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

AI Thread Summary
To calculate the spring constant (k) from the given velocity and compression data, the relationship between kinetic energy and potential energy in the spring must be established. The kinetic energy of the particle can be determined using its velocity at the moment of impact, while the potential energy stored in the spring when compressed is given by the formula Fsp = -k(s). The problem also introduces a scenario with a particle of double the mass, prompting a discussion on how this affects the spring's compression. Understanding the conversion of energy between the moving particle and the spring is crucial for solving both parts of the problem. The key takeaway is the need to relate kinetic energy at impact to the potential energy in the spring to find the spring constant and subsequent compression.
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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.
 
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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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