A particle P of mass m kg is attached to two fixed points A and B by two identic

Question

A particle P of mass m kg is attached to two fixed points A and B by two identical model springs, each of stiffness k and natural length I0. The point A is at a height 1/4/0 above the point B. The particle is free to oscillate vertically under gravity. The stiffness of each spring is given by k = 4mgll0. The horizontal level passing through the fixed point A is taken as the datum for the gravitational potential energy. The particle P is initially released from rest at a distance I0 below A. When m = 4.54 kg and I0 = 4.59 m, calculate the total mechanical energy (can be either positive or negative) of the system, in joules. Give your answer to 3 decimal places and take g = 9.81 ms-2.

Explanation / Answer

The gravitational potantial energy=-M*g*lo The energy of spring A would be zero The energy of spring B=1/2*4*M*g/lo*lo^2/16 The energy of spring=MgLo/8 Total energy=-7/8*M*g*Lo Total energy=178.9N

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