# Akoranga 24 Mahi Tuatahi

- Write the date in your books
- Discuss with the person next to you:
- What does the law of conservation of energy state?
- What unit is energy measured in?

## Ngā Whāinga Ako

- Define
**work**. - Name the unit of work and give its symbol.
- Use $W = Fd$.

Write ngā whāinga ako in your book

## Work

The amount of energy transferred/transformed.

E.g. When you lift your backpack off the ground you are transferring some **chemical potential energy** in your muscles into **gravitational potential energy** in the backpack. You are doing **work** on your backpack.

Work has the formula

\begin{aligned}
work &= force \times distance \

W &= F \times d
\end{aligned}

### Pātai Tahi: What is work measured in?

#### Whakatika Tahi

Work is measured in Joules (J) because it is defined as **the amount of energy transferred/transformed**.

### Pātai Rua

Sam has decided to take up weight lifting and starts by dead-lifting a $20kg$ mass from the ground to a height of $1m$. Calculate the work done for Sam to lift the weight.

- Formula
- Substitution
- Answer

#### Whakatika Rua

\begin{aligned}
W &= F \times d \

W &= (m \times g) \times d \

W &= (20 \times 10) \times 1 = 200J
\end{aligned}

### Pātai Toru

Jack has gone hiking up Avalanche Peak. He has a mass of $55kg$ and reaches a height of $1833m$, starting from $733m$. How much work has Jack done to reach the top?

- Formula
- Substitution
- Answer

#### Whakatika Toru

\begin{aligned}
W &= F \times d \

W &= (m \times g) \times d \

W &= (55 \times 10) \times (1833-733) = 605,000J
\end{aligned}

### Pātai Whā

- Get your mahi kāinga booklet and open it to Q31.
- Complete Q31
- What do you notice about the
*distance*value used? Is it horizontal or vertical? Why do you think that is?

- Formula
- Substitution
- Answer

#### Whakatika Whā

\begin{aligned}
W &= F \times d \

W &= (m \times g) \times d \

W &= (62 \times 10) \times 46.2 = 28,644J
\end{aligned}

We use the vertical distance, not the horizontal distance. Energy is not transferred/transformed when moving horizontally!

### Homework / *Mahi Kāinga*

- Due Monday, October 19th
- Mahi Kāinga Booklet Q30, Q35

# Akoranga 25 Mahi Tuatahi

Recall that **work is the amount of energy transferred/transformed**. Two skiers ride the 6-chair. One descends to base via Jan’s Face and the other via Fascination/Broadway. Describe the change in their energies and how they are similar/different.

## Te Whāinga Ako

- Use $W = Fd$ and $Ep = mgh$ to determine amounts of energy transfer.

Write te whāinga ako in your book

### Matapaki: How are these two formula similar/different?

\begin{aligned} W &= F \times d \end{aligned}

\begin{aligned} E_{p} &= m \times g \times h \end{aligned}

### Whakatika

- Work is
**the amount of energy transferred/transformed** - It is just a measure of energy
- In the vertical direction,
**it is exactly the same as**$E_{p}$! - You can use either formula

### Pātai Tahi

A rocket is launched with an acceleration of $90ms^{-2}$. It has a mass of $5kg$ and it reaches a height of 2000m. **How much work did the rocket do to get the rocket to this height?**

- Formula
- Substitution
- Answer

#### Whakatika Tahi

All energy is transformed from chemical potential **to gravitational potential**.

\begin{aligned}
W = E_{p} &= m \times g \times h \

&= 5 \times 10 \times 2000 = 100,000J
\end{aligned}

### Pātai Rua

Open your mahi kāinga booklet to Q33 about Ian and Chris on a diving platform.

- Formula
- Substitution
- Answer

#### Whakatika Rua

a) *How much work does Chris (48 kg) do when he climbs up the stairs to the 2m diving platform?*

\begin{aligned}
W = E_{p} &= m \times g \times h \

&= 48 \times 10 \times 2 = 960J
\end{aligned}

b) *Ian’s mass is 52 kg. Why did Ian do more work climbing up the 5 m ladder compared to Chris climbing up the 2 m ladder?*

Because $W=mgh$, if $m$ increases, the work increases. Also if $h$ increases, so does the work. Ian:

\begin{aligned}
W = E_{p} &= m \times g \times h \

&= 52 \times 10 \times 5 = 2600J
\end{aligned}

# Akoranga 26 Mahi Tuatahi

Get ready to Kahoot!

## Ngā Whāinga Ako

- Define
**power**. - Name the unit of power and give its symbol.
- Calculate the power of a device from given data.

Write the date and ngā whāinga ako in your book

## Power

The rate at which energy is transferred/transformed.

- A higher power means more energy is transferred each second.
- A lower power means less energy is transferred each second.

- Power is measured in Joules per second ($J/s$), which is also known as a Watt ($W$)

\begin{aligned}
power &= \frac{work}{time} \

P &= \frac{W}{t} \

\end{aligned}

### Pātai Tahi

You go to school but leave the light in your bedroom on all day. The lightbulb uses $1,134,000J$ of energy while you are away at school for 7 hours. Calculate the **power** of the bulb.

- Formula
- Substitution
- Answer

#### Whakatika Tahi

\begin{aligned}
P &= \frac{W}{t} \

&= \frac{1,134,000}{25,200} \

&= 45Js^{-1} = 45\frac{J}{s} = 45W
\end{aligned}

### Pātai Rua

Chris (48 kg) climbs 2m up some stairs to a diving board. He completes the climb in 5s. **What is Chris’ power?** *Hint: find work first, and then power.*

- Formula
- Substitution
- Answer

#### Whakatika Rua

\begin{aligned}
W &= F \times d \

&= (48 \times 10) \times 2 = 960J
\end{aligned}

\begin{aligned}
P & = \frac{W}{t} \

&= \frac{960}{5} = 192Js^{-1} = 192\frac{J}{s} = 192W
\end{aligned}

### Pātai Toru

Mahi Kāinga booklet Q36. *Hint: find work first, and then power.*

- Formula
- Substitution
- Answer

#### Whakatika Toru

\begin{aligned}
W &= F \times d \

&= (62 \times 10) \times 46.2 = 28,644J
\end{aligned}

\begin{aligned}
P & = \frac{W}{t} \

&= \frac{28644}{525} = 54.56Js^{-1} = 54.56\frac{J}{s} = 54.56W
\end{aligned}