lecture6_ch4

# lecture6_ch4 - How do we describe motion Speed = distance...

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Unformatted text preview: How do we describe motion? Speed = distance traveled in a given time Velocity = speed and direction Acceleration = change in velocity (speed or direction) in a given time Car accelerates when its speed increases Car accelerates when it turns(direction changes) Car accelerates when its speed decreases Acceleration owing to gravity is same for all objects Near Earthʼ s surface gravity increases the downward velocity by about 10 meters per second each second (g = 9.8 m/s/s) Momentum = (mass) x (velocity) The only way to change an objectʼs momentum is to apply a force to it How is mass different from weight? 1 Mass = total amount of matter in an object Weight = the force that gravity exerts on an object The weight reading on a scale changes as an elevator accelerates, even though mass stays constant If the elevator falls freely, you experience weightlessness Theory of gravity united heavens and Earth in one universe Laws of motion laid the foundation of physics How did Newton change our view of the universe? Also: Invented calculus Built 1st reﬂecting telescope Explored nature of light Isaac Newton Newton’s First Law What are Newton’s three laws of motion? An object moves at constant velocity unless a force acts to change its speed or direction 2 Newton’s Second Law Force = mass x acceleration Newton’s Third Law For any force, there is an equal and opposite reaction force (F = ma or a = F/m) Conservation of Momentum In any interaction, the total amount of momentum does not change Forces merely transfer momentum from one object to another Newton’s 3rd law of motion equivalently, conservation of momentum is consistently violated in Hollywood movies. (Send examples to me!) What keeps a planet rotating and orbiting the Sun? Gravity constantly exerts forces (=transfers momentum) between planets and Sun. 3 Objects orbit around their common center of mass because the total amount of momentum must stay ﬁxed Angular momentum = (mass) x (velocity) x (radius) Conservation of Angular Momentum In any interaction the total amount of angular momentum does not change Keplerʼs second law is an example of conservation of angular momentum The orbital velocity increases as the radius of the orbit decreases (see animation kepler_2_area..) As skaterʼs radius decreases, her spin velocity must increase IMPORTANT IDEA! Conservation of Energy Where do objects get their energy? Energy can be converted from one form into another, but the total amount of energy never changes. IMPORTANT IDEA! 4 Forms of Energy • Kinetic energy: energy of motion • Potential energy: stored energy – Gravitational (can fall from a height) – Chemical (food, gasoline) – Mass-energy (E = mc2) • Radiative energy: energy of light Definition: Temperature Kelvins: temperature unit T (K) is directly proportional to the random Kinetic Energy of the gas particles “Absolute zero” means zero motion 0 K = -460 deg F = -273 deg C A Kelvin is the same size as a Celsius degree. Keplerʼs second law is also an example of conservation of energy As the orbitʼs radius decreases, gravitational potential energy is converted into kinetic energy What determines the strength of gravity? The nature of an orbit depends on the total amount of energy Objects with lots of kinetic energy follow trajectories that do not return Escape velocity speciﬁes the speed needed to escape an objectʼs surface The force of gravity between two objects depends on the product of their masses and the square of the distance between them (KE = 1/2 mv2) (Gravity is an inverse square law.) Orbit trajectory cannonball 5 Astronauts in orbit are essentially falling around the Earth They feel weightless because they feel no force opposing gravity Kepler’s First Law Revisited How did Newton’s gravity extend Kepler’s laws? Kepler’s Second Law Revisited The shape of an orbit depends on the total amount of energy Orbits with lots of kinetic energy never return The speed of an object in its orbit is governed by conservation of energy and angular momentum Kepler’s Third Law Revisited: Newton’s version of Kepler’s 3rd Law p2 = 1 (M1 + M2) a3 How does gravity cause tides? Measuring the orbital period (p) in years and average separation (a) in AU of an orbiting system tell us its total mass (M1 + M2) in solar masses (1 solar mass = 2 x 1030 kg) IMPORTANT IDEA! 6 Gravity of Moon pulls harder on the near side of the Earth than on the far side, stretching the Earth Tides occur because water deforms more than land Tides generally occur twice a day as Earth rotates under Moon Tides are strongest when Sun, Earth, and Moon are aligned Tides are weakest when Sun and Moon form a right angle with Earth When is the LOWEST low tide? A. new/full moon B. 1st/3rd quarter moon 7 ...
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