Question

An anvil has a volume of 0.037m^3 and a density of 7838 kg/m^3. If it is dropped into a swimming pool 3.21 m deep, how much energy is lost during the fall and while striking the ground? Answer in joules.
subtle hint: As the anvil falls, an equal volume of water is displaced. This water must rise to the surface of the pool, raising the level of the water very slightly.

Answer 1

The potential energy of the anvil is transferred into the potential energy of the water of volume V_a, which is raised from the bottom of the pool to the surface, and the final kinetic energy of the anvil.
Mass of the anvil
m_a=ρ_a∙V_a=7838 kg/m^3 ∙0.037m^3=290 kg
Mass of the water (ρ_w=1000 kg/m^3):
m_w=ρ_w∙V_a=1000 kg/m^3 ∙0.037m^3=37 kg
Thus
m_a∙g∙h=m_w∙g∙h+E_k,
where E_k – kinetic energy of the anvil before hit, g=9.8 m/s^2 – acceleration due to gravity.
Since anvil stops after striking the bottom, all the kinetic energy is lost:
E_k=(m_a-m_w )∙g∙h=(290 kg-37 kg)∙9.8 m/s^2 ∙3.21 m=7959 J