A rocket has an initial total mass (including fuel) of m(0) = 4 * 10^3 kg. The v

Question

A rocket has an initial total mass (including fuel) of m(0) = 4 * 10^3 kg. The velocity of the exhaust gas is v(rel) = 3000 m/s. a) Consider the rocket at t = 0 just as it starts. How much mass must be expelled per second (how large must u be) for the rocket to have an initial acceleration g upwards in the gravitational field of the Earth? Let us now consider another rocket of the same design (same initial mass and relative velocity). Let us furthermore assume that the rocket engine works in such a way that the mass of the rocket head (hull + fuel) decreases according to the formula m(t) = m(0)exp(-bt). b) Determine the vale of b such that the rocket is able to just keep itself hovering in the gravitational field of the Earth.

Explanation / Answer

follow this The idea of a potential energy function is that it keeps track automatically of the work done by a force always present in a particular problem. The gravitational potential energy represents the work done by the weight mg of an object. So, if you use potential energy, you do not count the work weight does, that is ?K+?U=Wext where Wext is the work done by all forces other than gravity, in your example that is you. So, to lift the book you must exert a force upward of magnitude mg for a distance h and so the work you do is Wext=mgh; since kinetic energy has not changed, ?U=mgh.

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