Understanding Energy Equations: Mass, Gravity & Velocity

[jaredogden]

So I have just been sitting around trying to relate equations to units to maybe understand their derivation. I feel like it is more beneficial to understand a subject and be able logically come to a conclusion and not just memorize formulas.

We know that energy is measure in Joules which of course are a kg*m^2/s^2. This makes equations for energy much easier to understand for example potential energy which is the measure of energy stored in an object due to its position in a force field and is directly proportional to an objects mass in kg times the force of gravity (the force field) in m/s^2 times the objects height in meters. This obviously translates into the correct units of joules or kg*m^2/s^2.

Now I was thinking about kinetic energy and since it is the amount of energy an object possesses due to its motion. It makes sense that mass would still have to be used and that the objects velocity would come into play since it is a measure of energy due to motion, and since velocity is measured in m/s squaring the velocity would be necessary to produce m^2/s^2.

My only question for kinetic energy is why we take half the product of the objects mass times velocity squared? Is this just simply because (1/2) is a constant that matches the calculated value up with experimental data or am I missing something? Thanks for any help ahead of time.

 

[Fewmet]

Try considering that work is done to anybody to change its kinetic energy. In the simplest case it is work done to bring a mass m from an inital velocity of 0 rest to a final velocity v. The work done equals the change in kinetic energy.

W=Fd
W=mad
From v_f²-v_i²=2ad and v_i=0
we get d = v_f²/2a
Substituting in W=mad and making vf into v:
W = mv²/2
or
Kinetic energy =mv²/2