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.

单项选择题
阅读理解

Climate change is making it harder than usual for scientists to figure out what the future will bring and what impact weather changes will have on society and the economy. An upsurge of severe weather events has already destroyed homes, businesses and lives. Some fairly simple changes may reduce the toll.

In a laboratory test, a house built with conventional techniques is falling apart in hurricane-force winds.

The survivor has stronger shingles, thicker roof boards, and metal straps holding floors together.

Wind tunnel tests were done by the Insurance Institute for Business & Home Safety. It says stronger construction costs a little more, but holds up much better to extreme weather.

The growing number of unusually strong storms, like Typhoon Haiyan, has convinced the Chairman of the U. S. Senate Homeland Security Committee, Tom Carper, that extreme weather is the “new norm标准).”

"Extreme weather events have increased in frequency over the past 50 years and are expected to become even more common, more intense, and more costly," said Carper.

Hurricane Sandy hit beachfront businesses along the U.S. East Coast, including Carper's home state. Insurance companies had to pay out huge claims. To limit such losses, the insurance industry can raise premiums(保险费) for businesses in vulnerable(易受攻击的)locations and offer discounts to clients who make their buildings more resilient with upgraded construction techniques.

Managing risks is the job of insurance brokers like Kevin Connelly of the Graham Company, who spoke to VOA via Skype.

“We are either going to price your insurance at a huge markup, or we are not going to write (sell it) it at all, which is just as bad obviously," said Connelly.

Drought is another suspected consequence of climate change, and dry ground means more wildfires in California. Current mathematical models of climate change do a poor job of predicting the economic impact of drought and other weather events, says Massachusetts Institute of Technology Professor Robert Pindyck, who spoke via Skype.

“I think all we can do, taking all of that into account, is come up with some very rough numbers, very rough estimates, "said Pindyck. "Consensus estimates that maybe experts provide, that give us a view of what would the catastrophic outcome look like if we don’t do anything?”

To help deal with this serious problem, Pindyck says policymakers should take actions such as imposing a tax on carbon dioxide emissions. A carbon tax would encourage companies and families to use less energy and generate fewer of the gases thought to be driving changes in the climate. But other analysts say it is unlikely a new tax will get approval in the U.S. Congress any time soon.

小题1:What can be inferred from the passage?

A.There are many severe weather events destroying homes, businesses and lives.

B.Stronger construction will save the expense in the long run.

C.Government should be totally responsible for the weather change.

D.Typhoon Haiyan hit Tom Carper's home state.小题2:What natural disasters are not mentioned in the passage?

A.Drought

B.Hurricanes

C.earthquakes

D.wildfires小题3:In a laboratory test , what kind of houses can stay up?

A.a house built with conventional techniques

B.A house with stronger shingles

C.A house with thinner roof boards

D.a house with metal floors .小题4:What won’t insurance companies do to limit such losses?

A.pay out huge claims

B.raise premiums(保险费) for businesses in vulnerable(易受攻击的)locations

C.offer discounts to clients who make their buildings more resilient with upgraded construction techniques.

D.price insurance at a huge markup小题5:What is the attitude of other analysts towards the new tax on carbon dioxide emissions?

A.supportive

B.doubtful

C.indifferent

D.positive