A massless spring of constant k = 64.4 N/m is fixed on theleft side of a leveltrack. A block of mass m = 0.50 kg ispressed against thespring and compresses it a distance ofd. The block(initially at rest) is then released andtravels toward a circularloop-the-loop of radius R = 1.5m. The entire track andthe loop-the-loop are frictionless, exceptfor the section of trackbetween points A and B.Given that thecoefficient of kinetic friction between the block andthe trackalong AB is µk = 0.33, and that thelength of AB is 2.5 m,determine the minimum compressiond of the spring thatenables the block to just make itthrough the loop-the-loop atpoint C. [Hint: The force ofthe track on the block willbe zero if the block barely makes itthroughthe-loop-the-loop.]
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A massless spring of constant k = 64.4 N/m is fixed on theleft side of a leveltrack. A block of mass m = 0.50 kg ispressed against thespring and compresses it a distance ofd. The block(initially at rest) is then released andtravels toward a circularloop-the-loop of radius R = 1.5m. The entire track andthe loop-the-loop are frictionless, exceptfor the section of trackbetween points A and B.Given that thecoefficient of kinetic friction between the block andthe trackalong AB is µk = 0.33, and that thelength of AB is 2.5 m,determine the minimum compressiond of the spring thatenables the block to just make itthrough the loop-the-loop atpoint C. [Hint: The force ofthe track on the block willbe zero if the block barely makes itthroughthe-loop-the-loop.]
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