如图甲所示,电阻不计的光滑平行金属导轨相距L=0.5m,上端连接R=0.5Ω的电阻,下端连着电阻不计的金属卡环,导轨与水平面的夹角θ=300,导轨间虚线区域存在方向垂直导轨平面向上的磁场,其上、下边界之间的距离s=1Om,磁感应强度B﹣t图如图乙所示.长为L且质量为m=0.5kg的金属棒ab的电阻不计,垂直导轨放置于距离磁场上边界d=2.5m处,在t=O时刻由静止释放,棒与导轨始终接触良好,滑至导轨底端被环卡住不动.g取10m/s2,求:                                                                                                                        

                                     

(1)棒运动到磁场上边界的时间;                                                                             

(2)棒进人磁场时受到的安培力;                                                                             

(3)在0﹣5s时间内电路中产生的焦耳热.                                                                

                                                                                                                                    


跳水运动是我国体育运动的强项之一,其中高台跳水项目要求运动员从距离水面10m的高台上跳下,在完成空中动作后进入水中.若某运动员起跳瞬间重心离高台台面的高度为1m,斜向上跳离高台瞬间速度的大小为3m/s,跳至最高点时重心离台面的高度为1.3m,入水(手刚触及水面)时重心离水面的高度为1m,如图所示,图中虚线为运动员重心的运动轨迹.已知运动员的质量为50kg,不计空气阻力:                                                          

(1)以水面为零势能面,求运动员在起跳瞬间所具有的重力势能;                             

(2)求从跳离高台瞬间到跳至最高点的过程中,运动员克服重力所做的功;                      

(3)根据机械能守恒定律,求运动员入水(手刚触及水面)时速度的大小.                      

                                                                                           

                                                                                                                          


质量为m边长为l的正方形线框,从有界的匀强磁场上方由静止自由下落,线框电阻为R,匀强磁场的宽度为H(H>l),磁感强度为B,线框下落过程中ab边与磁场界面平行.已知ab边刚进入磁场和刚穿出磁场时都作减速运动,加速度大小均为a=g/3.试求:                                                                                                                

(1)ab边刚进入磁场时,线框的速度;                                                                             

(2)cd边刚进入磁场时,线框的速度;                                                                             

(3)线框经过磁场的过程中产生的热能.                                                                          

                                                                                               

                                                                                                                                      

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