PHY1020

BASIC CONCEPTS IN PHYSICS I

How can we predict the motion of everyday objects? 1

The Problem of Motion

Zeno and his paradoxes 2

ZENO (CA. 490–430 BC) AND ONENESS

Motion is impossible!

If “all is one” as

Parmeinides said then

motion is just an illusion

Zeno put together a number

of paradoxes to show that

motion does not really occur

Achilles Arrogance 3

ACHILLES AND THE TORTOISE

Set-up: Achilles lets the tortoise start a little ahead of him to give him a

head start

During the race: Achilles must first get to the position where the

tortoise started, during which time the tortoise has moved forward by

some distance. Achilles then moves through this distance during which

again the tortoise moves forward by some distance

Conclusion: Achilles will never reach the

tortoise no matter how fast he runs!

The horse that couldn’t 4

THE DICHOTOMY PARADOX

Imagine a horse tried to run some distance, she must first run half that

distance, but before that a quarter of the distance and so

This motion is impossible! (it seems)

The nature of measurements 5

THE SOLUTION TO THE PARADOX

Mathematical Reason:

Physics Reason: Observers measure distances between objects, the real

world does not. Thus its not that we have half of the

final destination distance covered but that half of some

distance has been past. Nature has no pre-destined aim!

Not us!

Objects tend to their natural place 6

ARISTOTLE (CA. 384–322 BC) AND MOTION

Axiom’s of Aristotle’s Theory of Motion:

1. No motion without a mover in contact with

moving body

2. Distinction in mover:

i. Natural motion - mover is internal to

moving body

ii. Forced motion - mover is external to

moving body

Held that objects tend to their natural place

unless forced motion is imposed upon them

Speed depends on applied force and medium resistance

7

ARISTOTLE’S LAW OF MOTION

Factors in his law of motion:

F – Force (weight) of mover

R – Viscosity or resistance of medium (Antiquity – Nature abhors

vacuums [Horror vacui])

V – Speed (Not velocity)

If F = R (or less than) then no motion occurs, but

if F > R then

How do objects fall? 8

PROBLEMS Question: What hits the ground first a 1Kg ball or a 10Kg ball?

Aristotelian Prediction: the 1Kg ball will take 10 times the time to fall the

same length

Reasoning: For some distance let T be the time taken to traverse that

distance

V1, V10 – Velocity of objects; T1, T10 – Falling time of objects

because

because

Thus or

Enter Strato and the idea of demonstrations 9

STRATO (CA. 335-269 BC) AND ACCELERATION

- Emphasized the need for demonstrations (experiments)

- Strato defined acceleration as the traversing of equal distances at

shorter times

- Claimed that Aristotle is correct but that during motion bodies

accelerate

Experimental demonstration 10

PROOF OF ACCELERATION

Strato used the water moving out of a

Spout to show that force produces

some acceleration since the drops

must slow down to form separate

entities from the main stream

How do objects fall? 11

JOHN PHILOPONUS (CA. 490–570)

But this [view of Aristotle] is completely

erroneous, and our view may be completely

corroborated by actual observation more

effectively than by any sort of verbal argument.

For if you let fall from the same height two

weights, one many times heavier than the other

you will see that the ratio of the times

required for the motion does not depend

[solely] on the weights, but that the difference

in time is very small. ... —John Philoponus'

refutation of the Aristotelian claim that the

elapsed time for a falling body is inversely

proportional to its weight

- Refutation of Aristotle’s inverse

relation

- Strengthening of experimental

side

- Proposal that objects fall at

approximately the same rates

irrespective of weight

[1]

[1] Cohen, W. R. and Drabkin, I.E., A Source Book in Greek

Science (Cambridge, MA: Harvard University Press, 1992)

Battle of the Force – Internal or Medium Driven 12

RESISTANCE TO MOTION

Aristotle thought that motion was maintained by means of a force

transferring ‘power’ to a surrounding medium which then maintains the

propagation

Philoponus on the other hand reasoned

that the ‘power’ that propels an object

forward must be internal and so self-

maintained meaning that objects could

move through vacua

How do objects start to moving and what stops them? 13

Jean Buridan (CA. 1300–1358)

Following Philoponus Buridan held that motion after

being caused is maintained by the object in question

This was done by defining an inertia for moving bodies,

that is an initial impetus that sets the object in motion

causes a sustained mechanism that maintains motion

This effective ‘driving power’ would depend in some way on the initial

speed and amount of matter

This idea has the added effect that it can explain how objects stop

moving as well, the resistance by a medium produces this stopping effect

This is very close to our modern explanation of motion!

Motion should be thought of in terms of observables 14

GALILEO GALILEI (CA. 1564–1642)

Constructed a model of motion using

geometrical concepts such as distance and

more importantly changes in this quantity

The core of Galileo is that he thought of

motion in concrete terms of change and so

observation instead of philosophical reasoning

"Nature is written in the grammar of

mathematics and its characters are triangles,

circles and other geometrical figures."

The beginnings of Galilean relativity 15

UNIFORM MOTION

"By steady or uniform motion, I mean one in which

the distances traversed by the moving particle during

any equal intervals of time, are themselves equal."

Definition: Uniform motion is when the distance

traversed is proportional to time of travel

Claim: Uniform motion is undetectable

under certain conditions.

What knock on effects could this have for

the Earth, could it be in motion?

Is the same true of acceleration or is this special? 16

UNIFORM ACCELERATION

Galileo’s definition: "A motion is said to be uniformly accelerated when

starting from rest, if it acquires, during equal time-intervals, equal

increments of speed."

Speed is proportional to time of travel or

This means

where k is some constant

The same distance is covered in equal times 17

MEAN SPEED

Introduced the idea of ‘mean speed’, which would be the speed

needed to traverse the same distance in some particular time

speed

speed

time

Hence,

Back to falling bodies 18

FREE FALL

Galileo proposed that bodies fall with uniform acceleration (with the

proviso that there is no wind currents or extra medium resistance as

for example through water)

This means that bodies fall with the same acceleration as long as the

medium (air/water) does not pose too much resistance

Thus,

This means feathers and rocks fall at the same speed!

No mass factor!

Galileo's Leaning Tower of Pisa experiment 19

THE EXPERIMENTAL TEST

Galileo dropped two spheres of different masses from the top of the

Tower of Pisa and found that they hit the ground at the same time

Results:

1. Aristotle’s theory of gravity is wrong, different weights fall at the

same rate, or at least not as an inverse proportionality

2. Galileo’s theory of motion with uniform acceleration correctly

predicted the measured results

How fast can we fall? 20

CONCEPT OF TERMINAL VELOCITY

Remembering Aristotles idea of when Force = Medium Resistance no

motion can occur, Galileo said this for acceleration

When Force = Medium Resistance no further acceleration occurs no

matter the weight and a Terminal uniform Velocity is achieved

The Speed limit 21

PROBLEM WITH GALILEO

Set-up: Imagine a sphere falling down an infinitely long inclined plane, the

sphere will accelerate ad infinitum.

This contradicts what happens in experiments when scientists try to

speed particles past the speed of light thus disproving the high velocity

extreme of Galileo’s theory of motion

Bringing everything together 22

NEWTON (CA. 1642–1727)

- There is only one kind of force and it is linked

to acceleration in a different way

- Force produced acceleration!

- and similarly acceleration produces a force

- Did not differentiate between internal and

external forces

- Using a new notion of calculus he managed

to intertwine concepts of position, speed and

acceleration

Newton’s Model of how Motion occurs 23

NEWTON’S LAWS OF MOTION

Newton proposed three laws under which all motion

could be described

First law: An object remains at constant velocity

unless acted upon by a force

Second law: The acceleration of an object is directly proportional to the

force applied on it and inversely proportional to the mass of the object.

Furthermore the direction of acceleration is parallel to the force

Third law: For every (force) action there is an equal and opposite

reaction

Newton’s Apple 24

FALLING BODIES

Keeping Galileo’s idea of uniform

acceleration of falling bodies, Newton

managed to articulate this into a general

principle (called the Equivalence

Principle)

The Age of Absolutes 25

GALILEAN RELATIVITY AND NEWTON’S AXIOMS

Galilean relativity lies on the principle that the laws of motion are the

same in all inertial (non-accelerating) frames

On this Newton formed his axioms:

1. An absolute space exists in which

motion can occur

2. All inertial observers share a

universal measurement of time

Light must travel instantaneously to

satisfy the second condition

The Universal Speed Limit 26

EINSTEIN IN THE HIGH ENERGY REGION

In the high velocity regime Galilean relativity breaks down and Einstein’s

relativity theory must be used

The principles here are changed to:

1. The Principle of Relativity – The underlying laws of motion are not

affected by the inertial frame in which measurements are made

2. The Principle of the Invariance of the Speed of Light – The speed of

light is measured to be the same in every inertial frame

Einstein weakened Newton’s absolute space and time axioms and said

that it may be that different observers measure the length and period of

events differently!

Quantum Nature 27

A SHORT NOTE ON QUANTUM THEORY

An electron collides with a Hydrogen

atom and scatters two further electrons

Over short distances particles jump from place to place, however on

the large scale it appears as continuous motion

CERN 28

THE CURRENT STATE OF AFFAIRS

The current problems in motion theory stem from trying to reproduce

Einstein’s relativity predictions (which are known to work) using the

quantum theory