Newton’s Law of Universal Gravitation

Newton’s Law of Universal Gravitation•The force of gravity between two masses

in the universe is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centres

•Sounds complicated right?

In summary,•The heavier the two objects are, the

greater the force of attraction•The forces of attraction decreases rapidly

as objects move apart•No matter how large the distance is, the

force of attraction will NEVER BE ZERO•Every object in the universe exerts a force

of attraction on all other objects near or far

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In Mathematical Terms,

•FG = the magnitude of the force of gravitational attraction between 2 objects (N)

•G – BIG G - universal gravitational constant ▫G = 6.67 x 10-11 N۰m2/kg2

•m1 & m2 – mass of each object (kg)•r = distance between the 2 objects

centres (m)

221

dmmG

FG

221

dmmG

FG

Videos•https://www.youtube.com/watch?v=Jk5E-

CrE1zg

Limits to the Equation•Cannot be applied to all shapes•The equation is valid for:

▫2 spheres (i.e. the earth and sun)▫a particle/object and a sphere (i.e. a person

and the earth)▫2 objects/particles whose sizes are much

smaller than the distance between them (2 people 2 km away from each other)

Example 1:•Two people are sitting on a bench 0.60 m

apart. If one has a mass of 80 kg and the other has a mass of 55 kg, what is the force of gravitational attraction between them?

Example 2:•Your parents are walking down the street.

Your mother has a mass of 60kg and your father has a mass of 90kg. If they are 1.2m apart, how attracted are your parents to each other (what force attracts them)?

Gravitational Field Strength•We can simplify this equation to find a

planet specific value to calculate gravitational force

•In this formula:▫G is constant▫M is the mass of the planet▫R is the radius of the planet

•g represents the gravitational field strength OR acceleration due to

gravity on the planet’s surface!!!

Example 1:•Using the following values for the Earth,

what is the gravitational field strength on Earth?▫rEarth = 6371.0 km▫MEarth = 5.97219 x 1024 kg

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Example 2:•You are standing on a basketball that has

a radius of 15cm and a mass of 2.3kg. What is the gravitational field strength attracting you to the basketball?

•Complete:▫Universal gravitation assn▫Universal Law of Gravitation problems