Physics 1901 Advanced

1
Physics 1901 (Advanced)

• A/Prof Geraint F. Lewis
• Rm 557, A29
• gfl_at_physics.usyd.edu.au
• www.physics.usyd.edu.au/gfl/Lecture

2
Physics_at_Sydney

• World renowned research
• Astronomy Astrophysics
• Optics Photonics
• Theoretical Physics
• Plasma High Energy Physics
• Brain Medical Physics
• Take advantage of this expertise

3
Physics 1901 (Advanced)

• Three module course consisting of
• Mechanics (15 lectures)
• Thermal Physics (10 lectures)
• Waves Chaos (13 lectures)
• It is assumed you have prior physics knowledge.
• Stream changes made by the HECS deadline.

4
Learning

• What you learn from this course depends upon the
  effort you put in
• Lectures are a guide to course material
• University Physics by Young Freeman
• Online resources WebCT Junior Physics
• 6hrs/week independent study

5
Tutorials

• Interactive Workshop Tutorials
• Work in small groups (upto 4)
• Worksheets Hands-on demonstrations
• A chance to ask questions
• A place to clarify ideas
• Not assessed up to you.
• No worksheets if you dont attend.

6
Labs

• Labs are 3 hours
• Work in groups of 4
• Read in advance
• Get it done faster
• Better chance of learning something
• Level 4, Carslaw Building
• Lab manuals from the CO-OP

7
Assessment

• Lab 20
• Mastering Physics 10
• Progressive Test 5
• Lab Skills Test 5
• Exam 60
• It is important to know concepts ideas, not
  just manipulate formulae.
• It is important to know the meaning of Academic
  Honesty

8
If you need help

• Talk to me or a duty tutor
• Consult the web resources
• Serious personal problems or illness it is
  important to complete a Special Consideration
  Form ASAP!

9
Physics 1901 Mechanics
10
Physics

• is the study of the changeable properties of
  natural objects
• Position, mass, temperature, charge
• Physics is predictive
• Know the properties of something now,
• calculate the properties of something later

11
Classical Mechanics (why classical?)

• Modern physics
• General Relativity
• Quantum Mechanics
• Classical mechanics
• Physics of human experience

12
Classical Mechanics (what why?)

• Simply put, classical mechanics is how do things
  respond to forces?
• The concepts of classical mechanics underpin the
  rest of physics
• Have implications in all sciences!
• Applied classical mechanics Engineering?

13
Course Layout
14
Kinematics (Review Ch 1-3)

• Kinematics is the description of motion
• Lets start with motion in one dimension
• xo is the initial position of an object
• vo is the initial velocity of an object
• a is the (constant) acceleration of an object
• What are its properties after a time t ?

15
Velocity Acceleration
Velocity is the change of distance over time
Acceleration is the change of velocity over time
(Differential equations!)
16
Kinematic Equations
You do not need to memorize such equations as
they will be given in an exam. You should be able
to derive them from the definitions of velocity
and acceleration!
17
Non-Constant Acceleration

• We will consider only constant acceleration.
• Remember this is not generally true.

is called the jerk
Can use these to derive more general kinematic
equations.
18
More than one dimension Vectors

• Once we consider motion in more than one
  dimension, vectors make life simpler.

The kinematic equations can be applied in each
direction separately. You decide the coordinate
system!
19
Decomposing Vectors
Vectors have a length direction. To use them we
need to decompose the vector into its components.
(this is important!)
20
Adding Vectors
21
Monkey Hunter
22
Galileo Inertia
The Principle of Inertia If a body is left
along, it remains where it is or continues along
with uniform motion. Why the universe behaves
like this is a mystery, but without it science
would be quite tricky.
23
Isaac Newton

• Developed concept of Dynamics
• Considered the motion of a body as it is being
  influenced by something.
• Developed three fundamental laws of motion.
• Amongst the most powerful scientific laws!

24
What is the something?

• In order to use Newtons laws, we have to find
  some formula for the force these laws say pay
  attention to the forces. If an object is
  accelerating, some agency is at work find it
• Richard Feynman
• Lectures on Physics

25
Universal Forces

• Gravity
• Electro-magnetic Forces
• Strong Force
• Weak Force
• All forces are some form of the above!

26
Newtons First Law

• A body acted on by no net force moves with
  constant velocity (which may be zero) and zero
  acceleration
• This just reiterates Galileos ideas of inertia.

27
Newtons Second Law

• If a net external force acts on a body, the body
  accelerates. The direction of the acceleration is
  the same as the direction of the net force. The
  net force vector is equal to the mass of the body
  times its acceleration

28
What is Mass?

• The amount of substance in a body
• The source of gravity
• The coefficient of inertia
• Why these quantities are the same is another
  mystery of the Universe.

29
Newtons Third Law

• If body A exerts a force on body B (an
  action), then body B exerts a force on body A
  (a reaction). These two forces have the same
  magnitude but are opposite in direction. These
  two forces act on different bodies

(Be careful with the minus sign! This is a vector
equation!)
30
Newtons Third Law
31
Using Newtons Laws

• With no net force, a body remains at rest or at
  constant velocity.
• With a net force, a body accelerates in the
  direction of the net force, dependent upon its
  mass.
• To every action, there is an equal and opposite
  reaction.

32
Complications Weight

• All masses are attracted to the centre of the
  Earth.
• Gravity produces an acceleration of g9.8m/s2
  which means the force is

For example a 51kg gymnast has a weight of 500N
(remember your units).
33
Complications Normal Forces

• Weight acts through the centre of mass, but as I
  am not accelerating when I stand on the ground,
  the net force0!
• Hence, there is another force balancing weight,
  supplied by the ground, called the normal force.
• Are weight the normal force represent an
  Action-Reaction pair?

34
Complications Normal Forces

• Normal forces are due to the repulsion of atoms
• Normal forces are normal to a surface

35
Complications Tension

• Tension occurs in ropes and strings and depends
  upon the particular configuration of the forces.
• For a massless rope, the tension is the same
  throughout the rope.

36
Complications Tension
37
Complications Tension

• When considering a rope with mass, its weight
  must be considered. In the static case

Remember, weight is a force so its direction is
important!!
38
Free-Body Diagrams

• Split the problem into smaller pieces.
• Consider the forces on particular parts.
• Keeping track of action-reaction pairs is vital.

39
Free-Body Diagram
40
Free-Body Diagram Example

• A trolley of mass m1 is place on a slope inclined
  at 15o. It is attached via a light string and
  pulley to a hanging sand bucket. What mass of
  sand m2 is needed such that the trolley possesses
  uniform motion?
• (Assume no friction)

41
Free-Body Diagram Example
42
Solving Problems A Guide

• Draw a free-body diagram
• Consider all of the forces acting
• Choose axes to ease the solution
• Decompose the forces
• Equations of motion

43
Complications Friction

• Microscopically, surfaces are not smooth but
  consist of pits peaks.
• When you try and move something these can lock
  like a jigsaw puzzle and resist movement.
• What force is actually causing the friction?

44
Complications Friction

• Metals can have a more complicated friction.
• As surfaces come into contact, atoms undergo cold
  welding. Pull these apart adds to the friction.
• The number of atoms in contact depends upon how
  hard the surfaces are pressed together.

45
Complications Friction

• Experimentally the amount of friction is found to
  be proportional to the component of weight
  perpendicular to the surface (equivalently the
  normal force).
• Static Friction The frictional force resisting a
  force attempting to move an object.
• Kinetic Friction The frictional force experience
  by a moving object.

46
Static Friction

• As the object is not moving, there must be no net
  force.

where ?s is the coefficient of static friction.
The frictional force Ff balances the applied
force until a point where FFf.
47
Kinetic Friction

• Kinetic friction opposes a moving object.

where ?K is the coefficient of kinetic friction.
Unlike static friction, kinetic friction has a
fixed value independent of the applied force. (Is
this really true?)
48
Friction
49
Coefficients of Friction
Generally, ?s is larger than ?K (e.g. steel upon
steel ?s0.74 and ?K0.57)
50
Worked Example (5-91)

• Block A, with a weight of 3w, slides down an
  inclined plane S of slope angle 36.9o at a
  constant speed, while plank B with weight w rests
  on top of A. The plank is attached by a cord to
  the top of the plane.
• Draw a diagram of the forces acting on block A
• If the coefficient of kinetic friction is the
  same between A B and A A, determine its value.

51
Complaining Horse
The horse claims that due to Newtons third law,
no matter how hard I pull on the cart, the cart
pulls back on me with the same force. How can I
ever move the cart!
52
Complications Circular Motion

• Consider a ball on a string, moving in a circle
  with uniform speed.
• What are the forces acting on the ball?

53
Complications Circular Motion

• The forces are not in equilibrium, and hence the
  ball must be accelerating!
• The acceleration points towards the centre of the
  circle.
• DO NOT add fictitious forces! (more on that in a
  moment)

54
Complications Circular Motion

• The length of the velocity vector remains
  constant, and so the acceleration is changing its
  direction.
• For an object traveling with speed v to move in a
  circle of radius r the centripetal acceleration
  must be

(review chapter 3)
55
Fictitious Forces

• Newtons laws work perfectly in inertial frames
• These are observers who are stationary or are in
  uniform motion with respect to the situation
  being examined, although quantities (such as
  velocity) are relative.
• When we consider accelerating (or rotating)
  frames (non-inertial), Newtons laws apparently
  dont hold anymore!

56
Fictitious Forces

• BUT we can make Newtons laws hold in
  non-inertial frames by inventing fictitious
  forces that do not exist (by which we mean there
  is no physical source for the force).
• Hence in a rotating frame, we can add a
  centrifugal force to balance the centripetal
  force!
• (So, what is the force that you feel on a stick
  to the wall fairground ride?)

57
Non-constant Forces

• In general, forces are not constant. An example
  of this is Hookes law for a spring, where the
  force is

k is the spring constant.
To calculate Newtons laws with non-constant
forces, we need to integrate the various vector
quantities (a very messy process). What we will
see next is that such problems are more simply
tackled using concepts of work energy.