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28 March, 05:17

At a carnival, you can try to ring a bell by striking a target with a 8.91-kg hammer. In response, a 0.411-kg metal piece is sent upward toward the bell, which is 3.88 m above. Suppose that 21.9 percent of the hammer's kinetic energy is used to do the work of sending the metal piece upward. How fast must the hammer be moving when it strikes the target so that the bell just barely rings?

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  1. 28 March, 06:23
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    4 m/s

    Explanation:

    M = mass of the hammer = 8.91 kg

    m = mass of the metal piece = 0.411 kg

    h = height gained by the metal piece = 3.88 m

    Potential energy gained by the metal piece is given as

    PE = mgh

    PE = (0.411) (9.8) (3.88)

    PE = 15.6 J

    KE = Kinetic energy of the hammer

    Given that:

    Potential energy of metal piece = (0.219) Kinetic energy of the hammer

    PE = (0.219) KE

    15.6 = (0.219) KE

    KE = 71.2 J

    v = speed of hammer

    Kinetic energy of hammer is given as

    KE = (0.5) M v²

    71.2 = (0.5) (8.91) v²

    v = 4 m/s
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