A given planet has twice the radius of earth but the same density (i.e. the same
ID: 2017048 • Letter: A
Question
A given planet has twice the radius of earth but the same density (i.e. the same mass per unit of volume). The volume of a sphere is given by the formula 4/3R^3
What is the potental energy of a 100 kg spacecraft located on this planet's surface?
a) -2.5 * 10^10 J
b -4.3 * 10^10J
c) -1.3 * 10^10 J
d) -7.4 * 10^10J
e) -6.1 * 10^10 J
Find the minimum kinetic energy necessary for this 100 kg space craft to leave the gravitational pull of this planet. Neglecting the effects of the atmosphere
Find the weight of this spacecraft as it rests on this planets surface
a) 981 N b)3924 N c) 490 N d) 245 N e) 1962N
Explanation / Answer
radius of the planet r = 2R where R = Radius of earth = 6.38 * 10 ^ 6 m So, r = 2 * 6.38 * 10 ^6 m Density of planet = Density of earth m / [4/3r^3] = M / [4/3R^3] m / r^ 3 = M / R ^ 3 m / [8R^3 ] = M / R^ 3 m = 8M = 8 * 5.98 * 10 ^ 24 kg Since mass of earth M = 5.98 * 10 ^ 24 kg the potental energy of a 100 kg spacecraft located on this planet's surface U = -Gmm' / r where m ' = mass of space craft = 100 kg G = Gravitational constant = 6.67 * 10 ^ -11 Nm^ 2/ kg^ 2 plug the values weget U = - 2.5 * 10 ^ 10 J (b). the minimum kinetic energy necessary for this 100 kg space craft to leave the gravitational pull of this planet K = 2.5 * 10 ^ 10 J (c). the weight of this spacecraft as it rests on this planets surface = m ' g where g = gravity on the surface of the planet = Gm / r^ 2 = G*8M / ( 2R ) ^ 2 = G * 8M / 4R^ 2 = 2GM / R^ 2 = 2* gravity on earth = 2 * 9.81 m / s^ 2 = 19.62 m / s^ 2 So, the weight of this spacecraft as it rests on this planets surface = 100 kg * 19.62 m / s^ 2 = 1962 NRelated Questions
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