[خلف الجميلي]

A mass m is pushed against a spring of spring constant k = 12000 N/m. The mass slides on a horizontal smooth surface except for a rough one meter long section, and then it encounters a loop of radius R as shown in the figure. The mass just barely makes it around the loop without losing contact with the track (i.e. the normal force at the top of the loop is zero). The coefficient of kinetic friction (k) between the mass and the rough surface is 0.35, m = 2 kg and R = 1 m.
a) Calculate the speed of the mass at the top of the loop.
b) Calculate the energy of the mass lost due to friction.
c) Calculate the distance the spring was compressed.


you can see the figure here

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