Chapter 4 – Gravity, Projectiles, Satellites PHS 116 Chapter 4 – Gravity, Projectiles, Satellites

Activity 1 [Gravity and reaction time]

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

4.1 Universal Law of Gravity Newton: The moon “falls” away from straight line motion

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 G = 6.67 x 10-11 N m2/kg2 That’s 0.0000000000667

Henry Cavendish First to calculate “G” independently G = __F___ (m1m2/d2)

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 kg d = Earth’s radius = 6.4 x 106 m [on board]

4.2 Effect of Distance on Gravity Gravity is weak to begin with weakest of the four fundamental forces gravity, electromagnetic, weak & strong nuclear forces As distance increases, gravity falls off by 1/d2 Similar example: spray paint

9 1/9 16 1/16

Worksheet page 27

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”

Weight You only weigh as much as the amount of support force you feel

Weightlessness

Artificial Gravity http://www.youtube.com/watch?v=J0bnL3HyfUo

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

F = G mass1 x mass2 (distance)2 J. Locke 1632 - 1704

Worksheet page 28

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

The vertical component acceleration due to gravity dvertical = ½ g t2

Combined

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?

Worksheet page 29, 30

dideal - dparabola = ½ g t2 = 5 t2

Launching Projectiles What trends do you notice? What’s the ideal launch angle?

What other effects? air resistance (lower angle = less air resistance) Spin for golf balls (lower angle = less spin)

Time of Flight deceleration of g = acceleration of g time up = time down

Worksheet pages 31, 32

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

above atmosphere

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

PE = mgh KE = ½ mv2

W =F x d

Worksheets pages 33-35

4.9 Escape Velocity Fire an object vertically What normally happens?

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 Jupiter 318 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

Chapter 4 Homework Exercises: 1, 2, 5, 6, 9, 12, 13, 20, 22, 27, 30, 32, 36, 37, 40, 49 Problems: 1, 2, 3, 8