1)Zero, a hypothetical planet, has a mass of 5.0 x10^23, a radius of 3.0 x 10^6,
ID: 1681637 • Letter: 1
Question
1)Zero, a hypothetical planet, has a mass of 5.0 x10^23, a radius of 3.0 x 10^6, andno
atmosphere. A 10 kg space probe is launched verticallyfrom its surface.
(1.5 points)
a)If the probe is launched with an initial kinetic energy of 5.0 x10^7 J, what will be its
kinetic energy when it is 4.0 x 10^6 m from the center ofZero?
(1.5 points)
b)If the probe is to achieve a maximum distance of 8.0 x10^6 m from the center of Zero,
with what initial kinetic energy must it be launched from thesurface of Zero?
Explanation / Answer
mass M = 5.0 x10^23 radius R = 3.0 x10^6 Mass of probe m = 10 kg Initial kinetic energy K = 5* 10 ^ 7 J Kinetic energy at heigt h is K ' = 4* 10^ 6 J from law of conservation of energy , K = K ' + Potentialenergy at height h K = K ' + [ GMm / ( R + h ) ] GMm / ( R + h ) = K - K ' = 46* 10 ^ 6 J where G = Gravitational constant = 6.67 * 10 ^ -11 N m^2/ kg ^ 2 from above ( R + h ) = GMm / ( 46 * 10 ^ 6 ) =7.25* 10 ^ 6 m from this required height h = 4.25* 10 ^ 6 m (b). maximum height H = 8* 10 ^6 m Required kinetic energy = potential energy at height H = GMm / ( R + H ) = 30.31* 10 ^ 6 J Mass of probe m = 10 kg Initial kinetic energy K = 5* 10 ^ 7 J Kinetic energy at heigt h is K ' = 4* 10^ 6 J from law of conservation of energy , K = K ' + Potentialenergy at height h K = K ' + [ GMm / ( R + h ) ] GMm / ( R + h ) = K - K ' = 46* 10 ^ 6 J where G = Gravitational constant = 6.67 * 10 ^ -11 N m^2/ kg ^ 2 from above ( R + h ) = GMm / ( 46 * 10 ^ 6 ) =7.25* 10 ^ 6 m from this required height h = 4.25* 10 ^ 6 m (b). maximum height H = 8* 10 ^6 m Required kinetic energy = potential energy at height H = GMm / ( R + H ) = 30.31* 10 ^ 6 JRelated Questions
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