Energy is required to to movea 1070 kg mass from the Earth\'s surface to an alti

Question

Energy is required to to movea 1070 kg mass from the Earth's surface to an altitude 2.01 timesthe Earth's radius RE. The acceleration due to gravityis 9.8 m/s2. The radius of teh Earth is6.37*106 m. What amount of energy is required toaccomplish this move? Answer in units of J. I do not understand where I went wrong. This iswhat I did: Work = F x r Work = mg * (3.01RE -RE) Work = (1070 kg)(9.8m/s2)(2.01*(6.37*106 m)) Work = 1.342595982E11 J Thanks in advance. Energy is required to to movea 1070 kg mass from the Earth's surface to an altitude 2.01 timesthe Earth's radius RE. The acceleration due to gravityis 9.8 m/s2. The radius of teh Earth is6.37*106 m. What amount of energy is required toaccomplish this move? Answer in units of J. I do not understand where I went wrong. This iswhat I did: Work = F x r Work = mg * (3.01RE -RE) Work = (1070 kg)(9.8m/s2)(2.01*(6.37*106 m)) Work = 1.342595982E11 J Thanks in advance. Work = mg * (3.01RE -RE) Work = (1070 kg)(9.8m/s2)(2.01*(6.37*106 m)) Work = 1.342595982E11 J Thanks in advance.

Explanation / Answer

Given that The mass of the earth (ME) =5.98*1024kg The mass of the object is (m) = 1070kg The universal gravitational constant(G) =6.67*10-11N.m2/kg2 The radius of the Earth is (ri)= 6.37*106 m. The height above which the object is moved is (rf)= 2.01RE                                                                            = 12.80*106m Therefore the amount of energy is required to accomplishthis move is                         E = Ef -Ei                                =-GMEm/2rf -(-GMEm/2ri)                               =-GMEm/2(1/rf -1/ri) Now substitute all the above values to get the requiredanswer The radius of the Earth is (ri)= 6.37*106 m. The height above which the object is moved is (rf)= 2.01RE                                                                            = 12.80*106m Therefore the amount of energy is required to accomplishthis move is                         E = Ef -Ei                                =-GMEm/2rf -(-GMEm/2ri)                               =-GMEm/2(1/rf -1/ri) Now substitute all the above values to get the requiredanswer                                                                            = 12.80*106m Therefore the amount of energy is required to accomplishthis move is                         E = Ef -Ei                                =-GMEm/2rf -(-GMEm/2ri)                               =-GMEm/2(1/rf -1/ri) Now substitute all the above values to get the requiredanswer

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