问题 填空题

质量为m的物块与水平面间的动摩擦因数为μ,为使物块沿水平面做匀速直线运动,则所施加的拉力至少应为多大?

答案

解析:取物块为研究对象,在与水平面夹θ角斜向右上方的拉力F作用下,物块沿水平面向右做匀速直线运动,此时,物块的受力情况如图所示,建立起水平向右为x轴正方向、竖直向上为y轴正方向的直角坐标系,沿两坐标轴方向列出平衡方程为

Fcosθ-f=0

Fsinθ+N-mg=0.

考虑到动摩擦力f与正压力N间的关系,又有

f=μN.

由上述三个方程消去未知量N和f,将F表示为θ的函数,得:

F=

μmg
cosθ+μsinθ

对上述表达式作变换,又可表示为

F=

μmg
cos(θ-α)
1+μ2

其中tanα=μ.

由此可知,当θ=arctanμ时,拉力F可取得最小值

Fmin=

μmg
1+μ2

答:所施加拉力的最小值为

μmg
1+μ2

阅读理解

阅读理解。

     When he took office, George W. Bush, son of former president George Herbert Walker Bush, became the

first son to follow his father into the White House since John Quiney Adams followed John Adams in the early

19th century.

     Bush was born on July 6, 1946, in New Haven, Connecticut, the first child of George Herbert Walker Bush

and Barbara Pierce Bush. Although George Herbert Walker Bush began his career in the oil industry, he finally

served as a congressman (国会议员), and vice president and president of the United States.

     At the age of two, Bush moved with his parents from Connecticut to Odessa, Texas, where his father took

up the oil business. After a year in Texas, the family moved to California for business reasons. A year later, the

family returned to Texas and settled in Midland, where Bush lived from 1950 to 1959.

     In 1959, again for business reasons, the family moved to Houston, Texas. In 1961 Bush left Texas and

went to Andover, Massachusetts, to attend Phillips Academy, a boarding school (寄宿学校) that his father had

also attended.

     At Phillips, Bush played basketball, baseball, and football. He was best known for being head cheerleader.

In 1964 he enrolled at Yale University in Connecticut; his father and grandfather had also attended Yale. At

Yale, Bush was considered an average student, but he was popular with his classmates.

     Bush graduated from Yale with a bachelor's degree in history in 1968. Then he joined the Air National

Guard and remained in the Guard until 1973. After earning his MBA from Harvard in 1975, Bush returned to

Midland. Like his father, he first entered the oil industry as a"landsman (新手)". However, Bush's oil companies never enjoyed great success. He took more interest in politics. He helped his father to become president and in

1994 he himself was elected governor of Texas.

     In the summer of 1999, Bush began to run for the president of the USA and on January 20, 2001, George

W. Bush, hand raised, took the oath(宣誓)of office to become the 43rd president of the US.

1. What does the writer intend to tell us in the first paragraph?

A. George W. Bush is the first son in American history to follow his father into the White House.

B. George W. Bush is the first son of former president George Herbert Walker Bush.

C. John Quincy Adams and his father were both former American presidents.

D. George W. Bush is the second one in American history to follow his father into White House.

2. We may learn from the text that young Bush __________.

A. got on very well at the universities

B. was very good at basketball, baseball and football

C. did everything as his father had done

D. was a very successful politician like his father

3. Which of the following is NOT true about George W. Bush?

A. Young Bush lived with his family in Texas from 1948 to 1961.

B. He once studied at a university that his father and grandfather had also attended.

C. He once ruled over an American state before he entered the White House.

D. He once served at the Air National Guard for about five years.

判断题