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16 May, 00:27

A 60 kg bungee jumper jumps from a bridge. She is tied to a bungee cord that is 15 m long

when unstretched and falls a total distance of 31 m. Calculate

(i) the spring constant of the bungee cord.

(ii) the maximum acceleration experienced by the jumper

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Answers (1)
  1. 16 May, 01:09
    0
    (i) 140 N/m

    (ii) 28 m/s²

    Explanation:

    (i)

    At the top of the jump, the bungee jumper has gravitational potential energy.

    At the bottom of the jump, the bungee jumper has elastic potential energy.

    mgh = ½ kx²

    (60 kg) (9.8 m/s²) (31 m) = ½ k (31 m - 15 m) ²

    k = 140 N/m

    (ii)

    At the bottom of the jump:

    ∑F = ma

    kx - mg = ma

    (140 N/m) (31 m - 15 m) - (60 kg) (9.8 m/s²) = (60 kg) a

    a = 28 m/s²
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