An object of mass m is lowered at constant velocity at the end of a string of negligible mass. As it is lowered a vertical distance h, its gravitational potential energy changes by
?Ug = -mg h
However, its kinetic energy remains constant, so that if we de?ne E = K + Ug, we ?nd ?E = -mg h. Why isn't the total energy E conserved?
1. In reality, all objects are massless, so that m = 0 and ?E = 0.
2. An external force is doing work on the system.
3. The net force on the system is not zero.
4. E is useless in real-world examples like this.
5. Because the universe is accelerating in its expansion, the object is actually at rest and not descending ... the earth moves away as fast as it moves "down."
6. The acceleration of the system is zero.
7. The total energy is indeed conserved, since ?E = ?Ug.
8. Ug is de?ned incorrectly as if gravity were a constant force.