A mass-spring system oscillates with an amplitude of 5.80 cm. If the spring constant is 275 N/m and the mass is 582 g,?

A mass-spring system oscillates with an amplitude of 5.80 cm. If the spring constant is 275 N/m and the mass is 582 g,

1. determine the mechanical energy of the system.

2. Determine the maximum speed of the object.

3. Determine the maximum acceleration.

2 Answers

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  • Anonymous
    4 months ago
    Favorite Answer

    1)

    E = 1/2 k A^2

    E = 0.5 * 275 * 0.058^2 = 0.46 J

    2)

    v = w A = sqrt(k/m) A

    v = sqrt(275/0.582) * 0.058 = 1.26 m/s

    3)

    a = w^2 A = (k/m) A

    a = (275/0.582) * 0.058 = 27.41 m/s^2

  • 4 months ago

    To solve this problem, I will assume the spring is moving horizontally. The following equation is used to calculate the mechanical energy.

    ME = ½ * k * d^2 = ½ * 275 * 0.058^2 = 0.46255 J

    2. Determine the maximum speed of the object.

    The maximum speed occurs when all of the mechanical energy has been converted into kinetic energy.

    KE = ½ * 0.582 * v^2 = 0.291 * v^2

    0.291 * v^2 = 0.46255

    v = √(0.46255 ÷ 0.291)

    This is approximately 1.59 m/s.

    3. Determine the maximum acceleration.

    The maximum acceleration occurs when the spring is exerting the maximum force. The equation for the maximum force is shown below.

    Maximum force = k * d

    F = 275 * 0.058 = 15.95 N

    15.95 = 0.582 * a

    a = 15.95 ÷ 0.582

    This is approximately 27.4 m/s^2. I hope this is helpful for you.

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