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A roller coaster with a mass of 973 kg at some point in time has a height of 24 m and rolls down the track at 25 m/s. What is the TOTAL energy of the roller coaster in Joules?

User Maulin
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1 Answer

19 votes
19 votes

The total energy refers to the kinetic energy plus the potential energy.

The kinetic energy depends on the velocity, and the potential energy depends on the position (height in this case).

The formulas are


\begin{gathered} K=(1)/(2)\cdot m\cdot v^2 \\ U=\text{mgh} \end{gathered}

Where m = 973 kg, h = 24 m, and v = 25 m/s.


\begin{gathered} K=(1)/(2)\cdot973\operatorname{kg}\cdot(25\cdot(m)/(s))^2=486.5\operatorname{kg}\cdot625\cdot(m^2)/(s^2)=304,062.5J \\ U=973\operatorname{kg}\cdot9.8\cdot(m)/(s^2)\cdot24m=^{}228,849.6J \end{gathered}

At last, we have to add these energies to find the total.


E_{\text{total}}=304,062.5J+228,849.6J=532,912.1J

Therefore, the total energy is 532,912.1 Joules.

User Mike Pone
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