问题 问答题

如图所示,一个绝缘光滑圆环竖直放在水平向右的匀强电场中,圆环半径大小为R=1.0m,电场强度大小为E=6.0×106V/m,现将一小物块由与圆心O等高的位置A点静止释放,已知小物块质量为m=1.6kg,电荷量为q=+2.0×10-6C,释放后滑块将沿着圆环滑动.小物块可视为质点,g取10m/s2.求:

(1)当物块滑到圆环最低点B时对轨道的压力大小;

(2)若在圆环最低点B点给小物块一个水平向左的初速度vB=9m/s,那么物块能否紧贴圆环在竖直平面内做圆周运动.(写出详细分析、判定过程)(已知:sin37°=0.6;cos37°=0.8)

答案

(1)物块由A运动到B的过程中,重力做正功,电场力做负功.

由动能定理可得:mgR+(-qER)=

1
2
m
v2B

解得:v

2B
=2gR-
2qER
m
=2×10×1.0-
2×2.0×10-6×6.0×106×1.0
1.6
=5(m/s)2

在B点由 FN-mg=m

v2B
R

解得:FN=m

v2B
R
+mg=1.6×(
5
1.0
+10)N=24N

由牛顿第三定律可得物块对轨道的压力大小为:

F′N
=24N

(2)设在C位置时重力与电场力的合力恰好指向圆心提供物块做圆周运动向心力时,物块刚好脱离圆环.

此时有:

(mg)2+(qE)2
=m
v20
R

解得:v0=

5
2
2
m/s,

OC与竖直方向夹角为370,若在圆环最低点B点给小物块一个水平向左的初速度vB=9m/s,在由B到C的运动过程中由动能定理可得:-mgR(1+cos37°)+(-qERsin37°)=

1
2
m
v2C
-
1
2
m
v2B

可解得:vc=6m/s>v0=

5
2
2
m/s.

因此物块能够紧贴圆环在竖直平面内做圆周运动.

答:(1)当物块滑到圆环最低点B时对轨道的压力大小为24N;

(2)若在圆环最低点B点给小物块一个水平向左的初速度vB=9m/s,物块能够紧贴圆环在竖直平面内做圆周运动.

多项选择题
单项选择题

Computer programmer David Jones earns £35,000 a year designing new computer games, yet he cannot find a bank prepared to let him have a check card. Instead, he has been told to wait another two years, until he is 18.

The 16-year-old works for a small firm in Liverpool, where the problem of most young people of his age is finding a job. David’s firm releases two new games for the expanding home computer market each month.

But David’s biggest headache is what to do with his money. Despite his salary, earned by inventing new programs within fight schedules, with bonus payments and profit-sharing, he cannot drive a car, take out a mortgage, or obtain credit cards.

He lives with his parents in their council house in Liverpool, where his father is a bus driver. His company has to pay £150 a month in taxi fares to get him the five miles to work and back every day because David cannot drive.

David got his job with the Liverpool-based company four months ago, a year after leaving school with six O-levels and working for a time in a computer shop. "I got the job because the people who run the firm knew I had already written some programs," he said. "I suppose £35,000 sounds a lot but actually that’s being pessimistic. I hope it will come to more than that this year." He spends some of his money on records and clothes, and gives his mother £20 a week. But most of his spare time is spent working.

"Unfortunately, computing was not part of our studies at school," he said. "But I had been studying it in books and magazines for four years in my spare time. I knew what I wanted to do and never considered staying on at school. Most people in this business are fairly young, anyway." David added, "I would like to earn a million and I suppose early retirement is a possibility. You never know when the market might disappear.\

He left school after taking 0-levels because ().

A. he did not enjoy school

B. he wanted to work with computers and staying at school did not help him

C. he was afraid of getting too old to start computing

D. he wanted to earn a lot of money