A spring is hanging from the ceiling, and an object of mass 2kg is hanging from

Question

A spring is hanging from the ceiling, and an object of mass 2kg is hanging from it, undergoing harmonic motion, with an amplitude of 0.5m. At the highest point in the motion, the spring is at the length that would be its equilibrium length if no object were attached.

(a)[6 pt(s) ]If the spring/mass system were oriented horizontally, and the mass were oscillating with this same amplitude, what would be the total energy of the system?

(b)[8 pt(s) ]For the object at its lowest point, its equilibrium point, and its highest point, calculate the elastic potential energy of the spring.

(c)[7 pt(s) ]For the object at its lowest point, its equilibrium point, and its highest point, calculate the kinetic energy of the object.

(d)[7 pt(s) ]For the object at its lowest point, its equilibrium point, and its highest point, calculate the gravitational potential energy of the earth/object system. Set the gravitational potential energy to zero when the object is 0.25m above the equilibrium of motion.

Explanation / Answer

a) Umax = m*g*(2*A)

= 2*9.8*(2*0.5)

= 19.6 J

b) U_lowest = 19.6 J

U_equilibrium = 19.6/2 = 9.8 J

U_higest = 0

c) KE_lowest = 0 J

KE_equilibrium = 9.8 J

KE_higest = 0

d) U_lowest = m*g*(-0.25) = 2*9.8*(-0.25) = -4.9 J

U_equilibrium = m*g*(0.25) = 2*9.8*(0.25) = 4.9 J

U_highest = m*g*(0.75) = 2*9.8*(0.75) = 14.7 J

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