mid3-sample_sol

# mid3-sample_sol - the escape speed at that radius 3 4 Mary...

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3. A rocket is launched from the surface of a planet with unknown mass M , and radius r = 6 . 67 · 10 5 [m]. It is known that the planet is orbited by a small moon, which orbits the planet at a distance of R = 6 . 67 · 10 7 [m] from the center of the planet with an orbital speed of v = 100 m/s. The rocket is propelled by rocket boosters, which provide a total work of W = 5 · 10 7 [J] during the trajectory from the surface (distance r ) to a distance of 2 · r . (a) What is the mass of the planet? Use the fact that gravity provides the centripetal acceleration, v 2 R = G M R 2 M = v 2 · R G = 10 4 · 6 . 67 · 10 7 / (6 . 67 · 10 - 11 ) = 10 22 (b) Assume that the rocket (mass m =100 [kg]) starts with v = 0. What is the speed of the rocket at a distance of 2 · r ? Use conservation of energy: W = 1 2 m · v 2 + ( - G · M · m 2 · r + G · M · m · r ) = 1 2 m · v 2 + G · M · m 2 · r v 2 = W · 2 m - G · M r = 10 8 / 10 2 - 6 . 67 · 10 - 11 · 10 22 / (6 . 67 · 10 5 ) = 10 6 - 10 6 = 0 (c) (Extra points) Will the rocket excape the gravitational pull of the planet, and why? No, since at 2 · r its velocity is zero. In order to escape it will need to have a speed larger than

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Unformatted text preview: the escape speed at that radius. 3 4. Mary is vacationing in Salt Lake City, which is near a famous lake known for its high concentration of salt in the water. Mary has a mass of m =55 [kg], and an average body density of ρ = 950 [kg m-3 ]. When bathing in the lake, she notices that 30% of her body is above the water level, while the remaining 70% is below the water level. (a) What is the density of Salt Lake? Use the balance between buoyant force and weight: ρ · V · g = ρ SL · (0 . 7 · V ) · g ⇒ ρ SL = ρ . 7 = 1357 (b) (Extra points) Is the knowledge of Mary’s mass necessary? And why? No, only the knowledge of the density is suFcient. USE±UL CONSTANTS: G = 6 . 67 × 10-11 [N kg-2 m 2 ] g =9.8 [m s-2 ] 4...
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mid3-sample_sol - the escape speed at that radius 3 4 Mary...

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