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问题 问答题

如图所示，平板A长l=10m，质量M=4kg，放在光滑的水平面上．在A上最右端放一物块B（大小可忽略），其质量m=2kg．已知A、B间动摩擦因数μ=0.4，开始时A、B都处于静止状态（取g=10m/s2）．则

（1）若加在平板A上的水平恒力F=6N时，平板A与物块B的加速度大小各为多少？

（2）要将A从物块B下抽出来，则加在平板A上的水平恒力F至少为多大？

（3）若加在平板A上的水平恒力F=40N时，要使物块B从平板A上掉下来F至少作用多长时间？

答案

对系统，假设AB之间不发生滑动．则

F=（M+m）a

解得a=

F
M+m
=
6
4+2
m/s2=1m/s2

对B而言，ma＜μmg

所以假设成立．

平板A与物块B的加速度大小为aA=aB=1m/s2

（2）对B，根据牛顿第二定律有μmg=ma0

解得a0=μg=0.4×10m/s2=4m/s2．

对系统：F=（M+m）a0=（4+2）×4N=24N．

所以加在平板A上的水平恒力F至少为24N

（3）设F的作用时间为t1，撤去F后，经过t2时间达到相同速度．

对B：

v共=gμ(t1+t2)
SB=
1
2
gμ(t1+t2)2

对A：

vA=a1t1
v共=vA-a2t2
F-mgμ=Ma1
mgμ=Ma2

则A的位移sA=

1
2
a1t12+vAt2-
1
2
a2t22

因为sA-sB=l，

解得t1=

3
s．

答：（1）平板A与物块B的加速度大小都为1m/s2．

（2）加在平板A上的水平恒力F至少为24N．

（3）要使物块B从平板A上掉下来F至少为

3
s．

问答题

如图是某化肥的标签，请列式计算，以解决如下问题：

（1）通过计算碳酸氢铵的含氮量，说明此标签是否有错误．

（2）据国家标准，碳铵化肥的NH4HCO3含量不得低少于95%．陈红同学利用下图装置和如下反应进行了三次实验，且假设杂质不发生反应：NH4HCO3

  △  
.
 
NH3↑+H2O+CO2↑       NH3+H2SO4═（NH4）2SO4

实验次数123平均值
使用样品的质量（克）8.008.008.008.00
硫酸溶液增加的质量（克）1.711.691.701.70
实验结果如下：

①陈红认为硫酸溶液增加的质量是氨气（NH3）的质量，根据陈红的分析，请利用实验平均值计算出该化肥中碳酸氢铵的百分含量．

②这个结果能否说明这种化肥合格与否，请说明原因．
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单项选择题

Today’s low gasoline prices make consumers willing to indulge their preference for larger cars, which consume greater amounts of gasoline as fuel. So United States automakers are unwilling to pursue the development of new fuelefficient technologies aggressively. The particular reluctance of the United States automobile industry to do, so, however, could threaten the industry’s future.
Which of the following, if true, would provide the most support for the claim above about the future of the United States automobile industry

A．A prototype fuel-efficient vehicle, built five years ago, achieves a very high 81 miles per gallon on the highway and 63 in the city, but its materials are relatively costly.

B．Small cars sold by manufacturers in the United States are more fuel efficient now than before the sudden jump in oil prices in 1973.

C．Automakers elsewhere in the world have slowed the introduction of fuel-efficient technologies but have pressed ahead with research and development of them in preparation for a predicted rise in world oil prices.

D．There are many technological opportunities for reducing the waste of energy in cars and light trucks through weight, aerodynamic drag, and braking friction.

E．(E) The promotion of mass transit over automobiles as an alternative mode of transportation has encountered consumer resistance that is due in part to the failure of mass transit to accommodate the wide dispersal of points of origin and destinations for trips.
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