Roller Coaster problem, suppose the vertical loop has a radius of unknown. The l

Question

Roller Coaster problem, suppose the vertical loop has a radius of unknown. The linear speed of the roller coaster has to be the top of the loop for the passengers to feel weightless is unknown. At the top of the loop, the force of gravity and the normal force acting on a passenger, their sum these two forces is the net force, which has equal the centripetal force in circular motion. However, the liner speed of the roller coaster at the bottom (6 o'clock) is 17.146 m/s. Could you know the total energy of 6 o'clock? Could you know the total energy of the 0 o'clock? Then, finally, could you tell me the radius of the vertical loop of this roller coaster? (At 0 o'clock, F_g = mg, F_c = m v^2/r, and F_net = F_g = F_c).

Explanation / Answer

The total enrgy at top is equal to the total energy at bottom. However, at top only PE is there and bottom only KE

Since K.E=PE

=>1/2mv2=mg2r

=>(1/2)17.146^2=2gr

=> r=7.49 m

Since at top Fc=mg

=mv12/r=mg

=>v12/r=g

=>v1=sqrt(9.8*r)=sqrt(9.8*7.49)=8.567 m/s

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