Conservation of Energy in a Block-Spring System

AI Thread Summary
In a block-spring system with a constant spring constant and amplitude, the total mechanical energy is determined by the amplitude and spring constant, not the mass of the block. Given an initial energy of 24 J with an amplitude of 4.5 cm, replacing the block with one of double the mass does not change the energy, as energy is proportional to the square of the amplitude. The energy remains at 24 J because the parameters affecting energy (spring constant and amplitude) are unchanged. The misconception that doubling the mass would double the energy is clarified, emphasizing that energy is independent of mass in this context. Thus, the energy of the system remains 24 J.
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Homework Statement



A block–spring system vibrating on a frictionless, horizontal surface with an amplitude of 4.5 cm has an energy of 24 J. If the block is replaced by one whose mass is twice the mass of the original block and the amplitude of the motion is again 4.5 cm, what is the energy of the system?

Homework Equations



E= K+U = .5mv^2 + .5kx^2 = .5kA^2

The Attempt at a Solution



So if the spring constant doesn't change and the amplitude doesn't change, will the energy of the system stay constant even though the mass (m) is doubled? Initially I thought the energy of the system would be doubled, because I thought it made sense that it would take more energy to move a more massive object, but that was incorrect. Thanks in advance for any assistance
 
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