# Mahi Tuatahi

\begin{aligned} F=ma \end{aligned}

- State what each letter stands for
- Give the units for each letter
- Rearrange the equation for $m$ and $a$
- Derive the SI units for F (not Newtons)

For a car of **mass 1500kg** which is accelerating at $3.7ms^{-2}$:

- What net force is needed to maintain this acceleration?

\begin{aligned} & && \text{Knowns} \newline & && \text{Unknowns} \newline & && \text{Formula} \newline & && \text{Sub and Solve} \end{aligned}

- If the engine is producing $6000N$ of thrust, what is the difference and what happened to it?

# Torque ($\tau$)

Torque can be thought of as the **turning effect** around a **pivot**.
Torque is sometimes known as **moment** or **leverage**.

\begin{aligned} \tau &= Fd_{\bot} \newline torque &= Newtons \times metres \newline torque &= \text{Newton meters (Nm)} \end{aligned}

- $F =$ force in Newtons
- $d_{\bot} =$ perpendicular distance of force from pivot

# Torque ($\tau$)

- A small force at a small distance produces a small torque,
- the same small force at a larger distance produces a larger torque.

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# Pātai 1

A force of $9N$ acting up at a distance of $10cm$ is needed to lift the top off a bottle of soft drink. Start by drawing a rough diagram. **Calculate the torque applied.**

\begin{aligned} & && \text{Knowns} \newline & && \text{Unknowns} \newline & && \text{Formula} \newline & && \text{Sub and Solve} \end{aligned}

# Pātai 1: Whakatika

A force of $9N$ acting up at a distance of $10cm$ is needed to lift the top off a bottle of soft drink. **Calculate the torque applied.**

\begin{aligned} & \tau = Fd_{\bot} \newline & \tau = 9 \times 0.1 \newline & \tau = 0.9 \text{Nm anticlockwise} \newline \end{aligned}

# Pātai 2

Calculate the torque applied if the lever is stretched to $75cm$.

\begin{aligned} & && \text{Knowns} \newline & && \text{Unknowns} \newline & && \text{Formula} \newline & && \text{Sub and Solve} \end{aligned}

# Pātai 2: Whakatika

Calculate the torque applied if the lever is stretched to $75cm$.

\begin{aligned} & \tau = Fd_{\bot} \newline & \tau = 9 \times 0.75 \newline & \tau = 6.75 \text{Nm anticlockwise} \newline \end{aligned}

# Pātai 3

Calculate the torque applied if the lever is compressed to $1cm$.

# Pātai 3: Whakatika

Calculate the torque applied if the lever is compressed to $1cm$.

\begin{aligned} & \tau = Fd_{\bot} \newline & \tau = 9 \times 0.01 \newline & \tau = 0.09 \text{Nm anticlockwise} \newline \end{aligned}

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# Question 4: Does torque have a direction?

Yes, and you must always state which direction it is acting in.

**Clockwise or Anticlockwise**

# Torque & Equilibrium

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# But, What Is Equilibrium?

*Newton’s First Law* tells us equilibrium is when an object is **at rest** or **moving uniformly**.

For this to occur we need two things:

- Sum of all forces to be 0
- Sum of all torques to be 0

# Okay, So Where Do We Use It?

Building bridges, setting up scaffolding, see-saws and more!

# Question 1

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$m_{1}=2kg$, $d_{1}=15cm$, $m_{2}=1kg$, $d_{2}=30cm$

- Calculate the clockwise and anticlockwise torques
- Are they in balance?

# Question 2

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$m_{1}=7kg$, $d_{1}=65cm$, $m_{2}=13kg$, $d_{2}=35cm$

- Calculate the clockwise and anticlockwise torques
- Are they in balance?

# Question 3

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The rock has mass $1100kg$ and is at distance $50cm$ from the pivot. If Ash exerts $70N$ of downward force at a distance of $8m$ from the pivot can he move the rock?

Archimedes once said: *“Give me a place to stand and I will move the world”*

**Question**: Assuming the mass of the Earth is $5.972\times 10^{24} kg$ at a distance of 1km from the pivot and Archimedes’ mass is $75kg$, how long would his lever have to be?

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# Mahi Tuatahi

![](../assets/torque-mahi tuatahi.png){ width=50% }

- Calculate the clockwise torque
- Calculate the anticlockwise torque
- Is it balanced?

# Torque & Equilibrium

The plank may not be massless. You may need to take it into account.

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- The mass of the plank acts through its
**center of gravity** - Because the plank is uniform, this is the middle of the plank

# How To Solve A Torque Problem

- Draw and label all forces on a diagram
- Draw and label the distances between all forces and the
**pivot** - Calculate all clockwise torque
- Calculate all anticlockwise torque
- Balance torques & forces

# Pātai

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- $d_{1}=30cm$, $d_{2}=70cm$, $m_{1}=900g$, $m_{2}=300g$, see-saw mass = $100g$.
- Calculate the total anticlockwise moment
- Calculate the total clockwise moment
- Is it balanced?

# Pātai: Case Study

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- Assume the system is in equilibrium ($\tau_{clockwise} = \tau_{anticlockwise}$)
- $d_{1}=0.5m$, $d_{2}=1.5m$, $F_{1}=2.5N$, see-saw mass = $0.5kg$, $F_{2}=?$.
- Draw the weight force of the see-saw on your diagram
- Find the unknown force, $F_{2}$

## Whakawai / Practise

Textbook: Force, Equilibrium and Motion - Q7, 8, 10, 11, 12