Gravity
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Gravity. Force at Impact. 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.

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Gravity

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Gravity

Gravity


Force at impact

Force at Impact

  • 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


Force is not motion

Force is Not Motion

  • 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


Third law law of reaction

Third Law: Law of Reaction

  • 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


Equal and opposite

Equal and Opposite

  • 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


Universal gravity

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.

Universal Gravity


Surface gravity

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.

Surface Gravity


Variations

Variations

  • 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


Effect of height

Effect of Height

  • 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


Latitude changes

Latitude Changes

  • 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


Earth s rotation

Earth’s Rotation

  • 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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