 # Introduction to Physical Science Monday, Wednesday, Thursday Tom Burbine

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Introduction to Physical Science Monday, Wednesday, Thursday Tom Burbine tomburbine@astro.umass.edu

Quiz #2 Momentum = mv Conservation of momentum Work = Force*distance Potential energy = mgh Kinetic energy = ½ mv 2 Conservation of energy F = G M 1 M 2 d 2

Newton’s Universal Law of Gravitation Every mass attracts every other mass through the force called gravity Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses

Formula Newton came up with this formula Force is proportional to M 1 M 2 d 2 M 1, M 2 are the masses of the two objects d is the distance between the objects

If you want to calculate actual forces F = G M 1 M 2 d 2 M 1, M 2 are the masses of the two objects d is the distance between the objects G = constant = 6.67 x 10 -11 m 3 /(kg  s 2 )

So what should you know about this formula F = G M 1 M 2 d 2 The force of attraction between any two objects is directly proportional to the product of their masses The force of attraction between two objects decreases with the square of the distance between their centers G is a very small number

assume all mass is concentrated in the center of a body d d

What is the attraction of two people in this room? F = G M 1 M 2 d 2 Say their masses are both 100 kg Their distances are 10 meters apart F = 6.67 x 10 -11 m 3 /(kg  s 2 ) * 100*100 kg 2 /(10*10 m 2 ) F = 6.67 x 10 -9 N = 0.0000000067 N Remember the person weighs 980 N

F = G M 1 M 2 d 2 The value of G was determined by Henry Cavendish between 1797-1798 G = 6.67 x 10 -11 m 3 /(kg  s 2 ) http://blogs.howstuffworks.com/2009/04/13/diy- calculate-the-gravitational-constant-like-cavendish- did/http://blogs.howstuffworks.com/2009/04/13/diy- calculate-the-gravitational-constant-like-cavendish- did/ http://www.makingthemodernworld.org.uk/learning_modules/maths/06.TU.02/illustrations/06.IL.09.gif

Inverse Square Law The Force is a function of 1/ d 2

F = G M 1 M 2 d 2 How would the force between the two people change if they were only 5 meters apart instead of 10 meters? A) Stay the same B) Double (Increase by a Factor of 2) C) Quadrupul (Increase by a Factor of 4) D) halve (decrease by a factor of 2)

F = G M 1 M 2 = G M 1 M 2 = 4 G M 1 M 2 (d/2) 2 d 2 /4 d 2 How would the force between the two people change if they were only 5 meters apart instead of 10 meters? A) Stay the same B) Double (Increase by a Factor of 2) C) Quadrupul (Increase by a Factor of 4) D) halve (decrease by a factor of 2)

Acceleration of gravity (g) M is the Earth’s mass F = ma = G Mm d is the Earth’s radius d 2 m is the mass of an object F is the force a is the acceleration a = G M d 2 g = a = G M d 2

Acceleration of gravity (g) M is the Earth’s mass g = G M d is the Earth’s radius d 2 g = 6.67 x 10 -11 m 3 /(kg  s 2 ) * (6.0 x 10 24 kg) (6.4 x 10 6 m) * (6.4 x 10 6 m) g = 9.8 m/s 2

Gravitational Acceleration Gravitational acceleration is different on different planets because they have different sizes and masses Gravitational acceleration (on Moon) = 1.6 m/s² (0.165 g) Gravitational acceleration (on Jupiter) = 24.8 m/s² (2.53 g)