Physics 1901 (Advanced)

Semester 1 2009 http://www.physics.usyd.edu.au/~gfl/Lecture

Physics 1901 (Advanced)

Prof Geraint F. LewisRm 560, [email protected]/~gfl/Lecture


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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.


Learning

What you learn from this course depends upon the effort you put in

Lectures are a guide to course material Read your module/unit outlines University Physics by Young & Freeman Online resources: WebCT & Junior Physics 6hrs/week independent study


Tutorials

Interactive Workshop Tutorials Work in small groups (up to 4) Worksheets & Hands-on

demonstrations A chance to ask questions A place to clarify ideas

Not assessed; up to you. No worksheets if you don’t

attend.


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


AssessmentLab 20%Mastering Physics 10%Progressive Test 5%Lab Skills Test 5%Exam 60%

It is important to know concepts & ideas, not just manipulate formulae; look at previous exam papers.

It is important to know the meaning of Academic Honesty


If you need help

Talk to me; Email me your question or to make

an appointment (no walk-ins) See a duty tutor Consult the web resources Serious personal problems or

illness it is important to complete a Special Consideration Form ASAP!


Physics 1901: Mechanics


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


Classical Mechanics (why classical?)

Modern physics General Relativity Quantum Mechanics

Classical mechanics Physics of “human experience”


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?


Course Layout

Lecture Content1-3 Kinematics, dynamics & Newton’s Laws

4-5 Applications of Newton’s Laws

6-7 Work & Kinetic Energy

8-9 Potential Energy & Energy Conservation

10 Momentum, Impulse & Collisions

11-12 Rotation of Rigid Bodies

13-14 Dynamics of Rotational Motion

15 Gravitation


Kinematics (Review Ch 1-3) Kinematics is the description of motion

Let’s 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 ?


Velocity & Acceleration

Velocity is the change of distance over time

Acceleration is the change of velocity over time

(Differential equations!)


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!


Non-Constant AccelerationGenerally, we will consider only constant acceleration (cos this makes life easier).

Remember this is not generally true.

is called the jerk

Can use these to derive more general kinematic equations.


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!


Decomposing VectorsVectors have a length & direction. To use them we need to decompose the vector into its components.

(this is important!)


Adding Vectors


Monkey & Hunter


Galileo & Inertia

The Principle of Inertia

If a body is left alone, 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.


Isaac NewtonDeveloped 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!


What is the ‘something’?

“In order to use Newton’s 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 FeynmanLectures on Physics


Universal Forces

Gravity Electro-magnetic Forces Strong Force Weak Force

All forces are some form of the above!


Newton’s First Law

“A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration”

This just reiterates Galileo’s ideas of inertia.


Newton’s 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”


What is Mass?

The amount of substance in a bodyThe source of gravityThe ‘coefficient’ of inertia

Why these quantities are the same is another mystery of the Universe.


Newton’s 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!)


Newton’s Third Law


Using Newton’s 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.


Complications: WeightAll masses are attracted to the centre of the Earth.

Gravity produces an acceleration of g=9.8m/s2 which means the force is

For example: a 51kg gymnast has a weight of 500N (remember your units).


Complications: Normal Forces

Weight acts through the centre of mass, but as I am not accelerating when I stand on the ground, the net force=0!

Hence, there is another force balancing weight, supplied by the ground, called the normal force.

Do weight & the normal force represent an Action-Reaction pair?


Complications: Normal Forces Normal forces are

due to the repulsion of atoms

Normal forces are normal to a surface


Complications: TensionTension 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.


Complications: Tension

More correctly, the rope is said to be the state of tension.

This results in forces at rope “edges”.

It’s important to remember that the resultant forces need not be in the same direction (or of the same magnitude).


Complications: TensionWhen considering a rope with mass, its weight must be considered. In the static case

Remember, weight is a force so its direction is important!!


Free-Body DiagramsSplit the problem into smaller pieces.

Consider the forces on particular parts.

Keeping track of action-reaction pairs is vital.


Free-Body Diagram


Free-Body Diagram: ExampleA 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)


Free-Body Diagram: Example


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


Complications: FrictionMicroscopically, 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?


Complications: FrictionMetals 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.


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.


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 F=Ff.


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?)


Friction


Coefficients of FrictionGenerally, s is larger than K (e.g. steel upon steel; s=0.74 and K=0.57)


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 & S, determine its value.


Complaining Horse

The horse claims that “due to Newton’s 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!”


Complications: Circular Motion

Consider a ball on a string, moving in a circle with uniform speed.

What are the forces acting on the ball?


Complications: Circular MotionThe 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)


Complications: Circular MotionThe 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)


Fictitious Forces

Newton’s 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), Newton’s laws apparently don’t hold anymore!


Fictitious Forces

BUT we can make Newton’s 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?)


Non-Constant ForcesIn general, forces are not constant. An example of this is Hooke’s law for a spring, where the force is

& k is the spring constant.

To calculate Newton’s 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.

Physics 1901 (Advanced)

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