A 4000kg lunar lander is in orbit 50km above the surface of the moon. It needs to move out to a 300km high orbit in order to link up with the mother ship. How much work must the thrusters do?
Using the principle of conservation of energy, we can write that -
Total work done by both internal and external agents = Total change in energy of the system (in our case the lunar lander is the system. Internal agent being the engine that is providing the thrust)Δ(PE)
So, Total work done = W_thrusters.
Total change in energy will be only due to change in Kinetic and Potential energies as only these 2 forms of energy is possessed by the system.
Now, initial and final kinetic energy will be 0 as our system is at rest at both these instants.