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How to calculate the mass of a ball based on a video

  1. Jan 24, 2017 #1
    1. The problem statement, all variables and given/known data
    I would like to know how I calculate mass of a ball based on a video. I can measure the speed of the ball at any point using Coach 3 (computer program). I know g=9.81m/s2 for the rest i don't know anything. I would like to know the way to calculate the mass of the ball in this video:


    2. Relevant equations
    F=m*a ?
    E=mc2 ?


    3. The attempt at a solution
    I have no clue, i only know the velocity of the ball.

    Thanks in advance for reacting to this thread.
     
  2. jcsd
  3. Jan 24, 2017 #2

    berkeman

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    Staff: Mentor

    Welcome to the PF.

    It would seem that you would need to know the spring constant of the spring mechanism below the ball, and the initial deflection of the mechanism. Once in flight, all masses will behave the same (ignoring air resistance)...
     
  4. Jan 24, 2017 #3

    gneill

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    The trajectory of the ball may be a distraction. Perhaps the key is that the ball and cart start out as one object accelerating together, then become separated leaving only the cart to accelerate horizontally. I think you'd need to know something about the mass of the falling weight and perhaps details of the pulley if its moment of inertia is significant. You'd also need to know if any friction values are significant.
     
  5. Jan 24, 2017 #4

    CWatters

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    This is unlikely to work in practice but...

    If you know the horizontal velocity at various points in time you can work out how fast it decelerates due to air resistance. Then if you know the diameter of the ball I suppose you might be able to estimate it's mass using aerodynamics. However I don't think the answer would be very accurate.

    My money is on it being very light weight. Something like a painted table tennis ball perhaps?
     
  6. Jan 25, 2017 #5
    Okay, so I now know the mass of the falling weight is 0.5kg and it falls at an acceleration rate of 1.8m/s2 before ejecting the ball, and at an acceleration rate of 3.2m/s2 after the ball is ejected. How can I calculate the mass of the ball with this information?
     
  7. Jan 25, 2017 #6

    gneill

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    Start by finding an equation for the acceleration for the simple case where there are two masses: M on the table and m falling. You've got two scenarios then, one where the mass M would represent both the cart and the ball and one where it is the cart alone. Determine M for each case.
     
  8. Jan 25, 2017 #7
    Thanks for the reply, do you happen to know 'this equation'?
     
  9. Jan 25, 2017 #8

    gneill

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    It's the one you'll have to derive yourself. After all, this is your homework. :smile:

    As usual, draw Free Body Diagrams and identify the forces. Proceed from there.
     
  10. Jan 25, 2017 #9
    I want to say thank you for your support, I figured out how to do it (or at least how I think the problem is solved):

    m1 = xkg
    m2 = 0.5kg
    a1 = 1.8m/s2
    a2 = 3.2m/22

    So the amount of force from the falling weight is 0.5x9.81=4.9N
    F=m1 *a ---> 4.9 = x*1.8 ---> 4.9/1.8=2.7kg (before launch of the ball)
    F=m1 *a ---> 4.9 = x*3.2 ---> 4.9/3.2=1.5kg

    2.7-1.5 = 1.2kg = the mass of the ball.
     
  11. Jan 25, 2017 #10

    gneill

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    Careful, there are two masses accelerating: One force accelerates the total mass.
     
  12. Jan 25, 2017 #11
    I see, so:
    4.9 = (m1+m2)*1.8 = 0.9m1 --> 4.9/0.9= 5.4kg
    and
    4.9 = (m1+m2)*3.2 = 1.6m1 --> 4.9/1.6= 3kg

    5.4-3 = 1.4kg = the mass of the ball

    Is this the right way the solve this problem?
     
  13. Jan 25, 2017 #12

    gneill

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    I'm not sure how you're carrying out your calculations. Can you show one in detail using symbols only? Let F be the force due to gravity on the falling weight, a be the measured acceleration.
     
  14. Jan 25, 2017 #13
    I did something wrong here (again),
    m2 is the mass of the falling weight
    m1 is the mass of the cart (+ the mass of the ball on t=x)

    it should be:

    F=m*a --> m2*g = 0.5*9.81= 4.9N
    Fres = m*a ---> 4.9N = (m2+m1)*a1 --->
    4.9-m2 = m1*a1 --->
    (4.9-m2)/a1= m1(t=x)

    Fres = m*a ---> 4.9N = (m2+m1)*a2 --->
    4.9-m2 = m1*a2 --->
    (4.9-m2)/a2 = m1(t=y)

    m1(t=x) - m1(t=y) = m3 (mass of the ball)
     
  15. Jan 25, 2017 #14

    gneill

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    How did you move m2 to the left hand side? Note that it is multiplied by a1 on the right hand side. Also, you end up subtracting a mass from a force, so the units don't match. You need to do a bit more algebra to isolate m1 properly.
     
  16. Jan 25, 2017 #15
    So when 4.9N = (m2+m1)*a1 ---> m1(t=x) = (4,9/a1) - m2 and
    4.9N = (m2+m1)*a2 ---> m1(t=y) = (4,9/a2) - m2 ?
     
  17. Jan 25, 2017 #16

    gneill

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    Yes, that looks better.
     
  18. Jan 25, 2017 #17
    Thanks a lot for helping me with this problem!
     
  19. Jan 25, 2017 #18

    gneill

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    Staff: Mentor

    You're very welcome!
     
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