Question

如圖所示，將邊長為a、質(zhì)量為m、電阻為R的正方形導線框豎直向上拋出，穿過寬度為b、磁感應強度為B的勻強磁場，磁場的方向垂直紙面向里．線框向上離開磁場時的速度剛好是進人磁場時速度的一半，線框離開磁場后繼續(xù)上升一段高度，然后落下并勻速進人磁場．整個運動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．求：

（1）線框在下落階段勻速進人磁場時的速度V₂； 
(2）線框在上升階段剛離開磁場時的速度V₁； 
（3）線框在上升階段通過磁場過程中產(chǎn)生的焦耳熱Q．

Answer 1

（1）線框在下落階段勻速進入磁場瞬間
mg = f +                                                                        ①
解得     v₂ =                                                                          ②
（2）線框從離開磁場至上升到最高點的過程
(mg + f ) h = mv₁ ²                                                              ③
線框從最高點回落至磁場瞬間
(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