posted by Brandon .
When an 81.0 kg adult uses a spiral staircase to climb to the second floor of his house, his gravitational potential energy increases by 2.25 103 J. By how much does the potential energy of a 17.0 kg child increase when the child climbs a normal staircase to the second floor?
It makes no difference of the staircase is spiral or "normal". What matters is the top to bottom elevation change.
The PE gain will be proportional to the person's mass.
Mulltiply 2.25*10^3 J by 17/81 (the mass ratio) and you will get the child's PE change
Grav PE of the adult = mgh = 2X10^3 J 81gh = 2X10^3 J gh = 2X10^3 / 81 Child's grav PE = mgh = 18 x 2x10^3 /81 = 444.4J