Skip to main content

# Mahi Tuatahi

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

1. State what each letter stands for
2. Give the units for each letter
3. Rearrange the equation for $m$ and $a$
4. Derive the SI units for F (not Newtons)

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

1. 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}

1. 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. { width=50% }

# 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 $1cm$.

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

# 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} { width=50% }

# Question 4: Does torque have a direction?

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

Clockwise or Anticlockwise

# Torque & Equilibrium { width=75% }

# 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:

1. Sum of all forces to be 0
2. 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 { width=50% }

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

1. Calculate the clockwise and anticlockwise torques
2. Are they in balance?

# Question 2 { width=50% }

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

1. Calculate the clockwise and anticlockwise torques
2. Are they in balance?

# Question 3 { width=50% }

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? { width=50% }

# Mahi Tuatahi

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

1. Calculate the clockwise torque
2. Calculate the anticlockwise torque
3. Is it balanced?

# Torque & Equilibrium

The plank may not be massless. You may need to take it into account. { width=50% }

• 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

1. Draw and label all forces on a diagram
2. Draw and label the distances between all forces and the pivot
3. Calculate all clockwise torque
4. Calculate all anticlockwise torque
5. Balance torques & forces

# Pātai { width=50% }

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

# Pātai: Case Study { width=50% }

• 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