问题 计算题

如图(甲)所示,一对足够长平行光滑轨道放置在水平面上,两轨道间距l=0.5m,左侧接一阻值为R=1的电阻;有一金属棒静止地放在轨道上,与两轨道垂直,金属棒及轨道的电阻皆可忽略不计,整个装置处于垂直轨道平面竖直向下的匀强磁场中。t=0时,用一外力F沿轨道方向拉金属棒,使棒以加速度a=0.2 m/s2做匀加速运动,外力F与时间t的关系如图(乙)所示。

(1)求金属棒的质量m

(2)求磁感强度B

(3)当力F达到某一值时,保持F不再变化,金属棒继续运动3秒钟,速度达到1.6m/s且不再变化,测得在这3秒内金属棒的位移s=4.7m,求这段时间内电阻R消耗的电能。

答案

由牛顿第二定律得:

(2)3分。   棒做匀加速运动,

所以,解得:

(3)9分。    F变为恒力后,金属棒做加速度逐渐减小的变加速运动,经过3秒钟,速度达到最大,此后金属棒做匀速运动。

时,

代入,求出变加速运动的起始时间为:

该时刻金属棒的速度为:

这段时间内电阻R消耗的电能:

阅读理解

阅读理解。

     Andrew Carnegie was a 19th century steel tycoon (大亨) who became one of the 20th century's most

famous philanthropists (慈善家). His life story is one of the most famous rags-to-riches accounts in United

States history.

     Carnegie was born in Dunfermline, Scotland, on November 25, 1835. The son of a weaver, he came with

his family to the United States in 1848 and settled in Allegheny, Pennsylvania. At age thirteen, Carnegie went

to work as a bobbin (线轴) boy in a cotton mill (纱厂). He then moved rapidly through a succession of jobs

with Western Union and the Pennsylvania Railroad. In 1865, he resigned to establish his own business

enterprises and eventually organized the Carnegie Steel Company, which started the steel industry in Pittsburgh.

At age sixty-five, he sold the company to J. P. Morgan for $ 480 million and devoted the rest of his life to his

philanthropic activities and writing, including his autobiography (自传).

     Many persons of wealth have contributed to charity, but Carnegie was perhaps the first to state publicly

that the rich have a moral obligation to give away their fortunes. In 1889 he wrote The Gospel (福音) of

Wealth, in which he asserted that all personal wealth beyond what was required to supply the needs of one's

family should be regarded as a trust fund to be administered for the benefit of the community.

     Carnegie set about giving away his fortune through innumerable personal gifts and through the establishment

of various trusts. In his thirties, Carnegie had already begun to give away some of his fast accumulating funds.

His first large gifts were made to his nature town. Later he created seven philanthropic and educational

organizations in the United States, including Carnegie Corporation of New York, and several more in Europe.

     One of Carnegie's lifelong interests was the establishment of free public libraries to make available to

everyone a means of self-education. There were only a few public libraries in the world when, in 1881,

Carnegie began to promote his idea. He and the Corporation subsequently (随后) spent over $56 million to build

2,509 libraries throughout the English-speaking world. After this program was ended in 1917, the Corporation

continued for about forty years an interest in the improvement of library services. Other major programs in the

Corporation's early history included adult education and education in the fine arts.

     During his lifetime, Carnegie gave away over$350 million. He died in Lenox, Massachusetts on August 11,

1919.

1. Carnegie became wealthy by ____.

A. his investment in weaving industry

B. his father's financial support

C. starting his steel business from nothing

D. his philanthropic activities

2. What is the correct order of events related to Carnegie?

    a. He sold his company.

    b. He organized the Carnegie Steel Company.

    c. He worked in a cotton mill.

    d. He came to the United States.

    e. He wrote The Gospel of Wealth.

A. c,d,e,b,a

B. c,b,a,d,e

C. d,c,b,e,a

D. d,b,a,e,c

3. Which of the following is TRUE about Carnegie?

A. He was the first wealthy person who contributed to charity.

B. He believed that it was the duty of the wealthy to help society.

C. He called on the wealthy to give away all of their fortune to help the poor.

D. He was willing to give personal gifts only to his friends and relatives.

4. Carnegie established public libraries in order to ____.

A. become famous

B. earn more money

C. improve library services

D. help people educate themselves

单项选择题