It is not only purely mechanical transfers of energy that follow this law of the conservation of energy, but all biological organisms must abide by this universal law as well. Take, for instance, the process of photosynthesis, which is considered the primary provider energy to almost all of life on Earth. Very simply put, "photosynthesis is the process of converting light energy to chemical energy and storing it in the chemical bonds of sugar" (Carter 1996). The process itself is actually quite complex, but basically several different pigments in plants (most essentially chlorophyll) absorb different wavelengths of light, which excites their electrons and causes chemical reactions to take place within specific molecules in the plant. These reactions ultimately result in the recombination of atoms into sugars, whose bonds can be broken to release energy when the plant needs it.

Plants are then eaten by other organisms, and te energy stored in the plant is converted yet again in the digestive process. One of the most basic processes for this conversion in many animals is the Krebs or citric acid cycle, which for animals is analogous to photosynthesis in plants (Kyrk 2008). The chemical process is again quite complex, but the principle of the conservation of energy remains the same. Glucose, the main sugar created by plants that is digestible for animals, is broken down, releasing the energy that the plants had stored in the sugar molecules during photosynthesis. Like any other reaction, some of the energy is lost to heat, but...

The rest of the energy is used to cause further chemical reactions, eventually resulting in the formation of adenosine triphosphate, which contains bonds that are very high in stored energy. These bonds can be broken to create kinetic and chemical energy within cells, powering movement and the many chemical process and reactions that are necessary for the existence of life. The fact that we heat up during exercise is evidence of the conservation and conversion of energy; as we "use up" our energy in kinetic movement, a great deal of the chemical energy in our cells and food is converted to heat.
Taken together, photosynthesis and the Krebs cycle provide a large-scale example of the conservation of energy. Sun energy is converted to chemical energy by plants (with some loss to heat). The chemical energy of plants is used by animals (including humans) to create more efficient carriers of chemical energy, and is eventually converted into kinetic energy (and more heat). Thus, the energy from the sun never disappears, but is converted multiple times into the kinetic energy of an arm pushing a cue stick into a ball.

References

Carter, J. (1996). "Photosynthesis." Accessed 25 May 2009. http://biology.clc.uc.edu/Courses/bio104/photosyn.htm

Kyrk, J. (2008). "Krebs cycle." Accessed 25 May 2009. http://www.johnkyrk.com/krebs.html

Nave, C. (2005). "Hyperphysics: Heat and thermodynamics." Accessed 25 May 2009. http://hyperphysics.phy-astr.gsu.edu/HBASE/hframe.html