问题 问答题

一轻质弹簧,两端连接两滑块A和B,已知mA=0.99kg,mB=3kg,放在光滑水平桌面上,开始时弹簧处于原长.现滑块A被水平飞来的质量为mC=10g,速度为400m/s的子弹击中,且没有穿出,如图所示,试求:

(1)子弹击中A的瞬间A和B的速度

(2)以后运动过程中弹簧的最大弹性势能

(3)B可获得的最大动能.

答案

(1)子弹击中滑块A的过程,子弹与滑块A组成的系统动量守恒有:

mCv0=(mC+mA)vA

  vA=

mCv0
mC+mA
v0=4m/s

子弹与A作用过程时间极短,B没有参与,速度仍为零,故:vb=0.

故子弹击中A的瞬间A和B的速度分别为:vA=4m/s,vb=0.

(2)对子弹、滑块A、B和弹簧组成的系统,A、B速度相等时弹性势能最大.

根据动量守恒定律和功能关系可得:

mCv0=(mC+mA+mB)v

由此解得:v=

mC
mC+mA+mB
v0=1m/s

根据功能关系可得:

EP=

1
2
(mC+mA)vA2-
1
2
(mC+mA+mB)v2=6 J  

故弹簧的最大弹性势能为6J.

(3)设B动能最大时的速度为vB′,A的速度为vA′,则

(mC+mA)vA=(mC+mA)vA′+mBvB

当弹簧恢复原长时,B的动能最大,根据功能关系有:

1
2
(mC+mA)
v2A
=
1
2
(mC+mA)
v′A
2
+
1
2
mB
v′B
2

解得:

v′B
=
2(mC+mA
(mC+mA)+mB
=2m/s

B获得的最大动能:

EKB=

1
2
mB 
v′B
2
=6J.

故B可获得的最大动能为:EKB=6J.

单项选择题 案例分析题

Questions 11 to 15 are based on the following passage.

Scratchy throats, stuffy noses and body aches all spell misery, but being able to tell if the cause is a cold or flu (流感) may make a difference in how long the misery lasts.

The American Lung Association (ALA) has issued new guidelines on combating colds and the flu, and one of the keys is being able to quickly tell the two apart. That’s because the prescription drugs available for the flu need to be taken soon after the illness sets in. As for colds, the sooner a person starts taking over-the-counter remedy, the sooner relief will come.

The common cold and the flu are both caused by viruses. More than 200 viruses can cause cold symptoms, while the flu is caused by three viruses—flu A, B and C. There is no cure for either illness, but the flu can be prevented by the flu vaccine (疫苗), which is, for most people, the best way to fight the flu, according to the ALA.

But if the flu does strike, quick action can help. Although the flu and common cold have many similarities, there are some obvious signs to look for.

Cold symptoms such as stuffy nose, runny nose and scratchy throat typically develop gradually, and adults and teens often do not get a fever. On the other hand, fever is one of the characteristic features of the flu for all ages. And in general, flu symptoms including fever and chills, sore throat and body aches come on suddenly and are more severe than cold symptoms.

The ALA notes that it may be particularly difficult to tell when infants and preschool age children have the flu. It advises parents to call the doctor if their small children have flu-like symptoms.

Both cold and flu symptoms can be eased with over-the-counter medications as well. However, children and teens with a cold or flu should not take aspirin for pain relief because of the risk of Reye syndrome (综合症),a rare but serious condition of the liver and central nervous system.

There is, of course, no vaccine for the common cold. But frequent hand washing and avoiding close contact with people who have colds can reduce the likelihood of catching one.

 

According to the passage, to combat the flu effectively, ()

A.one should identify the virus which causes it

B.one should consult a doctor as soon as possible

C.one should take medicine upon catching the disease

D.one should remain alert when the disease is spreading

单项选择题