Goal-less Exemplar

This system consists of a suspended platform (h=50 m)and a bungee cord that is 20m when hanging freely (no tension). 

The spreadsheet used to create the graphs above is available to edit as a copy of the original. Open the following link and create your own copy of the spreadsheet: Reverse Slingshot

The Perfect model assumes 100% Mechanical energy (GPE, KE, EPE) conservation. This would be a model almost completely separated from reality. 

The process was to define the total mechanical energy by the stating the maximum height the launched rider can achieve. This determined the GPE and therefore the total mechanical energy, EPE and KE are both 0 J at the highest point. 

The second data set added was the GPE, as this is a linear function of the height. The equation is =$C$1*$C$2*B6 where $C$1 is the mass of the rider (the $ locks the formula onto the cell C1) $C$2 is the Gravitational Field strength (9.8 N/m) and B6 is the height (this will change with the cell).

The third data set added was the Elastic Potential Energy. This was the next logical step due to the ability to calculate it easily from the eq EPE=1/2(mv^2). The rather complicated eq of: =if(B6>$F$3,0,0.5*($C$3)*($F$3-B6)^2). The =IF(B6>$F$3,0 portion compares the current height with that of the max extension of the bungee cord, if B6>$F$3, the formula returns 0 as the EPE as the cord has contracted as much as possible. The remainder of the formula is the equation for EPE, $F$3-B6 accounts for the extension of the bungee cord. 

Finally, the KE was determined by using the Law of Conservation of energy: if E_mech=GPE+EPE+KE, then KE=E_mech-(GPE+EPE). 

Many of the equations are tied (by use of locking onto cells $), to the variables at the top of the page. This allows you to change the conditions of the scenario, without having to recalculate everything.