The owners of a fun-park are designing a new ride. This will have a section in the form of a helix whose central axis is directed horizontally. Patrons will travel along the helical path in carriages whose speed is a fixed value, u. The carriages will be upside down when they are at a high point on the helix and the designers want to ensure that patrons are only just on the point of falling from their seats at this point (even though they are strapped in!). They can do this by ensuring that the centripetal acceleration just equals the acceleration due to gravity, g. The parameters that the designers can change are the radius of the helix p and its pitch p, which is the horizontal distance between neighbouring helical sections of the same orientation.(adsbygoogle = window.adsbygoogle || []).push({});

Show that, with suitable choice of axes, a carriage’s trajectory can be modelled as:

r(t) = (p cos wt, p sin wt, qt)

and find a relationship for the pitch p in terms of the modelling parameters w and q. Find a relation for the carriage speed u and the centripetal acceleration in terms of the modelling parameters p, w and q. By requiring that the centripetal acceleration should equal the acceleration due to gravity, find a relationship between p and p (involving u) that will assist in design decisions.

thats the problem that i am stuck with. i havent got far with it either. any help would be appreciated.

since the helix's are circular it would be that 2(pi)r = p x (number of sections)

centripetal accelaration equals the accelaration due to gravity, would that equal v^2/r = 9.8 ??

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# Homework Help: Rollercoaster ride problem, involving centripetal accelaration

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