# Akoranga 24 Mahi Tuatahi

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

## Ngā Whāinga Ako

1. Define work.
2. Name the unit of work and give its symbol.
3. 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

#### 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

#### 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

1. Get your mahi kāinga booklet and open it to Q31.
2. Complete Q31
3. What do you notice about the distance value used? Is it horizontal or vertical? Why do you think that is?
• Formula
• Substitution

#### 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

1. 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

#### 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

#### 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

## Ngā Whāinga Ako

1. Define power.
2. Name the unit of power and give its symbol.
3. 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

#### 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

#### 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