F.6 物理
2007-07-29 2:07 am
A wooden board pivoted freely at one point undergoes small sngular iscillation in a vertical plan. the period of oscillation T is given by L^2-AT^2L=B, where L is the distance between the centre of gravity of the board and the axis of oscillation , and A, B are constants. Determine the dimensions and units of A and B. suggest what physical quantities they may be related to.
回答 (1)
2007-07-29 8:13 am
✔ 最佳答案
依量綱的性質，在式中的每一項量綱都應該相同，所以[L^2] = 長度^2
[AT^2L] = [A] x 時間^2 x 長度 = 長度^2
[A] = 長度 x 時間^-2
[B] = 長度^2
所以
A 的單為是 ms^-2
B 的單位是 m^2
因此
A 的單位是加速度，可能是重力加速度。
B 的單位是 m^2，可能是板的面積。
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