问题 计算题

如图所示,质量m的物体(可视为质点)在竖直轻质弹簧上做简谐运动,当振幅为A时,木块对弹簧压力的最大值为木块重力的1.5倍,求:

(1)木块对弹簧压力的最小值为多少?

(2)欲使木块不脱离弹簧,其振幅不能超过多少?

答案

解:因为木块在竖直方向上做简谐运动,依题意木块在最低点时对弹簧的压力最大,在最高点对弹簧的压力最小

(1)在最低点根据牛顿第二定律有FN-mg=ma,代入数据解得a=0.5 g

由最高点和最低点相对平衡位置对称,加速度大小等值反向,所以最高点的加速度大小为a′=0.5 g

在最高点根据牛顿第二定律有mg-FN′=ma′

故FN′=mg-ma′=0.5 mg

(2)要使木块不脱离弹簧,设其振幅不能超过A′,此时木块振到最高点恰在弹簧原长处,此时的最大加速度为g,由a=-x知:

当振幅为A时,在最低点有0.5 g=-A

当振幅为A′时,在最高点有g=-A′

由此可得A′=2A

阅读理解

阅读理解

     Ask savvy investors(投资者) how they learned their first lessons about money, and they'll probably tell you lessons their parents taught them.

     The money values we learn as children stay with us the rest of our lives. If you are a parent, teaching

your children the value of saving and investing will benefit them the rest of their lives. Here's what you can

do:

     Help your child begin to save. Open savings accounts for your children, and teach them how the bank

adds interest to their savings that makes their money grow. Encourage your children to save a little from

every bit of money they receive, such as allowances, birthday gifts, etc. You may even want to set up a

matching program, contributing fifty cents for each dollar your child saves.

     Teach your child about stocks(股票).  A child in elementary school can start learning  about  how

businesses work. Once your child understands the basics, ask him or her to think about some of  the

businesses that might be good stock investments. Then use Morningstar Mutual Fund Guide(available

at your library) to find a quality mutual fund that holds some of these companies, or a mutual fund that

caters to children such  as  the Stein  Roe  Young  Investor Fund. Many funds  accept regular monthly

investments as low as $50 a month, so these funds can be a good way to teach children about the stock

market while saving for their college education.

     Encourage early IRA(个人退休金账户)saving. The new Roth IRA is a great way for children who

are working in summers or after school to begin saving for their future. Imagine how much money you'd

have today if you had saved $3,000 a year since you were a teenager!

     Let your kids handle their own money. We all learn by doing, so letting your kids manage a segment

of  their budget(预算)will let them earn valuable financial lessons.They may make mistakes, but they will

be small mistakes that may help them avoid larger mistakes as adults.

1.Which would be the best title for this passage?

A.Why to Teach Your Children to Save

B.How to Teach Your Children to Save

C.Tips for Saving for Children

D.Start Good Saving Habits Early

2.A matching program means ________.

A.that you should set a good example to your children

B.that you should provide enough money for children so that they can save some

C.that you encourage your children to compete with each other in saving

D.that you encourage your children by giving some extra money for them to save

3.According to the author, you should teach your children about investment when he/she is ________.

A.in the kindergarten  

B.in primary school

C.in middle school  

D.in college

单项选择题