Gravitational Force

You already know about gravitational force “The Earth’s gravitational pull on you” Your weight! w = mg

Newton’s law of Universal Gravitation Relates mass, distance and gravitational force between any two bodies G is a scaling constant: m1,m2 = masses r = distance between the two centers of mass

Practice Problems If an apple weighs 1N at the surface of the earth, how much does it weigh a distance of 2 earth radii from the center of the earth? 3 earth radii? Find Fg on a 3 kg rock at the Earth’s surface. How does the force exerted by the Earth on the rock compare to the force exerted by the rock on the Earth? Me=6x10^24kg Re=6x10^6m

G is the gravitational constant everywhere in the universe It scales Fg appropriately (gives it the correct units) It does not vary from place to place, object to object in the universe g is freefall acceleration on Earth, due to Earth’s gravitational pull on other objects

Charge, conservation of charge, acquisition of charge Electrostatics Charge, conservation of charge, acquisition of charge

Where does charge come from? Atoms are made of positive, negative, and neutral sub particles Neutrons (neutral charge) and protons (positive charge) are located in a tight cluster at the center of the atom – the nucleus Electrons (negative charge) move in clouds (spherical shells) around the nucleus These charged particles exert forces on each other, and on the charged particles in surrounding atoms

Charge Protons have greater mass than electrons, but both have the same magnitude of charge (1.6 x 10^-19 C) To create an object with positive charge, you must remove electrons To create an object with negative charge, you must add extra electrons Most atoms and objects are electrically neutral – the # of electrons = # of protons Like charges repel, opposite charges attract

Some atoms/molecules hold on to their electrons more tightly than others Eek! Chemistry. Example: Atoms in hair and fur give up electrons more easily than atoms in plastic, so if you rub a piece of plastic on fur or hair, electrons are pulled off of the fur and stick to the plastic The plastic has more electrons than protons and is now negatively charged The fur has more protons than electrons and is now positively charged

Conservation of charge When we charge something, no electrons are created or destroyed electrons are merely transferred from one object or substance to another Any object that has electrical charge has an excess or deficiency of a whole number of electrons electrons are an elementary particle and can not be divided into smaller particles (charge is quantized)

Electric Force Coulomb’s Law: Relationship discovered in 1700s by Charles Coulomb F = force between two charged particles q1, q2 = quantity of charge of each particle r = distance between two particles (or distance between the CM of two charged objects) k = 9 x 10^9 N*m²/C²

What is q? Quantity of charge is measured by amount of charge provided by number of extra electrons or number of missing electrons (extra protons) q = +/- Ne

Comparison: Felec vs. Fgrav Force of gravity: Electric force: Similarities – mathematical form, decrease as d increases, both forces act on objects that are not in physical contact with each other Differences – size (G vs. k), attraction vs. repulsion

Charge and conductivity Conductor good conductors share outer valance electrons: outer layer electrons move in a single cloud around all of the atoms/molecules When conductors carry net charge, charge spreads out (as far from each other as possible) Insulator good insulators have tightly bound electrons: electrons don’t move around from atom to atom When insulators carry net charge, extra charge stays put

2 Ways to acquire an electric charge 1. Charging by contact transfer of charge from one object to another by physical contact Electrons “hop” from the substance (like fur) that gives up the electron to the substance (like plastic) that takes an extra electron Now the fur has less electrons than protons and is positively charged The plastic has more electrons than protons and is negatively charged

2. Charging by induction An object is charged by the attraction or repulsion of a nearby charged object, without physical contact. Conductor: Bring a charged object near a neutral conductor Electrons in the conductor move to one side under the influence of the electric force provided by the charged object. Ground the conductor or separate/break it to create a permanent charge

Electroscopes Concepts: conductor induction, like charges repel - - - Charged object - - - + + + + + + + + - Electroscope - conductor - - -

Charging by induction/polarization Insulator: charge polarization Atoms and molecules within the insulator are distorted so that centers of positive and negative charge in a neutral atom or molecule no longer align. Sticking a balloon to a wall