Collision and Spring Constant: Calculating Amplitude for a Mass-Spring System

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SUMMARY

The discussion focuses on calculating the amplitude of a mass-spring system following a collision. An 11.5 kg mass traveling at 2.4 m/s collides with another 11.5 kg mass at rest, which is attached to a spring with a force constant of 110 N/m. The incorrect application of the amplitude formula A = v * sqrt(m/k) led to a miscalculation of 1.097 m, while the correct approach requires considering the combined mass of 23 kg. The frequency of the system was correctly calculated as 0.348 Hz.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with Hooke's Law and spring constants
  • Knowledge of basic principles of momentum conservation
  • Ability to apply formulas for oscillatory motion
NEXT STEPS
  • Review the conservation of momentum in elastic and inelastic collisions
  • Study the derivation and application of the amplitude formula A = v * sqrt(m/k)
  • Explore the relationship between frequency and spring constant in mass-spring systems
  • Investigate the effects of mass and spring constant on oscillation characteristics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to mass-spring systems.

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Homework Statement



An 11.5kg mass is traveling to the right with a speed of 2.4m/s on a smooth horizontal surface when it collides with and sticks to a second 11.5 kg mass that is initially at rest but is attached to a light spring with force constant 110N/m.

Homework Equations



f=1/T
T=1/f
F=-kx
A=v*(sqrt(m/k))

The Attempt at a Solution



I tried to use the equation A=V*sqrt(m/k). I plugged in 2.4 m/s in for v, k is the force constant, 110N/m, and I used 23 kg for the mass (the two masses added together). Solving for this, I get 1.097m. However, this is incorrect.
Any ideas where I went wrong?

Also, in case it is necessary, I have already solved for the frequency: f=0.348 Hz.
 
Last edited:
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what exactly are we looking for? I don't see the original question.
 

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