II. Two of the 4 fundamental forces: 1. The _____________________ force, Fg, between 2 masses: gravitational Gm1m2 r2 Fg = attractive …is always ______________________ …is ___________________________ to the masses …is ______________proportional to ____________ of r …is _______________ , which can be seen because the constant G = __________________________ is __________ . directly proportional inversely the square very weak 6.67 x 10-11 N·m2/kg2 tiny electrical 2. The _______________________ force, Fe, between two charges Fe = ???

separated by a distance… Suppose two charges q1 and q2 repel each other with an electrical force Fe=___. Then experiments are done… 10 Exp. # using…. and…. separated by a distance… new Fe 1 q1 2q2 2 3q1 q2 3 2q1 3q2 4 5 6 20 30 60 10/4 10/9 10/16 What can you conclude about the form of the electrical force? It is directly proportional to the _____________ on each object, and ___________ proportional to the ____________________ _______________________________ charge inversely square of the distance between the two charges.

Coulomb’s Law: The electrostatic force, Fe, between two charges q1 and q2 separated by a center-to-center distance r is… q1 q2 r Fe = where k = ________________________________ = ________________________________ ________________________________

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Coulomb’s Law: The electrostatic force, Fe, between two charges q1 and q2 separated by a center-to-center distance r is… q1 q2 r kq1q2 r2 Fe = where k = ________________________________ = ________________________________ ________________________________

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Coulomb’s Law: The electrostatic force, Fe, between two charges q1 and q2 separated by a center-to-center distance r is… q1 q2 r kq1q2 r2 Fe = the electrostatic constant where k = ________________________________ = ________________________________ ________________________________ 8.99 x 109 N·m2/C2, with q in coulombs and r in meters

Charles-Augustin de Coulomb French physicist 1736-1806

Ex: Cavendish "Weighing the Earth" Experiment: When a ____ sphere (m2) was brought close to the barbells, the _______________ attraction caused the thin wire to _________ . Pb thin wire From the wire's properties, the ______________ needed to make the wire twist that much could be _____________ gravitational force, Fg r m2 m1 Pb barbells twist estimated Then Fg, r, m2 and m1 were substituted into: G m1 m2 r2 Fg = and this was solved to find ______ . G G Once _____ was known, an object of known mass m and weight w were used to find ___________ unknown mass Me using G m Re2 Me w = Earth's

Coulomb’s torsion (twisting) balance:

Ex: Coulomb “charge" Experiment: silk thread When a charged ball q2 was brought close to the charge q1, the _______________ attraction caused the thin wire to _________ . counterweight electrical q1 From the thread’s twisting, the ______________ needed to make the wire twist that much could be determined. twist r force, Fe q2 k q1 q2 r2 Fe = and this was solved to find k.

Note: Fe is… …directly proportional to ____________ …and inversely proportional to ______ the q’s r2 Fe Fe Fe q r m 2. Fe is ___________________ if the charges are “opposite” and_____________________ if the charges are “like” attractive repulsive 3. Fe is ___________stronger than the gravitational force because ________ is ____________________ than ______. MUCH k MUCH greater G 4. Fe is an ________________________________force. “at a distance”

Ex: Find the electrical force between two charges q1 = +3.4 x 10-6 C and q2 = -1.7 x 10-4 C whose centers are separated by a distance of 2.5 x 10-2 m. kq1q2 r2 Fe = (8.99 x 109 N·m2/C2) (+3.4 x 10-6 C) (-1.7 x 10-4 C) Fe = (2.5 x 10-2 m)2 (-5.2 N·m2) Fe = = -8300 N (6.25 x 10-4 m2) Is the force attractive or repulsive? Which charge exerts a stronger force? If released from rest, which would accelerate more? attractive neither You can’t tell, since the masses are not given.

Ex: Two _______________ masses: neutral Fg Fg like The same two masses with ___________ charges: Fg Fg Fe Fe The same two masses but with _______________ charge: opposite Fe Fg Fe Fg

Ex: Two electrons and a proton are located at the vertices of an equilateral triangle as shown below. The electrical force of the proton acting on one of the electrons is shown. Draw all other electric forces. Then draw and label the net (resultant) force acting on each particle. R e- p R R e-

Ex: Because gravity and the electrostatic force are ____ ____________ … so similar planet v Gravity ___________ holds the planets to the Sun (S): Fg S It was thought that the electrostatic force was responsible for allowing the electron to ____________________________ . orbit the nucleus v electron electrical The ____________ force binds electrons to the nucleus (N): Fe N

In reality, orbiting electrons ______________________ Why? are not possible! 1. Electrons in circular orbits ___________________. are accelerating 2. Accelerating charges ______________________ . radiate energy away lose 3. Therefore, orbiting electrons would ________ energy and _________________________________ and all matter would ___________________in a fraction of a second spiral into the nucleus collapse quantum mechanics A better theory was needed, so _______________________ was developed. It says that: 1. The electron _______________________ , but ___________________________ orbit. does not orbit occupies a “stationary” 2. The “orbit” only tells you where the electron is ____________________ to be found or the _____________________ of finding it somewhere! most likely probability

The electron "cloud" is the modern idea of an electron. Brighter areas are where the electron is more likely to be found, i.e., has a higher probability of being found. The electron does not "move around." lowest energy "orbit" higher energy "orbits"

Electron cloud model: Electron "cloud" is _________ where the electron is _______ _________ to be found. The ________ ____________ are spread out around in the cloud. electron cloud __________ densest most likely charge and mass = __________ nucleus