lecture15

# lecture15 - Phys 2101 Gabriela Gonzlez Newtons law: F =...

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Phys 2101 Gabriela González

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“Newton’s law”: F = Gm 1 m 2 /r 2 Explains why apples fall, why the planets move around the Sun,…
sciencebulletins.amnh.org And in YouTube!

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.. but it also predicts traveling away from moving masses! Explains just as well as Newtons’ why things fall and planetary motion… Einstein’s messengers, National Science Foundation video einsteinsmessengers.org
5 Newton’s gravitation law (not F=ma!!): G = 6.67 x 10 -11 N m 2 /kg 2

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6 We can add gravitational forces. We have to add them as vectors!! All particles have the same mass. What’s the direction of the force on the labeled particle in each arrangement? Which arrangement has the largest force on the labeled particle?
7 For solid bodies, we have to add up the forces from all parts in the body: integrals!! Luckily, for spherical shells, things get simplified: A uniform spherical shell of matter attracts a particle that is outside the shell as if all of the shell’s mass were concentrated in the center. A uniform spherical shell of matter exerts no net gravitational force on a particle located inside it. also solid spheres!

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8 If objects fall from a height h, the force is F = GMm/r 2 = GMm/(R+h) 2 = ma g , with “free fall acceleration” a g =GM/(R+h) 2 . Notice that the Earth also “falls” towards the apple, but with a much smaller acceleration! GMm/R 2 F N =mg g=GM/R 2 =6.67x10 -11 Nm 2 /kg 2 x 5.98 x10 24 kg /(6.37x10 6 m) 2 = 9.8 m/s 2 Normal force of earth on us is “weight”, and if we are just standing on a scale, it is equal to Earth’s attractive gravitational force.
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## lecture15 - Phys 2101 Gabriela Gonzlez Newtons law: F =...

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