A Very Brief History of Statics and Dynamics

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Edwin Barker
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1 UNIVERSAL GRAVITION

, when the Greeks were developing ideas about science.

2 A Very Brief History of Statics and Dynamics The idea that a force causes motion goes back to the 4 th century B.C., when the Greeks were developing ideas about science. Aristotle ( BC) studied motion, and believed that objects with more mass fell to the earth faster because they had a greater attraction to the earth.

3 Galileo Galilei Galileo, the premier scientist of the 17th century, determined that moving objects eventually stop because of a force called friction and that all objects regardless of their mass will fall at the same rate.

4 Johanas Kepler Also during the 17 th Century, a German mathematician and astronomer Johannes Kepler developed three laws of planetary motion that accurately predicted the location of the planets but did not explain why they change speed throughout their elliptical orbits.

the motion of an object falling on earth.

5 Enter Newton 18 th century Troubled by the lack of explanation for the planet's particular orbits, Newton eventually related the motion of the moon about the earth to the motion of an object falling on earth. He determined that both are acted on by the same force, Gravity. This realization led him to his Law of Youtubevideo Universal Gravitation.

proportional to the square of the distance separating the masses.

6 Universal Gravitation Newton recognized that the force of gravity between any two objects with mass is directly proportional to the product of the masses, and inversely proportional to the square of the distance separating the masses. Mass of object 1 Mass of object Force of Gravity F grav G m m 1 r Distance between objects (radius) Gravitational Constant

7 G - the universal gravitation constant The value of G was experimentally determined nearly a century later by Lord Henry Cavendish using a torsion balance.

8 G is 6.67 x N m /kg The value of G is an extremely small numerical value because the force of gravitational attraction is only appreciable for objects with large mass. The value for the gravitational force you exert on the earth and it exerts on you are equal. F grav G m you r m Earth Earth G m Earth r m Earth you

9 Where d g Come From??? Since an object s weight on Earth is the gravitational force that the earth exerts on the object, we can say, near sea level: Fg W m object g G m m object Earth rearth g G m r Earth Earth N m / kg ( kg m) g = 9.81 m/s

10 Notice: The acceleration due to gravity is only dependent on the mass of the Earth and the distance from the center of Earth.

Universal Gravitation is an inverse-square law The gravitational force between two objects only depends on: Mass- Direct Relationship Distance-Inverse

11 Universal Gravitation is an inverse-square law The gravitational force between two objects only depends on: Mass- Direct Relationship Distance-Inverse Relationship AND Squared F grav G m m 1 r Which variable has the greatest effect on the gravitational force Mass or Distance? Why? Distance because it is squared

12 About the Inverse Square

13 Implications of Universal Gravitation: If the mass of an object if doubled, then the force of gravity is. Doubled If the distance between two objects is doubled, then the force of gravity is One/fourth What happens to the force of gravity if there is half the original. Mass? It is halved Distance? It is quadrupled F grav G m m 1 r

14 Universal Gravitation explains Satellite motion Newton proposed that if you fired a cannon ball fast enough, it would orbit the Earth. Why is a satellite a projectile? Because the only force acting on it is gravity.

object s down, must be balanced (net F=0) with the Moon s

15 Remember, Newton had realized that the Moon orbits the Earth because the gravitational force of the Earth, which pull s all object s down, must be balanced (net F=0) with the Moon s inertia. Which cannon ball was fired with the greatest velocity? #4

16 What happens if the projectile has a. Launch Speed less than 8000 m/s Projectile falls to Earth Launch Speed equal to 8000 m/s Projectile orbits Earth Circular Path Launch Speed greater than 8000 m/s Projectile orbits Earth - Elliptical Path

17 Remember: Kepler had determined that planetary orbits are elliptical. In an elliptical orbit, a satellites velocity changes as it s distance from the object it orbits changes. Why? Force of gravity changes with the distance change. How else could the force of gravity on the satellite be changed? Change Mass

18 Using Newton s Law of Universal Gravitation, how could the force of gravity on a satellite be decreased? 1. Decrease the mass OR. Increase the distance

19 REMEMBER there are TWO types of force: Field Forces- Forces that affect objects motion without direct physical contact Example: Gravity Contact Forces- Forces that affect objects motion when in direct physical contact Example: Weight

20 Fundamental Forces of Physics All particles interact with each other and can be described by: Gravity - the attractive force that draws two masses toward each other. Electromagnetism - the interaction of particles with an electrical charge. Weak Nuclear Force -acts on the scale of the atomic nucleus and is responsible for radioactive decay. Strong Nuclear Force - keeps nucleons (protons & neutrons) bound together in the atomic nucleus. Notice: The EM, Weak and Strong force all act across short distances. Gravity is the only force that acts across large distances.

21 Gravity is the weakest of the fundamental forces since it s effects can only be seen by large masses. Just for comparison sake take two electrons 1m apart: Fgrav=( Nm/kg)( kg) /(1m) = N Felec= ( Nm/C)( C) /(1m) = N The electromagnetic force is 4*10^4 times larger

22 Fact of Gravity: Attractive force only Increases with a decrease of distance between objects All matter has gravity Increases with an increase of mass Gravity accelerates all objects at the same rate, regardless of their mass Gravity is a field force (exerts a force without contact) Gravity is the weakest of the four fundamental forces Gravity Applet

23 SIM Gravitational Force Simulation

Gravity. Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields

Gravity. Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields Gravity Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields Simulation Synchronous Rotation https://www.youtube.com/watch?v=ozib_l eg75q Sun-Earth-Moon System https://vimeo.com/16015937