Question
(a) Calculate the energy released by the destruction of 1.00 kg of mass. (b) How many kilograms could be lifted to a 10.0 km height by this amount of energy?
Final Answer
Solution video
OpenStax College Physics for AP® Courses, Chapter 28, Problem 64 (Problems & Exercises)
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This is College Physics Answers with Shaun Dychko. How much energy could be released with the destruction of 1.00 kilogram of mass? So the energy would be the mass lost times c squared. So that's 1.00 kilogram times 2.998 times 10 to the 8 meters per second squared and that is 8.99 times 10 to the 16 joules. If this energy was used to raise some mass to a height of 10.0 kilometers, how much mass could be raised? So 10.0 kilometers is 10.0 times 10 to the 3 meters and the mass will gain some potential energy equal to the mass times gravitational field strength times the height and we can solve this for m by dividing both sides by gh. So that's potential energy that we found in part (a) divided by the gravitational field strength— 9.81 newtons per kilogram— times the height of 10.0 times 10 to the 3 meters and that is 9.16 times 10 to 11 kilograms could be raised to a height of 10.0 kilometers.