Newton’s Law of Universal Gravitation Newton’s Law of Universal Gravitation states that: the force of gravity between two masses in the universe is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centers. In order to represent this as an equation we must introduce a constant G, called the universal gravitational constant. FG = Gm1 m2 d2 • where FG is the magnitude of the gravitational attraction between any two masses, in N • m1 is the mass of one object, in kg • m2 is the mass of the other object, in kg • Δd is the distance between the centers of the objects, in m • G is the universal gravitational constant, 6.67x 10-11 Nm2/kg2. Question: Two people are sitting on a bench 2m apart. If one has a mass of 60 kg and the other a mass of 80 kg, what is the force of gravitational attraction between them? Answer: 8.0 x 10-8 N Acceleration Due to Gravity All objects near the Earth fall with the same constant acceleration. This is referred to as acceleration due to gravity, which has a magnitude of approximately 9.8 m/s2 anywhere near the surface of the Earth. If an object is in free fall then the object will accelerate downward at 9.8 m/s2. Free Fall & Kinematic Equations r r r v −v g= 2 1 Δt and r 1r r Δd = gΔt 2 + v1Δt 2 An arrow is shot with a bow straight up into the air. It leaves the bow with an initial velocity of 11m/s. a) b) c) d) e) How long will it take for the arrow to reach its highest point? What will be the arrows maximum height? How long will the arrow take to fall back to the ground? What will be the total distance travelled by the arrow? How fast will the arrow be travelling the instant before it makes contact with the earth? PG 80. #1,#2. PG 81. #2.