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A meter stick is held vertically with one end on the floor and is then allowed to fall. Find the speed of the other end just before it hits the floor, assuming that the end on the floor does not slip. (Hint: Consider the stick to be a thin rod and use the conservation of energy principle.) Number Enter your answer in accordance to the question statement Units Choose the answer from the menu in accordance to the question statement

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Answer:

  v =  7.67 m/s  for L= 1m

Explanation:

Let's use the conservation of mechanical energy, at the highest point and the lowest point

Initial. Vertical ruler

       Em₀ = mg h

Final. Just before touching the floor

       [tex]Em_{f}[/tex] = K = ½ I w²

      Em₀ = [tex]Em_{f}[/tex]

      m g h = ½ I w²

The moment of inertia of a ruler that turns on one end is

      I = 1/3 m L²

Let's replace

      m g h = ½ (1/3 m L²) w²2

      g h = 1/6 L² w²

They ask for the speed of the end so the height h is equal to the length of the ruler

      g L = 1/6 L² w²

The linear and angular variables are related

      v = w r

     w = v / r

In this case the point of interest a in strangers r = L

     g L = 1/6 L² v² / L²

     v = √ 6 g L

Let's calculate

Assume that the length of the meter is L = 1 m

    v = √ (6 9.8 1)

   v =  7.67 m/s

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