问题 计算题

(18分).如图,阻值不计的光滑金属导轨MN和PQ水平放置,其最右端间距d为1m,左端MP,接有阻值r=4的电阻,右端NQ与半径R为2m的光滑竖直半圆形绝缘导轨平滑连接;一根阻值不计的长为L=1.2m,质量m=0.5kg的金属杆ab放在导轨的EF处,EF与NQ平行。在平面NQDC的左侧空间中存在竖直向下的匀强磁场B,平面NQDC的右侧空间中无磁场。现杆ab以初速度v0=12m/s向右在水平轨道上做匀减速运动,进入半圆形导轨后恰能通过最高位置CD并恰又落到EF位置;  (g取10m/s2)

求:(1)杆ab刚进入半圆形导轨时,对导轨的压力:

(2)EF到QN的距离;

(3)磁感应强度B的大小

答案

(1)30N(2)4m(3)

题目分析:(1)设杆ab刚进入半圆形导轨时速度为,到达最高位置CD位置时,速度为,由于恰能通过最高点,则: 

解得 

杆ab进入半圆形导轨后,由于轨道绝缘,无感应电流,则根据机械能守恒:  

解得 

设在最低点时半圆形轨道对杆ab的支持力为N,

则有 

(2)杆ab离开半圆形导轨后做平抛运动,设经时间落到水平导轨上

解得

则杆ab与NQ的水平距离

(3)设杆ab做匀减速运动的加速度为a

解得

对杆刚要到达NQ位置进行分析

点评:本题通过圆周运动知识分析物体经过最高点时的力学条件,通过机械能守恒定律最后换算处最低处的速度,最后通过支持力与重力合力提供向心力求出未知量。本题还涉及平抛运动,和常见的电磁感应类问题

阅读理解

阅读理解。

                                                    May: Happenings from the Past

     May 5,1884

     Isaac Murphy, son of a slave and perhaps the greatest horse rider in American history, rides Buchanan

to win his first Kentucky Derby. He becomes the first rider ever to win the race three times.

     May 9,1754

     Benjamin Franklin's Pennsylvania Gazette produces perhaps the first American political cartoon (漫画),

showing a snake cutsin pieces, with the words" Join or Dic" printed under the picture.

     May 11,1934

     The first great dust storm of the Great Plains Dust Bowl, the result of years of drought (干旱), blows

topsoil all the way to New York City and Washington, D.C.

     May 19,1994

     Jacqueline Lee Bouvier Kennedy Onassis, former first lady and one of the most famous people of the

1960s, died of cancer in New York City at the age of 64.

     May 24, 1844

     Samuel F.B Morse taps out the first message, "What Hath God wrought," over the experimental

long-distance telegraph line which runs from Washington, D,C, to Baltimore, Md.

1. We know from the text that Buchanan is _____.

A. Isaac's father

B. a winning horse

C. a slave taking care of horses

D. the first racing horse in Kentucky

2. What is the title of the first American political cartoon?

A. Join or Die

B. Pennsylvania Gazette

C. What Hath God Wrought

D. Kentucky Dorby

3. In which year did the former first lady Jacqueline die?

A. 1934

B. 1960

C. 1964

D. 1994

4. Which of the following places has to do with the first telegram in history?

A. Washington, D.C.

B. New York City.

C. Kentucky.

D. Pennsylvania.

单项选择题