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# 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. $E_{k} = \frac{1}{2}mv^{2}$

# 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
• sciPAD Page 46