A rifle fires a pellet straight upward, because the pellet rests on a compressed spring that is released when the trigger is pulled. The spr

Question

A rifle fires a pellet straight upward, because the pellet rests on a compressed spring that is released when the trigger is pulled. The spring has a negligible mass and is compressed by from its unstrained length. The pellet rises to a maximum height of 6.10 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant.

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Yến Oanh 5 months 2021-09-01T10:55:49+00:00 1 Answers 0 views 0

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    2021-09-01T10:57:27+00:00

    This question is incomplete, the complete question is;

    A rifle fires a 2.10 × 10⁻² kg pellet straight upward, because the pellet rests on a compressed spring that is released when the trigger is pulled. The spring has a negligible mass and is compressed by 9.10 × 10⁻² m from its unstrained length. The pellet rises to a maximum height of 6.10 m above its position on the compressed spring. Ignoring air resistance, determine the spring constant.

    Answer:

    the spring constant is 303.5 N/m

    Explanation:

    Given the data in the question;

    There is a potential energy associated with the spring;

    we know that potential energy = kinetic energy

    mgh = \frac{1}{2}kx²

    where k is the spring constant and x is the compression

    as the pallet is fired, the spring gives kinetic energy which is converted into gravitational potential energy

    so

    m = 2.10 × 10⁻²

    g = 9.81 m/s²

    h = 6.10 m

    x = 9.10 × 10⁻² m

    we substitute

    mgh = \frac{1}{2}kx²

    2.10 × 10⁻² × 9.81 × 6.10 =  \frac{1}{2} × K × ( 9.10 × 10⁻² )²

    1.256661 = 0.0041405 × K

    K = 1.256661 / 0.0041405

    K = 303.5 N/m

    Therefore, the spring constant is 303.5 N/m

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