18-Jun-16 Chapter 13 Universal Gravitation

18-Jun-16 Newton and the Moon Newton realized that Earth’s gravity was the centripetal force that kept the moon in orbit. Also discovered that gravity was weaker at that great distance. Gravity force

18-Jun-16 Gravity & Distance We don’t notice that gravity gets weaker as we move away from Earth because we rarely go very far. Moon is 30 Earth diameters away

18-Jun-16 Universal Law of Gravity Force of gravity has magnitude given by (Gravity Force) = (G) x Object A Object B ( Mass of Object A ) x ( Mass of Object B) ( Distance ) x ( Distance ) DISTANCE Force Equal and opposite forces (Newton’s Third law)

18-Jun-16 Universal Gravity Constant, G In the formula for gravity force, we have G = N m 2 / kg 2 = 6.67 x 10 –11 N m 2 / kg 2 The formula and the constant are called “universal” because, up to now, this theory predicts gravity anywhere in the universe.

18-Jun-16 Cavendish Experiment For non-astronomical objects gravity force is very small. Need sensitive balance to detect. First measured by Cavendish in his home laboratory in 1797.

18-Jun-16 “Intelligent Falling” "Things fall not because they are acted upon by some gravitational force, but because a higher intelligence, 'God' if you will, is pushing them down," The Onion, August 17, 2005 Universal Law of Gravity

18-Jun-16 Sample Problem Here is an example of using the formula (Gravity Force) = (G) x ( Mass of Object A ) x ( Mass of Object B) ( Distance ) x ( Distance ) DISTANCE = Earth’s Radius Force Object B (Earth) Object A (1 kg mass)

18-Jun-16 Sample Problem Find gravity force for a 1 kg mass on surface of Earth. (Force) = (6.67 x 10 –11 ) x Value comes out to 9.8 Newtons (check this with your calculator; it’s good practice). ( 1 ) x ( 6 x ) ( 6.38 x 10 6 ) 2 Universal Gravity Constant, G Earth’s Radius Earth’s Mass

18-Jun-16 Sample Problem (cont.) Find gravity acceleration on a 1 kg mass. Using Newton’s Second Law, (Acceleration) = = Answer is 9.8 m/s 2, which we’ve been rounding off as 10 m/s 2. (Force) (Mass) ( 9.8 N ) (1 kg )

18-Jun-16 Inverse Square Law Gravity force weakens with distance as the inverse of the square of the distance. Geometric property of area and distance. Outer circle is twice Earth’s radius so it has 4 times the area Earth Gravity 1/4 Earth Gravity

18-Jun-16 Physics 1 (Garcia) SJSU Demo: Perspective These four figures are equally spaced in distance and, in perspective, you are standing that distance from the first. At twice the distance, the face is ¼ the size. At four times the distance face is 16 th the size.

18-Jun-16 Demo: Perspective Cards Hold large card at arm’s length. Close one eye then hold small card at a distance such that it is same size as large card. That distance will be half way between your eye and large card Arm’s length Half

18-Jun-16 Weightlessness In deep space, far away from all stars, planets, etc. there is almost no gravity force. In orbit near Earth, gravity is still strong (only 10% less than on surface). Why are Shuttle and Space Station astronauts “weightless”? Earth is nearby

18-Jun-16 Freefall & Weightlessness Freefall is a state of weightlessness, even though gravity is present.

18-Jun-16 Movie: Roller Coaster

18-Jun-16 Check Yourself Sit in a seat on Ferris wheel. While it is rotating: Where do you feel heaviest? Where do you feel lightest? What if it stops? E A B C D Velocity Centripetal Force

18-Jun-16 Demo: Ferris Wheel in Hand Place a heavy object in your hand, hold your arm out and rotate your arm, palm upward, in a small circle. Object will feel lightest at the top of the circle and heaviest at bottom. Support Force Support Force

18-Jun-16 Demo: Falling Slinky Hold a Slinky and its weight stretches it out. Now drop it. In freefall it’s in a state of weightlessness so Slinky immediately contracts.

18-Jun-16 NASA’s “Vomit Comet” NASA has a special airplane for training astronauts in free- fall weightless conditions. The “Vomit Comet” nickname tells you it’s quite a wild roller-coaster ride. The plane flies between 20,000 and 30,000 feet, same as commercial flights.

18-Jun-16 Power Climb Weightless Freefall Pull out of Dive Flight of the “Vomit Comet” At the top of the arc, the plane’s trajectory is projectile motion. Boeing 707 (modified)