ch3 gravity in physics and technology for future presidents
TRANSCRIPT
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Chapter 3
Gravity, Rotational Motion
Physics for Future Presidents
September 15, 2015
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09/10/2015 YGK, PffP: Forces
Forces Contact forces
! Anything transferred by direct contact
"Weight, friction, springs, strings, etc.
Distance forces
! Forces that do not require direct contact
! Allfundamentalforces act over distance
"Gravity, electromagnetic, weak, and strong forces
"In classical physics, we talk about force field -- animaginary medium that transmits the force
"In quantum physics, we say the force is transmitted by
exchange of virtual particles
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09/15/2015 YGK, PffP: Gravity
Most Common Everyday Forces
Gravity (see next)
Weight
! E.g. atmospheric pressure: weight of molecules
above Earth surface
"15 pounds per square inch (large !)
"Water pressure: 15 psi per 30 ft of depth
Friction! Friction of surfaces (dry friction) and drag
"Friction depends on quality of surfaces
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09/15/2015 YGK, PffP: Gravity
The Gravity Force
The most common force in the Universe
On Earth: distance force that attracts us to the
surface
!
Points downwards!
towards the centerof Earth
! Causes all objects in free fall to move with the
same acceleration towards Earth
"Galileo
"One important caveat: this is true if there is no air
resistance or other forces
"In other words, in vacuum
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09/15/2015 YGK, PffP: Gravity
Free Fall
Universal acceleration on surface of Earth"g = 10 m/s2= 32 ft/s2
"Downward velocity changes by 32 ft/s everysecond
! Distance traveled grows quadraticallywith time
"Elevation change = gt2/2 (if no initial vertical velocity)
Always points downward
"Towards the center of Earth, i.e. perpendicular to Earth
surface (in most places)
Free fall is independent of horizontal velocity
But depends on initial verticalvelocity
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09/15/2015 YGK, PffP: Gravity
Free Fall by Numbers Relations between elevation, speed, time
! Jump/fall with no initial velocity
"Elevation change = H = gt2/2 (going downward)
"Speed change = v = gt (pointing down)
! Time to fall:
! Speed at impact
"E.g. H=1 m = 3 ft!t = 0.4 s, v = 4 m/s = 10 mph
"H = 5 m = 15 ft!t = 1 s, v = 10 m/s = 23 mph
"H = 100 m = t = 4.4 s, v = 45 m/s = 100 mph
t =
2H
g
v =
2gH
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Parabolic Trajectories
Objects thrown near surface of Earth followparabolic trajectories
! How far and how high depend on initial velocity
and angle
"Larger velocity!farther and higher
"Steeper angle!higher
! If start and end of trajectory are on same elevations
"Takes same time to go up as to come down
"Farthest distance for angle of 45 degrees
! All true as long as air resistance is negligible
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09/15/2015 YGK, PffP: Gravity
Drag Force Real objects on Earth experience dragdue to air
resistance
Drag resists motion!opposes velocity
Drag grows with speed
! Linear at small speeds
! Quadratic at larger speeds
! Depends on shape of object
"Bicycle helmets, some cars (e.g. Toyota Prius) are designedto minimize drag
! May become so large as to exactly cancel downward
gravity force!terminal velocity
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09/15/2015 YGK, PffP: Gravity
Terminal Speeds
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v > v1 =
gREarth = 8 km/s
09/15/2015 YGK, PffP: Gravity
Satellites
Parabolic trajectories: faster!
farther
Eventually, may go as far as the edge of the
Earth
!
That is, once curvature of the trajectory is smallerthan curvature of the Earth!the object doesnt
fall on the ground
"Satellites
How fast does a satellite have to move ?
! First space velocity
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09/15/2015 YGK, PffP: Gravity
Rocket and Satellite Motion
Based on 4 fundamental laws of physics! Momentum conservation
! Angular momentum conservation
!
Energy conservation! Universal law of gravity
Johannes Kepler Isaac Newton Konstantin Tsiolkovsky
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09/15/2015 YGK, PffP: Gravity
Rocket Propulsion
Momentum conservation, or 3rd
NewtonsLaw:
! Origin of thrust: action vs reaction
"Thrust = mass flow !velocity of ejected gas
Konstantin Tsiolkovsky Werner von Braunmicrogravity.grc.nasa.gov
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09/15/2015 YGK, PffP: Gravity
Orbital Motion & Angular Momentum
Momentum = mass * speed (=mv)! Describes linear motion
! Vector: points in direction of motion
! Conserved (constant) if no external forces
"Newtons 2ndlaw: F = ma = dp/dt
Angular momentum = mass * speed * lever (=mvr)
= moment of inertia * angular speed (=I")
! Describes circularmotion! (Pseudo) Vector: corkscrew law
! Conserved (constant) if no external torques
"Newtons 2ndlaw: #= I$= dL/dt
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09/15/2015 YGK, PffP: Gravity
Satellites
Orbit around centerof Earth Higher launch velocity!higher elevation
But higher elevation!longer time
! Low Earth Orbit (LEO) satellites: period = 85 min
! Period = 24 h!H %40,000 km %23,000 miles
"Geostationary satellites
"Geostationary satellites must orbit in equatorial planeand from west to east
Launch point matters
"Compare orbit speed with Earth rotation (0.5 km/s)
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09/15/2015 YGK, PffP: Gravity
Weight and Weightlessness
Weight!
force with which objects push onsupports
"E.g. force with which we push on scales
Force generated by gravity
"Weight = mg = mass*acceleration of free fall
"Measure in Newtons (N) or Pounds (lbs)
Free fall: not pushing on anything
"No weight!
weightlessness
"Astronauts appear weightless because they are in free fall
Equivalence of gravity and acceleration (Einstein)
"Fictitious forces (e.g. Centrifugal) and artificial gravity
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09/15/2015 YGK, PffP: Gravity
Universal Gravity
Newton: gravity is attractive force between anymassive objects
"Proportional to product of masses
"Decreases with square of distance between centers
"GN(Newton constant) = 7!1011N*m2/kg2
"Ex: 2 70-kg people staying 1 ft (30 cm) apart experience
mutual gravitational attraction of 4!106N = 8!107lbs
Gravity is extremely feeble
! Only strong near very massiveobjects
F = GNm1m2
r2
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09/15/2015 YGK, PffP: Gravity
Universal Gravity Einstein: theory of general
relativity
Gravity caused by distortion of
spacetime around massive
objects
! Curved space!curved
trajectories
Massless objects gravitate too
! Gravity depends on total energy,including mass energy
! Photons gravitate!deflected by
massive objects
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09/15/2015 YGK, PffP: Gravity
Escape Velocity
Satellites: larger velocity!
larger radius
Escape velocity (2ndspace velocity): infinite radius
"For Earth
"Satellite launched with speed of 11 km/s will leave Earth
forever
Escape velocity grows with mass of the planet/star
! When escape velocity exceeds speed of light!
nothing can escape
"Black holes
vescape =v2 =
2gR = 11 km/s
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09/15/2015 YGK, PffP: Gravity
Black Holes
Computer-generated image of Large Magellanic Cloud (2MASS survey) with black
hole simulation superimposed