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Torque & Equilibrium


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}


Torque ($\tau$)

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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 $1cm$.

\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}


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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:

  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

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

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

Question 2

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

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

Question 3

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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

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  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.

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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

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Pātai: Case Study

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Whakawai / Practise

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