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Finding height dropped from Force vs. Time graph

  1. Nov 29, 2016 #1
    1. The problem statement, all variables and given/known data

    A pumpkin was dropped from a balcony of a skyscraper. The pumpkin happened to land on a sidewalk force sensor and the below data was collected. The pumpkin weighs 2.7kg.

    a) From what height was the pumpkin dropped?

    b) From what floor of the skyscraper was the pumpkin probably dropped?

    upload_2016-11-29_13-40-39.png

    2. Relevant equations

    Potential Before = Kinetic After: mgh = (1/2)mv^2

    Solving for v gives: v = sqrt(2gh)

    a = F/m

    Vf = a*t+Vi
    Sf = .5*at^2+Vi*t+ Si

    3. The attempt at a solution

    First I used mgh = .5mv^2 and solved for v.

    This gave me v = sqrt(2gh)

    I figure that finding the area under the curve of the graph gives the total force on the pumpkin as it is hitting the ground. I haven't done this yet, but I am not too worried about getting an exact answer for this part. I more want to make sure I know how to solve the rest of the problem.

    I tried using kinematic equations to solve for height, but I ended up with h being 0, so I think I am not using the right concept and/or equation here.

    We are currently studying conservation of momentum, but I don't see how that is helpful here for determining the height the object was initially dropped from.

    Hopefully I am missing something obvious?
     
    Last edited: Nov 29, 2016
  2. jcsd
  3. Nov 29, 2016 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Hello. Welcome to PF!

    The area under the graph does not give you the "total force". It gives you something called "impulse". Review your notes or textbook for information about impulse and how it is related to momentum.
     
  4. Nov 29, 2016 #3
    Right, I was mistaken. I think I've got it now.

    The impulse is equal to the change in momentum over that time period.

    Change in momentum = area under the curve = impulse = J

    So, using that I solved change in momentum:

    2.7(v) - 2.7(0)
    2.7v = J
    v = J/2.7

    I estimated J by using Reimann Sum, got 49.72.

    Then I just used conservation of energy, mgh = .5*m*v^2 and got 17.29 meters for h.

    Hopefully this is right, I think I didn't quite understand impulse.
     
  5. Nov 29, 2016 #4
    I got J = 49.65 Nm and h = 17.24 m.
    I'm not sure what floor that was from, but when thinking "skyscraper", it was not very high.
    Once again, a problem with more drama and suspense needed. :)
     
  6. Nov 29, 2016 #5
    Thanks, I'm glad I was close!
     
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