Conservation & Power

total mechanical energy is the

sum of the potential energy (U) dependent on an object’s position and kinetic energy (K) dependent on an object’s speed

• E = U + K

• if the only conservative force on an object is the gravitational force exerted by the Earth, the total mechanical energy is written as E = mgh + ½ mv²

the total work done is the

sum of the work done by all kinds of forces (conservative and nonconservative) and represented by the equation W = Wc + Wnc = ∆K

if nonconservative forces do no work,

Wnc = 0, and thus -∆U + Wnc = ∆K, and thus -∆U = ∆K

• thus, the sum of ∆U (change in potential energy) and ∆K (change in kinetic energy) adds to 0 by the equation ∆U + ∆K = 0, thus ∆ (U + K) = 0, thus ∆E = 0

  • ∆E is the change in total mechanical energy

• the total mechanical energy in a system in which the nonconservative forces do no work is conserved (does not change, and this is the principle of the conservation of energy)

energy is converted from

potential form (U) to kinetic form (K) during motion

in order to claim that there is a conservation of total energy

• neglect air resistance

• neglect friction

at the highest point during a vertical jump, the

kinetic energy (K) turns into potential energy (U)

• kinetic energy lost from the release into a jump = the gain in potential energy from the jump

the energy conversion rule states that

energy cannot be created nor destroyed, it can only be changed from one form to another

• some forms of energy include:

  • kinetic energy (K)

  • gravitational potential energy (U)

  • elastic potential energy (springs)

  • electric potential energy (circuits)

  • electromagnetic energy (radiowaves)

  • chemical energy (batteries)

  • heat

• nonconservative forces (friction, air resistance) convert mechanical energy to heat, which is not fully reusable

average power is the

rate at which work (W) is done by a force, thus P = ∆W / ∆t

• SI units are in Watts = Joules/s = kg m²/s³

average power also measures the

rate at which energy (E) is converted from one form to another

• P = ∆E / ∆t

• physiological example is metabolic rates