A block sliding along a horizontal frictionless surface with speed v collides with a spring and compresses it by 2.0 cm. What will be the co

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A block sliding along a horizontal frictionless surface with speed v collides with a spring and compresses it by 2.0 cm. What will be the compression if the same block collides with the spring at a speed of 2v?

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Thu Thủy 3 years 2021-08-19T11:09:20+00:00 1 Answers 285 views 0

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    1
    2021-08-19T11:10:41+00:00

    Answer:

    4.0 cm

    Explanation:

    For the compression of the spring, the kinetic energy of the mass equals the elastic potential energy of the spring.

    So, 1/2mv² = 1/2kx² ⇒ x = (√m/k)v

    Since m and k are constant since its the same spring x ∝ v

    If our speed is now v₁ = 2v, our compression is x₁

    x₁ = (√m/k)v₁ = (√m/k)2v = 2(√m/k)v = 2x

    x₁ = 2x

    Since x = 2.0 cm, our compression for speed = 2v is

    x₁ = 2(2.0) = 4.0 cm

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