Question

如圖所示，將邊長(zhǎng)為a、質(zhì)量為m、電阻為R的正方形導(dǎo)線框豎直向上拋出，穿過寬度為b、磁感應(yīng)強(qiáng)度為B的勻強(qiáng)磁場(chǎng)，磁場(chǎng)的方向垂直紙面向里．線框向上離開磁場(chǎng)時(shí)的速度剛好是進(jìn)人磁場(chǎng)時(shí)速度的一半，線框離開磁場(chǎng)后繼續(xù)上升一段高度，然后落下并勻速進(jìn)人磁場(chǎng)．整個(gè)運(yùn)動(dòng)過程中始終存在著大小恒定的空氣阻力f且線框不發(fā)生轉(zhuǎn)動(dòng)．求：

（1）線框在下落階段勻速進(jìn)人磁場(chǎng)時(shí)的速度V₂； 

(2）線框在上升階段剛離開磁場(chǎng)時(shí)的速度V₁； 

（3）線框在上升階段通過磁場(chǎng)過程中產(chǎn)生的焦耳熱Q．

 

Answer 1

（1）線框在下落階段勻速進(jìn)入磁場(chǎng)瞬間

             mg= f +                                                                         ①

解得      v₂=                                                                           ②

       （2）線框從離開磁場(chǎng)至上升到最高點(diǎn)的過程

               (mg+ f ) h = mv₁ ²                                                               ③

線框從最高點(diǎn)回落至磁場(chǎng)瞬間

        (mg - f ) h = mv₂ ²                                                               ④

③、④ 式聯(lián)立解得

        v₁ =                                                                     ⑤

            =                                                            ⑥

（3）線框在向上通過通過過程中

             mv₀² - mv₁² = Q +（mg + f）(a + b)                                      ⑦

             v₀= 2 v₁                                                                                    

             Q= m [ (mg)² – f ²] -（mg + f）(a + b)                          ⑧

解析:略