Chapter 4: Newton and Universal Motion

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# Chapter 4: Newton and Universal Motion - PowerPoint PPT Presentation

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. Study of Motion (Mechanics).

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Presentation Transcript
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
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 on Moon =

mass on Earth

• 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”

weight on Moon =

1/6 weight on Earth

in space, force ofgravity isnot zero

Newton
• Laws of Motion
• Moving object keeps moving
• Same speed
• Same direction

Objects want to move in straight line

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

acceleration = force / mass

• 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
• 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

Gravity

Sun

Launching Rockets
• Fire Cannon Sideways; keep increasing velocity
• Rocket moves sideways; offsets falling
• Circular Orbit Speed =17,000 mph
• Escape Speed = 25,000 mph
Newton

M1 = mass 1st object (sun)

M2 = mass 2nd object (planet)

R = distance between them

G = Newton’s constant

(a number)

• Law of Gravity

Force = G M1M2 / R2

• 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 massdepends on: mass of sundistance
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

• 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 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)