5-2, p.81Ģ5 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. Notice that the force decreases as the square of the distance. Triumph for Newton!!Ģ4 Figure 5-2 The force on a 0.1-kilogram mass at various distances from Earth. 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”). Radius of orbit: r = 3.8 x 108 m circumference of orbit: 2pr = 2.4 x 109 m orbital period: T = 27.3 days = 2.4 x 106 sec orbital speed: v = (2pr)/T = 103 m/sec = 1 km/sec!Ģ1 Acceleration required to keep Moon on a circular orbit Radius of orbit: r = 3.8 x 108 m circumference of orbit: 2pr = ? m orbital period: T = 27.3 days = ? sec orbital speed: v = (2pr)/T = ? m/sec = ? km/sec! Even if its orbit were perfectly circular, the Moon would still be accelerated. Newton’s approximation: Moon is on a circular orbit. Gravity depends on: (1) MASSES of the two objects, (2) DISTANCES between the objects.ġ8 Newton’s question: can GRAVITY be the force keeping the Moon in its orbit? Newton’s Law of Gravity states that gravity is an attractive force acting between ALL pairs of massive objects. (Cookies reach a high speed while the Earth hardly budges.)ġ6 But…why do the cookies and the Earth exert a force on each other? SECOND Law states: acceleration = force divided by mass Mass of Earth = 1025 x mass of cookies Therefore, acceleration of cookies = x acceleration of Earth. Cookies pull on earth: F = 1 pound, upward.ġ5 THIRD Law states: force on Earth = force on cookies Remove hand! Earth pulls on cookies: F = 1 pound, downward. Hand pushes on cookies: F = 1 pound, upward. All forces come in pairs.Ĭookies push on hand: F = 1 pound, downward. Whenever A exerts a force on B, B exerts a force on A that’s equal in size and opposite in direction. In mathematical form: Or alternatively:Ī package of cookies has mass m = kilograms, And experiences gravitational acceleration g = 9.8 meters/second2 How large is the force acting on the cookies?įor every action, there is an equal and opposite reaction.
The acceleration of an object is directly proportional to the force acting on it, and inversely proportional to its mass. Examples: gravity = pull electrostatic attraction = pull electrostatic repulsion = push 1 Isaac Newton’s 3rd Law and the Universal Law of Gravitationįorce = a push or pull acting on an object.
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