An 800.0 kg roller coaster car is at rest at the top of a 95 m hill. It rolls down the first drop to a height of 31 m. When it travels to the top of the second hill, it is moving at 28 m/s. It then rolls down the second hill until it is at ground level.
What is the kinetic and potential energy at the top and bottom of each hill?
They presumably want to to assume total mechanical energy (kinetic + potential) is constant, even though that is not the case.
At the top of the 95 m hill, all of the energy is potential, and equals
M g H = 744,800 J. Use the height or velocity at the other location, and the total energy (748,800 J) , to determine kinetic and potential energies
PE1 = mgh1 = 800•9.8•95 =744800 J.
Total E1 = PE1+ KE1=744800 J.
PE2 = 800•9.8•31=243040
KE2 = PE1- PE2 =
=744800 - 243040=501760 J.
Total E2 = PE2+ KE2=744800 J.
KE3 =mv²/2= 800•(28)²/2 =313600 J.
PE3 =744800-313600 = 431200 J.
Total E3 = PE3+ KE3=744800 J.
KE4 = 744800 J.
Total E4 = PE4+ KE4=744800 J.
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