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

(distance)2

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 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

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

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

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