Chapter 4: Newton and Universal Motion

Mechanics

• Mechanics = laws of motion

• Aristotle– Rest = Natural State of Motion– Heavy objects fall faster

• Galileo– Object continues in motion

unless something pushes on it– Heavy and light objects fall

at same rate

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Study of Motion (Mechanics)• Velocity

– Change in locationSpeed (mph) and direction (NE)

• Acceleration– Change in velocity (speed and/or direction)

• Force– Push or pull (pounds)

• Mass– How much stuff (grams, kilograms)

Mass vs Weight• Mass Produces Gravity

– Mass intrinsic to object(never changes)

– Gravity proportional to mass

• Weight = Force of Gravity– Stand on scale

scale pushes back with equal force

– Weight proportional to mass

• Free-Fall (falling elevator, astronauts)– Acceleration of gravity = weight / mass

All objects fall at same rate

– Objects appear “weightless”

mass on Moon = mass on Earth

weight on Moon = 1/6 weight on Earth

in space, force of gravity is not zero

Newton

• Laws of Motion1. Moving object keeps moving

• Same speed

• Same directionObjects want to move in straight line

2. Change in motion (speed or direction) • caused by force

acceleration = force / mass

3. Equal, but opposite, forces between pairs of objectsPush on object; it pushes back (just as hard)

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Newton

• Invents mathematics (calculus)– Used to solve force equations

• Circular motion– Direction of motion changes– Requires force– Force changes direction; speed unaltered– Force points toward center of circle

Newton

• Gravity– Pulls apple toward earth – makes apple fall

Weight = force of gravity

• Orbits similar to circles• Newton’s Hypothesis

– All objects produce gravity– Sun’s gravity

• planets orbit sun

– Planet’s gravity • moon orbits planet

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Sun

Gravity

Launching Rockets

• Fire Cannon Sideways; keep increasing velocity– Rocket moves sideways; offsets falling

• Circular Orbit Speed =17,000 mph• Escape Speed = 25,000 mph

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Newton

• Law of Gravity

Force = G M1M2 / R2

– Double either mass: force increases by 2– Double distance: force decreases by 4

M1 = mass 1st object (sun)M2 = mass 2nd object (planet) R = distance between them G = Newton’s constant (a number)

•Larger (smaller) mass causes larger (smaller) gravitational force.

•Larger (smaller) distance causes smaller (larger) gravitational force.

Newton and Planets

• Law of Gravity

Force = G MsunMplanet / R2

Acceleration = Force / Mplanet = G Msun / R2

– Planet motion:• independent of planet mass

depends on: mass of sundistance

Newton and PlanetsLaws of motion + Gravity• Predicts Kepler’s Laws:

– 1st Law (orbits are ellipses)– 2nd Law (equal area in equal time)

• conservation of angular momentum– Skater pulls arms in; spins faster– Planet gets closer to sun; goes faster

– Extended 3rd Law a3 = M P2

• use to measure mass M (of central body)

M in solar masses

Consider a planet orbiting the Sun. If the mass of the planet doubled but the planet stayed at the same orbital distance, then the planet would take

a) more than twice as long to orbit the Sun.b) exactly twice as long to orbit the Sun.c) the same amount of time to orbit the Sun.d) exactly half as long to orbit the Sun.e) less than half as long to orbit the Sun.

Imagine a new planet in our solar system located 3 AU from the Sun. Which of the following best approximates the orbital period of this planet?

a) 1 yearb) 3 yearsc) 5 yearsd) 9 years

P2=a3, so if a=3, then a3=3x3x3=27; then P2=27, so P~5 (since 5x5=25)