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The force net of a spring system

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data

    A spring has a relaxed length of 20 cm (0.20 m) and its spring stiffness is 9 N/m. You glue a 80 gram block (0.08 kg) to the top of the spring, and push the block down, compressing the spring so its total length is 10 cm. You make sure the block is at rest, then at time t = 0 you quickly move your hand away. The block begins to move upward, because the upward force on the block by the spring is greater than the downward force on the block by the Earth. Calculate y vs. time for the block during a 0.21-second interval after you release the block, by applying the Momentum Principle in three steps each of 0.07-second duration.

    We will only consider the y components in the following calculations, because there is no change in x or z.

    STEP 1

    Force: Just after releasing the block, calculate the force exerted on the block by the spring, the force exerted on the block by the Earth, and the net force:

    Fspring,y = 0.9


    FEarth,y = -0.784


    Fnet,y = 0.116



    Momentum update: Just after releasing the block, the momentum of the block is zero. Calculate the average net force during the next time interval by the force you just calculated. At t = 0.07 seconds, what will the new momentum and velocity of the block be?

    py = .00812



    vy = 0.1015



    Position update: Initially the bottom of the block is at y = 0.10 m. Calculating the average velocity in the first time interval by the final velocity, what will be the new position of the bottom of the block at time t = 0.07 seconds?

    y = .107105



    -----------------------------------------------------------

    STEP 2

    Force: At the new position, calculate the force exerted on the block by the spring, the force exerted on the block by the Earth, and the net force:

    Fspring,y = 0.836055


    FEarth,y = -0.784


    Fnet,y = .052055



    Momentum update: Calculate the average net force during the next time interval by the force you just calculated. At time t = 2 × 0.07 = 0.14 seconds, what will the new momentum and velocity of the block be?

    py = 0.01176385


    vy = 0.147048125



    Position update: Calculating the average velocity in the second time interval by the final velocity, what will be the new position of the bottom of the block at time t = 2 × 0.07 = 0.14 seconds?

    y = .119357



    -----------------------------------------------------------

    STEP 3

    Force: At the new position, calculate the force exerted on the block by the spring, the force exerted on the block by the Earth, and the net force:

    Fspring,y = 0.72579


    FEarth,y = -0.784


    Fnet,y =



    Momentum update: Calculate the average net force during the next time interval by the force you just calculated. At time t = 3 × 0.07 = 0.21 seconds, what will the new momentum and velocity of the block be?

    py =


    vy =

    Position update: Calculating the average velocity in the third time interval by the final velocity, what will be the new position of the bottom of the block at time t = 3 × 0.07 = 0.21 seconds?

    y =

    2. Relevant equations



    3. The attempt at a solution
    For step three I am having problems with the net force. I tried adding both the force of the spring and the force of the earth but it keeps telling me it is incorrect.
     
  2. jcsd
  3. Sep 16, 2012 #2

    Simon Bridge

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    Don't forget to put the units on your numbers.
    Also please show your working - otherwise it looks like you are pulling numbers out of the air.

    You last position looks like 0.119357m from the base
    ... the force from the spring is given by (0.9N/m)(0.119357m)=0.10742N ... not what you got.
     
    Last edited: Sep 16, 2012
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