# If a total mass of 11.1 kg falls 5.23 m and all of the mechanical energy is converted to internal...

## Question:

If a total mass of 11.1 kg falls 5.23 m and all of the mechanical energy is converted to internal energy, by how much will the internal energy of the water increase? The acceleration of gravity is 9.81 m/s{eq}^2 {/eq}. Assume no energy is transferred as heat out of the vessel to the surroundings or from the surroundings to the vessel s interior. Answer in units of J.

## Conservation of Energy:

Energy cannot be created nor destroyed. The potential energy of the system was converted into other form of energy. This can be internal energy. In this particular situation, the amount of potential energy is equal to the change in the system's internal energy.

Before the object fell, it has a potential energy. That potential energy can be converted to change the system's internal energy. It has to be equal to the initial potential energy due to energy conservation.

\begin{align} \rm PE &= mgh\\ \rm PE &= (11.1 \ \rm kg)(9.81 \ \rm m/s^2)(5.23 \ \rm m)\\ \rm PE &= 569.5 \ \rm J\\ \end{align}

Thus, the change in the system's internal energy is {eq}569.5 \ \rm J{/eq}.