Conservation of Energy (Spring + Kinetic)

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SUMMARY

The discussion focuses on the conservation of energy principles applied to a mass-spring system. A 3.0 kg mass collides with a spring bumper, moving at a velocity of 3.0 m/s, and the spring constant is given as 335 N/m. The maximum compression of the spring is calculated using the equation for kinetic energy equating to spring potential energy, resulting in a compression of 0.081 m. Both the energy conservation equations presented are valid, with the second equation simplifying to the first under specific conditions.

PREREQUISITES
  • Understanding of kinetic energy (E_kin) and spring potential energy (E_spring)
  • Familiarity with the formula for kinetic energy: E_kin = 1/2 mv^2
  • Knowledge of Hooke's Law and spring constant (k)
  • Ability to manipulate algebraic equations for problem-solving
NEXT STEPS
  • Study the principles of conservation of mechanical energy in physics
  • Learn about Hooke's Law and its applications in spring mechanics
  • Explore more complex mass-spring systems and their dynamics
  • Investigate energy transformations in different physical systems
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Students studying physics, educators teaching mechanics, and anyone interested in understanding energy conservation in mass-spring systems.

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Tonight I've got so many hard problems...

A 3.0 kg mass slides across a frictionless surface and collides against a spring bumper with a velocity of 3.0 m/s as shown in the diagram. Determine the maximum amount of the spring compresses if it spring constant is 335 N/m.

For this one I don't know whether I should use E_kin = E_spring then solve from there or E_kin(i) + E_spring(i) = E_kin(f) + E_spring(f), but as for the former I got:

1/2 mv^2 = 1/2 k (delta) l^2
mv^2 = k(delta) l^2
(3)(3)^2 = (335) (l^2)
x = .081 m

Is that right? Thanks a lot for your help so far, everyone! I really appreciate your time and kindness. :smile:
 
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looks good.

except the spring epe is .5kx^2
 
Both the equations are valid. The second one reduces to the first one since E_spring(i) is zero and E_kin(f) is zero.
 

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