Some modern roller coasters are "launched" rather than slowly pulled to the top of a hill. One recent design is a coaster on a U-shaped track like that shown above. Each time the coaster passes through the acceleration zone, it receives a kick from an electric motor. Suppose that for the track shown above, the height H is 75 m. The acceleration zone has a width d = 25 m. If a coaster of mass m = 11,000 kg experiences an accelerating horizontal force of magnitude 0.5mg while it is in the acceleration zone, how many passes through the zone must the coaster make before it will reach the top of the track? (After this, the function of the motor will be reversed to decelerate the coaster.)
System: Coaster as point particle, plus the earth as a rigid body of infinite mass.
Interactions: The coaster and earth create a conservative interaction of gravity, which will be treated as a potential energy in the system. The system is also subject to a non-conservative interaction from the the electric motor.
Model: Mechanical Energy and Non-Conservative Work.
Approach: We begin with an initial-state final-state diagram and energy bar graphs.
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