1 What is the Newtonian synthesis? 1. All objects near the Earth free-fall with the same acceleration. 2. The combination of forces on each planet directed towards the Sun 3. The combination of all forces on a planet directed along its path 4. Gravity only happens on Earth. 5. The union of terrestrial laws and cosmic laws 2 What did Newton discover about gravity? 1. The stars, planets, and moon move in divine circles. 2. Any force on a planet would be directed along its path. 3. Gravity only happens on Earth. 4. Gravity is universal, which means it is not a phenomenon unique to Earth. 5. All objects near the Earth free fall with the same acceleration. 3 In what sense does the moon fall? 1. The moon moves in a straight line toward the Earth. 2. The moon falls away from the straight line it would follow if there were no forces acting on it. 3. Some stones on the moon drop from it toward the Earth. 4 According to some nineteenth-century geological theories (now largely discredited), the Earth has been shrinking as it gradually cools. If so, how would g have changed over geological time? 1. It would increase; g is inversely proportional to the square of the radius of the Earth. 2. It would decrease; the Earth s radius is decreasing. 3. It would not change; the mass of the Earth remained the same. Quest Chapter 12 What is synthesis? It is the combining of separate things to make something new. This can include discarding unneeded or incorrect things as well. What things did Newton bring together and what did he toss? Read the text or check your notes. How does the moon move? How could we use the word fall to describe that motion? If the Earth is shrinking, what dimension of the Earth is getting smaller? What happens to the gravitational force on an object as the radius is reduced?
5 How does the force of gravity between two bodies change when the distance between them doubles? 1. quadruples 2. drops to one quarter of its original value 3. remains the same 4. Unable to determine; the mass is needed. 5. halves 6. doubles 6 You weigh 471 N. What would you weigh if the Earth were four times as massive as it is and its radius were two times its present value? If the masses remain the same and only the radius changes by the multiple given in the problem, how will F g change? Analyze the problem. Deal with each change separately. What is your new weight after the first change? 7 If you moved to a planet that has the same mass as the Earth but twice the diameter, how would your weight be affected? 1. 8 times as much 2. ½ as much 3. 2 times as much 4. 4 times as much 5. the same 6. 1/6 as much 7. None of these 8. ¼ as much 8 If you moved to a planet that has twice the mass of the Earth and also twice the diameter, how would your weight be affected? 1. ¼ as much 2. 2 times as much 3. ½ as much 4. 1/6 as much 5. the same 6. 4 times as much 7. 8 times as much Using that new weight, what is your final weight after the last change? If the masses remain the same and only the radius changes by the multiple given in the problem, how will F g change? If the radius remains the same and only one of the masses change by the multiple given in the problem, how will F g change?
9 What do we call the gravitational force between the earth and your body? 1. mass 2. velocity 3. weight 4. Newton 5. gravitation 10 When at rest on the launching pad, the force of gravity on the space shuttle is quite huge. When in orbit, some 297 km above Earth s surface, what is the force of gravity on the shuttle? Neglect changes in the weight of the fuel carried by the shuttle. 1. nearly zero (micro-gravity) 2. nearly as much 3. zero 4. about half as much Think What you are being asked to determine is the weight change to an object when the radius changes. What number when mulitplied by the radius of the Earth gives yields the radius of the Earth + 297km? 11 (part 1 of 4) Calculate the force of gravity on a 73 kg person at the surface of the Earth. The acceleration of gravity is 9.8 m/s 2. 12 (part 2 of 4) What force of gravity exists at three times the Earth s radius? 13 (part 3 of 4) What force of gravity exists at five times the Earth s radius? 14 (part 4 of 4) What is the relationship exhibited on a gravitational force vs distance graph? 1. direct 2. quadratic 3. exponential 4. inverse square How much would the weight change for that multiple of the radius? Use the second law of motion. Use the Universal Law of Gravitation. What happens when you change the radius. Same hint. What is the relationship between gravity and distance? Recheck your notes.
15 Two spheres have equal densities and are subject only to their mutual gravitational attraction. Which quantity must have the same magnitude for both spheres? 1. velocity 2. acceleration 3. kinetic energy 4. displacement from the center of mass 5. gravitational force 16 An apparatus like the one Cavendish used to find G has a large lead ball that is 8.9 kg in mass and a small one that is 0.071 kg. Their centers are separated by 0.06 m. Find the force of attraction between them. The value of the universal gravitational constant is 6.67259 10 11 N m 2 /kg 2. Answer in units of N 17 Two balls, each with a mass of 0.788 kg, exert a gravitational force of 9.79 10 11 N on each other. How far apart are the balls? The value of the universal gravitational constant is 6.673 10 11 Nm 2 /kg 2. 18 Mars has a mass of about 6.22 10 23 kg, and its moon Phobos has a mass of about 1.02 10 16 kg. If the magnitude of the gravitational force between the two bodies is 4.32 10 15 N, how far apart are Mars and Phobos? The value of the universal gravitational constant is 6.673 10 11 N m 2 /kg 2. 19 Tom has a mass of 77.6 kg and Sally has a mass of 49.9 kg. Tom and Sally are standing 18.5 m apart on a massless dance floor. Sally looks up and she sees Tom. She feels an attraction. If the attraction is gravitation, find its magnitude. Assume both can be replaced by spherical masses and that the gravitational constant is 6.67259 10 11 N m 2 /kg 2. Answer in units of N What. Substitute and solve for F g. Substitute and solve for F g.
20 The gravitational force of attraction between two students sitting at their desks in physics class is 4.13 10 8 N. If one student has a mass of 42.2 kg and the other has a mass of 64.1 kg, how far apart are the students sitting? The universal gravitational constant is 6.673 10 11 N m 2 /kg 2.