Question

L- Pivot Point 13.) A uniform, thin rod of length L and mass M is allowed to pivot about its end, as shown in the figure above (a) Using integral calculus, derive the rotational inertia for the rod around its end to show that it is ML2/3 The rod is fixed at one end and allowed to fall from the horizontal position A through the vertical position B. (b) Derive an expression for the velocity of the free end of the rod at position B. Express your answer in terms of M, L, and physical constants, as appropriate. An experiment is designed to test the validity of the expression found in part (b). A student uses rods of various lengths that all have a uniform mass distribution. The student releases each of the rods from the horizontal position A and uses photogates to measure the velocity of the free end at position B. The data are recorded Length (m) 02500.5 .00 25 1.50 Velocity (m/s) 2.7 384.65.25.8 6.3 (c) Indicate below which quantities should be graphed to yield a straight line whose slope could be used to calculate a numerical value for the acceleration due to gravity g. Horizontal axis: Vertical axis: Use the remaining rows in the table above, as needed, to record any quantities that you indicated that are not given. Label each row you use and include units. (d) Plot the straight-line data points on the grid below. Clearly scale and label all axes, including units as appropriate. Draw a straight line that best represents the data. し-」- -+-+-+-+ -+-+-+-+- +-+-+ + +-+-+ +-+-+-+-+-+-十 +-+-+-+- -+-+-++-+-+-+-+一 -+ i. Using your straight line, determine an experimental value for g i. Describe two ways in which the effects of air resistance could be reduced.

Answer 1

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e.ii To reduce air resistance, the rod should be as thin as possible.