A massless spring with spring constant k=980N/m is hanging from the ceiling. A m

Question

A massless spring with spring constant k=980N/m is hanging from the ceiling. A mass of 1kg is attached to the bottom of the spring. The spring is compressed by 0.5 cm and it is released. Use positive y to be downward and assume that y=0 corresponds to the unstreched position. You can assume that the elastic potential energy and gravitational potential energy are 1/2ky^2 and -mgy respectively where y is measured from the unstreched position of the spring.

What is the maximum length by which the spring is extended? and At what value of y does the mass have its maximum kinetic energy and what is its value?

Explanation / Answer

maximum length ,
mgh = 1/2 kx^2
1*9.8*y = 1/2 *980 * (y^2- .05^2)
y=.132m

KE max when
mg = kh
h = mg/k = 1*9.8/980 = .01m

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