Chapter 5 projectile motion and satellites
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Chapter 5 Projectile Motion and Satellites. Projectile Motion. Describe the motion of an object in TWO dimensions Keep it simple by considering motion close to the surface of the earth for the time being Neglect air resistance to make it simpler. Projectile Motion.

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Chapter 5 projectile motion and satellites
Chapter 5Projectile Motion and Satellites


Projectile motion
Projectile Motion

Describe the motion of an object in TWO dimensions

Keep it simple by considering motion close to the surface of the earth for the time being

Neglect air resistance to make it simpler


Projectile motion1
Projectile Motion

The ball is in free fall vertically and moves at constant speed horizontally!!!








Projectile motion8

What happens when we add air resistance?

Adds a new force on the ball

The force is in the opposite direction to the ball’s velocity vector and is proportional to the velocity at relatively low speeds

Need calculus to sort out the resulting motion

Lowers the angle for maximum range

Projectile Motion


Projectile motion9

The trick to maximum range is just to keep the object off the ground for as long as possible.

This allows the horizontal motion to be a maximum since x = vxt

Make range longer by going higher for your starting point

Make range longer by having more velocity

Projectile Motion


Projectile motion10
Projectile Motion the ground for as long as possible.


Satellites

Curvature of the earth enters into our calculations the ground for as long as possible.

Satellites

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


Satellites1
Satellites the ground for as long as possible.

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


Satellites2
Satellites the ground for as long as possible.

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 satellites

Farther out you go, the bigger the circumference of the orbit

It takes longer for the trip

Also, gravity weakens by inverse square law the farther out you go

Make the distance so that it takes 24 hours for the orbit

Satellite is stationary in the sky!!!

Communications Satellites


The moon

Distance is about 240,000 miles orbit

Takes 27.3 days to make an orbit

The Moon


Elliptical orbits

Give the object a speed a bit greater than 8 km/sec and the orbit will be elliptical

Elliptical Orbits


Elliptical orbits1
Elliptical Orbits orbit will be elliptical


Elliptical orbits2
Elliptical Orbits orbit will be elliptical

Sum of distances from foci to point on the ellipse is a constant!!!


Kepler s laws

Each planet moves in an elliptical orbit with the sun at one focus of the ellipse.

The line from the sun to any planet sweeps out equal areas of space in equal time intervals

The squares of the periods of the planets are proportional to the cubes of their average distances from the sun

Kepler’s Laws


Kepler s laws1
Kepler’s Laws focus of the ellipse.


Energy conservation
Energy Conservation focus of the ellipse.


Energy conservation1
Energy Conservation focus of the ellipse.


Energy conservation2
Energy Conservation focus of the ellipse.


Escape speed
Escape Speed focus of the ellipse.

Throw at > 11.2 km/sec and ball escapes the pull of the earth!!!


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