A block of mass 6o kg is sitting on a platform that in turn sits on a spring wit

Question

A block of mass 6o kg is sitting on a platform that in turn sits on a spring with a spring constant k=2500 N/m. The block is initially at rest. Assume that the gravitational
potential energy and elastic potential energy of the system is zero at this point.

a. What is the total mechanical energy of the system?

The platform is depressed a distance of 0.3 m and held there.

b. What are the kinetic, gravitational potential, and elastic potential energies of the system?

c. What is the new mechanical energy of the system?

The platform is released, ejecting the block in the vertical direction .

d. What are the kinetic, gravitational potential, and elastic potential energies when the mass reaches its highest point?

e. How high above the platform does the mass go (measure from the original un-depressed position)?

Explanation / Answer

The mass of the block m = 60 kg The spring constant k = 2500 N/m (a) When the platform is depressed 0.3 m    then the total energy E = mgh + 1/2 kx^2                                       = (60)(9.8) (0.3) + (0.5)(2500)(0.3)^2                                       = 288.9 J (b) The kinetic energy K = 0     The gravitational potential energy U = mgh = (60)(9.8) (0.3) = 176.4 J    The ealstic potential energy E' = 1/2 kx^2 = (0.5)(2500)(0.3)^2 = 112.5 J (c) From law of conservation of energy    the energy remains constant so the new energy E = 288.9 J (d) At the heightest point the velocity is zero    so the kinetic energy is zero so it have only gravitational and elastic potential energies The gravitational potential energy at heighest point is        U = mgh = (60)(9.8) (0.3) = 176.4 J and elastic potential energy       E' = 1/2 kx^2 = (0.5)(2500)(0.3)^2 = 112.5 J (e) The height it reached                176.4 J = mgh then h = 0.3 m about the mean position                                     

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