Maurice Tutor

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  • MCS,PHD
    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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  • Professor
    Phoniex University
    Oct-2001 - Nov-2016

Category > Management Posted 18 Jan 2018 My Price 6.00

single loop of the cycloid

Consider a single loop of the cycloid (6.26) with a fixed value of a, as shown in Figure 6.11. A car is released from rest at a point P0 anywhere on the track between O and the lowest point P (that

is, Po has parameter 0 θ0π). Show that the time for the cart to roll from P0 to P is given by the integral

and prove that this time is equal to  Since this is independent of the position of Po , the cart takes the same time to roll from P0, to P, whether P0 is at O, or anywhere between O and P, even infinitesimally close to P. Explain qualitatively how this surprising result can possibly be true. [Hint: To do the mathematics, you have to make some cunning changes of variables. One route is this: Write = Tr-2a and then use the relevant trig identities to replace the cosines of θ by sines of a. Now substitute sin a = u and do the remaining integral.]

 

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Maurice Tutor
(5)
Status NEW Posted 18 Jan 2018 07:01 PM My Price 6.00

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