Conservation of Energy in a Block-Spring System

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SUMMARY

The discussion centers on the conservation of energy in a block-spring system, specifically analyzing the impact of doubling the mass of the block while maintaining the same amplitude of 4.5 cm. The total mechanical energy of the system is given by the equation E = 0.5kA^2, where k is the spring constant and A is the amplitude. Since neither the spring constant nor the amplitude changes, the energy of the system remains constant at 24 J, regardless of the mass increase. This conclusion clarifies that energy in a spring system is independent of the mass when amplitude and spring constant are fixed.

PREREQUISITES
  • Understanding of mechanical energy conservation principles
  • Familiarity with spring constant (k) and amplitude (A) in harmonic motion
  • Knowledge of kinetic energy (K) and potential energy (U) equations
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the relationship between mass and energy in harmonic oscillators
  • Explore the implications of changing spring constants on energy in spring systems
  • Investigate energy transformations in different mechanical systems
  • Learn about the effects of friction on energy conservation in oscillatory motion
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation principles, as well as educators seeking to clarify concepts related to block-spring systems.

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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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