问题 计算题

(15分)光子具有能量,也具有动量。光照射到物体表面时,会对物体产生压强,这就是“光压”,光压的产生机理如同气体压强;大量气体分子与器壁的频繁碰撞产生了持续均匀的压力,器壁在单位面积上受到的压力就是气体的压强,设太阳光每个光子的平均能量为E,太阳光垂直照射地球表面时,在单位面积上的辐射功率为P0,已知光速为c,则光子的动量为,求:

(1)若太阳光垂直照射在地球表面,则时间t内照射到地球表面上半径为r的圆形区域内太阳光的总能量及光子个数分别是多少?

(2)若太阳光垂直照射到地球表面,在半径为r的某圆形区域内被完全反射(即所有光子均被反射,且被反射前后的能量变化可忽略不计),则太阳光在该区域表面产生的光压(用l表示光压)是多少?

答案

(1)

(2)

(1)时间t内太阳光照射到面积为S的圆形区域上的总能量

                                                                                    …………2分

解得                                                                          …………1分

照射到此圆形区域的光子数

                                                                                        …………2分

解得                                                                            …………2分

(2)因光子的动量

则达到地球表面半径为r的圆形区域的光子总动量

                                                                                       …………1分

因太阳光被完全反射,所以时间t内光子总动量的改变量

                                                                                       …………2分

设太阳光对此圆形区域表面的压力为F,依据动量定理

                                                                                        …………2分

太阳光在圆形区域表面产生的光压  …………1分

解得                                                                                …………2分

阅读理解

When Babbage was working at Cambridge, a new idea occurred to him. He wanted to construct a calculating machine to work out the solutions(解法)to maths problems not only with correctness but also with a speed beyond the power of any human mind. His machine could solve problems involving(涉及)long rows of figures in one continuous operation(运算).

In 1822 Babbage exhibited his invention and won a prize from the government. After that, he immediately started to work on a larger machine designed to solve more difficult problems. Although he received some money left by his father, the money was not enough to support his design. He wrote to the government about his plan and was given £2500 to start with, a sum worth much more in those days than it is now.

Babbage continued his work in London for four years. Then his health broke down, and he had to take a long holiday abroad. When he returned to London in 1828, he was at the end of his resources. Many bills remained unpaid. His chief assistant and co-workers quarreled with him and left with many expensive tools. For one year no work was done. During this period, Babbage, whose mind was always active, suddenly thought of a completely new idea for the machine. He rushed to meet the government officials to explain his new idea. But this time, they were unwilling to help him. For eight years, they refused to say whether they wanted the machine or not, and their final answer was “No.”

From 1828 to 1839, Babbage held the position of professor at Cambridge very successfully. But his greatest work was the unfinished calculating machine which stood covered in dust in his house. It was the beginning of the modern computer.

60.The machine Babbage designed would solve difficult maths problems _________.

A.in one operation with few mistakes

B.in more than one operation without any mistakes

C.in more than one operation with slight mistakes

D.in one operation without any mistakes

61.Babbage failed to continue his research work in 1828 mainly because _______.

A.he was in poor health                B.he almost ran out of money

C.his co-workers argued with him         D.he spent all his money on his bills

62.Babage explained his new idea to the government officials, expecting that _________.

A.they would agree to his plan             B.they would pay for his new idea

C.they would support him with money    D.they would exhibit his new design

63.From the passage, we can infer that __________.

A.Babbage failed to be a famous scientist at Cambridge

B.Babbage always had new ideas but gave them up easily

C.Babbage always needed support from the government officials

D.Babbage was the first designer of the modern computer

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