问题 计算题

(19分)在竖直平面内存在如图所示的绝缘轨道,一质量为m=0.4kg、带电量为q=+0.4C的小滑块(可视为质点)在外力作用下压缩至离B点0.05m,此时弹性势能=17.25J,弹簧一端固定在底端,与小滑块不相连,弹簧原长为2.05m,轨道与滑块间的动摩擦因数.某时刻撤去外力,经过一段时间弹簧恢复至原长,再经过1.8s,同时施加电场和磁场,电场平行于纸面,且垂直x轴向上,场强E=10N/C;磁场方向垂直于纸面,且仅存在于第二、三象限内,最终滑块到达N(6m,0)点,方向与水平方向成30º斜向下.(答案可用π表示,

(1)求弹簧完全恢复瞬间,小滑块的速度;

(2)求弹簧原长恢复后1.8s时小滑块所在的位置;

(3)求小滑块在磁场中的运动的时间.

答案

(1)7.5m/s (2)小滑块此时刚好到达坐标原点(3)s  

题目分析:(1)如图所示,弹簧释放到恢复原长经过位移s到达D点,根据能量关系,有:

                         (2分)

其中

解得:=7.5m/s                                            (1分)

(2)此后小滑块沿斜面向上做减速运动,由牛顿第二定律得:

                                 (2分)

解得小滑块的加速度大小为:=7.5                      (1分)

设小滑块运动到E点的速度为0,上升的位移为,则运动时间为:

=                                                  (1分)

上升的位移为:==3.75m                               (1分)

接着小滑块沿斜面下滑,运动时间为:=(1.8-1)s=0.8s

由牛顿第二定律有:               (1分)

解得:=2.5                                          (1分)

则下滑的位移为:=                            (1分)

由图中几何关系知:BD+=BO+                             (1分)

即小滑块此时刚好到达坐标原点.                             (1分)

(3)施加电场和磁场后,由题中数据知:

即小滑块只受洛伦兹力作用,做圆周运动到P(0,m)点,然后做匀速直线运动运动到N(6m,0).

小滑块进入磁场的速度为:=2m/s

洛伦兹力提供向心力:                               (2分)

由图中几何关系知小滑块做圆周运动的半径为:r=2m             (2分)

解得:=1T                                          (1分)

运动周期为:

在磁场中运动的时间为:==s                         (1分)

填空题
阅读理解

American cities are similar to other cities around the world; In every country. Cities reflect the values of the culture. American cities are changing, just as American society is changing.

After Wolld Wa Ⅱ,the population of most large American cities decreased; bowever. The populaton In omthe Sun Belt cities increased. Los Angeles and Houston are eitit where populatfon shife(转移)to and from the oity reflect the changing values of Amorican society. In the late 1940s and early 1950s,city residents(居民)became wealthier. They had more children so they needed more space, They moved out of their apartments in the city to buy their own homes. They bought houses in the suburbs(郊区).

Now things are changing. The children of the people who left the cities in the 1950s are now adults. Many, unlike their parents, want to live in the cities. They continue to move to Sun Belt cities and older ones of the Northeast and Midwest. Many young professionals are moving back into city. They prefer the city to the burbs because their jobs are there; or they jus enjoy the excitement and possibii that the city offers.

his  people     shift is bringing problems as well as benefits. Countless poot people  must leave  their apartments in the city because the owners want to sell the buildings or make apartments for sale instead of for rent. In the 1950s, many poor people did not have enough money to move to the suburbs; now many of these same people do not have enough money to stay in the cities.

Only a few years ago, people though that the older  American cities were dying. Some city residents now see a bright,  new fiture,  Others see only problems and comfiels the thing is sure many dying cities are alive again.

1. What does the author  think of cities all over the world?

A. They are alive.                        B. They are hopeless.

C. They are similar.                            D. They are different.

2.Why did American city residents want to live in the suburbs after World War Ⅱ?

A. Because older American cities were dying.

B. Because they were richer and needed more space.

C. Because cities contained the wont pare of society.

D. Because they could hardly afford a live in the city.

3. According to the 4th paragraph, a great many poor people in American cities_________.

A. are faced with housing problems

B. are forced to move to the suburbs

C. want to sell their buildings

D. need more money for daily expenses

4. We ear comude  from the text that ________.

A. American cities are changing far the worse

B. people have different views on American cities

C. many people are now moving from American cities

D. the population is decreasing in older American cities