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Gravity

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Gravity

- A falling ball on a paper surface can break through.
- The ball is exerting a force

- A falling ball on a hard surface rebounds.
- The surface is exerting a force

- There are forces both ways at contact.

force of the ball on the surface

force of the surface on the ball

- The ball breaking paper doesn’t stop.
- The force needed to break through is small.
- But that small force is also exerted on the ball.

- On a rebound the ground doesn’t move.
- The force needed to break through is large
- A force acted in both ways

force of the ball on the surface

force of the surface on the ball

- For every action there is an equal and opposite reaction.
- Forces between two objects act in pairs.
- F12 = -F21 (Newton’s third law)

reaction force acts on the rocket

rocket

hot gas is forced out

rocket and gas are both affected

- Newton’s law of reaction also applies to the force of gravity.
- The Earth pulls the Moon
- The Moon pulls the Earth

- Newton used this to describe a Law of Gravity.

FEM

Moon

FME

Earth

Newton realized that all objects obey that Law.

Other planets

Apples

People

The gravitational force is universal.

The gravitational constant is G = 6.67 x 10-11 Nm2/kg2.

What is the gravitational force between two students sitting in adjacent seats?

Assume the students have a mass of 70 kg each.

Assume that they are separated by 1m.

F = (6.67 x 10-11 Nm2/kg2) x (70 kg)2 / (1 m)2

F = 3.3 x 10-7 N.

The force of gravity on a mass is its weight.

The force of gravity compared to the mass is the field strength.

Consider the force on an unknown mass m.

Use Earth’s mass M and Earth’s radius R

Calculate the field strength.

g = F/m = GM/R2

M = 5.97 x 1024 kg

R = 6.37 x 106 m

g = 9.81 N/kg = 9.81 m/s2

This field strength g only applies at Earth’s surface.

Approximately, g is equal to 9.8 N/kg or 9.8 m/s2.

- Gravity varies over the surface of the Earth.
- The height of the surface varies – so the radius does, too
- The material under the surface is not uniform
- The earth isn’t exactly round
- The tides affect the earth as well as the oceans

- One unit of gravitational acceleration used on the Earth is the Galileo.
- 1 Gal = 1 cm/s2 = 0.01 m/s2 = 0.01 N/kg.
- g = 981 Gal

- High areas have a greater distance from the center of the Earth.
- An increase of 1 km should decrease g by 300 mGal.
- Type of rock affects g.

USGS

- As the Earth spins the equator slightly bulges.
- The radius is about 22 km bigger compared to the pole.
- Expect a few Gal difference from equator to pole.
- Equator: 9.780 m/s2
- North Pole: 9.832 m/s2

Colorado School of Mines

- The earth is made of layers of different types of rock.
- These rocks can move due to daily tides.
- Much less than ocean tides
- Period is 12 hours like the ocean

- The force of gravity from the Moon is countering some of the force of the Earth.

Colorado School of Mines

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