Dynamics work and energy

Question

why are there different formulas used for work-energy in dynamics?

Answer 1

Hi Karoulin!

 

There is one bedrock principle of the interaction between work and energy, and that often called the work-energy (or work-kinetic energy) theorem.  This states that the net work done on an object is equal to the change in that objects kinetic energy:

 

W_net = ΔKE = KE_f - KE_o

 

So, if positive net work is done on an object, it gains kinetic energy (speeds up).  If negative net work is done, the object loses kinetic energy (slows down).

 

This is true no matter which kinds of forces act on the object.  However, if -- in addition -- all the forces are conservative, there is a further relationship.

 

Conservative means the forces act to conserve the mechanical energy of the system they affect.  Mechanical energy is the sum of kinetic plus potential energy in the system (ALL kinds of potential energy, including gravitational, spring, and electric, as applicable).

 

If only conservative forces act, the work done by the conservative forces also relates to the change in potential energy, as:

 

W_c = -ΔPE

 

So, if the conservative forces do positive work, the potential energy of the system decreases, and, if they do negative work, the potential energy of the system increases.  

 

In general, conservative forces doing positive work is associated with the system going the way it naturally wants to go.  For example, if an object is falling straight down in free fall under gravity, the force of gravity is doing positive work (because the force is in the direction of displacement as the object falls).  All else being equal, objects naturally will fall under gravity.  And this corresponds to decreased gravitational potential energy.  If the object is being lifted (due to the intervention of some other force), the work done by gravity is negative, and the object gains gravitational potential energy by moving opposite the way it would naturally go (without any other forces present).

 

I hope that helps!  If that is not what you meant, or if you want to go into more detail, just let me know.

Answer 2

There are two main types of energy in work-energy dynamics: kinetic and potential.  Once formula emphasizes on the speed of the object since energy is affect by motion, whereas the other formula emphasizes on elevation and gravity

 

KE = mv²/2

 

PE = mgh