Box-Spring Collision: How Much Compression?

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SUMMARY

The discussion focuses on calculating the compression of a spring when a 1.5 kg box sliding at 12 m/s collides with it. The spring constant (k) is 2000 N/m. The kinetic energy (KE) of the box is determined to be 108 J, which is converted into the potential energy stored in the spring. The correct compression distance for the spring when stopping the box is calculated to be 0.3 m, while the compression when the box's speed is halved requires further analysis.

PREREQUISITES
  • Understanding of Hooke's Law (Fs = -kx)
  • Knowledge of kinetic energy (W = 1/2 mv^2)
  • Familiarity with potential energy in springs (W = 1/2 kx^2)
  • Basic principles of conservation of energy
NEXT STEPS
  • Calculate spring compression for varying initial speeds using the formula W = 1/2 kx^2.
  • Explore the effects of different spring constants on compression distances.
  • Investigate real-world applications of spring compression in engineering.
  • Learn about energy conservation principles in elastic collisions.
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of spring systems and energy conservation principles.

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Homework Statement


1.5kg box sliding on frictionless surface with a speed of 12m/s approaches a horizontal spring. The spring has a k of 2000N/m. How far will the spring be compressed in stopping the box? How far will the spring be compresses when the box's speed is reduced to half its initial speed?


Homework Equations


Fs=-kx
W=1/2kx^2


The Attempt at a Solution



Not sure if I needed this but I found the KE to be 108J. I tried to solve for x by 1.5kgx9.80m/s^2/2000N/m= .007m. Not sure!
 
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Try this - http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html

One is correct about the kinetic energy. Without dissipative forces, e.g. friction, the kinetic energy of the traveling mass will be transformed into the stored mechanical energy of the spring.

The acceleration of gravity is not part of this.
 
I put in the 2000N/m and 108J and got 0.3m?
 

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