ME, A, K, Max Speed, M: Physics?

An oscillating block-spring system has a mechanical energy of 8.3 J, an amplitude of 0.60 m, and a maximum speed 3.2 m/s. Spring constant k is 4.61×101 N/m.

What is the mass of the block?

**Can someone give me a formula and step by step?

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  • 8 years ago
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    The equation below is for the conservation of energy of the block – spring system.

    ½ * k * A^2 = ½ * k * d^2 + ½ * m * v^2

    A = amplitude, which the greatest distance that the spring is stretched or compressed.

    At this position, the potential energy of the spring is the maximum.

    ½ * k * A^2 is the maximum potential energy of the block.

    k = 4.61 * 10^1 N/m, A = 0.60 m

    Maximum PE = ½ * 4.61 * 10^1 * 0.60^2 = 8.298 J

    This is the total energy of the block – spring system.

    As the block moves from this position, the velocity of the block increases. The block is moving at the maximum speed, when the block passes through the equilibrium position. So, the kinetic energy of the block is the maximum as the block passes through the equilibrium position. At the equilibrium position, the spring is relaxed. So, the potential energy of the spring is 0 J, at the equilibrium position.

    At this position, Maximum KE = Maximum PE

    Maximum KE = ½ * m * (Maximum velocity)^2 = ½ * m * 3.2^2

    ½ * m * 3.2^2 = 8.298

    Solve for the mass of the block.

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