We have a toy gun with a spring constant of 50 N/m. The spring is compressed by 0.2 m. If you neglect friction and the mass of the spring, a

Question

We have a toy gun with a spring constant of 50 N/m. The spring is compressed by 0.2 m. If you neglect friction and the mass of the spring, at what speed will a 2 g projectile be ejected from the gun

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Nick 3 months 2021-07-29T14:28:18+00:00 1 Answers 16 views 0

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    2021-07-29T14:30:07+00:00

    Answer:

    31.6\:\mathrm{m/s}

    Explanation:

    The elastic potential energy of a spring is given by Us=\frac{1}{2}kx^2, where k is the spring constant of the spring and x is displacement from point of equilibrium.

    When released, this potential energy will be converted into kinetic energy. Kinetic energy is given by KE=\frac{1}{2}mv^2, where m is the mass of the object and v is the object’s velocity.

    Thus, we have:

    Us=KE,\\\frac{1}{2}kx^2=\frac{1}{2}mv^2

    Substituting given values, we get:

    \frac{1}{2}\cdot 50\cdot 0.2^2=\frac{1}{2}\cdot 0.002\cdot v^2,\\v^2=\frac{50\cdot 0.2^2}{0.002},\\v^2=1000,\\v\approx \boxed{31.6\:\mathrm{m/s}}

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