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01 A car goes around a curve of radius r at a constant speed v. Then it goes around a curve of radius 2r at speed 2v. What is the centripetal force on the car as it goes around the second curve, compared to the first? (A) four times as big (B) twice as big (C) one-half as big (D) one-fourth as big Centripetal Force Solution...

02 Solution... Two objects attract each other gravitationally. If the distance between their centers is cut in half, the gravitational force (A) is cut to one fourth. (B) is cut in half. (C) doubles. (D) quadruples Universal Gravitation Solution...

03 Two objects, with masses m1 and m2, are originally a distance r apart. The magnitude of the gravitational force between them is F. The masses are changed to 2m1 and 2m2, and the distance is changed to 4r. What is the magnitude of the new gravitational force? (A) F/16 (B) F/4 (C) 16F (D) 4F Universal Gravitation Solution...

04 A hypothetical planet has a mass of half that of the Earth and a radius of twice that of the Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the Earth? (A) g (B) g/2 (C) g/4 (D) g/8 g in terms of G Solution...

05 Two planets have the same surface gravity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of planet B? (A) 0.707m (B) m (C) 1.41m (D) 4m g in terms of G Solution...

06 Satellite A has twice the mass of satellite B, and rotates in the same orbit. Compare the two satellite's speeds. (A) The speed of B is twice the speed of A. (B) The speed of B is half the speed of A. (C) The speed of B is one-fourth the speed of A. (D) The speed of B is equal to the speed of A. Universal Gravitation Centripetal Force Solution...

7 What is the gravitational force on a 70-kg person standing on the Earth, due to the Moon? The mass of the Moon is 7.36 × 1022 kg and the distance to the Moon is 3.82 × 108 m. (A) 0.24 N (B) 0.024 N (C) 0.0024 N (D) 0.00024 N Universal Gravitation Solution...

8 The mass of the Moon is 7.4 × 1022 kg and its mean radius is 1.75 × 103 km. What is the acceleration due to gravity at the surface of the Moon? (A) 2.8 × 106 m/s2 (B) 9.80 m/s2 (C) 1.6 m/s2 (D) 0.80 m/s2 g in terms of G Solution...

9 An object weighs 432 N on the surface of the Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earth's surface, what is its weight? (A) 432 N (B) 48 N (C) 27 N (D) 0 N Universal Gravitation Solution...

10 Solution... The Earth has radius r. A satellite of mass 100 kg is at a point 3r above the Earth's surface. What is the satellite's weight? (A) 61 N (B) 109 N (C) 9000 N (D) 16000 N Universal Gravitation Weight Solution...

11 A satellite is in a low circular orbit about the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The mean radius of the Earth is 6.38 × 106 m.) (A) 5.9 km/s (B) 6.9 km/s (C) 7.9 km/s (D) 8.9 km/s Centripetal Force Weight Solution...

12 The hydrogen atom consists of a proton of mass 1.67 × 10-27 kg and an orbiting electron of mass 9.11 × 10-31 kg. In one of its orbits, the electron is 5.3 × 10-11 m from the proton. What is the mutual attractive force between the electron and proton? (A) 1.8 x 10-47 N (B) 3.6 x 10-47 N (C) 5.4 x 10-47 N (D) 7.0 x 10-47 N Universal Gravitation Solution...

01 A car goes around a curve of radius r at a constant speed v. Then it goes around a curve of radius 2r at speed 2v. What is the centripetal force on the car as it goes around the second curve, compared to the first? Centripetal Force

02 Two objects attract each other gravitationally. If the distance between their centers is cut in half, the gravitational force Universal Gravitation The law of universal gravitation is an inverse square law. If the distance between two objects is cut in half, the force between them is reduced to one quarter.

03 Two objects, with masses m1 and m2, are originally a distance r apart. The magnitude of the gravitational force between them is F. The masses are changed to 2m1 and 2m2, and the distance is changed to 4r. What is the magnitude of the new gravitational force? Universal Gravitation

05 Two planets have the same surface gravity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of planet B? g in terms of G

on the satellite’s mass 06 Satellite A has twice the mass of satellite B, and rotates in the same orbit. Compare the two satellite's speeds. Centripetal Force Universal Gravitation Speed does not depend on the satellite’s mass

7 What is the gravitational force on a 70-kg person standing on the Earth, due to the Moon? The mass of the Moon is 7.36 × 1022 kg and the distance to the Moon is 3.82 × 108 m. Universal Gravitation

8 The mass of the Moon is 7.4 × 1022 kg and its mean radius is 1.75 × 103 km. What is the acceleration due to gravity at the surface of the Moon? g in terms of G

9 An object weighs 432 N on the surface of the Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earth's surface, what is its weight? Universal Gravitation The law of universal gravitation is an inverse square law. If the distance between two objects is increased by a factor of three, the force is reduced by a factor of 9

10 The Earth has radius r. A satellite of mass 100 kg is at a point 3r above the Earth's surface. What is the satellite's weight? Universal Gravitation The law of universal gravitation is an inverse square law. If the distance between two objects is increased by a factor of three, the force is reduced by a factor of 9 Weight The weight of the satellite on Earth is The weight of the satellite 3r.

11 A satellite is in a low circular orbit about the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The mean radius of the Earth is 6.38 × 106 m.) Centripetal Force Weight

12 The hydrogen atom consists of a proton of mass 1.67 × 10-27 kg and an orbiting electron of mass 9.11 × 10-31 kg. In one of its orbits, the electron is 5.3 × 10-11 m from the proton. What is the mutual attractive force between the electron and proton? Universal Gravitation