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# Roller Coaster Physics

There is a species of bug on the planet Mindbender called bugonians than can only hear over the frequency of 290Hz. Bugonians are blind and relies only on hearing to survive. The mass of Mindbender is 7.66 x10^25 kg and a radius of 2.46 x10^7m.
A pendulum with a frequency of 0.41Hz attached to the ceiling above the top of a miniature rollercoaster. The bob on the pendulum has a mass of 2.0 kg. It hits a toy cart with a weight of 4.0N at the top of a track, which is touching a spring, with a spring constant of 2.6N/m. It is positioned 0.15m from equilibrium when it rolls down the hill.
The height of the first hill is unknown, but it is equal in height to the first loop of the rollercoaster. The minimum velocity to keep the cart in the first loop is 1.656 m/s.
After the first loop, the cart moves up a ramp with a coefficient of friction of 0.009. The cart is producing a noise at the frequency of 250Hz. The ramp has a height of 0.20 m, where it drops off and the cart is launched as a projectile.
There is a Bugonian suntanning 4.6m from the end of the ramp. Can the Bugionian hear the approaching cart, if you consider the Doppler effect on the frequency of sound as the cart is hurdling through Minderbender space towards him?
You must assume complete energy conversions UNLESS there is friction

Posted by Sam

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