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Specific Forces

Fundamental Forces

Universal Gravitation

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Objectives• Calculate the gravitational force given two masses and

the distance between them.

· Calculate the change in gravitational force when the mass or distance is changed.

· Add gravitational force vectors

· Explain how a person's weight is related to the Law of Universal Gravitation.

· Define 'gravitational field strength' and relate it to the acceleration due to gravity

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SPECIFIC FORCES

Fundamental Forces

Gravitational Force

Centripetal Force

Restoring force

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What Are The Fundamental Forces?

Gravitational Force

Electromagnetic force

Strong Nuclear Force

Weak Nuclear Force

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Gravitational Force

• An attractive force that exists between all masses.• It is the basis of planetary motion.• It is the weakest force.• It acts over long distances • Is universal• We experience it as

– Weight

– Planetary orbits

– Satellite motion

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Comparing the Gravitational and Electromagnetic Forces

The gravitational force, which only attracts, is much weaker than the electric force.

electric force = 1035 gravitational force

Just as the space around a planet and every other mass is filled with a gravitational field, the space around every electric charge is filled with an electric field.

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Sir Isaac Newton

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THE LAW OF UNIVERSAL GRAVITATION

• Newton proposed that an attraction between bodies is universal.

• Gravitational force is extremely weak between ordinary objects.

• Objects with enormous mass have significant gravitational force.

Creates orbits

Creates tides

Is known as weight for objects on the surface.

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According to Newton's law of gravity, her weight (not mass) decreases as she increases her distance from the Earth's center (not surface).

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Equal and Opposite Forces

m1

-F

+F

m2 r

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Newton’s Correlations!Newton’s Correlations!

He hypothesized that the net force on a planet must vary inversely with the square of its distance from the sun.

F 1/d2

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WEIGHT ON A PLANET

Weight is dependent upon the acceleration due to gravity where the weight is measured.

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WEIGHT GRAPH

Universal Gravitation, and therefore weight, follow the inverse square law.

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Variation of g with Altitude

1 typical space

shuttle altitude2 altitude of

communication

satellites3 distance to the

moon

Altitude (km) G (m/s2)

0 9.83

5 9.81

10 9.80

50 9.68

100 9.53

4001 8.70

35,7002 0.225

380,0003 0.0027

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The math…

F = (G m1 m2)/ d2

Newton’s Inverse Square Law.

G = 6.67 10-11 N·m2/kg2

– It is the Universal Gravitation Constant.– Discovered later by Cavendish.

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Elmira

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Force Changes with the Inverse of the Distance Squared

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Force Changes with Mass

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A Gravity Concept

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How Can I be Weightless on Earth?

The sensation of weight (your apparent weight) equals the force with which you press against the supporting floor. If the floor accelerates up or down, your apparent weight varies.

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Both are "weightless".

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If a star collapses to half its radius and there is no change in its mass, gravitation at its surface would increase by a factor of four.

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Which falls toward the other, A or B? Do the accelerations of each relate to their relative masses?

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Gravitational Field Strength

• Is the gravitational force per unit of mass acting at a point

g = Fg / m

Units for gravitational field strength are N/kg

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Field lines represent the gravitational field about the Earth. Where the field lines are closer together, the field is stronger. Farther away, where the field lines are farther apart, the field is weaker.

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Calculations about Satellites

We can calculate the velocity of a satellite using the equation

_________

v = (Gme ) / r

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ESCAPE VELOCITY

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What is Escape Velocity?

• It is the slowest speed with which we can launch a projectile so that it will never fall back to the earth.

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What kinds of orbits?

• A launch speed of – 8 km/s will give a circular orbit

– 8 to 11.2 km/s will give an elliptical orbit

– 11.2 km/s orbit is parabolic, it escapes

– Above 11.2 km/s, the orbit is hyperbolic

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What about the Period of the Satellite?

We use the equation

___________

T = 2 (r3 ) / (Gme )

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Geosynchronous Orbits

• The satellite remains stationary above one place on the earth.

• Characteristics– Must have the same period as the earth’s period of

rotation

• Which is 24 hours.

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The Astronomical Unit

• This is a unit of measure equal to the average distance between the earth and the sun.

• It is designated as 1 A.U. • 1 A.U. = 93 million miles.• 1 A.U. = 1.5 X 10^11 m.• The A.U. is used to measure astronomical

distances.