2.1 Galileo and Newton.

2.1 Galileo and Newton Opening Question What are Newtons 3 Laws of Motion? Define them.
Answer: 1st Law An object at rest tends to stay at rest,and an object in motion tends to stay in motionunless acted upon by an unbalanced force 2nd Law The force acting on a body is equal tothe mass of that object times its acceleration (F= ma) 3rd Law For every action, there is an equal andopposite reaction Velocity and Acceleration
Aristotles motion Until Galileo, Aristotlestheory of motion stood Heavier objects fall faster Natural motion is towardEarth Any other motion wasviolent motion andrequired a force to moveit All objects fall at aconstant rate Velocity and Acceleration
Galileo - DisprovingAristotle Heavier objects donot fall faster Found that a fallingobject isACCELERATED Falls faster and fasterwith each passingsecond Velocity and Acceleration
Galileo and Motion Found falling bodies do not fall at constant rates, butare ACCELERATED This steady increase in the velocity of a falling bodyby 9.81 m/s/s (9.81 m/s2) is called the ACCELERATIONOF GRAVITY at Earths Surface Known as variable g Conceptual question: If you were to drop an object offthe Empire State building, how fast would it be moving at0 seconds? 1 sec.? 2 sec? 3 sec.? (Ignore air resistance) Velocity and Acceleration
Acceleration (a) is the change of a bodys velocity (v)with time (t) = An object experiences acceleration any time its speed ordirection of motion changes Conceptual question: An automobile has threeaccelerators, what are they? Acceleration of Gravity
Galileo also discovered thatthe acceleration due togravity does not depend onthe mass (weight) of theobject Experimented with droppingballs of iron and wood fromthe top of the Leaning Towerof Pisa at the same time Whats the problem withthis? 300 years later, Apollo 15Astronaut David Scottdemonstrated thisphenomena on the moon(dropped feather and steelhammer) Fell at the same rate Along Comes Newton From the work of Galileo, Kepler, and others,IsaacNewton was able to deduce three laws of motion Led to an understanding of gravity Newtons Laws of Motion First Law
Law of inertia An object at rest stays at rest and anobject in motion stays in motion with the same speedand in the same direction unless acted upon by anunbalanced force. For example, astronauts drifting in space will travel atconstant rates in straight lines forever if no forces act onthem This law also explains why a projectile continues tomove after all forces have been removed For example, an arrow continues to move after leavingthe bowstring The object continues to move because it has momentum Momentum Momentum (p) is a measure of an objects amount of motion
Equivalent to an objects velocity (v) times its mass (m) Equation p = mv Ex. A paper clip tossed across a room vs. shot at the speed of arifle bullet Ex. Tossing a paper clip vs. tossing a bowling ball Motion of Objects The quantities used to describe the motion ofcan be divided into two categories: Scalars are quantities that are fullydescribed by a magnitude (or numericalvalue) alone Example: speed Vectors are quantities that are fullydescribed by a magnitude and a direction Example: velocity Category Scalar Vector
Conceptual Questions Quantity 5 meters 30 meters/second,East 5 miles, North 20 degrees Celsius 256 bytes 4000 calories Category Scalar Vector Speed vs. Velocity Speed is rate of motion anddoes not have anydirection implied Equaton = Distance is how muchground an object hascovered during itsmotion Velocity is a speed with aspecific direction Equation = Displacement is how farout of place an object isor overall change inposition Distance/Displacement Example
What is the displacement of the cross-country team ifthey begin at the school, run 10 miles and finish back atthe school? The displacement of the runners is 0 miles. While they havecovered a distance of 10 miles, they are not "out of place"or displaced. They finish where they started. Round-tripmotions always have a displacement of 0. 2. What is the distance and displacement of the race cardrivers in the Indy 500? (Knowing that one full lap is 2.5 milesand drivers race for 200 laps) a. The displacement of the cars is somewhere near 0 miles sincethey virtually finish where they started. Yet the successful carshave covered a distance of 500 miles. Closing Question Mr. Cooper is driving his car at 55 mph on Route 28. Hisspeed is constant but velocity is changing. Why? (Hint:remember a vehicles three accelerators) Answer: Velocity is changing because his direction ofmotion is changing. Newtons Laws of Motion Second Law
Law of force and acceleration The force acting on an object is equalto the mass of that object times its acceleration. Equation F = ma In a way, the 2nd law is common sense Ex. Pushing a grocery cart gently (one with balloons vs. bricks in it)in a certain direction If you push on a cart that isnt moving, you expect it to beginmoving in the direction you push With this equation, you can calculate precise numerical acceleration ifyou know the amounts of mass and force acting on it Weight vs. Mass The difference between weight and mass:
Weight is the force of gravityon mass Mass is the amount of matter(atoms/molecules) in anobject. Weight changes if the force ofgravity changes, mass doesnot Fweight= mg m = mass g = acceleration due togravity (9.81 m/s2) Centripetal Acceleration
The inward acceleration of an object moving in acircle is known as centripetal acceleration. Equation = 2 v =tangential velocity (m/s) (linear speed ofsomething moving along a circular path) r = radius of the circle (m) Sample Problem Centripetal Acceleration
A rock tied to a string is traveling at a constant speedof 4 m/s in a circle of radius 1.5 m. Calculate themagnitude of the centripetal acceleration of the rock.What is the direction of the acceleration? = 2 =(4 ) = 10.7 m/s2 (direction always inwards toward thecenter) Newtons Laws of Motion Third Law
Law of action-reaction To every action, there is an equal andopposite reaction. In other words, forces must occur in pairs directed in oppositedirections The famous Newtons Cradle toy demonstrates this law ofmotion Conceptual Example: If you stand on a skateboard and jumpforward, the skateboard will shoot away in what direction? Answer: Backward. As you jump, your feet must exert a forceagainst the skateboard, which accelerates it toward the rear,and the skateboard exerts an equal but opposite force on yourfeet, accelerating you forward. Newtons Cradle Newtonian Gravity Newton wondered if the force holding the moon in orbitwas the same force causing apples to fall gravitational force Thought it would be weaker at greater distances assumed that its strength would decrease as the squareof the distance increased This relationship is known as the inverse square law,which was familiar to Newton from various studieswith light Proved to be correct A screen set up 1m from a candle flame receives a certain amount of light on each square meter. If that screen moved to 2m away, the now covered 4 square meters. Newtonian Gravity Example Problems
Example: Compared with the strength of gravity at Earthssurface, how much weaker is this strength at the followingdistances? 5 Earth radii from Earths center? _____________________ 7 Earth radii from Earths center? _____________________ 2 Earth radii from Earths center? _____________________ Example: Compared with the light received from the Sun atEarths distance (1 AU), how many times fainter would lightfrom the Sun be at the following distances? 2 AU from the Sun? ________________________ 1.5 AU from the Sun? _______________________ 8 AU from the Sun? ________________________ Universal Law of Gravitation
Every particle of mass in the universe are attracted to eachother through mutual gravitation Newtons 3rd Law says that forces always occur in pairs, so ifEarth pulls on the moon, the moon must pull on Earth The force of gravity (Fgrav) depends upon the mass of theobject(s) Larger masses have stronger gravitational force You also have your own personal gravitation field! https://www.youtube.com/watch?v=1ZB-AdZwz84 Universal Law of Gravitation
He calculated the famous formula for thegravitational force between two masses, m1 andm2 : Fgrav = G = the gravitational constant that connectsmass to gravity G = x m3/kgs2 r= distance between the masses Example: Calculate the force of gravity betweenthe Earth and the moon. (Hint: The moon is 3.84 x105 km from Earth, Earths mass is 5.97 x 1024 kg,moons mass is 7.35 x 1022 kg) The Suns Mass Newtonian Mechanics tells us the force keepingthe planets in orbit around the Sun is thegravitational force due to the masses of theplanets and Sun By combining Newtons 2nd Law, centripetalacceleration, and the ULG, along with othergiven numerical data, you can calculate themass of our Sun! Calculating The Suns Mass Surface Gravity The acceleration due togravity (g) on the surface of anobject can also be calculatedfrom Newtons Universal Law ofGravitation: = 2 G = gravitational constant; x m3/kgs2 r = radius of the object, inmeters Example: Compare theacceleration due to gravity atEarths surface with that ofMars. Closing Exercises A sled slides down a hill, reaches the level surface andeventually comes to a stop. The fact that the sledultimately comes to a stop can best be explained bywhat? Explain. Sophia, whose mass is 52 kg, experienced a net force of N at the bottom of a roller coaster loop during herschool's physics field trip to the local amusement park.Determine Sophia's acceleration at this location. Suppose two carts, one twice as massive as the other, flyapart when the compressed spring that joins them isreleased. How fast does the heavier cart roll compared tothe lighter cart? Closing Exercises - Answers
the presence of an unbalanced force (e.g. friction)can cause a moving object to stop. 34.6 m/s2 According to Newton's Third Law, the forces on thesetwo masses must be equal (and in oppositedirections). According to Newton's Second Law, F =m a, we find a = F / m. That means the accelerationof the twice-as-massive cart will be one-half theacceleration of the other.