Ch 13 Gravitational Interactions

Newton DID NOT discover gravity.

He discovered that gravity is universal.

- It pulls everything with the same force.

•He also discovered that all objects in the universe attract each other.

•A force field exerts a force on objects in its vicinity.

Gravitational Field (g)

A force field that exists in the space around every mass or groups of masses.

•The strength of a gravitational field is the force per unit mass.

g = F/m

Newton’s Law of Universal Gravitation

221

r

mmGFg

mR

MmG

m

Fg

2

Using the earth’s radius and mass we get 9.8 m/s2.

mR

MmG

m

Fg

2

Remember at or near the earth’s surface the gravitational field strength is 9.8 m/s2 or 10 m/s2.

The acceleration due to gravity, ‘g’, decreases with

distance from the earth’s center as 1/d2.

As an object moves away from the center

of the Earth, by a distance equivalent to

the earth’s radius.

Distance Force of Gravity

RE Fg

2 RE 1/4 Fg

3 RE 1/9 Fg

4 RE 1/16 Fg

5 RE 1/25 Fg

Gravitational Field Inside a Planet

•There exist a gravitational field inside the earth as well as outside.

•As you get closer to the center of the earth the gravitational acceleration decreases.

• When you get to the center of the earth your acceleration is zero.

• There is no gravitational field at the center of the earth

• The mass above and below you cancel each other out.

Weight (Fg)•The force of gravity. •The pressing against the earth is the sensation we interpret as weight.

•Think about being in an elevator.

Stage A

                         

Stage B

                           

Stage C

                           

Stage D

                             

Fnet = ma

Fnet = 0 N

Fnet = ma

Fnet = 400 N, up

Fnet = ma

Fnet = 400 N,

down

Fnet = ma

Fnet = 784 N,

down

FN equals Fg

FNorm = 784 N

FN > Fg by 400 N

FNorm = 1184 N

FN < Fg by 400 N

FNorm = 384 N

FN < Fg by 784 N

FNorm = 0 N

This last situation is the reasoning you might feel a little queasy in the stomach when you go over a good size bump in the road at a really fast speed or sudden drops on roller coasters. You catch a little air and the seat drops out from you briefly.

• Rather than define weight as the force of gravity that acts on you.

• We can say that it is the force you exert on a supporting floor.

Weightlessness• Is not the absence of gravity, rather it is the absence of a support force.

Newton showed that the ocean tides are caused by differences of the moon’s

gravitational pull on opposites sides of the

earth.

• When the sun, Earth, and the moon are all lined up, the tides due to the moon and sun coincide.

• Resulting in higher than average high tide and lower than average low tides.

These are called spring tides.

Lunar Eclipse• Is produced when earth is directly between the sun and the moon.

Solar Eclipse•Is produced when the moon is directly in between the earth and sun.

Neap Tides• When there is a half moon,

the sun and moon partly cancel each other out.

• Produces lower than average high tides and lower than average low tides.

Black Hole• A mass that has collapsed to so great a density that its enormous local gravitational field prevents light from escaping.

Anatomy of a Black Hole

Black Holes