问题 计算题

分某运动员做跳伞训练,他从悬停在空中的直升飞机上由静止跳下,跳离飞机一段时间后打开降落伞做减速下落。他打开降落伞后的速度时间图象如图a(t=0为打开伞瞬间)。降落伞用8根对称的绳悬挂运动员,每根绳与中轴线的夹角均为37°,如图b。已知人的质量为50kg,降落伞质量也为50kg,不计人所受的空气阻力,打开伞后降落伞所受阻力f与速度v成正比,即f=kv(g取10m/s2,sin53°=0.8,cos53°=0.6).求:

⑴打开降落伞前人自由下落的距离;

⑵阻力系数k;

⑶打开伞瞬间加速度a的大小和方向以及此时每根悬绳承受的拉力为多少。

答案

⑴h=20m;⑵k=200N·s/m;⑶a=30m/s2,方向竖直向上;T=312.5N。

题目分析:⑴由图a可知,打开降落伞瞬间人的速度为v0=20m/s

根据自由落体运动规律可知,打开降落伞前人自由下落的距离为:h==20m

⑵由图a可知,当运动员下落速度为v=5m/s时,速度不再变化,即匀速下落,此时对人和伞整体受重力(M+m)g和空气阻力f作用,根据平衡条件有:f=(M+m)g              ①

又因为有:f=kv                ②

由①②式联立解得:k==200N·s/m

⑶打开伞瞬间对人和伞整体,根据牛顿第二定律有:kv0-(M+m)g=(M+m)a

解得:a=-g=30m/s2,方向竖直向上

设此时每根绳的拉力为T,对运动员根据牛顿第二定律有:8Tsin53°-Mg=Ma

解得:T=312.5N

阅读理解

How many coins have you got in your pocket right now?Three?Two?Or one?With a phonecard you can make up to 200 calls without any change at all.

1.What do you do with it?

Go to a telephone box marked “Phonecard”.Put in your card,make your call and when you've finished,a screen tells you how much is left on your card.It costs no extra for the cards,and the calls cast 10 per unit,the same as any other payphone call.You can put them in units of 10,20,40,100 or 200.

2.Now appearing in a shop near you

Near each card phone place you'll find a shop where you can buy one.They're at bus,train and city tube stations.Many universities,hospitals and clubs,restaurants and gas stations on the highway and shopping centers.At airports and seaports.

3.No more broken payphones

Most broken payphones are like that they've been vandalized(破坏了的).There are no coins in Cardphone to excite thieves' interest in it.So you're not probably to find a vandalized one.Get a phonecard yourself and try it out.Or get a bigger wallet.

小题1:There are three sections in the passage.Which section do you think is about why phonecards are good?

A.Section 1.

B.Section 2.

C.Section 3.

D.Section 1&2.小题2:Choose the right order of the steps under“How to use a phonecard”.

a.Put in your phonecard.

b.Look at the screen to find out how many calls you can still make.

c.Go to a telephone box marked “Phonecard”.

d.Make your call.

A.a,b,c,d

B.c,a,d,b

C.a,d,c,b

D.c,d,a,b小题3:The last sentence “Or get a bigger wallet”means“_________”.

A.Phonecards are cheap

B.You cannot use all payphones

C.Thieves will not break card phones

D.People do not like carrying a lot of coins

单项选择题