Assume that the force of a bow on an arrow behaves like the spring force. In aiming the arrow, an archer pulls the bow back 50. cm and holds

Question

Assume that the force of a bow on an arrow behaves like the spring force. In aiming the arrow, an archer pulls the bow back 50. cm and holds it in position with a force of 150 N. If the mass of the arrow is 50. g and the “spring” is massless, what is the speed of the arrow immediately after it leaves the bow?

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Thu Giang 2 months 2021-07-30T01:33:55+00:00 1 Answers 2 views 0

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    2021-07-30T01:35:53+00:00

    Answer:

    v = 38.73 m/s

    Explanation:

    Given

    Extension of the bow, x = 50 cm = 0.5 m

    Force of the arrow, F = 150 N

    Mass of the arrow, m = 50 g = 0.05 kg

    speed of arrow, v = ? m/s

    We start by finding the spring constant

    Remember, F = kx, so

    k = F/x

    k = 150 / 0.5

    k = 300 N/m

    the potential energy if the bow when pulled back is

    E = 1/2kx²

    E = 1/2 * 300 * 0.5²

    E = 0.5 * 300 * 0.25

    E = 37.5 J

    The speed of the arrow will now be found by using the law of conservation of energy

    1/2kx² = 1/2mv²

    kx² = mv²

    v² = kx²/m, on substituting, we have

    v² = (300 * 0.5²) / 0.05

    v² = 75 / 0.05

    v² = 1500

    v = √1500

    v = 38.73 m/s

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