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Free-Fall Acceleration

  1. Sep 8, 2004 #1
    A measurement of free-fall acceleration,g, was made by throwing a glass ball straight up in an evacuated tube and letting it return. Let ΔTl be time interval between two passages of ball across a certain lower level, ΔTu the time interval between the two passes across an upper level, and H the distance between the two levels.

    Show that g=(8H)/(ΔTl^2-ΔTu^2)

    I have no idea how to begin this proof.

    I've attempted to draw a picture that is attached.
     

    Attached Files:

  2. jcsd
  3. Sep 8, 2004 #2
    Let the origin be at the lower mark, then the motion of the ball is given by x = v0t - (1/2)gt2. To find the time passed between the lower mark being triggered on/off, first find the two times it passes through this position. Repeat for the higher mark. At this point you will have two equations with two unknowns (g being one of them). Use algebra to eliminate the other unknown and then solve for g.
     
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