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Forces and Newton's Laws

  1. Oct 29, 2009 #1
    1. The problem statement, all variables and given/known data
    A 0.54kg ball falls from rest at a height of 26m and rebounds up 16m. If the contact between the ball and ground lasted 1.8ms, what average force was exerted on the ball?


    2. Relevant equations
    F=ma
    v²=v0²+2a(x-x0)
    v=v0+at
    1000ms=1s (1.8ms is 0.0018s)

    3. The attempt at a solution
    (numbers are shortened for convenience but end results are with actual numbers)
    Calculated for velocity:
    v²=v0²+2a(x-x0)
    v²=0+2(9.8)(26)
    v=22.6m/s

    Calculated acceleration as ball hits ground:
    v=v0+at
    0=22.6+a0.0018
    a=12,541m/s²

    Calculate for force:
    F=ma
    F=(0.54)(12,541)
    F=6772.3N

    This is the answer I would try but it is wrong and I am missing something, like the 16m bounce up.

    I then tried to subtract the force calculated with the force exerted when the ball bounced back up, which had a force of:
    v²=v0²+2a(x-x0)
    v²=0+2(9.8)(16)
    v=17.7m/s

    v=v0+at
    0=17.7+a0.0018
    a=9838.2m/s²

    F=ma
    F=(0.54)(9838.2)
    F=5312.6N

    This is upward force so the resultant for is a downward (6772.3-5312.6)=1459.67N.
    This is also wrong and might have some assumptions in it.

    What is wrong with the calculations? Is there something that I didn't understand about the questions or the use of the equations?
     
  2. jcsd
  3. Oct 29, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    Through out the problem acceleration is g.
    Your v1 = 22.6 m/s is correct. v2 = 17.7 m/s is correct.
    Now the average force is equal to (final momentum - initial momentum)/time of contact.
    Note that two momentum have opposite direction.
     
  4. Oct 30, 2009 #3
    v1=22.6
    v2=17.7

    (final momentum - initial momentum)/time
    (v2×m - v1×m)/time
    (17.7×0.54 - 22.6×0.54)/0.0018
    (9.56 - 12.2)/0.0018
    -2.63/0.0018
    -1459.67

    Is this correct?
     
  5. Oct 30, 2009 #4
    Remember that v1 and v2, and hence their respective momenta, are in opposite directions.
     
  6. Oct 30, 2009 #5
    v1=-22.6
    v2=17.7

    (final momentum - initial momentum)/time
    (v2×m - v1×m)/time
    (17.7×0.54 - (-22.6)×0.54)/0.0018
    (9.56 - (-12.2))/0.0018
    21.76/0.0018
    12088.9

    Is this right?
     
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