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Work–energy with variable mass
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Energy bookkeeping with changing mass needs care for internal energy.
With changing mass, you must define the system and include internal energy changes. Applying ½mv² naively to a leaking cart or rocket gives wrong results.
In a rocket the exhaust gains kinetic energy too.
Energy conservation can still be used if all bodies are tracked.
In more detail
With variable mass, the work-energy relation must include the energy carried by the mass that enters or leaves the system. This makes the simple kinetic energy change insufficient.
Real-world uses
- Rockets and jets change mass as they burn fuel, so their energy budgets include the exhaust.
- Chutes that collect material gain mass as they move, changing their energy balance.
- A rocket shedding mass or a conveyor belt with changing load needs careful energy accounting, because part of the energy goes into the expelled material.
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Frequently asked questions
Can I use ordinary work-energy for a rocket?
Only if you include the energy of the exhaust, which is carried away at its own speed.
Why does exhaust energy matter?
Because energy carried by the expelled mass is part of the total energy budget.
Is energy conserved when mass changes?
Yes, but you must include the energy carried away by the mass that leaves the system.
Related topics in Work, Energy & Power
Conservation of energy in collisions · Virial theorem · Principle of virtual work · Hamiltonian as total energy · Lagrangian mechanics intro · Euler–Lagrange equations