C01 Universal Gravitation.notebook May 26, 2016

Transcription

1 Newton's law of Universal Gravitation 1

2 So...how do we know the Earth spins, anyway? By 1851 it was well known that the Earth was spinning. Observational evidence included Earth's "polar flattening" and "equatorial bulge". 2

3 Foucault suggested that a pendulum set up at a pole would continue to swing in the same plane as the Earth spun around it. Observers on the Earth would see the plane of the pendulum as moving 360 degrees in a day. 3

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5 Foucault pendulums are often set up in museums with huge masses and long pendulum arms. Depending on the latitude, it can take longer than a day for the pendulum plane to move through a circle. At this latitude it takes 2 days to move through 360 degrees. 5

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7 Newton's Law of Universal Gravitation Newton's brilliance was in realizing that the forces that cause objects to fall on Earth was the same force that caused objects in the heavens to move in their orbits. 7

8 Graphing activity: F g as a function of distance Distance (r) Gravitational Force (F) 1.0 F 2.0 F/4 3.0 F/9 4.0 F/ F/25 What does the graph tell us about the relationship between distance and gravitational force? 8

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10 Any two objects, 1 and 2, in the universe exert gravitational forces of equal magnitude but opposite direction on each other. The forces are directed along the line joining the centres of both objects. The magnitude of the gravitational force is given by: Magnitude of gravitational force (N) F g = G m 1 m 2 r 2 Distance between the centres of the objects (m) Universal gravitational constan 6.67 x N. m 2 /kg 2 Mass of object (kg) This law is an "inverse square" law. 10

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12 Practice Problems, #1 2, p

13 The Cavendish Experiment (p. 205) In 1798 Henry Cavendish confirmed experimentally that Newton's law of gravitation is valid and measured the value of G using his torsion balance apparatus. 13

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15 Example 4.2, p. 208 Object A exerts a gravitational force of 1.3 x N on object B. Determine the magnitude of the gravitational force if the separation distance is doubled, m A increases by 6 times, and m B is halved. 15

16 Practice Problems, p. 209 #1 2 Check and Reflect, p. 215, # etest 16

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19 Example 4.3, p. 209 During a lunar eclipse, Earth, the Moon, and the Sun are aligned on the same plane. Using the data in the chart, calculate the net gravitational force exerted by both the Moon and the Sun on Earth. 19

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21 Space Shuttle Grade: 11 Subject: Physics 20 Date: 21

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24 Gravitational Force Grade: 11 Subject: Physics 20 Date: 24

25 1 Which of the following free body diagrams illustrates the gravitational forces exerted by the Earth on the Sun and the Sun on the Earth? A C Earth Sun Earth Sun B Earth Sun Earth Sun D 25

26 Measuring the Earth: Once the value of G was known, we could determine the mass of the Earth using the two equations for F g that we know. 26

27 What makes planets go around the sun? At the time of Kepler some people answered this problem by saying that there were angels behind them beating their wings and pushing the planets around an orbit...the answer is not far from the truth. The only difference is that the angels sit in a different direction and their wings push inwards. Richard Feynman, The Character of Physical Law Discuss what Feynman means in this quotation using physics discussed in this unit. Diagrams may be applicable. 27

28 Newton's Version of Kepler's 3rd Law: What force causes the planets to move in "circular" motion around the Sun? animation shows the paths of th Voyager 1 and 28

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