combined mass is $$60kg$$ and she is moving at $$60km/h$$ ($$16.67ms^{-1}$$). Calculate her kinetic energy.

#### Whakatika Tua

We know $$m=60kg$$ and $$v=16.67ms^{-1}$$, and we are looking for $$E_{k}$$.

\begin{aligned} E_{k} = \frac{1}{2} \times 60 \times 16.67^{2} \\ E_{k} = 8336.667J \end{aligned}

## Whakamātau: Finding Your Kinetic Energy

Open the whakamātau document on Google Classroom!

## Extra Work

• Homework: Education Perfect due Monday 29th 11:25am