Newton and Forces

Isaac Newton Issac Newton (1642-1727) was the father of modern physics and astronomy. Some of his accomplishments include. Laws of Motion Co-inventor of Calculus Discoveries in optics and light Universal Gravitation

Newton and Galileo Newton recognized that he was able to make his discoveries by building on the work of those before him. He acknowledged that is was Galileo’s work with falling bodies that helped him understand gravity. Galileo’s understanding of inertia helped Newton explain his 1st law of motion.

Galileo’s Law Falling Bodies Galileo found that objects fall or roll down an incline with a constant acceleration. Falling objects fall using the “Odd Number Rule”. The distance a falling object travels with uses the equation d = ½gt2. Galileo was close to understanding gravity!

Galileo’s Idea of Inertia Inertia measures the tendency of an object to resist changes in motion. Galileo came up with the idea of inertia Objects do not want their motion to change Mass measures how much inertia an object has (More mass = More inertia)

Newton’s First Law of Motion (Law of Inertia) If no unbalanced forces act on a moving object, then the object will continue to move with a constant velocity (constant speed in a straight line). If an object is at rest it will stay at rest. Newton took his concept of forces and combined it with Galileo’s idea of inertia

What is a Force? A force is a push or pull acting on an object that changes the motion of the object.

Newton’s Second Law of Motion Newton discovered the idea of a Force He found the Force is proportional to the Acceleration of an object (more Force = more Acceleration) He found the Force is proportional to the mass of the object (more mass = more force needed). The direction of the force is the same as the direction of the acceleration.

Newton’s Second Law of Motion Moving objects accelerate when an unbalanced force (F) acts on them. The stronger the force, the greater the acceleration (a). Also, the greater the mass (m) the greater the force required to change the motion. Force = mass x acceleration F = ma

S.I. Unit For Force The Unit for Force is a Newton (N) 1N = 1kg m/s2 A Newton (N) is defined as the amount of force required to accelerate 1 kg of mass at a rate of 1 m/s2.

Newton’s Third Law of Motion States: Every Action has an equal and opposite Reaction. Forces always come in pairs! Action-Reaction Forces always occur between two objects.

Mass and Weight Mass is amount of matter that an object possess. Mass does not change with location. Weight is the gravitational force that a large body (such as a planet) exerts on another object.

Weight Weight is a Force! It is measured in Newtons. Weight = Mass x Acceleration due to Gravity (Newton’s 2nd law) W = mg Weight does change with location! (“g” will change with location)

Four Fundamental Forces of Nature Gravity – Force of attraction between any two masses. Weakest of the fundamental forces but acts over the largest distances. Electromagnetic Force (EMF) – force between charged particles. Stronger than gravity but does not reach as far. (Like charges repel, opposite charges attract)

Four Fundamental Forces of Nature 3. Strong Nuclear Force – Force of attraction between subatomic particles inside the nucleus. Strongest force in Nature but only acts inside the nucleus (shortest distance). Holds the atom together.

Four Fundamental Forces of Nature Weak Nuclear Force – is the force observed in the radioactive decay of some elements Unification Theory – This theory looks to unify all the fundamental forces to a single unified force.

Universal Gravitation After Galileo and Kepler, the heliocentric model gained acceptance but scientists still did not know what causes the motion of the planets! The stage was set in 1666 for Issac Newton to use his concept of a force and his Three Laws of Motion to explain the force behind planetary motion

Universal Gravitation Newton named this force Gravity He suggested Gravity is a force of attraction between any two masses and that each mass pulls on the other with an equal and opposite force

Universal Gravitation The Force of Gravity is directly proportional to the mass of each object F a m The Force of Gravity is inversely proportional to the square of the distance between the center of the masses F a 1/d2 (Inverse Square Law)

Universal Gravitation Equation Newton used his Law of Gravity (Universal Gravitation) to make the following equation: Fg = G m1 m2 d2 Where “G” is the Universal Gravitational Constant! G = 6.67 x 10-11 Nm2/kg2

Universal Gravitation Equation Note: In using the Universal Gravitation Equation, One mass(m1) doubles - Fg is doubled Both masses(m1, m2) double– Fg is quadrupled (multiplied by 4) Distance(d) doubles – Fg is divided by 4 (22 = 4) Note: d has to be measured from center to center! (Not center to SURFACE!)

Useful Information for Universal Gravitation Calculations G = 6.67 x 10-11 Nm2/kg2 ME = 5.96 x 1024 kg (Mass of Earth) RE = 6.37 x 106 m (Radius of Earth) MS = 2.0 x 1030 kg (Mass of Sun) dE-S = 1.5 x 1011 m = 1A.U. (Distance Earth to Sun) dE-M = 3.9 x 108 m (Distance Earth to Moon)

Universal Gravitation and Acceleration Due to Gravity Show why g = -9.8 m/s2 What affects the acceleration due to gravity (g)? Answer: 1) Mass of the planet. 2) Distance from the center of the object to the center of the planet

Calculating “g” on a Planet To calculate the acceleration due to gravity on the surface of any planet or moon, you need the mass of the planet and its radius. gp = G Mp/Rp2 Mp = Mass of the planet in kilograms (kg) Rp = Radius of the planet in meters (m) G = 6.67 x 10-11 Nm2/kg2

Universal Gravitation and Acceleration Due to Gravity The acceleration due to gravity (g) changes if you go to another planet or moon or as you move away from the surface of Earth g = 9.8 m/s2 at the surface of the Earth g will be greater on a larger planet (Jupiter gJ = 25 m/s2) g will be smaller on a smaller planet (Mercury gM = 3.78 m/s2)

Universal Gravitation and Acceleration Due to Gravity The Acceleration Due to Gravity Away from the Surface of the Earth (g/ ) can be found with the Equation: g/ = g (RE)2 (d)2 Note: d has to be measured from center to center! (Not center to SURFACE!)

Using Universal Gravitation Orbital Velocity – is the speed required for an object (satellite) to orbit a large central mass at a given distance. vorbital = square root (GMcm/r) G = Universal Gravitatonal Constant Mcm = Central Mass the object moves around r = the distance from the center of each object

Using Universal Gravitation Orbital Velocity – is the speed required for an object (satellite) to orbit a large central mass at a given distance. vorbital = square root (GMcm/r) G = Universal Gravitatonal Constant Mcm = Central Mass the object moves around r = the distance from the center of each object

Using Universal Gravitation Escape Velocity – is the speed required for an object (satellite) to escape from the surface of a large central mass at a given distance. vescape = square root (2GMcm/r) G = Universal Gravitatonal Constant Mcm = Central Mass the object moves around r = the distance from the center of each object Similar to Orbital Velocity but different by a square root (2)

Satellites After Newton formulated his Theory of Universal Gravitation, A question was presented to him regarding his theory. If Gravity is the same force that pulls an apple to the ground from a tree and also keeps the Moon in orbit, what keeps the moon from crashing into the Earth like an apple?

Newton’s Thought Experiment Newton answered the question with a thought experiment (Because you really cannot do this experiment with air resistance). Answer: The Moon is falling, but since it has a horizontal speed tangent to the orbital path, the Moon misses the Earth as it falls and is falling around the Earth!

Newton’s Thought Experiment Newton’s thought experiment explains how any satellite stays in orbit! Satellites are difficult to put into orbit but easy to get back to Earth. Just slow the satellite down! Note: A satellite is any object (Natural or Man-made) traveling around another object

Satellites The Moon is a satellite of the Earth! The Earth is a satellite of the Sun! Jupiter’s Moons are satellites of Jupiter! We put up man-made satellites around the Earth and other planets! Most of the man-made satellites going around the Earth are Geosynchronous (have a period, T = 24 hours)

Satellites There are 3 Equations we can derive for Satellites: vS = 2pr/t vS = [Square Root (GmE/r)] vS = RE [Square Root (g/r)] Note: r has to be measured from center to center! (Not center to SURFACE!)

Using Universal Gravitation Calculate the Period of the Moon – Newton’s Proof of the validity of his Universal Gravitational Equation Newton’s Version of Kepler’s 3rd law T2 = 4p2r3/GMcm

Weight and Weightlessness Why do the astronauts in the space shuttle experience weightlessness (zero gravity)? Microgravity – Is the situation when objects experience the illusion of weightlessness because they are all falling at the same rate Astronauts orbiting the earth are falling around the earth at a rate of “ g/ ”!

Einstein’s Theory of Gravity Einstein looked at gravity differently! Einstein suggested that instead of gravity being a force, he said that gravity is an effect of space itself. Mass puts a dent in space and tries to pull in everything in to this dent. (Mattress Example) Suggested how large masses can deflect light and the existence of Black Holes! Formulated his theory of Special Relativity and later his theory of then General Relativity.