knowledge, science, and the universe chapter 1 - Physical Science ...

More documents

Recommendations

Info

SECTION 3–6 The Law of Universal Gravitation 33 TIDES figure 3.5 Going in orbit or falling to the ground only depends on how much horizontal velocity the projectile has. orbital acceleration of the moon and have it agree with the value of g, gravity had to diminish as the distance squared. In Newton's time, both the radius of the Earth and the distance from the Earth to the Moon were known. The ratio of these distances was 1/60. Newton used geometry to show that the Moon's centripetal acceleration was 3600 times smaller than the gravitational acceleration g measured near the surface of the earth. The gravitational acceleration was smaller by a factor of 3600, which is 60 2 . This was exactly the inverse squared relationship he hoped to find. 3–5 GRAVITy ANd ThE ThIRd LAw Of MOTION Because the force of gravity depends on distance, water in oceans nearer to the moon experiences more of the Moon’s gravitational force than the Earth as a body does, because the Earth overall is farther away from the Moon. This greater force causes the water to bulge toward the moon, creating a high tide. However, the Earth itself is closer to the Moon than water in the oceans farthest Newton’s Third Law of Motion says two forces arise from any interaction between bodies, one force acting on each of the bodies. Throwing a rock off a cliff clearly shows the acceleration of the rock. What about Earth The rock is pulling up on Earth at the same time Earth is pulling down. Does Earth accelerate toward the rock in response Yes. But as we discussed in Chapter 2, Newton’s Second Law tells us the amount of acceleration on Earth is inversely proportional to its mass and therefore is so tiny it can hardly be measured, much less observed. But consider the Moon. Its gravity pulls on Earth with the same force that Earth’s gravity is pulling on it. With a mass of only 1.2% of Earth’s mass, the Moon accelerates much more than Earth. But while the Moon’s mass is considerably less than Earth’s, it is still enough to make Earth accelerate noticeably. As a result, Earth wobbles in and out of its orbit around the Sun, always pulled toward whichever side the Moon is on. Newton understood that gravity between two objects depends on the mass of both objects, not just one or the other. By looking at the symmetry inherent in the Third Law of Motion, Newton inferred that if the force of gravity on a boulder falling to Earth was proportional to the mass of the boulder, then the force ought to be proportional to Earth’s mass as well. He theorized that just as rocks with half the mass feel half the force, a planet with half the mass would create a gravitational attraction that is also half as strong. With this realization, the foundation for a universal law of gravity was finally complete. 3–6 Force of Moon’s gravity Far Oceans Earth Near Oceans ThE LAw Of uNIVERSAL GRAVITATION So far we have determined two important facts. First, the force of gravity is proportional to the masses of both of the objects on which it acts. Second, this force weakens as the square of the distance between their centers. Newton unified these insights into the Law of Universal Gravitation, or just the Law of Gravity. It can be stated as follows: Every object in the universe attracts every from the Moon, and therefore these oceans are not pulled towards the Moon as much as the Earth itself. The result is that oceans on the opposite side from the Moon also appear to bulge upward, creating high tides on opposite sides of the Earth. The Law of Gravity Expressed by the mathematical formula F=GmM/d 2 that describes the strength of the force of gravity between two objects of mass M and m separated between their centers by the distance d.
34 C h A p T E R 3 The Gravitational Interaction Gravitational Constant A number relating the strength of the gravitational force to the masses being attracted and their distance apart. henry Cavendish British scientist known for his work with hydrogen and his experiment that measured the gravitational force between two masses in order to calculate the density of the Earth. MIRROR other object by a long- range gravitational interaction that obeys Newton’s Third Law. The strength of the attractive force, F, varies with the masses, M and m, of the two objects and the distance, d, between their centers according to the relationship F = GmM/d 2 The number G that appears in the equation is the gravitational constant. G relates the amount of mass to the strength of the force. In Newton’s day no one knew the value of G. It can only be found through experiment and is so small, 6.67 ¥10 –11 in the metric system, that the gravitational force between two 100-kilogram balls placed 30 centimeters apart is about one-millionth of a pound. Only if one of the interacting objects has a large mass, like Earth, does the force become appreciable. The first public test of Newton’s universal Law of Gravity (and his laws of motion as well) came when he used them to successfully calculate the time and place of the return of a comet which the English astronomer, Sir Edmund Halley, suspected was orbiting the Sun. When “Halley’s” comet appeared just as Newton had predicted, the science of using mathematics based on universal laws to know future motion was born. Using the heavens as a testing ground was successful. But one could still argue that gravity emanated only from the Sun and planets and was not present in ordinary objects, such as buildings or rocks. It was a leap of faith for LIGHT SOURCE SCALE figure 3.6 A Cavendish balance. When the large spheres are in the position outlined by dashes, they exert no measurable force on the smaller suspended spheres. When the larger spheres are rotated to the position shown, their gravity attracts the suspended spheres. The amount of attraction is measured by the light beam’s displacement along the scale. Newton to hypothesize, without being able at that time to prove, that a force of gravity universally exists between any two objects that have mass. This aspect of the law was confirmed 70 years after Newton’s death by Henry Cavendish (1731–1810), who developed a method of measuring the minute gravitational attraction between such ordinary objects as metal balls. In Newton’s day no one knew what the mass of Earth was. So there were two unknown values, G and M, in any formula expressing the force of Earth’s gravity. An experiment was needed to measure the force of gravity between two known masses so that the value of G could be determined. (Then the mass of Earth could be found.) In the late 1700s the shy, eccentric Cavendish did just that (see Figure 3.6). Cavendish used two small gold or platinum spheres mounted on opposite ends of a lightweight metal bar suspended in the middle by a very fine wire. The wire had a mirror mounted in the middle of it. A focused light beam reflected off the mirror and onto a scale across the room. As two large lead spheres were brought near the small spheres, the gravitational attraction between the small and large spheres twisted the wire just enough to move the light spot on the scale. In this way the force required to twist the wire was determined, the force between the large and small spheres was inferred, and the Universal Law of Gravitation was used to calculate G from G = Fd 2 /Mm. 3–7 ACCELERATION REVISITEd There is a final point regarding the value of the acceleration of gravity, g, that needs to be cleared up. At the beginning of the chapter we found that g did not change for a rock as it fell off a cliff. Every second its velocity increased by the same amount. From this we concluded the force on the rock was the same at the top of the cliff as at the bottom. But the Law of Gravity clearly says the force of gravity gets stronger as the distance between objects decreases. Therefore g should be larger at the bottom of the cliff than at the top! As it turns out, the force of gravity is stronger at the base of the cliff than at the top by the amount that the Law of Gravity predicts, but the effect is very slight. A beach at sea level is 6,378 km from Earth’s center. The top of a
Page 1 and 2: KNOWLEDGE, SCIENCE, AND THE UNIVERS
Page 3 and 4: 4 C h A p T E R 1 Knowledge, Scienc
Page 9 and 10: 10 C h A p T E R 1 Knowledge, Scien
Page 11 and 12: 12 C h A p T E R 1 Knowledge, Scien
Page 13 and 14: 14 C h A p T E R 1 Study Guide 2. W
Page 15 and 16: LAWS GOVERNING MOTION I f I h a v e
Page 17 and 18: 18 C h A p T E R 2 Laws Governing M
Page 25 and 26: 26 C h A p T E R 2 Study Guide a. 1
Page 27 and 28: THE GRAVITATIONAL INTERACTION M i l
Page 29 and 30: 30 C h A p T E R 3 The Gravitationa
Page 31: 32 C h A p T E R 3 The Gravitationa
Page 35: 36 C h A p T E R 3 The Gravitationa
Page 38: Study Guide 39 7. The Sun has much

knowledge, science, and the universe chapter 1 - Physical Science ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?