Name: _________________________ Physics 11 Block: _____ Date: _______________ DYNAMICS Newton’s Law of Gravitation Gravitational Force / Force of Gravity: • An attractive force that causes objects with mass to be pulled towards each other. • An “action-at-a-distance” force since it acts without the objects making contact. • Its strength varies with distance. Your WEIGHT on the top of Mt. Everest is slightly different than your weight in class. Your MASS however, never changes. Newton’s Equation: Newton found that the gravitational force between two objects varied with distance. More specifically, that there was in INVERSE-SQUARED relationship between the force of gravity and distance: where: F = Force (N) d = distance to an object’s centre of mass (m) Example 1 – The force of gravity on an astronaut when orbiting around the earth is 100N. If the astronaut doubles his orbital distance, what is the new force he feels? a) 400 N b) 25 N c) 200 N d) No change Example 2 – The force of gravity on a satellite orbiting around the earth, decreases from 900N to 100N. If you compare his initial orbital distance (di) to his final orbital distance (df), you will find that: a) di = df b) 9 × di = df c) 3 × di = df d) di = 9 × df Physics 11 Newton also found that the gravitational force was DIRECTLY PROPORTIONAL to the mass of each body. where: M = mass of larger object (kg) m = mass of the smaller object (kg) Example 3 – If the force of gravity between a planet and its moon was 3.0x104 N, how much would the force be if an asteroid caused the moon to lose ½ of its mass? a) No change b) 1.5x104 N c) 3.0x102 N d) 6.0x104 N By combining these two ideas, he produced the following equation: Fg = force of gravity / gravitational force (N) G = Universal gravitational constant = 6.67x10-11 N*m2/kg2 r = distance between the centre of mass of the two objects (metres). M = mass of larger object (kg) m = mass of smaller object (kg) Example 4 – An 100 kg satellite is sitting 6.4x107 km away from the centre of the earth. a) What is the force of gravity on the satellite? b) If it were instead sitting 6.4x107 km above the earth’s surface, what would you need to change?
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