Forces, Energy and Motion Notes

8 Forces, energy and motion

  • Content Description: Investigating Newton’s laws of motion and quantitatively analysing the relationship between force, mass, and acceleration of objects (AC9S10U05).
  • Source: F–10 Australian Curriculum 9.0 (2024–2029) extracts © Australian Curriculum, Assessment and Reporting Authority; reproduced by permission.

Lesson Sequence

  • 8.1 Overview
  • 8.2 Average speed, distance, and time
  • 8.3 Measuring speed
  • 8.4 Acceleration and changes in velocity
  • 8.5 Forces and Newton’s First Law of Motion
  • 8.6 Newton’s Second Law of Motion
  • 8.7 Newton’s Third Law of Motion
  • 8.8 Work and energy
  • 8.9 Conservation of energy
  • 8.10 Designing safety devices
  • 8.11 Thinking tools — Cycle maps
  • 8.12 Project — Rock and rollercoaster
  • 8.13 Review

Science Inquiry and Investigations

  • Science inquiry is a central component of the Science curriculum.
  • Investigations, supported by a Practical investigation eLogbook and teacher-led videos, are included in this topic to provide opportunities to build Science inquiry skills through undertaking investigations and communicating findings.

8.1 Overview

8.1.1 Introduction

  • The thrill of a rollercoaster ride allows experiencing sudden changes in motion.
  • The laws of motion are vital for people in many fields and form the basis of calculations for the construction of vehicles, precision sports measurements, and safe theme park rides.
  • Any further study of physics will require a thorough understanding of this topic.

8.1.2 Think About Forces, Energy, and Motion

  1. Could a kangaroo win the Melbourne Cup?
  2. How do radar guns measure the speed of cars?
  3. Why do you feel pushed to the left when the bus you are in turns right?
  4. Why do space rockets seem to take forever to get off the ground?
  5. Why does it hurt when you catch a fast-moving ball with your bare hands?
  6. What does doing work really mean?
  7. Why can’t a tennis ball bounce higher than the height from which it is dropped?
  8. Why are cars deliberately designed to crumple in a crash?

8.1.3 Science Inquiry: A World of Forces, Energy, and Motion

  1. Model each of the following motions with a small toy car or a motorised car and then describe the movement a passenger in a car would feel when it:
    • a. accelerates suddenly
    • b. stops suddenly
    • c. takes a sharp left turn.
  2. Copy and complete the following table to list the forces acting on each of the people shown in the photos in figure 8.2. The number of forces acting on each of them is provided in brackets.
PersonForces acting on the person
a. Bungee jumper(3)
b. Parachutist(3)
c. Cyclist(5)
d. Skier(2)
e. Swimmer(4)
f. Skater(5)
g. Reader(2)
  1. Some of the people in the photographs in figure 8.2 are speeding up; others may be traveling at a steady speed or slowing down.
    • a. Which three of the people are the most likely to be speeding up? How do you know?
    • b. Which three people are most likely to be moving at a non-zero constant speed? How do you know?
  • c. Which three people are clearly losing gravitational potential energy? According to the Law of Conservation of Energy, energy cannot be created or destroyed. It can only be transformed into another form of energy or transferred to another object.
    • d. What happens to the lost gravitational potential energy of each of the three people referred to in part c.? What happens if they reach a steady speed?
  1. Use a plastic or paper bag (or other appropriate material) and string to create a parachute. Attach a small mass at the end to represent the person.
    • a. Were you able to observe all the forces you listed in question 2?
    • b. Which forces would be classed as non-contact forces? How do you know?
    • c. Compare dropping your parachute inside to dropping it outside. What differences do you notice in the movement of a parachute and the forces acting on it?
    • d. Add more mass to the bottom of your parachute. What do you notice? Does this change the forces acting on the parachute?

8.2 Average Speed, Distance and Time

  • Learning Intention: To explain the meaning of average speed and be able to use the average speed formula to calculate speed, distance or time. Also, to be able to describe the vector quantities of displacement and velocity.

8.2.1 Calculating Speed

  • Speed is a measure of the rate at which an object moves over a distance.
  • v is used to represent speed.
  • Speed is usually measured in kilometers per hour (km/h) or meters per second (m/s).
  • Speed and velocity are often used interchangeably in everyday life; however, they have very different meanings in science.
  • Average speed (v_{av}) is based on how far travelled in the total time of the journey.
  • It does not take into account the fluctuations in speed that occurred during the journey.
  • Average speed is calculated by dividing the total distance travelled by the total time taken.
  • Average speed = \frac{total \ distance \ travelled}{total \ time \ taken}
  • In symbols: v_{av} = binom{d}{t}, where:
    • v_{av} is the average speed
    • d is the total distance travelled
    • t is the total time taken
  • Example 1: Calculating average speed in m/s
    • Cheetah sprints after a young impala, covering 150 metre distance in 6 seconds.
    • Average speed = \frac{150 \ m}{6 \ s} = 25 \ m/s (approximately 90 \ km/h)
  • Example 2: Calculating speed in cm/min
    • The average speed of a snail that takes 10 minutes to cross an 80 centimetre concrete paving stone in a straight line is:
    • v = binom{d}{t} = binom{80 \ cm}{10 \ min} = 8 \ cm/min

8.2.2 Converting Between Units of Speed

  • Speed of a vehicle is usually expressed in kilometers per hour (km/h).

  • The internationally accepted scientific units of speed are meters per second (m/s).

  • Speed must, however, always be expressed as a unit of distance divided by a unit of time.

  • km/h\ = km/h \ (or \ km \cdot h^{-1})

  • m/s = m/s \ (or \ m \cdot s^{-1})

  • mm/week = mm/week \ (or \ mm \cdot week^{-1})

  • When converting into different units, you may:

    1. Convert the distance and time into the correct units first and then calculate the average speed.
    2. Use a conversion to convert between units of speed.

  • Converting between km/h and m/s

  • Example 3: Calculating average speed in km/h and m/s

    • The average speed of an aeroplane that travels from Perth to Melbourne, a distance of 2730 kilometers by air, in 3 hours is:
    • v_{av} = binom{d}{t} = binom{2730 \ km}{3 \ hours} = 910 \ km/h
    • To express the speed in metres per second (m/s) by converting kilometres to metres and hours to seconds:
    • v = binom{d}{t} = binom{2730000 \ m}{3 \ \times \ 3600 \ s} = 253 \ m/s

  • Activity: Converting from m/s to km/h

    • Convert 25 \ m/s into km/h.

8.2.3 Calculating Distance and Time

  • The formula used to calculate speed can also be used to calculate the distance travelled or the time taken.
  • v_{av} = binom{d}{t}
  • To calculate the distance, assuming constant speed, distance becomes the subject of the equation:
  • d = v_{av} t
  • To calculate how long a journey should take:
  • t = binom{d}{v_{av}}
  • When using the speed formula to calculate distance or time, the units used for distance and time must be the same as those used in the unit for speed.
  • Example 4: Calculating distance when speed and time are known
    • The distance covered in two and a half hours by a train traveling at an average speed of 70 \ km/h is:
    • d = v \times t = 70 \ km/h \times 2.5 \ h = 175 \ km
  • Example 5: Calculating time when distance and speed are known
    • The time taken for a giant tortoise to cross a 6-metre-wide deserted highway at an average speed of 5.5 \ cm/s is:
    • t = binom{d}{v_{av}} = binom{6 \times 100 \ cm}{5.5 \ cm/s} = 109 \ s \ approx 1 \ min \ 49 \ s

8.2.4 Stopping and Braking Distances

  • Stopping Distance = Reaction Distance + Braking Distance
  • Reaction distance is the distance travelled by the car once the driver sees the hazard, before applying the brakes.
  • Braking distance is the distance travelled once the brakes have been applied and the vehicle stops.
  • A car traveling at 40 \ km/h, with a driver reaction time of 0.8 seconds, and a braking time of 0.9 seconds, stops at a total distance of:
    • Reaction distance: d = v_{av} \times t = (40 \div 3.6) \times 0.8 = 8.9 \ m
    • Braking distance: d = v_{av} \times t = (40 \div 3.6) \times 0.9 = 10 \ m
    • Stopping distance = 8.9 + 10= 18.9 \ m
  • If the car was traveling at 50 \ km/h instead, with a driver reaction time of 0.8 seconds, and a braking time of 0.9 seconds, then the total stopping distance of the car would be:
    • Reaction distance: d = v_{av} \times t = (50 \div 3.6) \times 0.8 = 11.1 \ m
    • Braking distance: d = v_{av} \times t = (50 \div 3.6) \times 0.9 = 12.5 \ m
    • Stopping distance = 11.1 + 12.5 = 23.6 \ m

8.2.5 When the Direction Matters

  • Speed is a measure of the rate at which distance is covered.
    • It has a size or magnitude only.
    • It is described as a scalar quantity because it only has ‘scale’ or size information.
  • Velocity is a measure of the rate of change in position.
    • Velocity has a direction as well as a magnitude (size)
    • It is known as a vector quantity.
    • The overall change in position of an object, including the direction, is known as displacement.

8.2.6 Displacement, Distance, Velocity and Speed

  • Displacement and velocity are both vector quantities, and therefore, are described by both a magnitude and direction.
  • Displacement is the change in position of an object.
  • The symbol s can also be used to represent displacement.
  • The displacement of an object that has moved from position x1 to position x2 is:
  • \Delta x = x2 - x1
    • \Delta x is the change in position
    • x_1 is the initial position
    • x_2 is the final position
  • Velocity is the rate of change of position, calculated by dividing the change in position by time.
    • v = binom{\Delta x}{t} = binom{x2 - x1}{t}
    • v is the velocity
    • \Delta x is the displacement
    • t is the time taken
  • In order to perform calculations using vectors, the direction is indicated using positive and negative numbers.
    • When dealing with motion in a straight line, it is important to define which direction will be represented by positive numbers and which direction will be represented by negative numbers.
  • Common conventions are:
    • North \rightarrow +
    • South \rightarrow -
    • Up \rightarrow +
    • Down \rightarrow -
    • West \rightarrow -
    • East \rightarrow +
    • Left \rightarrow -
    • Right \rightarrow +
    • Backwards \rightarrow -
    • Forwards \rightarrow +

8.2.7 Using Position-Time and Velocity-Time Graphs

  • Position-time graphs are also know as displacement-time graphs
  • A steeper slope represents a faster speed.

8.3 Measuring Speed

  • Learning Intention: To describe how speed is measured with the help of different devices and understand the importance of controlling speed on the roads for safety.

8.3.1 Keeping Track of Speed

  • The instantaneous speed is the speed at any particular instant of time.
  • Formula one racing - the average speed does not provide much information about the speed at any particular instant during the race.
  • By using more stopwatches and placing them closer together, a more accurate estimate of instantaneous speed can be obtained.

8.3.2 Measuring Speed: Ticker Timers

  • A ticker timer provides a simple way of recording motion in a laboratory.
  • When the ticker timer is connected to an AC power supply, its vibrating arm strikes its base 50 times every second.
  • Each marked interval on the tape represents five-fiftieths of a second — that is, 0.1 seconds.
  • The average speed between each pair of dots is determined by dividing the distance between them by the time interval.
  • v_{av} = \frac{4.2cm}{0.1s} = 42cm/s

8.3.3 Measuring Speed: Motion Detectors

  • Sonic motion detectors send out pulses of ultrasound at a frequency of about 40 \ kHz and detect the reflected pulses from the moving object.
  • The device uses the time taken for the pulses to return to calculate the distance between itself and the object. A small computer in the motion detector calculates the speed of the object.
  • The same technology can be used to measure speed and can also be found in light gates. When an object passes through the ‘gate’ where the beam is, a detector in the gate can no longer sense the light, so triggers a timer.
  • When the object leaves the gate, the beam is now detected so the timer stops. By knowing the length of the object (usually a piece of card attached to a trolley) and the length of time as recorded by the gate, the speed of the object can be calculated.

8.3.4 Measuring Speed: Speedometers

  • The speedometer inside a vehicle has a pointer that rotates further to the right as the wheels of the vehicle turn faster.
  • It provides a measure of the instantaneous speed.
  • Older speedometers use a rotating magnet that rotates at the same rate as the car’s wheels.
  • Newer electronic speedometers use a rotating toothed wheel that interrupts a stationary magnetic field. An electronic sensor detects the interruptions and sends a series of pulses to a computer, which calculates the speed using the frequency of the pulses.
  • Car speedometers are not 100% accurate.

8.3.5 Measuring Speed: GPS

  • The global positioning system (GPS) uses radio signals from at least four of up to 32 satellites orbiting Earth to accurately map your position, whether you are in a vehicle or on foot.
  • GPS navigation devices usually calculate speed about once every second.
  • To do this, they measure the small perceived change in frequency of the received radio waves due to your motion relative to them. This is called the Doppler effect.

Science as a Human Endeavour: Speed and Road Safety

  • Police use three different methods to monitor driving speeds as accurately as possible to ensure that speeding drivers are penalised. These include:
    • Radar guns.
    • Laser guns.
    • Digitectors.

8.4 Acceleration and Changes in Velocity

  • Learning Intention: To describe what acceleration is and calculate acceleration of an object that is speeding up or slowing down.

8.4.1 Getting Faster

  • When an object moves in a straight line, its acceleration is a measure of the rate at which it changes velocity.
  • Average acceleration can be calculated by dividing the change in velocity by the time taken for the change:
    • a_{av} = \frac{v - u}{t} = \frac{\Delta v}{t}
      • where:
        • a_{av} is the acceleration (in m/s^2).
        • \Delta v is the change in velocity (in m/s).
        • v = final velocity (in m/s)
        • u = initial velocity (in m/s)
        • t is the time taken (in s).
  • The SI units of acceleration are m/s^2 (metres per second squared).
  • 10 \ m/s^2 means 10 metres per second faster every second.
  • Example 6: Calculating average acceleration
    • A car traveling at 60 \ km/h north increases its velocity to 100 \ km/h north in 5.0 seconds. The car has an average acceleration of:
    • a_{av} = \frac{100 \ km/h - 60 km/h}{5.0 s} = \frac{40 \ km/h}{5.0 s} = 2.2 m/s^2
    • That is, on average, the car increases its velocity by 2.2 \ m/s each second (2.2 \ m/s^2 north).

8.4.2 Slowing Down

  • If the acceleration of an object is in the opposite direction to its velocity, the object slows down, also known as deceleration.
  • Acceleration is simply the rate of change of velocity.
  • Example 7: Calculating negative acceleration
    • A truck is traveling at 35 \ m/s forwards at the bottom of a hill but 10 seconds later at the top of the hill it has a velocity of 15 \ m/s forwards. The truck has an acceleration of:
    • a_{av} = \frac{15 m/s - 35 m/s}{10 s} = -2.0 m/s^2
    • That is, on average, the truck decreases its velocity by 2 \ m/s each second, because its acceleration is in the opposite direction to its velocity.

8.4.3 Comparing Positive and Negative Acceleration

  • Example, drag racing

8.5 Forces and Newton’s First Law of Motion

  • Learning Intention: To explain what forces are and how an object will stay in its state of motion or rest unless an external unbalanced force is applied.

8.5.1 What is a Force?

  • A force is an interaction between two objects.

  • A force is a push, pull or twist applied to one object by another.

  • It is a vector quantity, which means it requires a magnitude and a direction to describe it.

  • The unit of force is the newton (N), named after Sir Isaac Newton.

  • The four fundamental forces in nature are:

    • Gravitational force: The force of attraction between two objects with mass.
    • Electromagnetic forces: Forces associated with electric and magnetic fields, describing interactions between charged particles. Can be split into magnetic forces and electrostatic forces.
    • Strong nuclear forces: Forces observed inside the nucleus of an atom.
    • Weak nuclear forces: Forces associated with particle transformations within the nucleus.

  • Other common forces include:

    • Normal force: The force applied by a surface at right angles to the surface in response to a push on it by an object.
    • Resistive forces: The forces applied to an object to prevent or oppose its motion (e.g., drag forces and frictional forces, including air resistance).
    • Thrust or driving forces: The forces causing an object to move or accelerate forward.
    • Tension or compression forces: The forces caused by pulling on an object to stretch it or pushing on an object to compress it.
      Calculating the force due to gravity at Earth’s surface

  • Commonly called weight

  • F_g = mg, where \textit{g} is Earth's gravitational field strength, which is equal to 9.8 m/s^2

  • F_g = mg

    • g = gravitational field strength (N/kg).

  • Mass or force due to gravity

  • Mass is the amount of matter in an object and is measured in kilograms (kg). It is a scalar quantity while force due to gravity is a vector quantity.

  • Example:

  • Force due to gravity on Earth: m = 50kg, g_{Earth} = 9.8 N/kg

    • Fg = m \times g{Earth} = 50 \times 9.8 = 490 N

  • Force due to gravity on the Moon: m = 50kg, g_{Moon} = 1.6 N/kg

    • Fg = m \times g{Moon} = 50 \times 1.6 = 80 N

8.5.2 Adding Forces

  • Forces are vector quantities, so direction is important.
  • When two forces are applied in the same direction, simply add the magnitudes.
  • If forces are acting in opposite directions, subtract their magnitudes.
  • If the net force is zero, the forces are balanced.
  • If the force in one direction is greater than the force in the opposite direction, the forces are unbalanced.

8.5.3 Newton’s Laws

  • Newton’s three laws of motion explain the effect of all of the forces acting on the motion of objects.
  • Newton’s Laws of Motion:
  1. Newton’s First Law of Motion states that an object will remain at rest, or will not change its speed or direction, unless it is acted upon by an outside, unbalanced force.
  2. Newton’s Second Law of Motion states that the acceleration of an object depends on the size of the net (total or resultant) force and the mass of the object.
  3. Newton’s Third Law of Motion states that for every force that exists, a second force of equal size and opposite direction also exists. That is, when an object applies a force to a second object, the second object applies an equal and opposite force to the first object.

8.5.4 Newton’s First Law

  • Newton’s First Law : An object will remain at rest, or will not change its speed or direction, unless it is acted upon by an outside, unbalanced force.
  • Forces are vectors, so because these forces are the same size but in opposite directions, the net force on the plane is equal to zero both horizontally and vertically.
  • This means that the plane travels at a steady velocity because it cannot accelerate without an unbalanced net force.
  • Inertia is the property of objects that makes them resist changes in their motion.
  • The greater the mass of an object, the more inertia it has.

EXTENSION: Newton’s First Law and Inertia

  • Inertia is the property of objects that makes them resist changes in their motion.
  • The greater the mass of an object, the more inertia it has.

8.5.5 Driverless Cars

  • A driverless car uses computers to make decisions about the size of the thrust and resistive forces on the car.
  • Manufacturers of driverless cars need to ensure the computers inside each car are receiving enough information from the car’s sensors and have information about appropriately sized forces to ensure a smooth ride for passengers.

8.6 Newton’s Second Law of Motion

  • Learning Intention: To apply Newton’s Second Law to determine the acceleration of an object.

8.6.1 Newton’s Second Law of Motion

  • Newton’s Second Law of Motion describes how the mass of an object affects the way that it moves when acted upon by one or more forces.
  • Newton’s Second Law of Motion states the acceleration of an object is equal to the total force on the object divided by its mass.
  • a = \frac{F_{net}}{m}
  • a is the acceleration (in m/s^2)
  • F_{net} is the net force on the object (in N)
  • m is the mass of the object (in kg).
  • When using Newton’s Second Law of Motion, it is important to remember that an object’s acceleration will always be in the same direction as the net force acting on the object.
  • When the total force on an object is zero, the acceleration of the object will also be zero.
  • This confirms and adds to Newton’s First Law, which states that an object only accelerates when the forces on it are unbalanced.

8.6.2 Newton’s Second Law in Action

  • Example launching space shuttle at Cape Canaveral, Florida.
  • a = \frac{F_{net}}{m}
  • If the thrust (upwards) is about 6.2 million newtons greater than the weight (downwards). That is, the net force on the spacecraft is about 6.2 million newtons upwards.
  • a = \frac{6200000 N}{580000 kg} = 10.7 m/s^2