问题 计算题

(12分)如图所示,水平传送带A、B两端点相距x=4m,以v="2" m/s的速度(始终保持不变)顺时针运转,今将一质量为100g小煤块(可视为质点)无初速度地轻放至A点处,已知小煤块与传送带间的动摩擦因数为0.4,g取10m/s2。由于小煤块与传送带之间有相对滑动,会在传送带上留下划痕,则小煤块从A运动到B的过程中

(1) 小煤块从A运动到B的时间是多少?

(2) 划痕的长度?

(3) 产生的热量?   

(4) 传送物体电动机多做的功?

答案

(1)2.25s (2)0.5m (3)0.2J (4)0.4J

题目分析:(1)煤块在传送带上滑动时,根据牛顿第二定律有:

;因此解得

当煤块速度和传送带速度相同时,位移为:

因此煤块先加速后匀速运动:

加速时间:

匀速时间:

所以从A到B的时间为

(2)在加速阶段产生相对位移即产生划痕,

固有:

(3)产生的热量为

(4)电动机做的功等于煤块产生的动能与系统产生的热量之和,所以为

点评:分析清楚物体运动的过程,先是匀加速直线运动,后是匀速直线运动,分过程应用运动规律求解即可,尤其是注意分析摩擦力的变化情况.

阅读理解

Easy Ways to Keep Your Brain Sharp

Everyone is forgetful, but as we age, we start to feel like our brains are slowing down a bit—and that can be a very annoying thing.小题1:    Read on for some techniques worth trying.

1. 小题2:   

People who regularly made plans and looked forward to upcoming events had a 50 percent

reduced chance of Alzheimer's disease (早老性痴呆症), according to a recent study.  小题3: 

Something as simple as setting a goal to have a weekly coffee date with a friend will do. There's evidence that people who have a purpose in life or who are working on long or short-term goals appear to do better. In other words, keep your brain looking forward.

2. Go for a walk.

Mildly raised glucose (葡萄糖) levels can harm the area of the brain that helps you form memories and physical activity can help get blood glucose down to normal levels. In fact,exercise produces chemicals that are good for your brain. 小题4:    

3. Learn something new.

Take a Spanish class online, join a drawing club, or learn to play cards. A study found that mental stimulation (刺激) limits the weakening effects of aging on memory and the mind. But the best thing for your brain is when you learn something new and are physically active at the same time.  小题5:    Or go dancing with your friends.

A.Focus on the future.

B.This can be especially harmful to the aged.

C.It should be something like learning gardening.

D.So take a few minutes each day to do some reading.E.But don't worry if your schedule isn't filled with life-changing events.

F.Luckily, research shows there is a lot you can do to avoid those moments.

G.In other words, when you take care of your body, you take care of your brain.

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