We can use the formula for gravitational potential energy:
PE = mgh
where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the change in height.
For the adult, we know that:
PE_adult = m_adult * g * h = 81.0 kg * 9.81 m/s^2 * 2.00 × 10^3 J = 1.59 × 10^4 J
For the child, we can use the same formula but substitute in the values for the child's mass and the change in height:
PE_child = m_child * g * h
We don't know the exact height of the staircase, but we can assume that it is similar to the height of the spiral staircase the adult climbed. Therefore, we can use the same value of h as before.
Substituting in the values, we get:
PE_child = 18.0 kg * 9.81 m/s^2 * 2.00 × 10^3 J = 3.53 × 10^3 J
Therefore, the potential energy of the 18.0-kg child increases by 3.53 × 10^3 J when the child climbs the normal staircase to the second floor
Hope this helps