Question

when the simulation, thermal energy, $e_{th}$, refers to the energy that is lost to the environment through heat as a result of friction between the skateboards wheels and the ramp. this means that the total energy of the skater, which is conserved, will be transformed into three different types of energies over time: kinetic, potential, and thermal. however, while kinetic and potential energy can be transformed into one another as the skater moves, whatever energy is turned into thermal energy is lost to the environment and cannot be transformed back.
this leaves us with the following revised mathematical model for the conservation of energy: $e_t=ke + pe+e_{th}$, where $e_t$ is constant and $e_{th}$ cannot decrease in value over time.
imagine that a skater is standing ($v = 0 m/s$) at the top of a ramp at $t = 0 s$. then, they step forward and ride down the ramp. use the mathematical model for the total energy of an object to calculate the missing values in the table.
enter your answers in the boxes.

Explanation:

Step1: Recall energy - conservation formula

The total energy formula is $E_T=KE + PE+E_{th}$, and $E_T$ is constant.

Step2: Calculate values at $t = 0$ s

Since $v = 0$ m/s at $t = 0$ s, $KE=0$ J. Given $E_T = 500$ J and $E_{th}=0$ J, then $PE=E_T - KE - E_{th}=500 - 0 - 0=500$ J.

Step3: Calculate values at $t = 1$ s

Given $KE = 100$ J, $E_{th}=10$ J and $E_T$ is constant ($E_T = 500$ J), then $PE=E_T - KE - E_{th}=500 - 100 - 10 = 390$ J.

Step4: Calculate values at $t = 2$ s

Given $KE = 200$ J, $PE = 260$ J, then $E_{th}=E_T - KE - PE=500 - 200 - 260 = 40$ J.

Step5: Calculate values at $t = 3$ s

Given $PE = 0$ J, $E_{th}=100$ J, then $KE=E_T - PE - E_{th}=500 - 0 - 100 = 400$ J.

Answer:

Time (s)	Kinetic Energy (J)	Potential Energy (J)	Thermal Energy (J)	Total Energy (J)
1	100	390	10	500
2	200	260	40	500
3	400	0	100	500