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19 January, 11:45

A spring-loaded pellet gun is designed to fi re 3.00-g projectiles horizontally at a speed of 45.0 m/s. (a) If the spring is compressed to its maximum design difference of 8.00 cm, what spring constant is required?

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  1. 19 January, 11:59
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    The spring constant required = 949.2 N/m

    Explanation:

    The energy stored in the spring is converted to kinetic energy of the projectiles fired.

    Energy stored in spring's = kx²/2

    Kinetic energy of bullets = mv²/2

    k = spring constant = ?

    x = maximum compression of the spring = 8 cm = 0.08 m

    m = mass of projectiles fired = 3.0 g = 0.003 kg

    v = velocity of projectiles fired = 45.0 m/s

    kx² = mv²

    k (0.08²) = 0.003 (45²) = 6.075

    k = 949.2 N/m

    The spring constant required = 949.2 N/m
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