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Homework Help: Mass Free Fall

  1. Jul 24, 2010 #1
    A 10 kg mass is in free fall with no air resistance. In order to slow the mass at a rate equal to the magnitude of g, an upward force must be applied with magnitude:


    F=ma



    F=(10kg)(9.81m/s2) = approximately 100N

    So in order to slow the mass at a rate equal to g it should be a force less than 100N?? Im not sure how to figure this out. Help!!!

    Thanks

    Jerry Zink
     
  2. jcsd
  3. Jul 24, 2010 #2

    rock.freak667

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    Let's start with the forces on the body falling.

    There are three forces acting or well two since we are ignoring air resistance. What are these two and what direction are they going in (up or down)?

    Since the body is moving downwards, the resultant force, ma, is downward. Can you formulate an expression for the resultant force ma?
     
  4. Jul 24, 2010 #3
    The two forces are

    1. gravitational force on the 10kg mass "going down"
    2. The upward force "going up"

    So the upward force must go against the force of gravity plus the force of the mass.

    The mass has a force of F=ma = 100N downward

    Since the upward force is in the opposite direction it has to counteract the downward force and slow it down to = g

    Im just having trouble formulating the expression for the upward force.
     
  5. Jul 24, 2010 #4
    Would the upward force be :

    F=m2a ?

    F=(10kg)(2)(9.81m/s2) = 196N

    is this correct?
     
  6. Jul 24, 2010 #5

    rock.freak667

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    Correct.
    Right but remember, the force of gravity is the 'force of the mass'.

    So you will have one going down and one going up (don't worry with the formulas for now, just use U for upwards and W for downward). If the mass is moving downwards, what direction should the resultant force be in?
     
  7. Jul 24, 2010 #6
    The resultant force should be in the upward direction
     
  8. Jul 24, 2010 #7

    rock.freak667

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    The mass is falling in which direction?
     
  9. Jul 24, 2010 #8
    OH! So the resultant force is in the downward direction.
     
  10. Jul 24, 2010 #9

    rock.freak667

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    Right so your resultant is

    ma = W-U

    and you identified the downward force as the force of gravity. So what is W equal to?

    They want the resultant acceleration to be equal to g. So what is 'a'?
     
  11. Jul 25, 2010 #10
    so W = ma + u

    a = 9.81m/s2

    so W is equal to the downward force of 100N?

    So this means u = W - ma

    U = 100N - (10kg)(9.81m/s2)

    U = 1.9N

    Is this right?

    Are you sure its not this "ma = U-W"

    This would make more sense because then U is = to around 200N
     
  12. Jul 25, 2010 #11

    rock.freak667

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    If your upward force is greater then your object is moving upwards and not falling.

    Normally what you have is

    ma = W-U-Fair resistance

    Sorry though, I interpreted one part wrong. They want the mass to fall at 'g' right? Which is essentially with the force of gravity, which is constant. Since it's acceleration is constant, the resultant force is ?
     
  13. Jul 25, 2010 #12
    Is the resultant force still the force of the mass 100N downwards?
     
  14. Jul 25, 2010 #13

    rock.freak667

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    No, the resultant force is the resultant of W and U. Since the mass is not accelerating anymore, the resultant force is zero.
     
  15. Jul 25, 2010 #14
    ?? So if the resultant force is zero how do we find the upward force?
     
  16. Jul 25, 2010 #15

    rock.freak667

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    If we have ma=W-U and ma=0, then wouldn't W-U=0 ?
     
  17. Jul 25, 2010 #16
    So if the upward force is equal to the downward force W=U

    Fw = (10kg)(9.81m/s2)

    W = 100N
    U = 100N

    This doesnt seem right?
     
  18. Jul 25, 2010 #17

    rock.freak667

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    Why not?
     
  19. Jul 25, 2010 #18
    Then wouldn't that implicate that the mass is not moving?
     
  20. Jul 25, 2010 #19

    rock.freak667

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    Not in this case. The body is falling. Which means it is traveling at a constant velocity.
     
  21. Jul 25, 2010 #20
    That makes sense, but the answer in my book says the upward force is equal to 200N. This is what is throwing me off. Maybe the book is wrong.

    I really appreciate your help rock.freak667

    Can you make any sense of the 200N answer?

    Thanks again

    Jerry Zink
     
  22. Jul 25, 2010 #21

    vela

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    This is correct.
    The fact that the mass is moving downward only tells you that the velocity vector points down. It doesn't tell you anything about the direction of the acceleration vector.

    For 1D motion, if the speed of the object is increasing, the acceleration points in the same direction as the velocity. If it's slowing down, the acceleration points in the direction opposite to the velocity.
     
  23. Jul 25, 2010 #22

    ehild

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    The body is slowing down at a rate of g from its downward velocity. It means that the acceleration is opposite to the velocity. Therefore it should point upward as Vela has explained, and its magnitude is g. Jerryez was right, the resultant force should be in the upward direction.

    ma=mg=F-mg

    ehild
     
  24. Jul 27, 2010 #23
    So if

    downward Force = mg = 100N

    ma=mg=F-mg

    (10kg)(9.81m/s2) = F - (10kg)(9.81m/s2)

    F = (98.1)+(98.1)
    F = approximately 200N

    So the upward force is twice as great as the downward force this makes the downward mass fall at g? Can someone explain the theory behind this?
     
  25. Jul 27, 2010 #24

    ehild

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    The upward force will make the falling body slow down at a rate of g till it loses all its downward velocity. After that, it will rise.

    ehild
     
  26. Jul 27, 2010 #25

    vela

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    You're not taking into account the direction of the acceleration. Let's use the usual convention of positive being the upward direction and negative being the downward direction. If only its weight mg acts on the mass, you get

    ma = -mg ⇒ a = -g

    The negative sign indicates the mass accelerates in the downward direction at a rate of 9.8 m/s2. With the upward force F of magnitude F=2mg acting as well, you get

    ma = F - mg = 2mg - mg = mg ⇒ a = +g

    Again the mass is accelerating at a rate of 9.8 m/s2, but this time it's accelerating in the upward direction.
     
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