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18 February, 20:24

A 2 kg rock is released from rest at a height of 20 m. Ignore air resistance and determine the kinetic energy, gravitational potential energy, and total mechanical energy at each of the following heights: 20, 10, and 0 m.

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  1. 18 February, 20:30
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    At 20 m kinetic energy is 0 J, Potential energy is 392.4 J and total energy is 392.4 JAt 10 m kinetic energy is 196 J, Potential energy is 196.2 J and total energy is 392.4 JAt 0 m kinetic energy is 392.4 J, Potential energy is 0 J and total energy is 392.4 J

    Explanation:

    Kinetic energy = 0.5 x Mass x Velocity²

    KE = 0.5mv²

    Potential energy = Mass x Acceleration due to gravity x Height

    PE=mgh

    Here m = 2 kg

    g = 9.81 m/s²

    Substituting

    KE = 0.5 x 2 x v² = v²

    PE = 2 x 9.81 x h = 19.62h

    At height 20 m:-

    v = 0 m/s

    h = 20 m

    Substituting

    KE = v² = 0² = 0J

    PE = 19.62 x 20 = 392.4 J

    Total energy = 0 + 392.4 = 392.4 J

    At 20 m kinetic energy is 0 J, Potential energy is 392.4 J and total energy is 392.4 J

    At height 10 m:-

    We have equation of motion v²=u²+2as

    v = ?

    u = 0 m/s

    s = 20 - 10 = 10 m

    a = 9.81 m/s²

    v²=0²+2 x 9.81 x 10

    v = 14 m/s

    v = 14 m/s

    h = 10 m

    Substituting

    KE = v² = 14² = 196 J

    PE = 19.62 x 10 = 196.2 J

    Total energy = 196 + 196.2 = 392.4 J

    At 10 m kinetic energy is 196 J, Potential energy is 196.2 J and total energy is 392.4 J

    At height 0 m:-

    We have equation of motion v²=u²+2as

    v = ?

    u = 0 m/s

    s = 20 - 0 = 20 m

    a = 9.81 m/s²

    v²=0²+2 x 9.81 x 20

    v = 19.81 m/s

    v = 19.81 m/s

    h = 0 m

    Substituting

    KE = v² = 19.81² = 392.4 J

    PE = 19.62 x 0 = 0 J

    Total energy = 392.4 + 0 = 392.4 J

    At 0 m kinetic energy is 392.4 J, Potential energy is 0 J and total energy is 392.4 J
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