Torque & Equilibrium

12PHYS - Mechanics

Finn LeSueur

2019

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.

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 \(1cm\).

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

Question 4: Does torque have a direction?

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

Clockwise or Anticlockwise

Torque & Equilibrium

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

\(m_{1}=2kg\), \(d_{1}=15cm\), \(m_{2}=1kg\), \(d_{2}=30cm\)

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

Question 2

\(m_{1}=7kg\), \(d_{1}=65cm\), \(m_{2}=13kg\), \(d_{2}=35cm\)

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

Question 3

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?

Mahi Tuatahi

  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.

  • 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

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

Pātai: Case Study

  • 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