PHS 116 Chapter 4 – Gravity, Projectiles, Satellites.
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Transcript of PHS 116 Chapter 4 – Gravity, Projectiles, Satellites.
Sir Isaac Newton
Did not “discover” gravity
First to realize that gravity is not confined to Earth
Forces must act on the planets
Netwonian synthesis
Law of Universal Gravitation
After observing Halley’s comet Came up with this relationship
F ~ mass1 x mass2
(distance)2
The Universal Gravitational Constant (G)
F ~ mass1 x mass2
(distance)2
F = G mass1 x mass2
(distance)2
G = 6.67 x 10-11 N m2/kg2
That’s 0.0000000000667
Sample Problem: Use “G” to calculate the mass of the Earth!
Assume you have a 1 kg mass.F = 9.8 N (we round to 10 usually)G = 6.67 x 10-11 N m2/kg2
m2 = 1 kgd = Earth’s radius = 6.4 x 106 m
[on board]
4.2 Effect of Distance on Gravity
Gravity is weak to begin withweakest of the four fundamental forcesgravity, electromagnetic, weak & strong
nuclear forces As distance increases, gravity falls off by
1/d2
Similar example: spray paint
Distance
Refers to the distance between the “center of mass” for the two objects
The greater an object’s distance from the Earth, the less it __________
The force of attraction approaches zero at very large distances, but can never reach zero
weighs
Question
You climb up a tree 4 m high and measure the force of gravity on your body.
You then climb up a tree 8 m high and measure the force of gravity on your body.
Do you weigh 4 times less (1/d2) when you’re up the 8 m tree?
4.3 Weight and Weightlessness Weight has no
meaning without the concept of “support force”
When you take away the support force you are “weightless” or in “freefall”
4.4 Universal Gravitation
Why are the planets round?
mass contained in the planet exerts gravity on other mass within the planet
a sphere is the best way to distribute gravity equally
[draw on board]
Planetary Perturbations
Planets influence other planet’s orbits
http://www.youtube.com/watch?v=-zJACUydNL8
4.5 Projectile Motion
Gravity causes the path of projectiles thrown horizontally to curve
To analyze properly, look at horizontal and vertical components of motion separately
The horizontal component
Object moves at constant velocity, no acceleration, due to its own inertia
if we ignore air resistance
dhorizontal = velocity x time
Projectiles Launched Horizontally The curved path is
called a parabola Follows parabolic
motion Object will hit the
ground at the same time an object dropped straight down will hit
Projectiles Launched at an Angle Up
Still follows parabolic motion
Object will hit the ground after object dropped straight down
Projectiles Launched at an Angle Down
Still follows parabolic motion
Object will hit the ground ______
the same object dropped straight down?
What other effects?
air resistance (lower angle = less air resistance)
Spin for golf balls (lower angle = less spin)
4.6 Satellites The earth is not flat If an object is projected fast enough, it can
“fall” all the way around the earth satellites 18,000 mph for a baseball
The Moon
a projectile that circles the Earth definitely influenced by Earth’s gravity, as
are other satellites Has enough velocity not to fall into the
Earth (or it would’ve done so long ago)
4.7 Circular Orbits
A satellite in orbit always moves in a direction perpendicular to the force of gravity acting on it
A very special form of free fall (no support force) The higher the orbit, the less the speed, the
longer the path, and the longer the period (time it takes to make one orbit)
8 km/s ensures a perfect circular orbit
4.8 Elliptical Orbits
If a projectile exceeds 8 km/s orbit will be an ellipse speed is not constant around the ellipse faster nearer massive object highest P.E. farthest from massive object
Escape Speed
The “initial burst” speed required to escape orbit
11.2 km/s for Earth (~25,000 mph) Leaves Earth, traveling slower and slower From any planet (or body):
v = (2 G M / d)1/2
Escape Speeds
Sun 333,000 Earth 620 km/s
Jupiter318 Earth 60.2 km/s
Earth 1 Earth 11.2 km/s
Mars 0.11 Earth 5.0 km/s
Moon 0.0123 Earth 2.4 km/s
Escape Speed
Only pertains to the initial thrust needed
Rockets could burn out if initially 11.2 km/s
You can actually escape at any speed if you’re willing to take enough time to do it