The total energy stored in a spring is expressed as (1/2)kA^2, where k represents the spring constant and A is the amplitude. The discussion clarifies that k can be defined as F/x, leading to the rearrangement (1/2)(FA^2/x). However, the correct interpretation of the energy equation requires understanding that F must equal mg when a mass is attached to a hanging spring. Thus, the expression (1/2)(mgA) is valid only under this specific condition.
PREREQUISITESStudents studying physics, particularly those focusing on mechanics and energy systems, as well as educators looking for clear explanations of spring dynamics.
yes, where F is the max force in the spring and A is the absolute value of x.JustinLiang said:Homework Statement
Since the total energy in a spring is
(1/2)kA^2
Can we rearrange this...
given k=F/x
(1/2)(FA^2/x)
Since x is also the amplitude, we have:
(1/2)(FA)
Only if F = mg, as when a mass is attached from a hanging spring and released.(1/2)(mgA)