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29 May, 18:11

The spring is released and a 0.10-kilogram plastic sphere is fired from the launcher. Calculate the maximum speed with which the plastic sphere will be launched. [Neglect friction.] [Show all work, including the equation and substitution with units.]

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  1. 29 May, 20:38
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    A) The elastic potential energy stored in the spring when it is compressed 0.10 m is 0.25 J.

    B) The maximum speed of the plastic sphere will be 2.2 m/s

    Explanation:

    Hi there!

    I've found the complete problem on the web:

    A toy launcher that is used to launch small plastic spheres horizontally contains a spring with a spring constant of 50. newtons per meter. The spring is compressed a distance of 0.10 meter when the launcher is ready to launch a plastic sphere.

    A) Determine the elastic potential energy stored in the spring when the launcher is ready to launch a plastic sphere.

    B) The spring is released and a 0.10-kilogram plastic sphere is fired from the launcher. Calculate the maximum speed with which the plastic sphere will be launched. [Neglect friction.] [Show all work, including the equation and substitution with units.]

    A) The elastic potential energy (EPE) is calculated as follows:

    EPE = 1/2 · k · x²

    Where:

    k = spring constant.

    x = compressing distance

    EPE = 1/2 · 50 N/m · (0.10 m) ²

    EPE = 0.25 J

    The elastic potential energy stored in the spring when it is compressed 0.10 m is 0.25 J.

    B) Since there is no friction, all the stored potential energy will be converted into kinetic energy when the spring is released. The equation of kinetic energy (KE) is the following:

    KE = 1/2 · m · v²

    Where:

    m = mass of the sphere.

    v = velocity

    The kinetic energy of the sphere will be equal to the initial elastic potential energy:

    KE = EPE = 1/2 · m · v²

    0.25 J = 1/2 · 0.10 kg · v²

    2 · 0.25 J / 0.10 kg = v²

    v = 2.2 m/s

    The maximum speed of the plastic sphere will be 2.2 m/s
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