Question

When the mass of the object decreases, explain the effect that change in mass has on the potential and kinetic energy of the object.

Answer 1

Use the usual formulas:

- Gravitational potential energy: U = m g h.
- Kinetic energy: K = 1/2 m v^2.

Immediate consequences (when height h and speed v are held fixed):
- Both U and K are proportional to the mass m. If m decreases, U and K decrease in direct proportion (halve the mass → each energy halves).

Other common situations to note:
- If the system has a fixed total energy (or fixed kinetic energy), reducing mass will increase the speed: v = sqrt(2K/m), so smaller m → larger v for the same K.
- In free fall (no air resistance) m cancels from m g h = 1/2 m v^2, so the fall speed v = sqrt(2 g h) does not depend on mass — lighter and heavier objects reach the same speed.
- If mass is lost by ejecting material (as in a rocket), the energetics are more complicated: energy carried away by the ejected mass matters, so the remaining object’s U and K cannot be found just by plugging a smaller m into the simple formulas without accounting for that transferred energy.

Example: a 10 kg object at h = 2 m has U = 10·9.8·2 = 196 J; if its mass drops to 5 kg (same height) U = 98 J. If its speed is 3 m/s, K drops from 1/2·10·9 = 45 J to 1/2·5·9 = 22.5 J.