Newton’s Law of Universal Gravitation AP Physics 1 McNutt Adapted from AP physics curriculum from Tenafly HS, New Jersey
Isaac Newton Late 1600s, England Shouldn’t everything want to fall?
Questions If the planets are orbiting the sun, what force is keeping them in orbit? What force keeps the moon in its orbit? Could the force of gravity be universal?
Why does the moon not fall straight down onto the earth?
The Thought Experiment We have all thrown a ball. We know the harder you throw it level to the ground the further it goes.
The Thought Experiment If you keep throwing the ball at faster speeds, no air, it would go further. (watch this video) Universial Gravitation.ppt
The Thought Experiment If you keep throwing the ball at faster speeds, no air, it would go further. If it is shot fast enough, it keeps on going Even faster it gets shot away Picture from: http://www.astro.virginia.edu/class/oconnell/astr1210/guide08.html
Newton’s Law of Universal Gravitation Any two objects attract each other with a gravitational force, proportional to the product of their masses and inversely proportional to the square of the distance between them. The force acts in the direction of the line connecting the centers of the masses.
Newton’s Law of Universal Gravitation http://scienceblogs.com/startswithabang/upload/2009/07/meet_our_second_moon/400px-NewtonsLawOfUniversalGravitation.svg.png
Henry Cavendish’s experiment determined the proportionality constant G in 1798. http://www.newscientist.com/data/images/archive/1639/16390101.jpg
The Value of G. G= 6.67 x 10-11 N m2 / kg2
Change of Gravitational Force with Distance Law of universal gravitation is known as an inverse square law.
Problem 1 Two spheres of mass 35kg are 60m apart. What force does one exert on the other? If the mass of one is tripled and the radius is quadrupled how does the force change?
Problem 1
Problem 1 cont.
Problem 1 cont.
Problem 1 cont.
Problem 1 cont.
Problem 1 cont.
Problem 2 Two spheres of equal mass have a force of gravity of 7.0x10-9 exerted on each other. Find their mass if the distance between them is 7.0m.
Problem 2
Problem 3 Find the value of the gravitational acceleration g. The mass of the earth is 6.0 x 1024kg.
Problem 3 continued
Problem 3 continued
Acceleration of Gravity
Watch this Video
Gravity’s Potential Energy
Gravity’s Potential Energy
Gravity’s Potential Energy
Potential Energy Practice The moon magically stops orbiting the earth and starts to fall in. Radius of average lunar orbit = r = 3.8E5 km mearth= 5.97E24 kg mmoon = 7.35E22 kg A) How much energy does the moon have? B) What would it’s speed be relative to the earth when it collides? (treat both as point masses)
Potential Energy Practice
Potential Energy Practice U = -7.7E28 J mmoon = 7.35E22 kg (the (-) means it would come toward the earth) B) What would it’s speed be relative to the earth when it collides? KE=change in PE If it hits the earth it lost all it’s distance so ½*mmoon*v^2= U v=√(2U/mmoon) v=1448 m/s = 1.5 km/s