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Homework Help: Why does Hooke's law not work here?

  1. Oct 20, 2015 #1
    1. The problem statement, all variables and given/known data
    1. A 1200-kg car moving on a horizontal surface has speed v = 85 kmh when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?
    2. Relevant equations

    3. The attempt at a solution
    I tried to find the average acceleration to slow the car from 85kmh to 0. I used the formula vfinal^2=vinitial^2 + 2ax, where velocity initial is 23.6m/s and x is 2.2m. This gave me an acceleration of -126m/s^2. Then I multiplied the acceleration by the mass to find the average force. This gave me -151200N. Then, I plugged that into Hooke's law with x being 2.2m. This gave the spring constant being 69000N/m.

    However, I am supposed to use the conservation of energy principle where KE=PE. This gives the correct answer. Why does my method not work?
  2. jcsd
  3. Oct 20, 2015 #2

    Ray Vickson

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    I does not work because the acceleration is not constant. Hook's Law works, but not your expression ##v_f^2 = v_i^2 + 2ax##.
    Last edited: Oct 20, 2015
  4. Oct 20, 2015 #3

    Mister T

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    By Hooke's law I assume you mean ##F=kx## where ##F## is the magnitude of the force and ##x## is the distance?

    In that formula ##F## is not the average force. It's the magnitude of the force when the spring is stretched (or compressed) a distance ##x##.

    If the force were constant, that would work, but the force is not constant. You could integrate the force, or use energy concepts.
  5. Oct 20, 2015 #4
    Oh, okay it makes sense now. Thank you both very much.
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