问题 问答题

取距地球无穷远处物体的重力势能为零,则地球周围物体的重力势能的表达式为:Ep=-G

Mm
r
,其中G为万有引力常量,M为地球的质量,m为物体的质量,r为物体到地心的距离,地球半径R=6400km,地球表面重力加速度g取10m/s2.试计算:

(1)质量为1×103kg的卫星绕地表飞行,其总机械能为多大?

(2)再补充多少能量可使它脱离地球的引力?

答案

(1)卫星在离地高度为H处环绕地球做匀速圆周运动,据万有引力提供向心力,列出等式:

GMm
r2
=m
v2
r
,r=R…①

根据根据在地面附近物体受到地球的万有引力近似等于物体在地面上的重力,列出等式:

GMm
R2
=mg…②

动能Ek=

1
2
mv2 ③

由①②③得:

万有引力势能的表达式:Ep=-G

Mm
r
…④

卫星的机械能应该是动能和势能之和.

所以E=Ek+Ep=-3.2×1010

(2)根据能量守恒,要使卫星能飞离地球,动能转化为引力势能,而且要飞到引力势能为零的地方,

所以需要补充3.2×1010J能量可使它脱离地球的引力.

答:(1)质量为1×103kg的卫星绕地表飞行,其总机械能为-3.2×1010J

(2)再补充3.2×1010J能量可使它脱离地球的引力.

完形填空

Directions: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.

This was no ordinary class. The students who came together were all science or engineering professors at Cornell University. They had interrupted their research to accept an invitation to take part in an unusual experiment: “an interesting week of poetry”. This class was part of a study to answer the questions: Why is science difficult for many non-science students?

The students in the poetry class listened to lectures and took notes. They had reading tasks and had to write three short papers. All students noticed one thing—the importance of spoken words. In science and engineering classes, the instructors put tables and drawings on the blackboard. But in this poetry class, the instructors just talked. They didn’t write anything on the board.

The scientists and engineers noticed one similarity between science and poetry. In both subjects, students need to find layers of meaning. Some layers are simple, clear, and on the surface; other layers are deeper and more difficult. This search for different levels of meaning doesn’t happen much in undergraduate science classes, but it is important later, in graduate school. And it is always important in humanities(人文科学).

Both the poetry instructors and their students learned something about teaching from this experience. One poetry instructor, for example, now sees the importance of using informational charts as he teaches. Most of the scientists agreed on several points. First, humanities classes might help science students to see patterns and decide which information is important. Second, the poetry class was fun. One engineer decided, “We need to change the way we teach engineering to make it an enjoyable experience for students.” But perhaps the most important result of the experience was this: All of the professors began to think about how they teach and how they can teach better.

(Note: Answer the questions or complete the statements in NO MORE THAN TWELVE WORDS.)

小题1:Why was this class very unusual?

小题2:The experiment was designed to help teachers find out ________.

小题3:The poetry class was different from science and engineering classes in that __________.

小题4:What influence did the experiment had on those professors?

单项选择题 案例分析题