Ch3 Gravity in physics and technology for future presidents

7/24/2019 Ch3 Gravity in physics and technology for future presidents

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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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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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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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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


7/1909/15/2015 YGK, PffP: Gravity

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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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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Terminal Speeds


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v > v1 =

gREarth = 8 km/s


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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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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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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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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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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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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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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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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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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Black Holes

Computer-generated image of Large Magellanic Cloud (2MASS survey) with black

hole simulation superimposed

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Ch3 Gravity in physics and technology for future presidents