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29 July, 20:27

Two 4.2 kg masses are connected to each other by a spring with a force constant of 28 N/m and a rest length of 1.0 m. If the spring has been compressed to 0.80 m in length and the masses are traveling toward each other at 0.42 m/s (each), what is the total energy in the system (in J) ?

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  1. 29 July, 20:43
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    The total energy of the system is 1.301 J

    Explanation:

    The total energy in the system is due to Kinetic of two 4.2 kg masses traveling at 0.42 m/s (each) and Elastic potential energy in the spring.

    Kinetic energy = ¹/₂mv²

    Kinetic energy for the two masses = 2 (¹/₂mv²)

    = 2 (0.5 * 4.2 * 0.42²)

    = 0.741 J

    Elastic potential energy, P. E = ¹/₂kx²

    where;

    k is the force constant = 28 N/m

    x is the extension in the spring = 1.0 - 0.8 = 0.2 m

    Elastic potential energy, P. E = ¹/₂kx² = ¹/₂ * 28 * (0.2) ² = 0.56 J

    Total energy of the system = P. E + K. E

    = 0.56 J + 0.741 J

    = 1.301 J
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