Forces, Motion, & Energy - Notes on Newton's Laws

Forces, Motion, & Energy

Goal

• Apply Newton’s three laws of motion.

• Success Criteria:

  • Describe the law of inertia (First Law)

  • Analyse the relationship between force, mass, and acceleration (Second Law)

  • Identify and label the action-reaction pair of forces (Third Law)

• How do car safety features protect you in a crash?

Area of Study 1: Forces, Motion, & Energy

• Lesson 9:

  • Model the force due to gravity, $F_g$, as the force of gravity acting at the centre of mass of a body.

  • Model forces as vectors acting at the point of application (with magnitude and direction), labelling these forces using the convention: $F<em>{\text{on A by B}} = -F</em>{\text{on B by A}}$.

  • Apply Newton’s three laws of motion to a body on which forces act.

Key Vocabulary

• Inertia

• Force

• Mass

• Acceleration

• Balanced

• Unbalanced

• Action - Reaction Pair

• Velocity

Newton's Laws

• 1st law: The Law of Inertia

  • An object at rest will stay at rest, unless acted on by a net external force.

• 2nd law: $F = ma$

  • The force on an object is equal to its mass times its acceleration.

• 3rd law: $F<em>{\text{on A by B}} = -F</em>{\text{on B by A}}$

  • All forces between two objects exist in equal magnitude and opposite direction.

Newton’s First Law: The Law of Inertia

• An object will not change its motion unless a net force acts on it.

  • Either a state of rest, or

  • Uniform motion

• An object will maintain a constant velocity unless an unbalanced, external force acts on it.

• Example 1: A student observes a box sliding across a surface and slowing down to a stop. From this observation what can the student conclude about the forces acting on the box?

• Example 2: Passengers on commercial flights are required to be seated and have their seatbelts fastened when the plane is coming in to land. Explain what would happen to a person who was standing in the aisle as the plane landed?

• Question 3: Explain why you should always wear a seatbelt.

  • Fact: According to… (state a relevant law / theory / equation / etc)

  • Reason: This means that… (describe the fact)

  • Outcome: In this case / instance / question / example…

Newton’s Second Law

• The force on an object is equal to its mass times its acceleration: $F = ma$

• Where:

  • F = Net force (N)

  • m = mass of the object (kg)

  • a = acceleration ($ms^{-2}$)

  • v = final velocity ($ms^{-1}$)

  • u = initial velocity ($ms^{-1}$)

  • t = time (s)

• Formula: $F = ma = m \frac{v - u}{t}$

Acceleration

• Acceleration due to gravity (g) is the acceleration of an object due to gravitational force.

• On the surface of Earth, $g = 9.81 ms^{-2}$.

• The value of g is different on different planets as they have different masses

Comparative Gravities

Examples

• Example 1: How much force is required to hold a piano (mass 545 kg) outside a third floor window?

• Example 2: Calculate the acceleration of a 45.0kg mass that has a 441N force acting on it.

• Example 3: A toy car with a mass of 55.9 kg starts at rest and accelerates north. The engine generates a force of 56.8N and it accelerates over 3.50seconds. What is the final velocity of the car?

• Question 4: Calculate the final velocity of a 60.0 kg mass moving at 2.67$ms^{-1}$ east, when a net force of 45.5N west acts on it for 2.80 seconds.

• Question 5: Mary is paddling a canoe. The paddles are providing a constant driving force of 45N south and the drag forces total 25N north. The mass of the canoe is 15 kg and Mary has a mass of 50.0kg.

  • a. Calculate the force due to gravity acting on Mary.

  • b. Find the net horizontal force acting on the canoe.

  • c. Calculate the magnitude of the acceleration on the canoe.

Practical Activity

• Complete the practical activity using the provided worksheet

• Draw your graphs neatly and in pencil

• Add a line of best fit to your graph

Newton’s Third Law

• $F<em>{\text{on A by B}} = -F</em>{\text{on B by A}}$

• All forces between two objects exist in equal magnitude and opposite direction.

• For every action, there is an equal and opposite reaction

  • If object A exerts a force of object B, then object B will exert a force, equal in size and opposite in direction, on object A.

• Newton realised that all forces exist in pairs, often referred to as action-reaction pairs

• Labelling Action-Reaction Pairs

• Example 1: The photo shows an astronaut orbiting Earth. Label the action-reaction pair of force between Earth and the astronaut.

• Example 2: Which best explains why we are able to accelerate forward when starting to run?

  • a. The runner's upper body quickly leans forward, causing the entire body to begin accelerating forward.

  • b. As one leg moves backward, it provides an equal and opposite force for the other foot to move forward.

  • c. The foot not touching the ground propels the entire body as it swings forward.

  • d. The striking foot pushes backward against the ground. The friction with the ground provides an equal and opposite force forward.

  • e. No acceleration takes place. Runners are always at a fixed velocity.

• Example 3: You and a friend are pulling on a rope in opposite directions as hard as you can. What is the "equal and opposite force" to the force of your hand pulling on the rope, as described by Newton's Third Law?

  • a. The force of the rope pulling your friend's hand

  • b. The force of your arm pulling back on your hand

  • c. The force of friction between the ground and your shoes

  • d. The force of your friend pulling on the rope in the opposite direction

  • e. The force of the rope pulling on your hand in the opposite direction

• Example 4: Why isn’t the car damaged when it hits a bug, but the bug is instantly flattened?

Year 10 Physics: Forces, Motion, & Energy

Area of Study 1: Forces, Motion, & Energy - Lesson 5

• Objectives:

  • Analyze graphically, numerically, and algebraically, straight-line motion under constant acceleration.

  • Apply the vector model of forces, including vector addition and components of forces.

Goal

• Apply Newton’s First Law of Motion both theoretically and mathematically.

Success Criteria

• I can:

  • Describe Newton’s First Law of Motion.

  • Calculate the net force acting on an object.

  • Determine the effect of the net force on an object with reference to Newton’s first law.

• Question: Why do objects change their speed?

Key Vocabulary

• Accelerate

• Net Force

• Inertia

Why Do Objects Change Their Speed?

• This question is central to understanding forces and motion.

Newton’s First Law

• Newton's First Law: Every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external, net force.

• Inertia: The tendency to resist changes in a state of motion.

Net Force

• Definition: The sum of all the forces acting on an object.

• Nature: Vector quantity (has both magnitude and direction).

• Formula: $F_{net} = \sum F$

• If two forces act in opposite directions, the net force is the difference between the greater and smaller force.

• The object will accelerate in the direction of the net force.

Balanced Forces

• Do not cause a change in motion (Newton’s First Law).

• Opposite in direction.

• Equal in magnitude.

Unbalanced Forces

• Occur when one force is greater in magnitude than the other.

• Shows the effect of force on the object - causes the object to accelerate.

• Can be in the same or opposite direction.

Free Body Diagrams

• Physicists use free body diagrams to represent complex objects with detail.

Representing Force

• Force is a vector quantity.

• Represented with an arrow:

  • The length of the arrow indicates the magnitude of the force.

  • The arrowhead shows the direction.

Application Questions (Net Force Examples)

• Examples with multiple forces acting on objects, requiring calculation of net force.

Changing Speed in a Car

• Illustrates real-world applications of forces and motion.

Braking Distance

• Braking distance depends on how fast a vehicle is traveling before the brakes are applied, and is proportional to the square of the initial speed.

• Even small increases in speed mean significantly longer braking distances.

• Wipe Off 5 Road Safety Campaign

  • Reduce speeding.

  • Educate road users about the dangers of traveling, even a little, over the speed limit.

  • Reducing average speed by 5 km/h could save lives and prevent serious injuries.

Review Questions

• What happens to the moose if you’re driving while on your phone?

• What happens to the moose if you’re travelling at a higher speed?

• Why do speed limits exist? Why are they different? (e.g., school zones vs. highways)

Forces, Motion, & Energy

Area of Study 1: Forces, Motion, &Energy - Lesson 3

• Identify parameters of motion as vectors or scalars.

• Analyze, graphically, non-uniform motion in a straight line.

Goal

• Analyze kinematics graphs (displacement-time, velocity-time, and acceleration-time).

Success Criteria:

• Define acceleration as a change in speed and/or direction (change in velocity).

• Calculate acceleration mathematically.

• Interpret information presented as kinematics graphs.

• Question: How do speed cameras work?

Acceleration

• The rate at which velocity changes with time, considering both speed and direction.

• Acceleration can occur if an object speeds up, slows down, or changes direction.

Speed & Velocity

• Speed: $s = \frac{d}{t}$

  • $s$ = speed (m/s)

  • $d$ = distance (m)

  • $t$ = time (s)

• Velocity: $v = \frac{\Delta x}{t}$

  • $v$ = velocity (m/s)

  • $\Delta x$ = displacement (m)

  • $t$ = time (s)

Acceleration (Continued)

• Acceleration due to gravity ($g$) is the acceleration of an object due to gravitational force.

• On the surface of Earth, $g = 9.81 \text{ m/s}^2$.

• The value of $g$ is different on different planets due to varying masses.

Acceleration Formula

• $a = \frac{\Delta v}{t}$

  • $a$ = acceleration (m/s²)

  • $\Delta v$ = change in velocity (m/s)

  • $t$ = time (s)

• $a = \frac{v<em>f - v</em>i}{t}$

  • $a$ = acceleration (m/s²)

  • $v_f$ = final velocity (m/s)

  • $v_i$ = initial velocity (m/s)

  • $t$ = time (s)

Displacement-Time Graphs

• For motion in 1-dimension.

Checkpoint: Acting out displacement-time graphs

• Place markers 1m apart from negative 4 to positive 4.

• Start the stopwatch and try to match your motion to the graph. The person timing you should give you feedback on how you went.

• Swap roles and repeat the activity until everyone in your group has had a turn.

• Finished early? Create your own to act out.

Velocity-Time Graphs

• For motion in 1-dimension.

• Includes positive acceleration, negative acceleration and zero acceleration

Converting between Kinematics Graphs

• It is possible to convert between displacement-time, velocity-time, and acceleration-time graphs for motion in one-dimension (left/right, up/down, north/south, etc.).

Checkpoint

• Use the velocity-time graph to draw a displacement (s) - time graph and an acceleration - time graph.

• Draw an approximate velocity-time graph and then use that to draw an approximate acceleration-time graph for the four displacement-time graphs.

Instantaneous vs. Average Speed

Instantaneous Speed

• The speed of an object at a particular moment in time.

• If direction is included, it becomes instantaneous velocity.

Average Speed

• The average speed formula is given by the total distance traveled divided by the time taken to cover that distance.

• Assume you’re being asked for average speed in VCE physics.

Okay, here's a simplified explanation of kinematics graphs:

• Displacement-Time Graphs: These graphs show how an object's position changes over time. A straight, sloped line means the object is moving at a constant velocity. A curved line indicates acceleration (changing velocity). The steeper the slope, the faster the object is moving.

• Velocity-Time Graphs: These graphs illustrate how an object's velocity changes over time. A straight, sloped line indicates constant acceleration. A horizontal line means the object is moving at a constant velocity. The area under the curve represents the displacement of the object.

• Acceleration-Time Graphs: These graphs show how an object's acceleration changes over time. A horizontal line indicates constant acceleration. The area under the curve represents the change in velocity of the object.

Area of Study 1: Forces, Motion, & Energy - Lesson 2

• Objective: Analyze straight-line motion under constant acceleration, identifying parameters as vectors or scalars graphically, numerically, and algebraically.

• Goal: Explore how changing distance and time affects speed/velocity.

• Success Criteria:

  • Differentiate between scalar and vector quantities.

  • Calculate speed and velocity.

  • Consider ways to improve accuracy and precision in data collection.

Key Vocabulary

• Distance

• Displacement

• Speed

• Velocity

• Scalar Quantity

• Vector Quantity

• Acceleration

Scalar and Vector Quantities

• Scalars: Quantities with only magnitude (size).

• Vectors: Quantities with both magnitude and direction.

Distance vs. Displacement

• Distance (d): A scalar quantity that measures the total distance traveled.

  • SI Unit: meters (m)

• Displacement (x): A vector quantity measuring the shortest distance between two points.

  • SI Unit: meters (m)

Speed vs. Velocity

• Speed (s): A scalar quantity indicating "how fast an object is moving."

  • It represents the rate at which an object covers distance.

• Velocity (v): A vector quantity referring to "the rate at which an object changes its position."

Speed and Velocity Equations

• Speed:

  • $s = \frac{d}{t}$

  • s = speed (m/s)

  • d = distance (m)

  • t = time (s)

• Velocity:

  • $v = \frac{\Delta x}{t}$

  • v = velocity (m/s)

  • $\Delta x$ = displacement (m)

  • t = time (s)

  • $\Delta$ = change = final - initial

Speed Equation

• $s = \frac{d}{t}$

  • s = speed (m/s)

  • d = distance (m)

  • t = time (s)

Helpful Hints: Unit Conversion

• Converting between km/h and m/s:

  • km/h ÷ 3.6 = m/s

  • m/s x 3.6 = km/h

Checkpoint Examples

• Example 1: A dog chases a ball 40m west in 5 seconds.

  • Calculate the speed of the dog.

  • Calculate the velocity of the dog.

  • V: List the variables

  • E: Which equation/s connects these variables?

  • G: Go! Substitute and solve

• Example 2: A cat runs around the neighborhood for 10 minutes at an average speed of 1.5 m/s. How far does the cat cover in this time?

  • V: List the variables

  • E: Which equation/s connects these variables?

  • G: Go! Substitute and solve

Your Turn Questions

• Question 1: A car travels 540 km north in 6 hours.

  • What speed did it travel at (in km/h)?

  • What is the car’s average velocity in m/s?

• Question 2: A whale swims at a constant speed of 8 m/s for 17 seconds. What distance did it travel?

• Question 3: How long does it take to travel a distance of 672 km at a speed of 96 km/h?

• Instructions:
  * V: List the variables
  * E: Which equation/s connects these variables?
  * G: Go! Substitute and solve
  * In your book write out the question and the answer, as well as working out (working out = the equation and full substitution as well as the answer)

How Fast Can You Run? Experiment

• What data will you need to determine your speed?

• How can you increase the precision and accuracy of your data?

  • Accuracy: How close a measurement is to the true value.

  • Precision: How close multiple measurements are to each other. Precise measurements have values close to the mean.

    • Repeating an experiment improves precision through statistical averaging, but doesn't affect accuracy, as systematic errors don't average out.

Experiment Procedure

• Perform at least three trials to measure running speed.

• Optional: Measure skipping, moonwalking, or rolling speed.

• Record data in a table:

  Distance (m)	Trial 1 (s)	Trial 2 (s)	Trial 3 (s)	Average time (s)	Speed (m/s)
  Running
  Moonwalking
  Rolling

Displacement Graphs

Motion

• Motion is an object's change in position relative to a reference point.

• Example:

  • Relative to the earth: Moving at 17,500 mph.

  • Relative to the shuttle: Not moving.

Distance vs. Displacement

• Distance: How far travelled.

• Displacement: How far from origin.

Distance and Displacement in 2D

• Example: Distance between Minnetonka High School and Niagra Falls, Canada.

  • Distance as the Crow Flies: $1170.297$

  • Distance by Land Transport: $1525.995$

  • Road journey time: 21 Hours, 11 Minutes

Practice Problem: Distance and Displacement

• Problem: You walked 5 km East, turned around and walked 2 km West, turned around again and walked another 4 km East.

  • What is your distance?

  • What is your displacement?

• Solution:

  • Distance: $5 + 2 + 4 = 11 \text{ km}$

  • Displacement: $7 \text{ km}$

Graphing Displacement

• The displacement can be graphed over time to visualize the motion.

  Variable to Find	Known Variables	SUVAT Equation	Rearranged Equation
  ss	uu, vv, tt	s=12(u+v)ts=21​(u+v)t	No rearrangement needed
  ss	uu, aa, tt	s=ut+12at2s=ut+21​at2	No rearrangement needed
  ss	vv, aa, tt	s=vt−12at2s=vt−21​at2	No rearrangement needed
  ss	uu, vv, aa	v2=u2+2asv2=u2+2as	s=v2−u22as=2av2−u2​
  uu	vv, aa, tt	v=u+atv=u+at	u=v−atu=v−at
  uu	ss, aa, tt	s=ut+12at2s=ut+21​at2	u=s−12at2tu=ts−21​at2​
  uu	ss, vv, tt	s=12(u+v)ts=21​(u+v)t	u=2st−vu=t2s​−v
  uu	vv, aa, ss	v2=u2+2asv2=u2+2as	u=v2−2asu=v2−2as​
  vv	uu, aa, tt	v=u+atv=u+at	No rearrangement needed
  vv	ss, uu, tt	s=12(u+v)ts=21​(u+v)t	v=2st−uv=t2s​−u
  vv	uu, aa, ss	v2=u2+2asv2=u2+2as	v=u2+2asv=u2+2as​
  vv	ss, aa, tt	s=vt−12at2s=vt−21​at2	v=s+12at2tv=ts+21​at2​
  aa	uu, vv, tt	v=u+atv=u+at	a=v−uta=tv−u​
  aa	ss, uu, tt	s=ut+12at2s=ut+21​at2	a=2(s−ut)t2a=t22(s−ut)​
  aa	uu, vv, ss	v2=u2+2asv2=u2+2as	a=v2−u22sa=2sv2−u2​
  aa	ss, vv, tt	s=vt−12at2s=vt−21​at2	a=2(vt−s)t2a=t22(vt−s)​
  tt	uu, vv, aa	v=u+atv=u+at	t=v−uat=av−u​
  tt	ss, uu, aa	s=ut+12at2s=ut+21​at2	Use quadratic formula: t=−u±u2−4(12a)(−s)2(12a)t=2(21​a)−u±u2−4(21​a)(−s)​​
  tt	ss, uu, vv	s=12(u+v)ts=21​(u+v)t	t=2su+vt=u+v2s​

  
  

• The example of walking 5 km East, then 2 km West, then 4 km East can be represented on a displacement graph with time on the x-axis.