问题 选择题

如图所示,质量分别为m1和m2的两物块放在水平地面上,与水平面间的动摩擦因数都为μμ≠0),用轻弹簧将两物块连接在一起。当用水平力F作用在m1上时,两物块均以加速度a做匀加速运动,此时,弹簧伸长量为x ;若用水平力F’仍作用在m1上,两物块均以加速度a’=2a做匀加速运动,此时,弹簧伸长量为x’。则下列关系正确的是:(   )

A、F’=2F       B、x’=2x

C、F’>2F       B、x’<2x

答案

答案:D

考点:

分析:本题可先对整体用牛顿第二定律列式求出加速度,再隔离出m2用牛顿第二定律列式求出弹簧弹力.

解答:解:拉力为F时,对两个物体整体,由牛顿第二定律得:

F-μ(m1+m2)g=(m1+m2)a    ①;

假设弹簧弹力为F1,对质量为m2的物体,有:

F1-μm2g=m2a                ②;

拉力为F’时,a’=2a,对两个物体整体而言,由牛顿第二定律得:

F’-μ(m1+m2)g=(m1+m2)2a   ③;

假设弹簧弹力为F1′,对质量为m2的物体,有:

F1′-μm2g=2m2a′④;

由①③两式可解得:F’<2F  ⑤;故AC错误;

由②④⑤三式可解得,F1′<2F1

由胡克定律公式得,F1=kx,F1′=kx′,因而有x′<2x,故B错误,D正确.

故选D.

点评:本题关键为拉力变为2倍,合力变得大于2倍;弹簧弹力与地面是否粗糙无关!

单项选择题
单项选择题

The Southdale shopping centre in Minnesota has an atrium, a food court, fountains and acres of parking. Its shops include a Dairy Queen, a Victoria’s Secret and a purveyor of comic T-shirts. It may not seem like a landmark, as important to architectural history as the Louvre or New York’s Woolworth Building. But it is. "oh, my god!" chimes a group of teenage girls, on learning that they are standing in the world’s first true shopping mall. "That is the coolest thing anybody has said to us all day. "

In the past half century Southdale and its many imitators have transformed shopping habits, urban economies and teenage speech. America now has some 1,100 enclosed shopping malls, according to the International Council of Shopping Centres. Clones have appeared from Chennai to Martinique. Yet the mall’s story is far from triumphal. Invented by a European socialist who hated cars and came to deride his own creation, it has a murky future. While malls continue to multiply outside America, they are gradually dying in the country that pioneered them.

Southdale’s creator arrived in America as a refugee from Nazi-occupied Vienna. Victor Gruen was a Jewish bohemian who began to design shops for fellow immigrants in New York after failing in cabaret theatre. His work was admired partly for its uncluttered, modernist look, which seemed revolutionary in 1930s America. But Gruen’s secret was the way he used arcades and eye-level display cases to lure customers into stores almost against their will. As a critic complained, his shops were like mousetraps. A few years later the same would be said of his shopping malls.

By the 1940s department stores were already moving to the suburbs. Some had begun to build adjacent strips of shops, which they filled with boutiques in an attempt to re-create urban shopping districts. In 1947 a shopping centre opened in Los Angeles featuring two department stores, a cluster of small shops and a large car park. It was, in effect, an outdoor shopping mall. Fine for balmy southern California, perhaps, but not for Minnesota’s harsh climate. Commissioned to build a shopping centre at Southdale in 1956, Gruen threw a roof over the structure and installed an air-conditioning system to keep the temperature at 75°F (24℃)—which a contemporary press release called "Eternal Spring". The mall was born.

Gruen got an extraordinary number of things right first time. He built a sloping road around the perimeter of the mall, so that half of the shoppers entered on the ground floor and half on the first floor-something that became a standard feature of malls. Southdale’s balconies were low, so that shoppers could see the shops on the floor above or below them. The car park had animal signs to help shoppers remember the way back to their vehicles. It was as though Orville and Wilbur Wright had not just discovered powered flight but had built a plane with tray tables and a duty-free service.

Why did critics complain that Gruen’s "shops were like mousetraps" ()

A. Gruen designed his shops in a way capable of luring customers in

B. Gruen designed his shops with an appearance of mousetrap

C. Gruen’s shops were famous for the mousetraps they sold

D. Gruen’s shops sold things much more expensive than that of other ones