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Finding the Mass of a Homogeneous Rod Using the Distance the Center of Gravity Moved

ÀÛ¼ºÀÚ Uploader : aloha ÀÛ¼ºÀÏ Upload Date: 2023-05-22º¯°æÀÏ Update Date: 2023-05-22Á¶È¸¼ö View : 89

When the length of the rod is L (m), an object of mass m (kg) is attached to one end, and when the center point moves toward the object by d (m), the mass ms (kg) of the rod can be obtained.

Since moment equilibrium is achieved at point d, the following equation holds.

(ms/L)(L/2+d)g(L/2+d)/2 = (ms/L)(L/2-d)g(L/2-d)/2 + mg*(L/2-d)

It can be rearranged as follows.

(ms/L)(L/2+d)^2 = (ms/L)(L/2-d)^2 + 2m(L/2-d)

ms(L/2+d)^2 = ms(L/2-d)^2 + 2mL(L/2-d)

ms((L/2+d)^2-(L/2-d)^2) = 2mL(L/2-d)

ms(2Ld) = 2mL(L/2-d)

ms = mL(L/2-d)/(Ld) = mL(L-2d)/(2Ld)


*** Âü°í¹®Çå[References] ***

ms = m*L*(L-2*d)/(2*L*d)
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