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Toy gun Spring Questions

  1. Oct 19, 2014 #1
    1. The problem statement, all variables and given/known data
    There are two problems, but I think that they are similar:

    A toy gun shoots a projectile straight up. The maximum height reached by the projectile is H when the spring is compressed x cm. For the projectile to reach a height of 2H, the spring of the gun should be compressed how much?

    The bumper of a car is connected to the body by a spring of spring constant k. When the car hits a cement wall with a speed of 1.0 km/h, the spring compresses 1.0 cm. If the car hits a cement wall with a speed of 2.0 km/h, the spring will compress by how much? (answer in cm)

    2. Relevant equations

    The work of the spring is Ws = -.5*k*x^2
    The force of the spring is F=-kx

    3. The attempt at a solution

    Problem 1: If work is force * distance, then the equation of the work of the spring can be set equal to the equation for the force of the spring * the distance H:

    -k*x*H = -.5*k*x^2
    after some algebra, you get to this equation:

    So if you wanted to double H, you would also double x.

    So in terms of x, the spring should be compressed 2x cm. However, this is not the correct answer, but I think my reasoning is correct. Can somebody point out the flaw?

    If -.5*k*x^2 = .5*m*v^2,
    you would plug in "2*v" for v because 2km/hr is double 1km/hr
    Thus, x would be 2 times the original x for 1km/hr, so the spring would compress 2cm.
    I'm not sure if this problem is correct, because the previous problem is incorrect so I'm not sure about spring problems.
  2. jcsd
  3. Oct 19, 2014 #2


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    2016 Award

    Staff: Mentor

    Where does the left side come from?
    And where did you take gravity into account?
    The projectile loses contact to the spring after the first x cm.

    The second solution is correct.
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