问题 计算题

用不等臂的天平来称量某物体,当物体放在左盘里,往右盘加m1的砝码时天平平衡;当把同一物体放在右盘里,往左盘里加m2的砝码时,天平平衡。试根据杠杆平衡条件证明:物体的实际质量:

答案

见解析

题目分析:设物体的质量为m,左盘的臂长为L1,右盘的为L2

第一次,左物右砝,砝码质量为m1,根据杠杆平衡有:mgL1=m1gL2,可得mL1=m1L2  (1)

第二次,左砝右物,砝码质量为m2,根据杠杆平衡有:m2gL1=mgL2,可得m2L1=mL2(2)

(1)(2)两式相除得:m/m2=m1/m,即

点评:对于杠杠问题,有几次杠杠平衡,根据杠杠平衡条件列几个等式,然后求解,一般都能解决问题.

填空题



For more than two centuries, American’s colleges and universities have been the backbone of the country’s progress. They have educated the technical, managerial, (1) and provided generation after generation of national leaders. Today educators from around the globe are turning to U. S. institutions of higher learning (2) . They are apt to find many reasons for the excellence of American universities, but (3) stand out as watersheds:
Education (4) : In 1862 Congress enacted the Land-Grant College Act, which essentially extended the opportunity of higher education (5) , including such disenfranchised groups as women and minorities. Each state was permitted to sell large tracts of (6) and use the proceeds to endow at least one public college.
(7) : Over the years, the decentralization and diversity of the America’s colleges and universities have promoted competition for students and resources. Competitive pressure first arose (8) . The academy’s impact really grew after World War II, when (9) commissioned by President Roosevelt argued that it was the federal government’s responsibility to (10) for basic research. Instead of being centralized in government laboratories, scientific research (11) in American universities and generated increasing investment. It also gave graduate students research opportunities and helped (12) far and wide, to the benefit of industry, medicine and society as a whole.
(13) : The end of the World War II saw passage of the Servicemen’s Readjustment Act of 1944. The law, which provided for (14) for returning veterans, made an already democratic higher-education system accessible in ways that were (15) in Europe, opening the doors of the best universities to men and women who had (16) of going to college.
(17) : The creation of federal loan guarantees and subsidy programs, as well as outright grants for college students brought (18) to higher education and further helped to democratize access. Since its founding (19) , the Federal Family Education Loan Program has funded more than 74 million student loans worth more than (20) .

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