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Work & Power

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?
  3. Write your joint conclusion in your books!

Ngā Whāinga Ako 🔗

  1. Define work.
  2. Name the unit of work and give its symbol.
  3. Use $W = Fd$.

Work 🔗

The amount of energy transferred/transformed (gained/lost).

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. If the overall energy does not change, no work is done.

Work has the formula:

$$ \begin{aligned} work &= force \times distance \newline
W &= F \times d \end{aligned} $$

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

Pātai 🔗

Rearrange the formula $W=F \times d$ to:

  1. Make $F$ the subject
  2. Make $d$ the subject

Ngā Whakatika 🔗

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

Pātai 🔗

  1. Sam does a deadlift and raises $20kg$ by $1m$. Calculate the work done.
  2. Sarah hikes up Avalanche Peak. They have a mass of $55kg$, they start at $733m$ and do $605,000J$ of work to reach the top. How high did they climb?.

$$ \begin{aligned} K:& \cr U:& \cr F:& \cr S+S:& \end{aligned} $$

Whakatika Tahi 🔗

$$ \begin{aligned} W &= F \times d \newline W &= (m \times g) \times d \newline W &= (20 \times 10) \times 1 = 200J \end{aligned} $$

Whakatika Rua 🔗

$$ \begin{aligned} W &= F \times d \newline W &= (m \times g) \times d \newline 605,000 &= (55 \times 10) \times d \newline \frac{605000}{55 \times 10} &= d = 1100m \end{aligned} $$

Whakawai / Practice 🔗

Complete and mark!

Matapaki/Discussion 🔗

Compare and contrast these formula with the person sitting next to you. Write your thoughts in your book.

$$ \begin{aligned} W &= F \times d \newline E_{p} &= m \times g \times h \end{aligned} $$

Pātai 🔗

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

$$ \begin{aligned} K:& \cr U:& \cr F:& \cr S+S:& \end{aligned} $$

Whakatika Whā 🔗

$$ \begin{aligned} W &= F \times d \newline W &= (m \times g) \times d \newline W &= (62 \times 10) \times 46.2 = 28,644J \end{aligned} $$

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

Whakatika 🔗

Tākaro / Game 🔗

Get ready to Kahoot!

Pātai: Rocket 🔗

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?

$$ \begin{aligned} K:& \cr U:& \cr F:& \cr S+S:& \end{aligned} $$

Whakatika 🔗

All energy is transformed from chemical potential to gravitational potential.

$$ \begin{aligned} W = E_{p} &= m \times g \times h \newline &= 5 \times 10 \times 2000 = 100,000J \end{aligned} $$

Whakawai / Practice 🔗

Complete Q33 then Q32 from your homework booklet.

$$ \begin{aligned} K:& \cr U:& \cr F:& \cr S+S:& \end{aligned} $$

Extra: Q28

Whakatika 🔗

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

$$ \begin{aligned} W = E_{p} &= m \times g \times h \newline &= 48 \times 10 \times 2 = 960J \end{aligned} $$

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:

$$ \begin{aligned} W = E_{p} &= m \times g \times h \newline &= 52 \times 10 \times 5 = 2600J \end{aligned} $$

Ngā Whāinga Ako 🔗

  1. Define power.
  2. Name the unit of power and give its symbol.
  3. Be able to do a variety of power calculations.

Power 🔗

The rate at which energy is transferred/transformed.

The rate at which work is done.

$$ \begin{aligned} power &= \frac{work}{time} \newline P &= \frac{W}{t} \newline \end{aligned} $$

Write this formula so that $W$ and $t$ are the subject.

Pātai 🔗

  1. You leave your bedroom light on day. It uses $1,134,000J$ while you are at school for 7 hours. Calculate the power of the bulb.
  2. Chris ($48kg$) climbs a $2m$ staircase with a power of $192W$. Calculate how long it took him to climb the stairs.

$$ \begin{aligned} K:& \cr U:& \cr F:& \cr S+S:& \end{aligned} $$

Whakatika Tahi 🔗

$$ \begin{aligned} P &= \frac{W}{t} \newline &= \frac{1,134,000}{25,200} \newline &= 45Js^{-1} = 45\frac{J}{s} = 45W \end{aligned} $$

Whakatika Rua 🔗

$$ \begin{aligned} W &= F \times d \newline W &= m \times g \times h \end{aligned} $$

$$ \begin{aligned} P &= \frac{W}{t} \newline P &= \frac{m \times g \times h}{t} \newline 192 &= \frac{48 \times 10 \times 2}{t} \newline t &= \frac{48 \times 10 \times 2}{192} = 5s \end{aligned} $$

Whakawai 🔗

Complete and mark Q36 from your Mahi Kāinga booklet. Hint: find work first, and then power.

$$ \begin{aligned} K:& \cr U:& \cr F:& \cr S+S:& \end{aligned} $$

Whakatika 🔗

$$ \begin{aligned} W &= F \times d \newline &= (62 \times 10) \times 46.2 = 28,644J \end{aligned} $$

$$ \begin{aligned} P & = \frac{W}{t} \newline &= \frac{28644}{525} = 54.56Js^{-1} = 54.56\frac{J}{s} = 54.56W \end{aligned} $$