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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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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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