When an 84.7 kg adult uses a spiral staircase to climb to the second floor of his house, his gravitational potential energy increases by 2.00E+3 J. By how much does the potential energy of a 17.3 kg child increase when the child climbs a normal staircase to the second floor?
m g h
same g
same h
(17.3 / 84.7) 2*10^3
To find the increase in potential energy for the child climbing a normal staircase, we need to use the formula for gravitational potential energy:
Potential Energy = mass * gravity * height
Since both the adult and the child are climbing to the same height (the second floor), we can assume that the height is the same for both cases.
Given:
Mass of the adult (m1) = 84.7 kg
Change in potential energy for the adult (ΔPE1) = 2.00E+3 J
Mass of the child (m2) = 17.3 kg
To find the change in potential energy for the child (ΔPE2), we can set up a ratio using the masses and the changes in potential energy:
ΔPE1 / m1 = ΔPE2 / m2
Plugging in the given values:
(2.00E+3 J) / (84.7 kg) = ΔPE2 / (17.3 kg)
To solve for ΔPE2, we can rearrange the equation:
ΔPE2 = (2.00E+3 J) * (17.3 kg) / (84.7 kg)
Calculating this, we find:
ΔPE2 ≈ 409.9 J
Therefore, the potential energy of the child increases by approximately 409.9 J when climbing a normal staircase to the second floor.