Physics 20 Lesson 22 Gravitational Field Strength

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Erick Daniel
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1 Physics 0 Lesson Gravitational ield Strenth Refer to Pearson paes 16 to 9 for a discussion of ravitational field strenth. I. Gravitational field strenth (acceleration due to ravity) Near the surface of the Earth all objects, reardless of size or shape, are subject to an averae acceleration due to ravity of 9.81 m/s actin downward toward the center of the Earth. Another name for this acceleration is ravitational field strenth. As you move away from the center of the Earth, the ravitational field strenth decreases in manitude, but its direction remains unchaned. The ravitational field strenth is different for different planets and moons. When we calculate the ravitational force of attraction between an object and the Earth, we could use the Universal Law of Gravitation equation m m G r 1 or we could use the more familiar m ma When we make these equations equal to one another, we et: mm ma G r 1 (reconizin that m = m ) mm m a G r a 1 m G r 1 (m cancels) (where r is the radius and m 1 is the mass of the planet) The ravitational field strenth or the acceleration due to ravity for a planet or moon is calculated usin this formula. Example 1 What is the ravitational field strenth on the surface of Neptune? rom the table at the end of this lesson we find the mass and radius of Neptune. m1 a G r 6 11 Nm ( k) a k 7 ( m) a = N/k or m/s Dr. Ron Licht - 1

2 Example What is the ravitational field strenth at a distance of x 10 7 m above the surface of the Earth? If a person weihs 400 N on the surface, what would he weih at this distance? rom the data table on the formula sheet we find the mass and radius of Earth. r = r E + altitude = 6.37 x 10 6 m x 10 7 m =.551 x 10 7 m a m G r 1 ( k) ( m) 4 11 Nm k 7 a a = N/k The person s mass can be calculated usin = m a (a = 9.81 N/k on the surface) m a 400N m 9.81 N k m 40.77k m = / = 400 N/(9.81 m/s ) = k The person s new weiht can be calculated usin: ma 40.77k(0.613 ) N k = 5 N at x 10 7 m above the Earth Dr. Ron Licht -

3 II. Gravitational force ravitational field strenth Some confusion may exist between the concepts of ravitational field strenth and ravitational force. Consider three objects like those depicted below. Each object experiences the same ravitational field strenth of 9.81 m/s, assumin that we are on Earth, but each object experiences a different force since each object has a different mass. 10 k 100 k 1000 k = 98.1 N = 981 N = 9810 N m III. Practice problems 1. What is the ravitational field strenth on the surface of Earth? What is the ravitational field strenth 100 km above the surface of Earth? (9.81 m/s, 9.53 m/s ). You are on a planet whose radius is known to be about 4500 km. You then perform the followin experiment: You drop a rock from a heiht of 10.0 m and measure the time of its fall to be.65 s. What is the mass of the planet? (8.65 x 10 3 k) Dr. Ron Licht - 3

4 IV. Hand-in assinment Use the data table below to help you do the followin problems. The Solar System Period of Period of Mass Radius of rotation Mean radius revolution of Object (k) object (m) on axis (s) of orbit (m) orbit (s) Sun 1.98 x x x 10 6 Mercury 3.8 x x x x x 10 6 Venus 4.83 x x x x x 10 7 Earth 5.98 x x x x x 10 7 Mars 6.37 x x x x x 10 7 Jupiter 1.90 x x x x x 10 8 Saturn 5.67 x x x x x 10 8 Uranus 8.80 x x x x x 10 9 Neptune 1.03 x x x x x 10 9 Pluto 6 x x x x x 10 9 Moon 7.34 x x x x x Calculate the acceleration due to ravity on Jupiter. (4 m/s ). If a man weihs 780 N on Earth, what would he weih on the moon? (19 N) 3. The instrument payload of a rocket weihs 890 N on Earth. What does it weih at an altitude of 550 km above the surface of the Earth? (35.3 N) 4. Calculate the acceleration due to ravity on Saturn. How much will a 60 k man weih on the surface of Saturn? (10.4 m/s, 64 N) 5. At the top of Mt. Robson in British Columbia, a 7.50 k turkey weihs 7.6 N. Calculate the manitude of the ravitational field strenth at this location. (9.68 N/k) Dr. Ron Licht - 4

V. Activity Read Pearson paes 6 to 8 and then do QuickLab 4-4. Problem What is the motion of water in a cup when the cup is dropped from several metres above Earth's surface?

5 V. Activity Read Pearson paes 6 to 8 and then do QuickLab 4-4. Problem What is the motion of water in a cup when the cup is dropped from several metres above Earth's surface? Materials paper cup pointed pen or pencil water food colorin stepladder thinkin students Procedure CAUTION: Do this activity outside. Have someone steady the ladder and be careful when climbin it. 1. Ask your kind and benevolent instructor for the materials for the activity.. Make two small holes on opposite sides of the cup near the bottom usin the pen or pencil. Cover the holes with your thumb and forefiner. Then fill the cup with colour water. 3. Hold the cup at shoulder heiht above the round and uncover the holes. Observe what happens to the water. Have a partner sketch the path the water takes. 4. Read step 5 but before proceedin with step 5, predict what will happen when you drop the cup. Explain your prediction. 5. Refill the cup, climb the ladder and drop the cup from a heiht of several metres. Observe the motion of the water durin the fall. Questions 1. Describe the path and motion of the water (a) when the cup was held stationary, and (b) when the cup was dropped from the ladder. Give a reason for your observations. How do you observations compare with your predictions? Explain. Dr. Ron Licht - 5

Physics 20 Lesson 21 Universal Gravitation

Physics 20 Lesson 21 Universal Gravitation Physics 0 Lesson 1 Universal Gravitation I. Gravity is More Than a Name We all know of the word ravity it is the thin which causes objects to fall to Earth. Yet the role of physics is to do more than to