Instructor: Dr. Tatiana Erukhimova Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lecture 4

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 (384-322 B.C.); Physics Archimedes (3rd century B.C.), the law of lever, the law of equilibrium for floating bodies Galileo Galilei (1564-1624), the basic law of motion

Archimedes (3rd century B. C 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

Buoyancy When a body is completely or partially immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body.

Galileo Galilei 1564-1642

“Father of modern science” Albert Einstein Stephen Hawking: Galileo probably bears more of the responsibility for the birth of modern science than anybody else. Was the first to apply a scientific method: Put forward a hypothesis, verify it by experiment, describe it with a mathematical model Insisted that language of mathematics should describe the laws of nature and experiments should prove it. No place for arguments based on beauty, religion etc.

Achievements in physics Verified that free-fall acceleration is independent on masses of bodies. This fact inspired Einstein’s General Relativity. Formulated the Principle of Relativity, which laid the framework for Newton’s laws and inspired Einstein’s Special Relativity. Proposed the Principle of Inertia, which was used (borrowed?) by Newton as his First Law. Found that the period of a pendulum is independent on its amplitude. He discovered it by observing swings of a bronze chandelier in the Cathedral of Pisa and using his pulse to measure the time!

Galileo's experiment with a feather and a coin Imagine you drop a light feather and a heavy coin from Albritton Bell Tower (138 ft.) Will they reach the ground at the same time? 384-322 B.C. Aristotle says : “No! The coin will land first because heavier objects fall faster than the lighter ones, in direct proportion to weight”. 1564-1642 1800 years later Galileo says : “Yes! A coin and a feather will land together if there is no air resistance!”

Free fall g=9.8 m/s2=32 ft/s2 g-positive! On planet Earth, if you neglect air resistance, any body which is dropped will experience a constant acceleration, called g, independent of its size or weight. g=9.8 m/s2=32 ft/s2 g-positive!

A New Era of Science

Newton’s law of gravitation

Clockwork universe Newtonian mechanics was so beautiful and clear that people believed that it explained everything. They thought that everything in the Universe worked like a perfect clock obeying Newton’s laws. To predict what happens in future, you just need to specify the initial positions and velocities for all objects.

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

Motion in One Dimension (Chapter 2) We consider a particle - as time goes, the position of the particle changes

Problems An experimental vehicle starts from rest at t=0 and accelerates at a rate given by a = 5 m/s3 t. What is its velocity and position 2 s later? A particle moves along the x axis. Its position as a function of time is given by x(t) = at+bt2 where t is in sec and x is in meters. A and b are constants. What is the acceleration as a function of time? a(t) = α t2. v(t = 0) = W; x(T) = D. α, T, W, and D are constants. Find the velocity and position as a function of time.

A ball is dropped vertically down (no air resistance) from height H. Find the position x(t) and velocity v(t) of the ball as a function of time. How long is the ball in the air?

If a=ac=Const:

Have a great day! Reading: Chapter 2