问题 计算题

如图所示,滑块质量为m,与水平地面的动摩擦因数为0.1,它获得一大小为3的水平速度后,由AB滑行5R,并滑上光滑的半径为R圆弧BC,在C点的正上方有一离C高度也为R的旋转平台,沿平台直径方向开有两个离轴心距离相等的小孔PQ,旋转时两孔均能达到C点的正上方,若滑块过C点后穿过P,又恰能从Q孔落下,则平台的角速度ω应满足什么条件?

答案

题目分析:滑块以速度,A开始向B运动

滑块由A滑到B过程中,由动能定理得:

得:滑块从B点到P点过程中机械能守恒,

得:得:

滑块穿过P孔后竖直上抛,上抛到落回的总共时间为

平台转过角度为角速度为

式中(n=0、1、2……)

点评:本题的易错点在于平台转动的角速度的多解性,注意运动的周期性往往带来多解性.

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阅读理解

     Christopher Thomas, 27, was a writer by night and a teacher by day when he noticed he was always

tired and was losing weight fast. Diagnosed with diabetes(糖尿病), Thomas would need to inject himself with insulin(胰岛素) three times a day for the rest of his life or risk nerve damage, blindness, and even

death. And if that weren't bad enough, he had no health insurance.

     After a month of feeling upset, Thomas decided he'd better find a way to fight back. He left Canton,

Michigan for New York, got a job waiting tables, nicknamed himself the Diabetic Rockstar, and created

diabeticrockstar.com, a free online community for diabetics and their loved ones-a place where over

1,100 people share personal stories, information, and resources.

    Jason Swencki's son, Kody, was diagnosed with diabetes at six. Father and son visit the online children's forums(论坛) together most evenings. "Kody gets so excited, writing to kids from all over, " says

Swencki, one of the site's volunteers. "They know what he's going through, so he doesn't feel alone."

     Kody is anything but alone: Diabetes is now the seventh leading cause of death in the United States,

with 24 million diagnosed cases. And more people are being diagnosed at younger ages.

     These days, Thomas's main focus is his charity(慈善机构), Fight It, which provides medicines and

supplies to people-225 to date-who can't afford a diabetic's huge expenses. Fightit.org has raised about

$ 23,000-in products and in cash. In May, Thomas will hold the first annual Diabetic Rockstar Festival

in the Caribbean.

     Even with a staff of 22 volunteers, Thomas often devotes up to 50 hours a week to his cause, while

still doing his fulltime job waiting tables. "Of the diabetes charities out there, most are putting money into

finding a cure, " says Bentley Gubar, one of Rockstar's original members. "But Christopher is the only

person I know saying people need help now."

1. Which of the following is TRUE of Christopher Thomas?

A. He needs to go to the doctor every day.

B. He studies the leading cause of diabetes.

C. He has a positive attitude to this disease.

D. He encourages diabetics by writing articles.

2. Diabeticrockstar.com was created for ________.

A. diabetics to communicate

B. volunteers to find jobs

C. children to amuse themselves

D. rock stars to share resources

3. According to the text, Kody ________.

A. feels lonely because of his illness

B. benefits from diabeticrockstar.com

C. helps create the online kid's forums

D. writes children's stories online

4. What can we learn about Fight It?

A. It helps the diabetics in financial difficulties.

B. It organizes parties for volunteer once a year.

C. It offers less expensive medicine to diabetics.

D. It owns a wellknown medical website.