11 Newton’s Third Law of Motion: For every action, there is an equal and opposite reaction.Whenever A exerts a force on B, B exerts a force on A that’s equal in size and opposite in direction.All forces come in pairs.
14 Example of Newton’s Third Law: Cookies push on hand: F = 1 pound, downward.Hand pushes on cookies: F = 1 pound, upward.Remove hand!Earth pulls on cookies: F = 1 pound, downward.Cookies pull on earth: F = 1 pound, upward.
15 THIRD Law states: force on Earth = force on cookies SECOND Law states: acceleration = force divided by massMass of Earth = 1025 x mass of cookiesTherefore, acceleration of cookies = x acceleration of Earth.(Cookies reach a high speed while the Earth hardly budges.)
16 But…why do the cookies and the Earth exert a force on each other? Newton’s Law of Gravity states that gravity is an attractive force acting between ALL pairs of massive objects.Gravity depends on:(1) MASSES of the two objects,(2) DISTANCES between the objects.
18 Newton’s question: can GRAVITY be the force keeping the Moon in its orbit? Newton’s approximation: Moon is on a circular orbit.Even if its orbit were perfectly circular, the Moon would still be accelerated.
19 The Moon’s orbital speed: radius of orbit: r = 3.8 x 108 mcircumference of orbit: 2pr = ???? morbital period: T = 27.3 days = ???? secorbital speed:v = (2pr)/T = ??? m/sec = ? km/sec!
20 The Moon’s orbital speed: radius of orbit: r = 3.8 x 108 mcircumference of orbit: 2pr = 2.4 x 109 morbital period: T = 27.3 days = 2.4 x 106 secorbital speed:v = (2pr)/T = 103 m/sec = 1 km/sec!
21 Acceleration required to keep Moon on a circular orbit
23 Bottom Line Triumph for Newton!! If gravity goes as one over the square of the distance,Then it provides the right acceleration to keep the Moon on its orbit (“to keep it falling”).Triumph for Newton!!
24 Figure 5-2 The force on a 0.1-kilogram mass at various distances from Earth. Notice that the force decreases as the square of the distance.Fig. 5-2, p.81
25 Figure 5-3 The sum of all the forces on the apple exerted by all portions of Earth acts as if all the mass were located at Earth’s center.Fig. 5-3, p.82
26 Figure 5-1 If the sphere’s radius is doubled, the sphere’s surface increases by a factor of 4. Fig. 5-1, p.80
27 Earth's surface 6.38 x 106 m 9.8 1000 km above surface 7.38 x 106 m LocationDistance fromEarth's center (m)Value of gm/s2Earth's surface6.38 x 106 m9.81000 km above surface7.38 x 106 m7.332000 km above surface8.38 x 106 m5.683000 km above surface9.38 x 106 m4.534000 km above surface1.04 x 107 m3.705000 km above surface1.14 x 107 m3.086000 km above surface1.24 x 107 m2.607000 km above surface1.34 x 107 m2.238000 km above surface1.44 x 107 m1.939000 km above surface1.54 x 107 m1.6910000 km above surface1.64 x 107 m1.4950000 km above surface5.64 x 107 m0.13
31 (4) Newton’s Law of Gravity: The gravitational force between two objectsF = gravitational forceM = mass of one objectm = mass of the second objectr = distance between centers of objectsG = “universal constant of gravitation”