Question

An electrical drill has 100 J of chemical energy. Of the 100 J, 45 J are transformed into kinetic energy and 20 J are transformed into sound. The remaining energy is given off as thermal energy. What is the thermal energy of the drill?

Answer 1

For the law of conservation of energy, the total output energy must be equal to the total input energy:
$E_{in} = E_{out}$ (1)
The input energy is the chemical energy of the drill:
$E_{in}=100 J$
The output energy is sum of kinetic energy Ek, sound Es and thermal energy Et:
$E_{out} = E_k+E_s+E_t$ (2)
We know the value of the kinetic energy: $E_k =45 J$ and of the energy converted into sound: $E_s=20 J$, so we can put together (1) and (2) to find the thermal energy:
$E_t=E_{in}-E_k-E_s=100 J-45 J-20 J=35 J$

Answer 2

For the law of conservation of energy, the total output energy must be equal to the total input energy:

(1)

The input energy is the chemical energy of the drill:

The output energy is sum of kinetic energy Ek, sound Es and thermal energy Et:

(2)

We know the value of the kinetic energy:  and of the energy converted into sound: , so we can put together (1) and (2) to find the thermal energy: