physics

A block of ice of mass 4.10 kg is placed against a horizontal spring that has force constant k = 210 N/m and is compressed a distance 2.60×10−2 m. The spring is released and accelerates the block along a horizontal surface. You can ignore friction and the mass of the spring.

Calculate the work done on the block by the spring during the motion of the block from its initial position to where the spring has returned to its uncompressed length.

What is the speed of the block after it leaves the spring?

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  1. The work done by the spring in decompressing to the uncompressed length is just the stored potential energy at the maximum compressed length, which is
    (1/2) k X^2.

    You don't need to know the mass of the ice, but you could use it to calculate the velocity.

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  2. 0.0625

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  3. 0.0625J is the answer for the 1st question
    W=1/2kx^2
    =1/2(200 N/m)(0.025)^2
    =0.0625J

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  4. sorry wrong post:

    Given:
    mass= 4.10 kg
    k= 210 N/m
    x= 2.60x10^2 m

    just substitute to W=1/2kx^2 and you'll get the answer for the 1st question

    sorry again

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  5. For the velocity remember that the work done on the ice by the spring is calculated as the change in Kinetic Energy of the block or:
    Work = (1/2)mass*velocity(final)^2 - (1/2)mass*velocity(initial)^2

    Plug in your Work answer from part a and substitute into the above equation. When solving for the velocity, remember that it starts from rest, or at a 0 velocity. This cancels out the initial Kinetic Energy portion of the equation.

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