Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Sections 801, 802, 803 Lecture 2

Mechanics Various forms of motion: -mechanical -electromagnetic -thermal, etc. Mechanical form of motion is connected with displacements of various bodies relative to each other and with changes of the shapes of the bodies

Historical Notes History of mechanics linked with history of human culture Aristotle ( B.C.); Physics Archimedes (3 rd century B.C.), the law of lever, the law of equilibrium for floating bodies Galileo Galilei ( ), the basic law of motion

Archimedes (3rd century B.C.), the law of lever, the law of equilibrium for floating bodies GIVE ME A PLACE TO STAND AND I WILL MOVE THE EARTH

Antikythera Mechanism decoded?! Found in 1901 near the Antikythera island in a Roman shipwreck dated 80 BC Remained a puzzle for over 100 years Recently deciphered using X-ray tomography, optical imaging, texture mapping

Nature, 30 November 2006 (page 587)

A sophisticated mechanical computer

Predicts: Lunar and solar cycles, taking into account ellipticity of the moon’s orbit Lunar and solar eclipses Accurate positions of the sun, moon, and planets Luni-solar calendar Unfortunately, the secret of making such devices was lost after the invasion of Romans. Next time when much simpler mechanisms of this kind appeared was in Islamic countries in 1300 AD (Al Biruni) Later they were imported to Europe and became clock mechanisms

a v a = g = const for all bodies independently on their masses Galileo Galilei ( ), the basic law of motion

A New Era of Science

Newton’s law of gravitation

Clockwork universe

1905 Albert Einstein "Gravitation cannot be held responsible for people falling in love.“ Albert Einstein

Overview of Today’s Class Derivatives Examples

Quiz 1. If f(x)=2x 3 what is the derivative of f(x) with respect to x? 6x 8x 2 I have no clue how to start 6x 2

1. If f(x)=2x 3 evaluate 2x 4 I have no clue how to start 0.5x 4 +Const 2x 2 /3

1. If f(x)=2x evaluate 2x 3 /3 I have no clue how to start 5 x 2 +Const

Derivatives A derivative of a function at a point is a slope of a tangent of this function at this point.

Derivatives

or Function x(t) is a machine: you plug in the value of argument t and it spits out the value of function x(t). Derivative d/dt is another machine: you plug in the function x(t) and it spits out another function V(t) = dx/dt

Derivative is the rate at which something is changing Velocity: rate at which position changes with time Acceleration: rate at which velocity changes with time Force: rate at which potential energy changes with position

Derivative is the rate at which something is changing -Size of pizza with respect to the price -Population of dolphins with respect to the sea temperature …………………

GDP per capita

Have a great day! Reading: Chapter 1