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Chapter 4

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University of Toronto Mississauga
John Lester

Chapter 4 - Understanding Motion, Energy & Gravity (Sept 23) How do we describe motion? - Speed = change in position/location in some amount of time = m/s - Velocity - not the same as speed - a change in location and direction in some amount of time - units are m/s - same as speed - ex. driving 100km/h west is not the same velocity as driving 100km/h north, although the speeds are the same - Acceleration = change in velocity in some amount of time = (m/s)/s = m/s^2 - increasing speed is an acceleration - decreasing speed is a deceleration - changing direction of motion at a constant speed is also an acceleration - ex. dropping a motionless object; v = 0m/s @ 0 s; ▯ ▯ ▯ ▯ ▯ ▯ v = 10 m/s @ 1 s --> a = (10m/s - 0m/s)/s ▯ ▯ ▯ ▯ ▯ ▯ = 10 (m/s)/s - Momentum = velocity x mass - note: momentum has direction because velocity has direction - changing velocity - changes momentum - changing mass also changes momentum (less common) - a force is needed to change momentum - NET (= total) force changes momentum Sept 26 What is Mass? - Mass = sum of all the matter (molecules and atoms) in an object - The number of molecules and atoms in an object is a HUGE number - One person has approx. 10^28 molecules + atoms - Instead, use a simple number = kilogram, to represent mass What is Weight? - Force of gravity on the mass of an object - Confusion: we often use the same unit (kg) for both mass and weight - Ex: an astronaut’s mass is the same on Earth and Moon, but the astronaut’s weight is different because the force is different Newton’s Laws of Motion 1st Law: If there is no net force, the momentum does not change 2nd Law: A new force changes momentum (usually changing velocity = acceleration) ▯ equation: net force = mass x acceleration 3rd Law: Forces come in opposite pairs ▯ force = reaction force Newton’s Law of Gravity - Gravity is a universal force between all objects having mass - Force of gravity depends on both masses - Force of gravity depends on separation - greater separation = weaker force - weakens as 1/(separation)^2 = inverse square but it never goes to zero Fg = G (M1M2/d2) Fg depends directly on each mass Fg depends inversely on the square of the separation G is a universal constant Fg extends forever, until the separation is infinite Fg is never canceled out because all masses are positive quantities Fg is extremely important in astronomy because of the huge masses and separations Gravity in Astronomy - Astronomy has huge masses - huge gravity - Astronomy has huge separations - weak gravity - Astronomy has small separations - huge gravity - Other forces can cancel out: + and - charges, North and South magnetic poles - Mass is always positive - gravity cannot cancel out - gravity never stops, even at the largest distances Kepler’s Laws, Again - Observed that the planets have elliptical orbits - Newton used his laws of motion and gravity to show why the orbits are elliptical - Kepler’s 3rd Law: p2 = a3 - Newton derived p2 = (4pi2 / G(M1+M2)a3 - p = how long it takes to orbit around an object - a = average separation (semimajor axis of elliptical orbit) - Very important in astronomy, observing p and a - derive M1 + M2 - if M2 is small, like a tiny moon, we can ignore it and learn the value of M1 Cosmic Calculation - Mass of Eris - Observe p = 15.774 days = 1.363 x 10^6 s - Observe a = 37,350 km = 3.735 x 10^7 m - Use the known values of G and pi - Ignore the mass of Dysnomia Sept 28 Conservation Laws - Conserved - indestructible - Ex: mass (paper burned) - Other conserved quantities: - momentum = mass x velocity - angular momentum = mass x vel x radius = regular momentum x orbit size - Conserving angular momentum explains how Lepler’s 2nd law works Tides - Recall F(gravity) depends on 1/(separation)^2 - Moon’s gravitational force is - strongest on the near side of Earth - average on the centre of Earth - weakest on the far side of Earth - Difference in force stretches Earth = tide - Note: Tides = stretch of Earth’s rocky body
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