论文部分内容阅读
老问题:用一架不等臂天平称一物体的质量,物体放在天平的左盘上称出其质量为M_1,物体放在右盘上称出其质量为M_2,求证物体的真实质量M=(M_1·M_2)~(1/2)。几乎所有的参考书上都是如下解法: 设天平左臂长为L_左,右臂长为L_右,依题意应满足如下关系: MgL_左=M_1gL_右(Ⅰ) MgL_右=M_2gL_左(Ⅱ) 由(Ⅰ),(Ⅱ)两式可得证。此解法虽可得推导结论,但操作过程并不完整。因为天平(无论是等臂的,还是不等臂的)在使用时必须先调好平衡。那么未载物前应满足平衡关系。 M_左gL_1=M_右gL_2(a) 式(a)中,M_左g为天平横梁左臂及左载物盘的重量,L_1为M_左g的力臂;M_右g为天平横梁右臂及右载物盘的重量,L_2为M_右g的力臂。
The old problem: use an inequality scale to weigh the mass of an object. The object is weighed on the left side of the scale and its mass is M_1. The object is weighed on the right disk and its mass is M_2 to verify the true mass of the object. =(M_1·M_2)~(1/2). Almost all reference books have the following solution: Set the left arm of the balance to be L_left and the right arm to be L_right. The meaning should satisfy the following relationship: MgL_left=M_1gL_right(I) MgL_right =M_2gL_left (II) can be obtained from (I) and (II). Although this solution can lead to conclusions, the operation process is not complete. Because the balance (whether it is equal arm, or not waiting for the arm) must first adjust the balance. Then balance should be satisfied before loading. M_left gL_1=M_right gL_2 (a) In formula (a), M_left g is the weight of the balance arm left arm and the left load plate, L_1 is the force arm of M_left g; M_right g is The weight of the right arm of the balance beam and the right load tray, L_2 is the arm of M_right g.