Roller Coaster Physics

Question

Calculate the potential energy, kemetic energy, total energy, and velocity for a marble of 1.24 m (height)

Answer 1

If a roller coaster applies work to move a marble from height zero to a height of 1.24 m, then the potential energy of that marble would be calculated from E_P = mgh = m(9.8)(1.24) = 12.2m That would also be the total energy.

If there are no frictional losses and the marble rolls back down to height zero, then ALL the potential energy will have been converted to kinetic energy (E_K) so E_K = 12.2m.

Since kinetic energy is calculated as E_K = 1/2mv² then, since E_K = E_P, 1/2mv² = 12.2m or (since the mass cancels):

1/2v² = 12.2

v² = 24.4

v = √24.4

v = 4.94 m/s