问题 计算题

(14分)如图所示,OAB是刚性轻质直角三角形支架,边长AB=20cm,∠OAB=30°;在三角形两锐角处分别固定两个不计大小的小球,A处小球质量为1kg。现将支架安装在可自由转动的水平轴上,使之可绕O点在竖直平面内无摩擦转动。装置静止时,AB边恰好水平。求:

(1)B处小球的质量;

(2)若将装置顺时针转动30°,至少需做多少功;

(3)若将装置顺时针转动30°后由静止释放,支架转动的最大角速度。

答案

(1)3kg(2)2–3(3)

题目分析:(1)mAgAOcos30°=mBgBOsin30°             2分

mB=mAcot230°=3kg                                           2分

(2)W=mAgAO sin30°- mBgBO(1- cos30°)  2=2–3 (J)              2分

(3)在平衡位置,物体的势能最小,动能最大,支架转动的角速度最大    2分

mA(ωAO)2+mB(ωBO)2= mAgAO sin30°- mBgBO(1- cos30°)            2分

ω= rad/s ="3.93" rad/s

点评:本题的关键是把握装置运动过程中的特殊状态,如在平衡位置是,势能最小,动能最大,角速度最大,根据动能定理分析解题

阅读理解

Gregg Bleakney’s dream was to travel the Americas from top to bottom. He got the idea after he finished a long bike ride. Gregg’s friend, Brooks Allen, also liked riding a bike. The two friends talked and made a plan: they would travel from Alaska to Argentina – by bike.

To pay for the trip, Gregg and Brooks worked to save money for a long time. Once they were on the road, they often camped outdoors and ate cheaply. In many places, local people opened their doors to the two friends and gave them food.

On their way, they passed deserts, rainforests and mountains. They visited modern cities and ancient ruins (遗迹) such as Machu Picchu in Peru. And they made many friends from all over the world.

In May 2007 – two years, twelve countries, and over 30,500 kilometres later – Gregg finally reached Ushuaia, Argentina. (Near Guatemala, Brooks had to go back and Gregg continued without him.)

The trip taught both men a lot about traveling. What did they learn? Here is some of Gregg’s advice:

Travel light. You should carry many things with you.

Be flexible (灵活). Don’t plan everything. Then you’ll be more relaxed, especially if there are problems.

Be polite. One traveler told Gregg, “Nobody wants to fight or cheat a nice man.” It’s true.

根据文章内容填写5个空处,每空不限一词。每题1分

小题1:Gregg Bleakney’s dream was to _______________________.

小题2:Before traveling, the two friends _____________________ to pay for the trip.

小题3:___________ got to Ushuaia, Argentina in May 2007.

小题4:According to the passage, if you don’t plan everything for a trip, ___________________.

小题5:One traveler told Gregg that nobody wants to __________________________.

单项选择题