Chapter 5 Projectile Motion and Satellites
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Transcript of Chapter 5 Projectile Motion and Satellites
Projectile MotionProjectile Motion
Describe the motion of an object in Describe the motion of an object in TWO dimensionsTWO dimensions
Keep it simple by considering motion Keep it simple by considering motion close to the surface of the earth for close to the surface of the earth for the time beingthe time being
Neglect air resistance to make it Neglect air resistance to make it simplersimpler
Projectile MotionProjectile Motion
The ball is in free fall vertically and moves at constant speed horizontally!!!
Projectile MotionProjectile Motion
x
yHorizontal (x)
x v x t
Vertical (y)
y y0 v0y t 12gt 2
v y v0y gt
Projectile MotionProjectile Motion
What happens when we add air What happens when we add air resistance?resistance?
Adds a new force on the ballAdds a new force on the ball The force is in the opposite direction to the The force is in the opposite direction to the
ball’s velocity vector and is proportional to ball’s velocity vector and is proportional to the velocity at relatively low speedsthe velocity at relatively low speeds
Need calculus to sort out the resulting Need calculus to sort out the resulting motionmotion
Lowers the angle for maximum rangeLowers the angle for maximum range
Projectile MotionProjectile Motion
The trick to maximum range is just to The trick to maximum range is just to keep the object off the ground for as keep the object off the ground for as long as possible.long as possible.
This allows the horizontal motion to This allows the horizontal motion to be a maximum since be a maximum since x = vx = vxxtt
Make range longer by going higher Make range longer by going higher for your starting pointfor your starting point
Make range longer by having more Make range longer by having more velocityvelocity
SatellitesSatellites
Curvature of the earth enters into Curvature of the earth enters into our calculationsour calculations
If I start 5 m above the surface, it will still be at 5 m after one second if it is moving 8000 m/sec
SatellitesSatellites
Throw at 8000 m/sec
This is about 18,000 mph
Earth circumference is 25,000 miles
Takes 25000/18000 = 1.4 hours = 84 minutes
Higher altitude longer
SatellitesSatellites
Force of gravity on bowling ball is at 90o to velocity, so it doesn’t change the velocity!!!
If no air resistance, gravity doesn’t change speed of satellite, only direction!!!
Communications Communications SatellitesSatellites
Farther out you go, the bigger the Farther out you go, the bigger the circumference of the orbitcircumference of the orbit
It takes longer for the tripIt takes longer for the trip Also, gravity weakens by inverse Also, gravity weakens by inverse
square law the farther out you gosquare law the farther out you go Make the distance so that it takes 24 Make the distance so that it takes 24
hours for the orbithours for the orbit Satellite is stationary in the sky!!!Satellite is stationary in the sky!!!
The MoonThe Moon Distance is about 240,000 milesDistance is about 240,000 miles Takes 27.3 days to make an orbitTakes 27.3 days to make an orbit
Elliptical OrbitsElliptical Orbits
Give the object a speed a bit greater Give the object a speed a bit greater than 8 km/sec and the orbit will be than 8 km/sec and the orbit will be ellipticalelliptical
Elliptical OrbitsElliptical Orbits
Sum of distances from foci to point on the ellipse is a constant!!!
Kepler’s LawsKepler’s Laws
Each planet moves in an elliptical orbit Each planet moves in an elliptical orbit with the sun at one focus of the ellipse.with the sun at one focus of the ellipse.
The line from the sun to any planet The line from the sun to any planet sweeps out equal areas of space in sweeps out equal areas of space in equal time intervalsequal time intervals
The squares of the periods of the The squares of the periods of the planets are proportional to the cubes of planets are proportional to the cubes of their average distances from the suntheir average distances from the sun