conservative and non-conservative forces
conservative forces
(eg. force of gravity, elastic forces)
don’t affect the mechanical energy of a system
path independence (the total work done isn’t affected by the path of the object’s motion)
work = change in potential energy (this is called the work-potential energy theorem)
W = ∆Ep = mg∆h
if the object being worked on also gains kinetic energy, work = change in potential energy + change in kinetic energy (this is the work-energy theorem)
W = ∆Ep + ∆Ek = mg∆h + (1⁄2)mv2
therefore… the car in the diagram below (if we assume it’s frictionless) will have the same speed at point Q no matter which ramp it glides down!
non-conservative forces
(eg. friction)
cause the energy of the system to change; thus energy is not conserved (no-brainer)
causes energy to leave the system via heat or sound
work done by friction = the product of the force of friction and the distance of the path traveled by the object
Wf = Ff∆d
therefore, in the same diagram above, because Ramp B has a longer distance, the car will lose more energy on Ramp B. and since potential energy will always be the same at the bottom (0), this loss in energy affects only the kinetic energy of the car.
the calculated value of Wf should always be negative, because friction always reduces the mechanical energy.
the amount of work done by friction thusly affects the total mechanical energy of the system:
but not all non-conservative forces reduce the mechanical energy within a system!
eg. motors add energy to a system
Em2 = Em1 + the total work done by all the external forces
this is another version of the same work-energy theorem.