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Janet asked in Science & MathematicsPhysics · 1 decade ago

Spring constant help needed?

a 0.60-kg metal sphere oscillates at the end of a vertical spring. As the spring stretches from 0.12 to 0.23 m (relative to its unstrained length), the speed of the sphere decreases from 5.70 to 4.80 m/s. What is the spring constant of the spring?

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  • 1 decade ago
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    use conservation of energy, knowing that the total energy at each point is the same

    call x1, v1 the values at x=0.12m and x2, v2 the values at x=0.23m, energy conservation tells us

    1/2k(x1)^2+1/2m(v1)^2=

    1/2 k(x2^2) + 1/2 m(v)^2

    dividing through by 1/2 and substituting values, we get

    k(0.12)^2+(0.6)(5.7)^2=

    k(0.23)^2+(0.6)(4.8)^2

    collecting terms:

    k[(0.23)^2-(0.12)^2]=

    0.6[(5.7)^2-(4.8)^2]

    and now just solve for k

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