How Is the Spring Constant Calculated from Velocity and Compression Data?

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SUMMARY

The spring constant (k) can be calculated using the formula Fsp = -k(s), where Fsp is the force exerted by the spring and s is the compression distance. In this discussion, a 6 kg particle with a velocity described by the equation v(t) = 15t^2 + 7 m/s compresses the spring by 8 cm at t = 8 seconds. The kinetic energy of the particle at this moment is converted into potential energy stored in the spring, allowing for the determination of k. Additionally, when a particle with double the mass impacts the spring with the same velocity, the compression distance can be calculated using the relationship between mass, velocity, and spring constant.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with Hooke's Law and spring mechanics
  • Basic knowledge of kinetic and potential energy concepts
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Calculate kinetic energy using the formula KE = 0.5 * m * v^2
  • Explore the relationship between kinetic energy and potential energy in spring systems
  • Learn about the implications of mass changes on spring compression
  • Study advanced applications of Hooke's Law in oscillatory motion
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Physics students, mechanical engineers, and anyone studying dynamics and energy conservation in spring systems.

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Homework Statement



The velocity of a 6 kg particle is found to be well fit by

v(t) = 15t^2 + 7 (velocity in units m/s)

a) If the particle hits a spring at t = 8 seconds, and compresses the spring 8 cm, what is the spring constant?

b) Suppose a particle with twice the mass, but the same velocity hits the (relaxed) spring. How far will the spring be compressed?


Homework Equations



Fsp = -k(s)


The Attempt at a Solution



The main problem I have with understanding this problem is one, the problem is asking for "k". I got that. It gives me "s" (8cm). I got that. I know that I have to use velocity with the time value given. The part that I'm not getting is relating the velocity equation given to finding the k unknown.

All my best.
 
Physics news on Phys.org
You have more equations you can use.

How much energy is in the system when the particle is moving, and how much energy is in the system when the spring is compressed? How are they related?
 

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