A space probe of mass is first lifted from the Earth’s surface to an altitude of and

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A space probe of mass 200 kg200\,\text{kg} is first lifted from the Earth’s surface to an altitude of 400 km400\,\text{km} and, after some time, is boosted further to an altitude of 1600 km1600\,\text{km}. Ignore any change in kinetic energy during each stage. (i) Calculate the work required for the first stage of the journey (surface to 400 km400\,\text{km}). (ii) Calculate the work required for the second stage (400 km400\,\text{km} to 1600 km1600\,\text{km}). (iii) Find the total work done in the two–stage process. (iv) Calculate the work that would be required if the probe were taken directly from the surface to 1600 km1600\,\text{km} in one single operation. Compare this value with your result in part (iii) and state what this indicates about the path taken.

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