Galileo Galilei

 

1.  Galileo Galilei
     a.  Born February 15, 1564
     b.  Died January 8, 1692
     c.  Theories
          i.  Heliocentrism
         ii.  Sunspots
        iii.  Astronomy
               1.  Phases of Venus
               2.  Moons of Jupiter
         iv.  Physics
               1.  Principle of inertia: “a body moving on a level surface will continue in the same

                    direction at  constant speed unless disturbed”
          v.  Inventions
               1.  Compasses
               2.  Balances
               3.  Telescopes
               4.  Microscopes 
         vi.  Equations
               1.  Law of Fall – falling bodies; ex: a stone falling for twice as long as another stone will

                    travel  four times the distance; bodies fall on earth at a constant acceleration and that

                    force of

                    gravity which causes all bodies to move downward is a constant force

                    a.  X = at2 ; where X is distance; a is a factor; and t is time

               2.  Principle of superposition—If a body is subjected to two separate influences, each

                    producing a characteristic type of motion, it responds to each without modifying its

                    response to the other.
                    a.  A + B = A + B ≠ A2 + B2
      d.  Contributions
           i.  Father of modern science – Einstein
          ii.  Father of observational astronomy
         iii.  Father of modern physics

 

 

 

 

Problem:

Galileo Galilei wanted to understand and explain the universe, but, like most major innovations to science, he was ahead of his time. Galileo wanted to explain that our universe is heliocentric, or revolves around the sun, as opposed to the common belief, of the time, that the earth was a fixed point at the center of the universe. Galileo looked to Mars, the Red Planet, for explanation. With his newly invented, improved telescope, he demonstrated that the planet appeared to be almost four times bigger during parts of its orbit. How can this be if the earth is fixed and all other planets are revolving around it? Galileo sought out to explain how this observation explains that the earth is not at the center of the universe and that Mars has a special retrograde movement regarding its orbit. The planet appears to be moving in a specific direction then retrogrades or changes direction then changes back to the original direction. One of Galileo’s other big problems was explaining his belief that a heavier body and a lighter body, in a vacuum, would fall down at the same speed. He needed a way to explain that time was the only factor, ignoring air resistance, affecting the speed of the falling objects. He got his idea from a swinging lamp inside of a church cathedral. He measured the swinging of the lamp with his heartbeat and measured the amount of beats it took to swing from one side to the other and back to the original side. This concept of periodicity lead him to use ramps to measure the time it took for bodies to roll down the incline of the ramp. This led him to believe that the only thing slowing the bodies down the ramp is a resisting force such as friction. Besides friction, the only thing affecting the speed of the body down the ramp was the amount of time it spent rolling. Thus, the higher the ramp, or the longer it took to roll, increased the speed. Hence, in a vacuum, with no air resistance, the only thing affecting the speed at which two bodies fell, whether they are a bowling ball and a feather, was the time at that they are released.

 

 

Galileo Galilei

Archimedes

 

1.  Galileo Galilei
     a.  Born c. 287 BC

     b.  Died c. 212 BC

     c.  Theories
           i.  Archimedes’ principle

            1.   Displacement from gold crown in bathtub. Had to figure out density of crown from  

                      dishonest goldsmith for King Hiero II

         ii.  Archimedes' screw

        iii.  Method of exhaustion

      d.  Contributions
           i.  "Eureka!"

    e.  Formula

           

 

           i.  where F = buoyant force of a given body; v = volume of displaced fluid; g = acceleration

               due to gravity; pf = density of the fluid; pg = density of the body

 

 

 

 

 

Problem:

 

 

Archimedes was given the task to figure out if his King’s newly acquired gold crown was actually made of gold because the King did not trust the town’s goldsmith. In ancient times, how could Archimedes compare two objects without knowing their chemical makeup? In his famous “eureka” moment, Archimedes discovered the principle that has taken his namesake. In his bathtub, gold crown in hand, Archimedes was pondering the problem that was given to him. Seemingly, by accident, the gold crown fell into the bathtub and knocked some water out. Archimedes had solved his problem. Archimedes principle states: “Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object”. In other words, the force of the object’s weight in a fluid (the weight of the crown) will displace the fluid that it is submerged in (bathtub water) in an equal amount. Thus, if he could measure the density of the crown by displacing it in water then he could compare that density with the density of a known piece of actual gold to compare.

 

Archimedes

Isaac Newton

 

1.  Isaac Newton
     a.  Born December 25, 1642
     b.  Died March 20, 1726
     c.  Theories
          i.  Classical mechanics for Physics
         ii.  Law of motion
        iii.  Law of universal gravitation
              1.  Apple falling on Newton's head - Voltaire
     d.  Contributions
           i. 
Co-discovered Calculus with Gottfried Leibniz

          ii.  Laws of motion

               1.  When viewed in an inertial reference frame, an object either remains at rest or continues to

                      move at a constant velocity, unless acted upon by an external force (inertia).

               2.  The vector sum of the external forces F on an object is equal to the mass m of that object  

                      multiplied by the acceleration vector a of the object: F = ma

               3.  When one body exerts a force on a second body, the second body simultaneously exerts a

                     force  equal in magnitude and opposite in direction on the first body (for every rxn there is an 

                     equal  but opposite rxn)

               4.  Newtonian telescope

               5.  Dispersive prism (Opticks (1706))

 

     e.   Equations
            i. 

 

               1.  Law of universal gravitation 

               2.  F = force between two masses; G = gravitation constant (6.673×10−11 N · (m/kg)2); m1 = first

                    mass;  m2 = second mass; r = distance between the centers of the masses

           ii.  Kinematic equations

               1.   d = vo • t + 0.5 • a • t2

               2.  vf = vo + a • t

               3.  vf2 = vo 2 + 2 • a • d
               4.  d = (vo + vf)/ 2 • t                                                                                                                                      
                    a.  where d = displacement; t = time; a = acceleration; vo = original velocity; vf = final velocity

 

 

 

 

 

 

 

 

Problem:

Galileo Galilei wanted to understand and explain the universe, but, like most major innovations to science, he was ahead of his time. Galileo wanted to explain that our universe is heliocentric, or revolves around the sun, as opposed to the common belief, of the time, that the earth was a fixed point at the center of the universe. Galileo looked to Mars, the Red Planet, for explanation. With his newly invented, improved telescope, he demonstrated that the planet appeared to be almost four times bigger during parts of its orbit. How can this be if the earth is fixed and all other planets are revolving around it? Galileo sought out to explain how this observation explains that the earth is not at the center of the universe and that Mars has a special retrograde movement regarding its orbit. The planet appears to be moving in a specific direction then retrogrades or changes direction then changes back to the original direction. One of Galileo’s other big problems was explaining his belief that a heavier body and a lighter body, in a vacuum, would fall down at the same speed. He needed a way to explain that time was the only factor, ignoring air resistance, affecting the speed of the falling objects. He got his idea from a swinging lamp inside of a church cathedral. He measured the swinging of the lamp with his heartbeat and measured the amount of beats it took to swing from one side to the other and back to the original side. This concept of periodicity lead him to use ramps to measure the time it took for bodies to roll down the incline of the ramp. This led him to believe that the only thing slowing the bodies down the ramp is a resisting force such as friction. Besides friction, the only thing affecting the speed of the body down the ramp was the amount of time it spent rolling. Thus, the higher the ramp, or the longer it took to roll, increased the speed. Hence, in a vacuum, with no air resistance, the only thing affecting the speed at which two bodies fell, whether they are a bowling ball and a feather, was the time at that they are released.

 

 

Isaac Newton