Question

n amusement park roller coaster cart is pulled up a steep incline 100 m high and is released down the track, traveling a maximum of 40 m/s. This diagram shows a portion of the track with a given point.



image




Assuming no friction and conservation of energy, which graph can be claimed to represent the kinetic and potential energy of the cart at the given point and what is the justification?



A.
Claim:

Justification: The cart has more potential energy than kinetic energy to climb the side of the loop.

B.
Claim:

Justification: The kinetic energy and potential energy are the same as the cart is halfway up the loop.

C.
Claim:

Justification: The cart is traveling at its maximum speed as it travels up the side of the loop.

D.
Claim:

Justification: The cart has more kinetic energy than potential energy to climb the side of the loop.

Answer 1

D.

Claim: The cart has more kinetic energy than potential energy as it climbs the side of the loop.

Justification: With no friction mechanical energy is conserved: Etotal = KE + PE = m g H (H = initial release height). At any height h the energies satisfy KE = Etotal − m g h. If h < H/2 then KE > PE (because Etotal − m g h > m g h ⇔ Etotal > 2 m g h). The shown point is below the halfway height of the original drop, so more of the total energy is kinetic than potential.