问题 问答题

运动员驾驶摩托车做腾跃特技表演是一种刺激性很强的运动项目.如图所示,AB是水平路面,BC是半径为20m的圆弧,CDE是一段曲面.运动员驾驶功率始终是P=1.8kW的摩托车在AB段加速,到B点时速度达到最大υm=20m/s,再经t=13s的时间通过坡面到达E点时,关闭发动机后水平飞出.已知人和车的总质量m=180kg,坡顶高度h=5m,落地点与E点的水平距离s=16m,重力加速度g=10m/s2.如果在AB段摩托车所受的阻力恒定,求

(1)AB段摩托车所受阻力的大小;

(2)摩托车过B点时受到地面支持力的大小;

(3)摩托车在冲上坡顶的过程中克服阻力做功.

答案

(1)摩托车在水平面上已经达到了最大速度,牵引力与阻力相等.则

P=Fυ=fυ

f=

P
υ
=90N

(2)摩托车在B点,进行受力分析,由牛顿第二定律得:N-mg=m

υ2
R

N=m

υ2
R
+mg=5400N

由牛顿第三定律得地面支持力的大小为5400N.

(3)对摩托车的平抛运动过程,有t=

2h
g
=1s

平抛的初速度υ0=

s
t
=16m/s

摩托车在斜坡上运动时,由动能定理得Pt-Wf-mgh=

1
2
m
υ20
-
1
2
mυ2

求得Wf=27360J

答:(1)AB段摩托车所受阻力的大小是90N;

(2)摩托车过B点时受到地面支持力的大小是5400N;

(3)摩托车在冲上坡顶的过程中克服阻力做功是27360J.

阅读理解

A kind of little cars may some day take the place of today’s cars. If everyone drives such cars in the future,there will be less pollution in the car. There will also be more space for parking cars in cities,and the streets will be less crowded. Three such cars can fit in the space now needed for one car of the usual size.

The little cars will cost much less to own and to drive. Driving will be safer,too,as these little cars can go only 65 kilometers an hour. The cars of the future will be fine for getting around a city,but they will not be useful for long trips. Little cars will go 450 kilometers before needing to stop for more gasoline.

If big cars are still used along with the small ones,two sets of roads will be needed in the future. Some roads will be used for the big,fast cars and other roads will be needed for the slower,small ones.

小题1:There is much pollution in the car today because ________.

A.people drive big cars

B.people drive little cars

C.the cars go 65 kilometers an hour

D.the cars can go 450 kilometers an hour小题2:The usual size of cars today is ________that of future cars.

A.much smaller than

B.much the same as

C.three times as large as

D.a little larger than小题3:We can learn from the passage that________.

A.big cars cost less to own and to drive

B.big cars are not useful for long trips

C.the cars of the future will be much smaller than today’s cars

D.small cars are faster than big ones小题4:The street will be less crowded because ________.

A.there will be fewer cars in the future

B.there will be fewer passengers in the street

C.driving future cars will be safe

D.future cars will be much smaller小题5:Two sets of roads may be needed in the future because ________.

A.there will be too many cars in the future

B.more and more people will get around a city

C.big cars and little cars may be used along with each other

D.it looks more beautiful to have two sets of roads

单项选择题 A1/A2型题