# Ch12-1 Newton’s Law of Universal Gravitation Chapter 12: Gravity F g = Gm 1 m 2 /r 2 G = 6.67 x 10 -11 Nm 2 /kg 2.

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Ch12-1 Newton’s Law of Universal Gravitation Chapter 12: Gravity F g = Gm 1 m 2 /r 2 G = 6.67 x 10 -11 Nm 2 /kg 2

Figure 12-2 Dependence of the Gravitational Force on Separation Distance, r

CT1: Suppose Earth had no atmosphere and a ball were fired from the top of Mt. Everest in a direction tangent to the ground. If the initial speed were high enough to cause the ball to travel in a circular trajectory around Earth, the ball’s acceleration would A. be much less than g (because the ball doesn’t fall to the ground). B. be approximately g. C. depend on the ball’s speed.

1.5 x 10 11 m 3.84 x 10 8 m Not to scale!  1.5 x 10 11 m  F EM F SM F P12.8 (p.389)

CT2: It is best to say that the Moon orbits the A. Earth. B. Sun.

Ch12-2 Gravitational Attraction of Spherical Bodies Chapter 12: Gravity

CT3: Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth’s center is twice that of satellite A. What is the ratio of the centripetal force acting on B to that acting on A? (F B /F A ) A. 2 B. 1/4 C. 1/2 D. 1/2 E. 4

CT4: In addition to using kinematics, the big picture principle in P12.20 (p.390) will be A. Newton’s laws. B. conservation of energy. C. conservation of momentum. D. the work-kinetic energy theorem.

Ch12-3 Kepler’s Laws Chapter 12: Gravity

Kepler’s First Law: The planets orbit the Sun in ellipses with the Sun at one of the foci. Semi-major axis = a. 2a 2a = 2r 2a

Kepler’s Second Law: The orbits sweep out equal areas in equal times.

greater v smaller v L = mvr is constant. Angular momentum is conserved because the central force of the Sun produces  net = 0.

Kepler’s Third Law: T  a 3/2, where a is the semi- major axis of the ellipse. For a circle, a = r.

CT5: In addition to using kinematics, the big picture principle in P12.28 (p.390) will be A. Newton’s laws. B. conservation of energy. C. conservation of momentum. D. the work-kinetic energy theorem.

CT6: For P12.31 (p.390), the period depends on A. the mass of the Earth. B. the mass of the satellite. C. both the mass of the Earth and the satellite. D. neither the mass of the Earth nor the mass of the satellite.

Ch12-4 and 5 Potential Energy and Energy Conservation U g = -GMm/r for two masses M and m separated by r E = K + U g is conserved when only the gravitational force is acting because the universal gravitational force is a conservative force Chapter 12: Gravity

CT7: In addition to using kinematics, the big picture principle in P12.41 (p.391) will be A. Newton’s laws. B. conservation of energy. C. conservation of momentum. D. the work-kinetic energy theorem.

P12.66 (p.392)

CT8: In addition to using kinematics, the big picture principle in P12.67 (p.392) will be A. Newton’s laws. B. conservation of energy. C. conservation of momentum. D. the work-kinetic energy theorem.

CT9: System A has masses m and m separated by r; system B has masses m and 2m separated by 2r; system C has masses 2m and 3m separated by 2r; and system D has masses 4m and 5m separated by 3r. Which system has the smallest attraction between the two masses? A. A B. B C. C D. D

CT10: System A has masses m and m separated by r; system B has masses m and 2m separated by 2r; system C has masses 2m and 3m separated by 2r; and system D has masses 4m and 5m separated by 3r. Which system has the next smallest attraction between the two masses? A. A B. B C. C D. D

CT11: System A has masses m and m separated by r; system B has masses m and 2m separated by 2r; system C has masses 2m and 3m separated by 2r; and system D has masses 4m and 5m separated by 3r. Which system has the greatest attraction between the two masses? A. A B. B C. C D. D

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