Transcript Document

Chapter 4: Newton and Universal Motion
Mechanics
• Mechanics = laws of motion
• Aristotle
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– 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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are needed to see this pictur e.
Study of Motion (Mechanics)
• Velocity
– Change in location
Speed (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)
mass on Moon =
mass on Earth
– Gravity proportional to mass
• Weight = Force of Gravity
– Stand on scale
scale pushes back with equal force
weight on Moon =
1/6 weight on Earth
– Weight proportional to mass
• Free-Fall (falling elevator, astronauts)
– Acceleration of gravity = weight / mass
All objects fall at same rate
– Objects appear “weightless”
in space, force of
gravity is not zero
Newton
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Laws of Motion
1. Moving object keeps moving
•
•
Same speed
Same direction
Objects 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 objects
Push on object; it pushes back (just as hard)
Newton
• Invents mathematics (calculus)
– Used to solve force equations
• Circular motion
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–
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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
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Weight = force of gravity
• Orbits similar to circles
• Newton’s Hypothesis
– All objects produce gravity
– Sun’s gravity
Gravity
• planets orbit sun
– Planet’s gravity
• moon orbits planet
Sun
Launching Rockets
• Fire Cannon Sideways; keep increasing velocity
– Rocket moves sideways; offsets falling
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• Circular Orbit Speed =17,000 mph
• Escape Speed = 25,000 mph
Newton
• Law of Gravity
Force = G M1M2 / R2
M1 = mass 1st object (sun)
M2 = mass 2nd object (planet)
R = distance between them
G = Newton’s constant
(a number)
– Double either mass: force increases by 2
– Double distance: force decreases by 4
•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 sun
distance
Newton and Planets
Laws 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
M in solar masses
• use to measure mass M (of central body)
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 year
b) 3 years
c) 5 years
d) 9 years
P2=a3, so if a=3, then a3=3x3x3=27; then P2=27, so P~5 (since 5x5=25)