Physics: Understanding

MotionYear 10 Core Science 2015

What do we need to learn?

How do we convert units?

What do these terms mean?

Distance, displacement, vector, scalar, speed, velocity, acceleration, force and momentum

How can we describe and analyse motion?

What do we need to learn?

How are changes in movement caused by the actions of forces?

What are Newton’s 3 laws of motion? How do we explain and apply them to the real world?

What is momentum and how does it apply to real life situations?

There’s lots to learn…

What’s going to help us?

Asking lots of Questions

Conducting experiments

Drawing graphs

Applying the theory to real life situations

1.0 An Ideal World

In the ideal world the laws of motion apply exactly, eg. objects which are moving will continue to move with the same speed unless or until something occurs to change this.

To make life easier for Physics students, situations or events which require mathematical analysis are often described as occuring in an ideal, frictionless world.

In the ideal world an object under the influence of Earth’s gravity will accelerate at 9.8 ms-2 throughout its journey never reaching a terminal velocity.

In the ideal world energy transformations are always 100% efficient, so that the potential energy of a pendulum at the top of its swing is all converted to Kinetic Energy (motion energy) at the bottom.

In the ideal world perpetual motion machines are common place.

Physics language Some units we will be

using.Quantity (Unit)

Fundamental Units

Force (Newton) Mass (kg), length (m), time (s)

Acceleration (ms-2)

Momentum (kgms-1)

Velocity (ms-1)

Work (Joule) Note: W = F.d

Length (m), time (s)

Mass (kg), length (m), time (s)

Mass (kg), length (m), time (s)

Length (m), time (s)

Standard International units are: meter, kilogram, second, ampere

Why do we need standard units?When things go wrong…

Why do we need standard units?

It is important that scientists can share their data and findings. To do this, they use a common set of units. The SI unit for both distance and displacement is the metre (m) and the SI unit for speed is metres per second (m/s).

You may have seen ‘metres per second’ also written as ‘ms−1’. This expression is derived from the rule for calculating speed:

Speed = distance = metres time taken seconds

When shifting the ‘seconds’ from the denominator to the numerator of the fraction, the index (or power) becomes negative. Hence, the seconds are written with an index of −1 in ms−1 (we’ll learn more about this later…)

What’s the difference?

Scalars have magnitude (size) only

Eg distance traveled is 300meters

Other scalar quantities:

Speed, mass, time, temp, energy

Vectors have magnitude and direction.

Eg distance traveled is 300m north

Shown by a

Line showing magnitude

arrow showing direction

Motion in motion

What is the relationship between

100 and 27.78

To change units from m/s to km/h

100km/h

27.78m/s

X 3.6

÷ 3.6

Convert the following1.40km/h to m/s 2.60km/h to m/s

3.80km/h to m/s 4.100km/h to m/s

5.110km/h to m/s 6.1m/s to km/h

7.10m/s to km/h 8.12m/s to km/h

9.60m/s to km/h 10.15m/s to km/h

Convert the following1.40km/h =

11.11m/s2.60km/h =

16.67m/s3.80km/h =

22.22m/s4.100km/h =

27.78m/s5.110km/h =

30.56m/s6.1m/s = 3.6km/h

7.10m/s = 36km/h 8.12m/s = 43.2km/h

9.60m/s = 216km/h 10.15m/s = 54km/h

Fundamental skills

Show that 1 ms-1 = 3.6 kmh-1

1m x 1km x 3600s s 1000m 1h

Two relevant conversion factors are: 1 km = 1000 m, 1 h = 3600 s

so 1 ms-1 = 3.6 kmh-1

Which ones to use ?Easy, you want to end up with km on the top line and h on the bottom

These can be written as:

1km1000

m

or1000

m1km

and

1h3600 s

3600s1hor

3.6

Who are these men?

Who are these men?

Who are these men?

So who is faster?

Did Usain Bolt run the 100m faster than Michael Johnson ran the 400m?

Calculate the speed of the two men.

Speed (m/s)= distance (m) ÷ time taken (sec)

World records

100m- Usain Bolt

9.58 seconds

How many meters per second? 10.44 m/s

How many km per hour? 37.59 km/h

400m Michael Johnson

43.18 seconds

How many meters per second? 9.26 m/s

How many km per hour? 33.34km/hSo the faster runner

was…Usain Bolt

MotionAim:

To convert:

meters per second (m/s or ms-1)

to

kilometers per hour (km/h or kmh-1) using a formula

Distance Time

Distance in

meters

Time in second

sm/s km/hr

100m 9.58

400m 43.18

1km 2:12

2km 4:45

20km 55:48

World records

Distance Time

Distance in

meters

Time in second

sm/s km/hr

100m 9.58 100 9.58s 10.44 37.58

400m 43.18 400 43.18s 9.26 33.34

1km 2:12 1000 132.96s 7.52 27.07

2km 4:45 2000 284.79s 7.02 25.28

20km 55:48 20000 3348s 5.97 21.51

World records

Converting units

Position & Displacement In order to specify the position of an object we first need to define an ORIGIN or starting point from which measurements can be taken.

For example, on the number line, the point 0 is taken as the origin and all measurements are related to that point.

-40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40

Numbers to the right of zero are labelled positiveNumbers to the left of zero are labelled negativeA number 40 is 40 units to the right of 0A number -25 is 25 units to the left of 0

Position Questions

1. What needs to be defined before the position of any object can be specified ?

A zero point needs to be defined before the position of an object can be defined

2. (a) What distance has been covered when an object moves from position +150 m to position + 275 m ?

Change in position = final position – initial position = +275 – (+150) = + 125 m. Just writing 125 m is OK

(b) What distance has been covered when an object moves from position + 10 m to position -133.5 m ?

Change in position = final position – initial position = -133.5 – (+10) = - 143.5 m. Negative sign IS required

Distance & Displacement

Distance is a measure of length travelled by an object. It has a Unit (metres).Distance is best defined as “How far you have travelled in your journey”

Displacement is the shortest possible length between the start and finish of the travelling object.Displacement is best defined as “How far from your starting point you are at the end of your journey”

Distance & Displacement

Distance is a scalar measurement.Remember:Scalar measurements are expressed only as a size, with no direction.

Displacement is a vector measurement.Remember:Vector measurements are expressed as a size and a direction

Distance & Displacement

The difference between distance & displacement is easily illustrated with a simple example. You are sent on a message from home to tell the butcher his meat is off.

2 km

At the end of the journey, Distance travelled = 2 + 2 = 4km

Positive Direction

while Displacement = +2 + (-2) = 0 km

At this point in the journey, Distance travelled = 2km and Displacement = + 2km

Let’s see if this makes

sense…

Lets read through pages 262-263 and

attempt some questions

Let’s recall distance and

displacement…

Distance

Is how far on object has traveled, from point A to point B.

Distance has only magnitude (scalar)

Eg the distance traveled by the runner was 9km

Displacement

Is the change in position or the shortest distance between two points.

Displacement has a magnitude and direction (vector)

Eg the runner ran 6km to the right and 3km down, (displacement 6.7km south east)

How far did the person travel?

6km

3km

start

finishDistance: 6 + 3 = 9km

Displacement: 6.7km south east

Let’s visualise the difference…

Speed and Velocity

So what’s the difference?

Speed & VelocityThese two terms are used interchangeably in the community but strictly speaking they are different:

Speed is the time rate of change of distance, i.e., Speed = Distance

Time

Velocity is the time rate of change of displacement, i.e.,

Velocity = Displacement

Time

Speed & VelocitySpeed is a SCALAR QUANTITY, having a unit (ms-1), but no direction.Thus a speed would be:100 kmh-1 or,27 ms-1

Velocity is a VECTOR QUANTITY, having a unit (ms-1) AND a direction.Thus a velocity would be:100 kmh-1 South or - 27 ms-1

Instantaneous & Average Velocity

The term velocity can be misleading, depending upon whether you are concerned with an Instantaneous or an Average value.

The best way to illustrate the difference between the two is with an example. You take a car journey out of a city to

your gran’s place in a country town 90 km away. The journey takes you a total of 2 hours.

The average velocity for this journey, vAV = Total Displacement = 90 = 45 kmh-1

Total Time 2

Questions

Instantaneous & Average Velocity

Recall:The average velocity for this journey, vAV = Total Displacement = 90 = 45 kmh-1

Total Time 2

However, your instantaneous velocity measured at a particular time during the journey would have varied between 0 kmh-1 when stopped at traffic lights, to, say 120 kmh-1 when speeding along the freeway. Average and Instantaneous velocities are rarely the same.

Unless otherwise stated, all the problems you do in this section of the course require you to use Instantaneous Velocities.

Questions

Speed and Velocity

Average speed- total distance by the total time

Velocity- is the displacement by the time taken

Average Speed = total distance traveled (m)

Total time taken (s)

Velocity = displacement (m)

time taken (s)

Speed vs. VelocitySpeed is simply how fast you are travelling…

Velocity is “speed in a given direction”…

This car is travelling at a speed of 20m/s-1

This car is travelling at a velocity of 20m/s-1 east

Quick questions

A female runner completes a 400 m race (once around the track) in 21 seconds what is: (a)Her distance travelled (in km), (b) her displacement (in km), (c) her speed (in ms-1) and (d) her velocity (in ms-1) ?

(a) Distance = 0.4 km(b) Displacement = 0 km(c) Speed = distance/time = 400/21 = 19ms-1

(d) Velocity = displacement/time = 0/21 = 0 ms-1

6km

3km

start

finishDistance= 9km

Displacement= 6km Speed= 18km/hr

Velocity= 12km/hr

The runner takes half and hour to finish

Motion pracLet’s collect some data. . . .

Motion by GraphsDistance

Time

(a)

Displacement

Time

(b)

Describe how the object moving?

Graphical RelationshipsGraphs are used to help give us an image of movement of an object

Graphs “tell you a story”.

You need to develop the skills and abilities to “read the story”.

There are two basic types of graphs used in Physics:

(a)Sketch Graphs – give a “broad brush” picture or show the “trend”.

(b) Numerical Graphs – give the exact relationship between the two variables graphed and may be used to calculate other values.

Sketch Graphs

Distance

Time

Sketch graphs have labelled axes but no numerical values, they show a “trend” between the quantities.

The Story:As time passes, the distance of the object from its starting point does not change. This is the graph of a stationary object

The Story:The object begins its journey at the origin at t = 0. As time passes its displacement increases at a constant rate (slope is constant). So time rate of change of displacement which equals velocity is constant.This is a graph of an object travelling at constant velocity

Displacement

Time

Velocity

Time

The Story:As time passes the velocity remains constant. This is a graph of an object travelling at constant velocity

The Story:As time passes its displacement gets larger at an increasing rate. This is the graph of an object moving with constant acceleration

Displacement

Time

Sketch Graphs

Distance versus time graph. As time passes displacement remains the same. This is the graph of a stationary object

Displacement versus time graph. As time passes its displacement is increasing in a uniform manner. This is a graph of an object travelling at constant velocity.

Distance

Time

(a)

Displacement

Time

(b)

Sketch GraphsVelocity

Time

(c) Velocity versus time

graph. As time passes the velocity of the object remains the same. This is a graph of an object travelling at constant velocity.

Displacement versus time graph. As time passes its displacement gets larger at an increasing rate. This is a graph of an accelerating object.

Displacement

Time

(d)

What a graph can tell you.The graphs you are required to interpret mathematically are those where distance or displacement, speed or velocity or acceleration are plotted against time.

The information available from these graphs are summarised in the table given below.

Graph TypeRead

directly from the graph

Obtained from slope of graph

Obtained from area under the

graph

Distance or Displacement

Vs Time

Distance or displacement

Speed or velocity

No useful information

Speed or Velocity Vs

Time

Speed or velocity Acceleration

Distance or displacement

Displacement-time graphs

40

30

20

10

0

20 40 60 80 100

4) Diagonal line downwards =

3) Steeper diagonal line =1) Diagonal line =

2) Horizontal line =

Distance

(metres)

Time/s

Moving forwards

Remaining stationary

Moving forwards faster

Returning to the starting position

20 40 60 80 100

1) What is the speed during the first 20 seconds?

2) How far is the object from the start after 60 seconds?

3) What is the speed during the last 40 seconds?

4) When was the object travelling the fastest?

Distance

(metres)

Time/s

Distance/time = 0.5 ms-1

0

10

20

30

40

40 m

Distance/time = 1 ms-

1

Between 40 & 60 seconds at 1.5 ms-1

Read from graph

Acceleration

Acceleration is defined as the time rate of change of velocity, i.e., Acceleration = Change in velocity

Time

a = ΔV = Vf - Vi

t t

Acceleration has units of (ms-2)

Acceleration simply means how much an object is speeding up by every second

Acceleration means an

increase in velocity over time,

while Deceleration means a

decrease in velocity over time.

a

v

When v and a are in the same direction,the car accelerates and its velocity will increase over time.

va

When v and a are in the opposite direction, the car decelerates and its velocity will decrease over time.

Acceleration

For example If an object has an acceleration of 2ms-2, this means that an object will increase its speed by 2ms-1 every second

If a= 2ms-2 and its initial speed is 10ms-1 then

t=0 v = 10ms-1

t=1 v = 12ms-1

t=2 v = 14ms-1

a

v

If a = -2ms-2 and its initial speed is 20ms-1, then

va

t = 0 v = 20ms-1

t = 1 v = 18ms-1

t = 2 v = 16ms-1

Acceleration

A roller coaster, at the end of its journey, changes it’s velocity from 36 ms-1 to 0 ms-1 in 2.5 sec. Calculate the roller coaster’s acceleration.

a =

=

= - 14.4 ms-2

Practice Acceleration questions

Acceleration = change in velocity (in m/s)

(in m/s2) time taken (in s)

1) A cyclist accelerates from 0 to 10m/s in 5 seconds. What is her acceleration?

2) A ball is dropped and accelerates downwards at a rate of 10m/s2 for 12 seconds. How much will the ball’s velocity increase by?

3) A car accelerates from 10 to 20m/s with an acceleration of 2m/s2. How long did this take?

4) A rocket accelerates from 1,000m/s to 5,000m/s in 2 seconds. What is its acceleration?

2 ms-2

120 ms-

1

5 s

2000 ms-2

Velocity-time graphs

10 20 30 40 50

Velocity

m/s

T/s

1) Upwards line =

2) Horizontal line = 3) Upwards line =

4) Downward line =

0

20

40

60

80

60

40

20

0

1) How fast was the object going after 10 seconds?

2) What is the acceleration from 20 to 30 seconds?

3) What was the deceleration from 30 to 50s?

4) How far did the object travel altogether?

10 20 30 40 50

Velocity

m/s

Time/s

Graphical Interpretation1) Given below is the Distance vs Time graph for a cyclist riding along a straight path.

010

20 30

40

50

60

A B C D

Time (s)

10

20

Distance (a) In which section (A,B,C or D) is the cyclist stationary ? (b) In which section is the cyclist travelling at her slowest (but not zero) speed ? (c) What is her speed in part (b) above ? (d) What distance did she cover in the first 40 seconds of her journey ? (e) In which section(s) of the graph is her speed the greatest ? (f) What is her displacement from her starting point at t = 50 sec ?

(a) Stationary in section C(b) Section B (c) Travels 10 m in 20 s speed = 10/20 = 0.5 ms-1

(d) 20 m (read directly from graph)(e) Section D (travels 20 m in 10 s) speed = 2 ms-1

(f) Displacement at t = 50 s is 0 m (i.e., back at starting point)

Graphical Interpretation2) Shown below is the Velocity vs Time graph for a motorist travelling along a straight section of road.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200

2

4

6

8

10

-2

-4

-6

-8

Time(s)

-10

Velocity (ms-1)(a) What is the motorist's displacement after 4.0 sec ?(b) What is the motorists acceleration during this 4.0 sec period ?(c) What distance has the motorist covered in the 20.0 sec of his journey ?(d) What is the motorist's displacement at t = 20.0 sec (e) What happens to the motorists velocity at t = 20.0 sec? Is this realistic ?(f) Sketch an acceleration vs time graph for this journey.

(a) Displacement = area under velocity time graph. Between t = 0 and t = 4 s. Area = ½ (10 x 4) = 20 m

(b) Acceleration = slope of velocity time graph

= (10 – 0)/(4 – 0) = 2.5 ms-2

(c) Distance = area under graph (disregarding signs) Total area = ½(10 x 4) + (6 x 10) + ½(10 x 2) + ½(9 x 2) + (6 x 9) = 20 + 60 + 10 + 9 + 54 = 153 m

(d) Displacement = area under graph (taking signs into account) = ½(10 x 4) + (6 x 10) + ½(10 x 2) - ½(9 x 2) - (6 x 9) = 20 + 60 + 10 - 9 – 54 = 27 m

Graphical Interpretation3) An object is fired vertically upward on a DISTANT PLANET. Shown below is the Velocity vs Time graph for the object. The time commences the instant the object leaves the launcher

Velocity (ms

-1)

Time (s)

30

-30

2 4 6 8 10 120

(a) What is the acceleration of the object ?(b) What is the maximum height attained by the object ?(c) How long does the object take to stop ?(d) How far above the ground is the object at time t = 10.0 sec ?

(a) Acceleration = slope of velocity time graph. Slope = (30 – 0)/(0 – 6) = -5.0 ms-2

(b) Displacement = area under velocity time graph = ½ (6 x 30) = 90 m

(c) Stops at t = 6.0 sec(d) The rocket has risen to a height of 90 m in 6 sec. It then falls a

distance of ½ (4 x 20) = 40 m, so it will be 90 – 40 = 50 m above the ground at t = 10 s

Measuring Acceleration with a ticker timer

Forced Change

What is a Force ?

First, a force is an "interaction". You can compare a force to another common interaction - a conversation.

"A force is an interaction between two material objects involving a push or a pull."How is this different from the usual textbook definition of a Force simply being a “push or a pull” ?

How is Force like a Conversation?A conversation is an interaction between 2

people involving the exchange of words (and ideas). Some things to notice about a conversation (or any interaction) are:To have a conversation, you need two people. One person can't have a conversation A conversation is something that happens between two people. It is not an independently existing "thing" (object), in the sense that a chair is an independently existing "thing".

How is Force like a Conversation?

In the definition, "(material) objects" means that both objects have to be made out of matter - atoms and molecules. They both have to be "things", in the sense that a chair is a "thing". A force is something that happens between 2 objects. It is not an independently existing "thing" (object) in the sense that a chair is an independently existing "thing".

Forces are like conversations in that:To have a force, you have to have 2 objects - one object pushes, the other gets pushed.

Force Questions1. A force is an interaction between 2 objects. Therefore a force can be likened to

A: Loving chocolate B: Fear of flyingC: Hatred of cigarettesD: Having an argument with your partner

2. Between which pair can a force NOT exist ?

A: A book and a tableB: A person and a ghostC: A bicycle and a footpathD: A bug and a windscreen

What Kinds of Forces Exist ?

2. Field Forces are forces in which the two interacting objects are not in contact with each other, yet are able to exert a push or pull despite a physical separation. Examples of field forces include Gravitational Forces, Electrostatic Forces and Magnetic Forces

For simplicity sake, all forces (interactions) between objects can be placed into two broad categories:1. Contact forces are types of

forces in which the two interacting objects are physically contacting each other. Examples of contact forces include frictional forces, tensional forces, normal forces, air resistance forces, and applied forces.

What Kinds of Forces Exist ?

Force is a quantity which is measured using the derived metric unit known as the Newton. One Newton (N) is the amount of force required to give a 1 kg mass an acceleration of 1 ms-2. So 1N = 1 kgms-2

 Force is a vector quantity, you must describe both the magnitude (size) and the direction.

Contact or Field Forces1. Classify the following as examples of either Contact or Field forces in

action (or maybe both acting at the same time).

EXAMPLE CONTACT FORCE

FIELD FORCE

(a) A punch in the nose

(b) A parachutist free falling

(c) Bouncing a ball on the ground

(d) A magnet attracting a nail

(e) Two positive charges repelling each other

(f) Friction when dragging a refrigerator across the floor

(g) A shotput after leaving the thrower’s hand

√

√√

√

√

√√

√√

What Do Forces Do ?Forces affect motion. They

can:• Begin motion• Change motion• Stop motion• Have no effect

BEGINNING MOTION:A constant force (in the same direction as the motion) produces an ever increasing velocity.

STOPPING MOTION:A constant force (in the opposite direction to the motion) produces an ever decreasing velocity.

CHANGING MOTION:A constant force (at right angles to the motion) produces an ever changing direction of velocity.

NO EFFECT:A total applied force smaller than friction will not move the mass

FR

Net Force1. A body is at rest. Does this necessarily mean that it has no force acting on it ? Justify your answer.

NO – A body will remain at rest if the NET FORCE acting is zero – it could have any number of forces acting on it. So long as these forces add to zero it will remain at rest.

2. Calculate the net force acting on the object in each of the situations shown.

1200 N N

900 N 75 N95 N

250 N

250 N

150 N

450 N

(a) (b)

(c) (d)

300 N Left 20 N Left

0 N 300 N Down

Mass V’s WeightWhat’s the difference?

MassMass is the matter that makes up an

object

WeightWeight is the outcome of a gravitational field acting on a mass

Weight is a FORCE and is measured in Newtons. Its direction is along the line joining the centres of the two bodies which, between them, generate the Gravitational Field.

Near the surface of the Earth, each kilogram of mass is attracted toward the centre of the earth by a force of 9.8 N.(Of course each kilogram of Earth is also attracted to the mass by the same force, Newton 3)So, the Gravitational Field Strength near the Earth’s surface = 9.8 Nkg-1

Weight and mass are NOT the same, but they are related through the formula:

W = mgWhere: W = Weight (N)m = mass (kg)g = Grav. Field Strength (Nkg-1)

1 kg

1 kg

1 kg

9.8 N

Weight vs MassEarth’s Gravitational Field Strength is 10N/kg. In other words, a 1kg mass is pulled downwards by a force of 10N.

W

gM

Weight = Mass x Gravitational Field Strength

(in N) (in kg) (in N/kg)

1) What is the weight on Earth of a book with mass 2kg?

2) What is the weight on Earth of an apple with mass 100g?

3) Dave weighs 700N. What is his mass?

4) On the moon the gravitational field strength is 1.6N/kg. What will Dave weigh if he stands on the moon?

Mass & WeightFill in the blank spaces in the table based on a persons mass of 56kg on earth.

PlanetMass on

planet (kg)

Grav Field Strength (Nkg-

1)

Weight on planet (N)

Earth 56 9.81

Mercury 0.36

Venus 0.88

Jupiter 26.04

Saturn 11.19

Uranus 10.49

56

56

56

56

56

549.4

20.2

20.2

1458.2

626.6

587.4

Your Mass & WeightFill in the blank spaces in the table based on your mass on earth.

Planet Mass on planet (kg)

Grav Field Strength (Nkg-

1)

Weight on planet (N)

Earth 9.81

Mercury 0.36

Venus 0.88

Jupiter 26.04

Saturn 11.19

Uranus 10.49

Newton’s Laws of Motion

Newton’s LawsNewton developed 3 laws which cover all aspects of motion (provided objects travel at speeds are well below the speed of light).

Law 1 (The Law of Inertia)A body will remain at rest, or in a state of

uniform motion, unless acted upon by a net external force. Law 2

The acceleration of a body is directly proportional to net force applied and inversely proportional to its

mass. Mathematically, a = F/m more commonly written as F = ma

Law 3 (Action Reaction Law)For every action there is an equal and opposite

reaction.

Motion at or near the speed of lightis explained by Albert Einstein’s Theory of Special Relativity.Newton, at

age 26

Newton’s 1st Law

Newton 1 deals with non accelerated motion.It does not distinguish between the states of “rest” and “uniform motion” (constant velocity).As far as the law is concerned these are the same thing (state).

There is no experiment that can be performed in an isolated windowless room which can show whether the room is stationary or moving at constant velocity.

Objects want to keep on doing what

they are doing

Newton’s 1st Law states:A body will remain at rest, or in a state of uniform motion, unless acted upon by a net external force.

If NO net external force exists

No Net Force means No

Acceleration

It requires an unbalanced

force to change the velocity of

an object

Another way of saying this is:

Most importantly: Force is NOT needed to keep an object in motion

Is this how you understand the world works ?

Newton’s 2nd LawNewton’s 2nd Law states:The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force FNET, in the same direction as the net force, and inversely proportional to the mass of the object.Mathematically, a = FNET/m more commonly written as FNET = ma

The Net Force on an object

equals the rate of change of its

momentum

Using the formula FNET = ma is only valid for situations where the mass remains constant

Newton actually expressed his 2nd law in terms of momentum.

So, FNET = change in momentum = Δp = mΔv =

ma change in time Δt Δt

Momentum (p) = mass x velocity

FNET is the VECTOR SUM of all the forces acting on an object.The acceleration and FNET are ALWAYS in the same direction.

Newton 2 deals with accelerated motion.

Force and acceleration

If the forces acting on an object are unbalanced then the object will accelerate, like these wrestlers:

Force (in N) = Mass (in kg) x Acceleration (in m/s2)

F

AM

Force, mass and acceleration

1) A force of 1000N is applied to push a mass of 500kg. How quickly does it accelerate?

2) A force of 3000N acts on a car to make it accelerate by 1.5m/s2. How heavy is the car?

3) A car accelerates at a rate of 5m/s2. If it weighs 500kg how much driving force is the engine applying?

4) A force of 10N is applied by a boy while lifting a 20kg mass. How much does it accelerate by?

F

AM

Newton’s 2nd LawUnbalanced force or Net force causes

Terminal Velocity

Consider a skydiver:

1) At the start of his jump the air resistance is _______ so he _______ downwards.

2) As his speed increases his air resistance will _______

3) Eventually the air resistance will be big enough to _______ the skydiver’s weight. At this point the forces are balanced so his speed becomes ________ - this is called TERMINAL VELOCITY

Terminal Velocity

Consider a skydiver:

4) When he opens his parachute the air resistance suddenly ________, causing him to start _____ ____.

5) Because he is slowing down his air resistance will _______ again until it balances his _________. The skydiver has now reached a new, lower ________ _______.

Velocity-time graph for terminal velocity…

Velocity

Time

Speed increases…

Terminal velocity reached…

Parachute opens – diver slows down

New, lower terminal velocity reached

Diver hits the ground

On the Moon

Newton’s 3rd LawNewton's 1st and 2nd Laws tell you what forces do. Newton's 3rd Law tells you what forces are.

"opposite" means that the two forces always act in opposite directions - exactly 180o apart.

This statement is correct, but terse and confusing. You need to understand that it means:"action...reaction" means that forces always occur in pairs. Single, isolated forces never happen.

For example, first Suzie annoys Johnnie (action) then Johnny says "Mommy! Suzie’s annoying me!" (reaction).This is NOT an example what is going on here! The action and reaction forces exist at the same time.

"action " and "reaction " are unfortunate names for a couple of reasons :

For every action there is an equal and

opposite reaction

1. Either force in an interaction can be the "action" force or the "reaction" force.

"equal" means :Both forces are equal in magnitude.Both forces exist at exactly the same time. They both start at exactly the same instant, and they both stop at exactly the same instant. They are equal in time.

2. People associate action/reaction with "first an action, then a reaction”

Questions

Spring 200889

Friction is a Force

Force on person by box

Force on floor by box Force on box by floor

It’s the sum of all the forces that determines the acceleration.Every force has an equal & opposite partner.

Force on box by person

Spring 2008

Friction Mechanism

Corrugations in the surfaces grind when things slide.Lubricants fill in the gaps and let things slide more easily.

Why Doesn’t Gravity Make the Box Fall?

Force of Earth acting on Box (weight)

Force of Floor acting on Box

Force from floor on boxcancels gravity.

If the floor vanished, thebox would begin to fall.

What’s missing in this picture?

Force on person by box

Force on floor by box Force on box by floor

Force on box by person

A pair of forces acting between person and floor.

Spring 200893

Don’t all forces then cancel?

How does anything ever move (accelerate) if every force has an opposing pair?

The important thing is the net force on the object of interest

Force on boxby floor

Force on box by person

Net Forceon box

Newton’s Laws29. At what speeds are Newton’s Laws applicable ?At speeds way below the speed of light

30. Newton’s First Law:A: Does not distinguish between accelerated motion and constant velocity motionB: Does not distinguish between stationary objects and those moving with constant accelerationC: Does not distinguish between stationary objects and those moving with constant velocityD: None of the above

31. Newton’s Second Law:A: Implies that for a given force, large masses will accelerate faster than small massesB: Implies that for a given force, larger masses will accelerate slower than smaller massesC: Implies that for a given force, the acceleration produced is independent of massD: Implies that for a given force, no acceleration is produced irrespective of the mass.

Newton’s 2nd Law

34. A car of mass 1250 kg is travelling at a constant speed of 78 kmh-1 (21.7 ms-1). It suffers a constant retarding force (from air resistance, friction etc) of 12,000 N

(a)What is the net force on the car when travelling at its constant speed of 78 kmh-1 ?

At constant velocity, acc = 0 thus ΣF = 0

(b) What driving force is supplied by the car’s engine when travelling at 78 kmh-1 ?

(c) If the car took 14.6 sec to reach 78 kmh-1 from rest , what was its acceleration (assumed constant) ?

At constant velocity ΣF = 0, so driving force = retarding force = 12,000 N

Use eqns of motionu = 0 ms-1 , v = 21.7 ms-1, a = ?, x = ?, t = 14.6 suse v = u + at -> 21.7 = 0 + 14.6(a) -> a = 1.49 ms-2

MomentumNewton described Momentum as the “quality of motion”, a measure of the ease or difficulty of changing the motion of an object.Momentum is a vector quantity having both magnitude and direction.

Mathematically,p = mv

Where,p = momentum (kgms-1)m = mass (kg)v = velocity (ms-1)

In order to change the momentum of an object a mechanism for that change is required.

Airbags/Crumple Zones

39. Explain why, in a modern car equipped with seat belts and an air bag , he would likely survive the collision whereas in the past, with no such safety devices, he would most likely have been killed.

The change in momentum in any collision is a fixed value thus impulse is also fixed, but the individual values of F and t can vary as long as their product is the that fixed value. In modern vehicles seat belts and crumple zones are designed to increase to time it takes to stop thus necessarily reducing the force needed to be absorbed by the driver because Impulse = Ft. This reduced force will lead to reduced injuries. In the old days the driver would have been “stopped” be some hard object like a metal dashboard and his time to stop would have been much shorter and thus the force experienced would have been larger leading to more severe injury and likely death.