Gravity Notes Part I

Take notes on your 6.1

History of Gravity

Greeks – believed things had natural places– levity = light– gravity = heavy

Newton 1700’s – first to extend the idea of gravity to the whole universe– came up with an equation to calculate gravity

Einstein 1900’s – gravity is the result of the warping of space-time

Universal Law of Gravitation – every particle attracts every other particle

m

dm

221

gd

mGmF

Force (N) mass (kg)

distance (m)

constant

G = 6.67x10-11 Nm2/kg2

Inverse square law – one quantity varies inversely as another quantity is squared

Suppose that two masses are a distance apart and are attracted by a force of 20 N.

m

dm

If the mass of one of the objects suddenly doubles, what is the force attracting them?

2m

dm

If the mass of both objects suddenly

doubles, what is the force attracting them?

If the distance between the object doubles, what is the force?

2m

d

2m

m

2dm

If the distance between the object doubles, and the

mass of one object triples, what is the force?

2dm

3m

221

gd

mGmF

4

3

2d

mG3mF 2

21g

Review Projectiles

The boy on the tower throws a ball, if there were no gravity it would go straight.

Gravity makes it fall. How far does it fall in 1 second?

dy= ½gt2

It will fall 4.9 m vertical in 1 second. However the speed of how fast he throws will determine how far horizontal it goes.

What if the boy throws the ball so fast that you have to take into account the curvature of the earth?

Every 8 km or 8000 m the earth drops roughly 4.9 m.

How fast would you have to throw a ball so it never hits the ground?

8 km/s or 8000 m/s (18000 mph)

http://www.uwlax.edu/faculty/sallmen/phy155/labs/cannonball_mass_vs_orbit.htm

• Projectiles A and B fall back to earth.

• Projectiles C and D achieve an orbit at a fixed height.

• Projectile E achieves escape velocity.

http://www.valdosta.edu/~cbarnbau/astro_demos/frameset_tides.html Click on “Gravity” then “Satellites in Orbit”

Newton, the Apple, and the Falling Moon

Newton compared the falling apple with the falling moon. He hypothesized that the moon was a projectile circling the earth because of gravity. The reason it doesn’t fall into the earth is because it has a large linear speed.

Escape Speed – minimum speed an object must have in order to escape from the gravitational pull of a mass.

r

2Gmv esc

velocity (m/s) mass (kg)

radius (m)

constant

Reminders

• 40s Green Gravity Worksheet due next Monday

• You are now able to do the POTW.

• If you missed last Thursday and need to make up the Torque Lab, do it by this Thursday.

• No school Friday