Energy is a very elusive concept but here are a couple of notes. First, energy is never created or destroyed, it just changes from one form to another and this really is the story of much of science, including biology. One form of energy is called mechanical energy and it’s the energy of doing work where work is the energy necessary to move an object over some distance. Work is equal to the force applied to the object times the distance the object moves4 \(W=FD\). A tree has to use energy to move xylem sap up its trunk and we say that it “does work on the xylem”. This work (mechanical energy) is the force applied to the xylem times the distance the xylem moves. The longer the distance the more work (given the same force). Another form of energy is kinetic energy which is the energy of a moving object, and is one-half of the product of the object’s mass and velocity squared5 \(KE = \frac{1}{2}M\nu^2\). When a cheetah runs, its hand and foot impact the ground with a certain amount of kinetic energy which suddenly goes to zero so this energy is transferred into the skeleton of the limbs. The cheetah will want a skeleton that can absorb and release this energy without permanently deforming or breaking the skeleton! Another form of energy is potential energy which comes in several forms. It could be the energy of an elevated mass in a gravitational field. Gravity makes the mass fall, which transfers this potential energy to kinetic energy. Or it could be the electrochemical energy in an ion gradient, such as the H\(^+\) gradient in a mitochondria. The potential energy of the H\(^+\) gradient is transferred into the kinetic energy of the ATP synthase mechanism which is then transferred into the potential energy of the phosphate bond in ATP. We will talk a lot about this kind of energy transfer.
Power is the rate of working or the rate that energy is used, so is equal to the Work divided by the time spent doing the work6 \(P=\frac{W}{T}\). It takes about the same amount of energy (work) for a cheetah to walk or to run a mile but the running cheetah expends this energy over a much shorter amount of time so running requires more Power. Note that since \(W=FD\) then \(P=F\frac{D}{T} = F\nu\), that is power is the product of force and velocity7 \(P=F\nu\). So high power activities are activities with high force at a high velocity or done over a short amount of time.