Quiz10_16solutions - Physics 221 Quiz 10 Spring 2016...

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Unformatted text preview: Physics 221 Quiz 10 Spring 2016 Name & Section Quiz 10A An astronaut lands on a new planet and sends out a report: “I measured my weight on the planet’s surface and found out that it was double my weight on the Earth’s surface” 1. What is the radius of this new planet? Assume that the average density (ρ) of this planet is exactly same as the average density of the Earth. The radius of the Earth is 6.37 x 106 m. Solution: Weight = GMpma/Rp2 G – Gravitational constant Mp – Mass of the planet ma – mass of the astronaut Rp -­‐ radius of the planet Mp = ρ(4/3)πRp3 Wp = G( ρ(4/3)πRp3)ma/Rp2 = (4/3)πρGmaRp WE = G( ρ(4/3)πRE3)ma/RE2 = (4/3)πρGmaRE Wp = 2WE Rp =2RE = 12.7 x 106 m 2. For returning home, the astronaut’s spacecraft escapes from the planet completely. What is the minimum launching speed (the escape speed) of a spacecraft to return home from this planet? The escape speed from the earth is 1.12 x 104 m/s. Solution: VE = (2GME/RE)1/2 = RE ((8/3)πρG) Vp = (2GMp/Rp)1/2 = Rp ((8/3)πρG) = 2RE ((8/3)πρG) = 2VE Vp = 2(1.12 x 104 m/s) = 2.24 x 104 m/s Physics 221 Quiz 10 Spring 2016 Name & Section Quiz 10B An astronaut lands a new planet and sends out a report: “I measured my weight on the planet’s surface and found out that it was half of my weight on the Earth’s surface” 1. What is the radius of this new planet? Let’s assume that the average density (ρ) of this planet is exactly same as the average density of the Earth. The radius of the Earth is 6.37*106m Solution: Weight = GMpma/Rp2 G – Gravitational constant Mp – Mass of the planet ma – mass of the astronaut Rp -­‐ radius of the planet Mp = ρ(4/3)πRp3 Wp = G( ρ(4/3)πRp3)ma/Rp2 = (4/3)πρGmaRp WE = G( ρ(4/3)πRE3)ma/RE2 = (4/3)πρGmaRE Wp = (1/2)WE Rp =(1/2)RE = 3.19 x 106 m 2. For returning home, the astronaut’s spacecraft escapes from the planet completely. What is the minimum launching speed (the escape speed) of a spacecraft to return home from this planet? The escape speed from the Earth is 1.12 x 104 m/s. Solution: VE = (2GME/RE)1/2 = RE ((8/3)πρG) Vp = (2GMp/Rp)1/2 = Rp ((8/3)πρG) = (1/2) RE ((8/3)πρG) = (1/2) VE Vp = (1/2)(1.12 x 104 m/s) = 0.56 x 104 m/s Physics 221 Quiz 10 Spring 2016 Name & Section Quiz 10C There is a planet which has the same average density as Earth but a radius which is double the Earth’s radius. An astronaut lands on this planet. 1. What is the acceleration due to gravity at the planet’s surface? The acceleration due to gravity at the Earth’s surface is 9.8 m/s2. Solution: g = GMp/Rp2 G – Gravitational constant Mp – Mass of the planet Rp -­‐ radius of the planet Mp = ρ(4/3)πRp3 gp = G( ρ(4/3)πRp3)/Rp2 = (4/3)πρGRp gE = G( ρ(4/3)πRE3)/RE2 = (4/3)πρGRE gp = gE(Rp/RE) gp = 2gE = 19.6 m/s2 1. For returning home, the astronaut’s spacecraft escapes from the planet completely. What is the minimum launching speed (the escape speed) of a spacecraft to return home from this planet? The escape speed from the Earth is 1.12 x 104 m/s. Solution: VE = (2GME/RE)1/2 = RE ((8/3)πρG)1/2 Vp = (2GMp/Rp)1/2 = Rp ((8/3)πρG)1/2 = 2RE ((8/3)πρG)1/2 = 2VE Vp = 2(1.12 x 104 m/s) = 2.24 x 104 m/s Physics 221 Quiz 10 Spring 2016 Name & Section Quiz 10D There is a planet which has the same average density as Earth but a radius which is half the Earth’s radius. An astronaut lands on this planet. 1. What is the acceleration due to gravity at the planet’s surface? The acceleration due to gravity at the Earth’s surface is 9.8 m/s2. Solution: g = GMp/Rp2 G – Gravitational constant Mp – Mass of the planet Rp -­‐ radius of the planet Mp = ρ(4/3)πRp3 gp = G( ρ(4/3)πRp3)/Rp2 = (4/3)πρGRp gE = G( ρ(4/3)πRE3)/RE2 = (4/3)πρGRE gp = (Rp/RE) gE gp = (1/2)gE = 4.9 m/s2 2. For returning home, the astronaut’s spacecraft escapes from the planet completely. What is the minimum launching speed (the escape speed) of a spacecraft to return home from this planet? The escape speed from the Earth is 1.12 x 104 m/s. Solution: VE = (2GME/RE)1/2 = RE ((8/3)πρG)1/2 Vp = (2GMp/Rp)1/2 = Rp ((8/3)πρG)1/2 = (1/2) RE ((8/3)πρG)1/2 = (1/2)VE Vp = (1/2)(1.12 x 104 m/s) = 0.56 x 104 m/s ...
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