Chapter 10 - Gravity and Motion. Newton’s First Law of Motion. A body continues in a state of rest or uniform motion in a straight line unless made to change that state by forces acting on it. The natural behavior of objects is to continue to move however they have been moving (inertia).
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Chapter 10 - Gravity and Motion
Path followed by the Moon
F = G M m / r2where
F is the gravitational force (in newtons)
M, m are the masses of the attracting bodies (in kilograms)
r is the distance between the (centers) of the bodies
G is a proportionality constant that depends on units
G = 6.67 x 10-11 N m2 / kg2
Example: Calculate the force of gravity exerted by the Earth on a 7-kg bowling ball.
Solution:F = GMm/r2
G = 6.67 x 10-11 Nm2/kg2
M = MEarth = 6 x 1024 kg
m = Mball = 7 kg
r = distance between centers = radius of Earth = 6,378,000 m
F = (6.67 x 10-11)(6 x 1024)(7)/(6,378,000)2 N
= 68.9 N(kg and m units all cancelled out)
Example: If the bowling ball from the previous example is dropped, how fast will it accelerate?
Solution:a = F/m
F = 68.9 N
m = 7 kg
a = (68.9)/(7) = 9.8 m/s2
The Earth also feels the force of 68.9 N but accelerates much less (essentially zero acceleration) because of its far larger mass.
Aristotle had claimed that heavier objects fell faster than lighter ones. Twice the weight would fall twice as fast he said.
Galileo did experiments that easily proved this was not true (although that he did the experiments/demonstration at the Leaning Tower of Pisa is believed to be a myth).
Perturbed orbit due to Jupiter
G = gravitational constant
M = mass of planet
R = radius of planet
G = 7 x 10-11 m3/(kg s2)
m = 6 x 1024 kg
r = 6 x 106 m
vesc2 = 2 (7e-11) (6e24) / (6e6) m2/s2
= 11,832 m/s
= 11,832 m/s (1 km/1000 m) = 11.8 km/s