中学物理仿真模拟实验

中央电大毕业设计毕业论文专业:计算机基础与应用年级：2004年春计算机本科学号：041060219姓名：倪亚非指导老师：李征2005年12月28日物理仿真模拟实验------碰撞实验倪亚非（中央电大计算机基础与应用2004年春本科）指导老师：李征【摘要】 随着计算机的发展，计算机的应用深入到各个领域，使用Visualbasic 6.0制作中学物理仿真模拟实验就是其中的一个领域。

【关键词】 仿真模拟；碰撞；Visual Basic 6.0;窗体;【引言】 随着计算机的发展，计算机的应用深入到各个领域，使用计算机做物理仿真模拟实验即节省资源，又便捷。

实验原理中学物理中，碰撞实验作为验证动量守衡的一种精确测量手段，而倍受推崇。

碰撞实验使用气垫导轨，数字毫秒计，游标卡尺，滑块等作为实验用具。

当两滑块在水平的导轨上沿直线作对心碰撞时，若略去滑块运动过程中受到的粘滞阻力和空气阻力，则两滑块在水平方向除受到碰撞时彼此相互作用的内力外，不受其它外力作用。

故根据动量守衡定律，两滑块的总动量在碰撞前后保持不变。

设如图1所示，滑块1和滑块2的质量分别为M1和M 2，碰撞前二滑块的速度分别为V10和V 20，碰撞后的速度分别为V1和V 2，则根据动量守衡定律有M1V10+M2V20=M1V1+M2V2若写成标量的形式，即M1V10+M2V20=M1V1+M2V2式中各速度均为代数值，各V 值的正负号决定于速度的方向与所选取的坐标轴方向是否一致，这一点要特别注意。

牛顿曾提出“弹性恢复系数”概念。

其定义为碰撞后的相对速度与碰撞前的相对速度的比值。

一般称为恢复系数，用e 表示，即：e=vv v v 201012--当e=1时为完全弹性碰撞，e=0时为完全非弹性碰撞，一般0<e<1为非完全弹性碰撞。

气轨滑块上的碰撞弹簧是钢制的，e 值在0.95-0.98，它虽然接近1，但是其差异也是明显的，因此在气轨上不能实现完全弹性碰撞(1). 非完全弹性碰撞 取大小二滑块（M1>M2），将滑块2置于A ，B 光电门之间，使V20=0 推动滑块1以速度V10去撞滑块2，碰撞后速度分别为V1，V2，则M1V10=M1V1+M2V2碰撞前后动能的变化为：v m v m v m E K 210122221121)(21-+=∆实际实验时，由于滑块运动受到一定的阻力，又由于导轨具有少许的弯曲，在A 门测出的速度V 1A ，在B 门测出的速度V 2B 和V 1B ，都和碰撞前后瞬间相应的速度有些差异，减少差异的方法之一，是尽可能缩短碰撞点到测速光电门间的距离。

办法之二是进行速度修正，因为滑块在“调平”气轨上运动时仍然有加速度。

可参照图2测出3个加速度，对相应的速度进行修正 图中滑块位置为碰撞前瞬间的位置，CD 为此时二滑块挡光片中点的位置，AB 为实验时光电门的正常位置。

1。

AC 间距离为S10，将B 门移至C ，测出滑块1在AC 间的加速度a10。

则V10=s a vA1010212+ (V 1A 是在Ａ门的速度)2。

CB 间距离为S1，将光电门置于C ，B 处，测出滑块1在CB 间的加速度a1，则Ｖ1=s a vB11212- (V 1Ｂ是在B 门的速度)3。

DB 间距离为S2，将光电门置DB 时，测出滑块2在DB 间的加速度则：V2=s a vB22222- (V 2B 是在B 门的速度)（2）。

完全非弹性碰撞 此时e=0，将滑块2置于光电门AB 间，而且V20=0，滑块1以速度V10撞向滑块2，碰撞后二滑块粘在一起以同一速度V2运动。

碰撞前后的动量关系为M1V10=(M1+M2)V2动能变化为v m v m m E K 2101222121)(21-+=∆核心算法在实验中，滑块的质量和挡片的长度是可以自行设置的，为了和实际相符，滑块１的速度也是可以设置的，即Ｖ10或V1A是可以设置的。

也就是说在实验开始时Ｍ１，Ｍ２，Ｖ１Ａ是以知的。

V1Ａ使用Scrollbar控件来控制，V1A=Scroll1.value. 那么，如何描述Ｖ1B（Ｖ1），Ｖ2B(V2)？由实验原理可知:1.当Ｍ１＝Ｍ２时，即：M1V1A= M2V2B V2B=V1A2.当Ｍ１≠Ｍ２时，有：M1V10=M1V1+M2V2 （其中Ｖ1A,M1,M2已知）设Ｍ１／Ｍ２＝X V2B/V1A=Y由最小二乘法求出：Ｙ＝a+bX 中a,b的值即当Ｍ1,M2,V1A给定后，就可求出V2B , V1B,V2B=V1A(a+bM1/M2)将上式代入碰撞方程就可求出 V1B=V1A(1-b-aM2/M1)也就是说知道了a,b后，就可知道V1B,V2B122B1A有最小二乘法可知：拟合直线Y=a+bX 的a,b 可由以下公式求出 a=ΣYi/n – b ΣXi/n b=)(22x x yx y x i n n iiiii∑-∑∑-∑由以上公式和数据可求出：a=0.517202515 b=0.437473235即：Y=0.517202515+0.437473235X到次，由实验以及最小二乘法求出了a,b 。

在实验开始时，M1,M2,V1A 已知，那么从以上公式就可以很容易得到其他的量。

代码Form1:（进入窗体）Private Sub Command1_Click()Unload MeForm2.ShowEnd SubPrivate Sub Form_Load()Form1.Caption = ":::::::::::::::::::::::欢迎使用中学物理仿真模拟实验::::::::::::::::::::::::"Timer1.Interval = 500End SubPrivate Sub Timer1_Timer() ‘运动字体由Timer1触发s = Form1.Captionb = Len(s)Form1.Caption = Right(s, b - 1) + Left(s, 1)End Sub此窗体中加了段会来回运动的字体，在标题栏里。

Form2: (主界面)Option ExplicitPublic flage As BooleanPublic direction1 As Boolean, direction2 As BooleanPublic v As Integer, dd As BooleanPrivate Sub Command1_Click()Dim i As Integer, j As Integer, t As IntegerIf Form8.Text1.Text = "" Or Form8.Text2.Text = "" Then ‘判断滑块质量输入数据t = MsgBox("请先设置滑块1的属性!", 16, "操作步骤错误") 的正确性BeepGoTo hui:End IfIf Form9.Text1.Text = "" Or Form9.Text2.Text = "" Thent = MsgBox("请先设置滑块2的属性!", 16, "操作步骤错误")BeepGoTo hui:End IfTimer1.Interval = 50 ‘设置触发时间间隔hui:End SubPrivate Sub Command2_Click() ‘实验器具位置初始化Image9.Visible = TrueImage6.Left = 960Image9.Left = 4800Timer1.Interval = 0Form13.Text1.Text = ""Form13.Text2.Text = ""Form13.Text3.Text = ""End SubPrivate Sub Command3_Click() ‘使用Slider控件来设置V1A Slider1.Visible = TrueCommand3.Visible = FalseSlider1.Left = 8520Slider1.Top = 960End SubPrivate Sub data_Click() ‘数据处理窗口显示Form5.ShowEnd SubPrivate Sub exit_Click() ‘退出实验EndEnd SubPrivate Sub Label2_Click() ‘滑块属性1设置窗口显示Form8.ShowEnd SubPrivate Sub Label3_Click() ‘滑块属性2设置窗口显示Form9.ShowEnd SubPrivate Sub Image2_Click() ‘光电门位置调整Form2.Image9.Visible = FalseIf direction1 = False ThenImage2.Left = Image2.Left + 2000direction1 = TrueElseImage2.Left = Image2.Left - 2000direction1 = FalseEnd IfEnd SubPrivate Sub Image3_Click() ‘光电门位置调整If direction2 = False ThenImage3.Left = Image3.Left - 2000direction2 = TrueElseImage3.Left = Image3.Left + 2000direction2 = FalseEnd IfImage9.Visible = FalseEnd SubPrivate Sub Image4_Click() ‘计时器窗口显示Form13.ShowEnd SubPrivate Sub Image6_Click() ‘滑块属性1设置窗口显示Form8.ShowEnd SubPrivate Sub Image7_Click() ‘调平窗口显示Form10.ShowForm12.ShowEnd SubPrivate Sub Image8_Click() ‘水平窗口显示Form12.ShowEnd SubPrivate Sub Image9_Click() ‘滑块属性2设置窗口显示Form9.ShowEnd SubPrivate Sub mudi_Click() ‘实验目的窗口显示Form3.ShowEnd SubPrivate Sub step_Click() ‘实验步骤窗口显示Form6.ShowEnd SubPrivate Sub form2_load()flage = FalseEnd SubPrivate Sub Timer1_Timer()v = Slider1.ValueDim vv As Singlevv = vIf flage = False Then ‘判断是完全非弹性碰撞还是非完全弹性碰撞If Val(Form8.Text1.Text) = Val(Form9.Text1.Text) Then ‘M1=M2时If Image6.Left < 3600 + (10 - Val(Form8.Text2.Text)) * 120 ThenImage6.Left = Image6.Left + vEnd IfIf Image9.Left < 7560 + (10 - Val(Form9.Text2.Text)) * 120 And Image6.Left > 3599 + (10 - Val(Form8.Text2.Text)) * 120 ThenImage9.Left = Image9.Left + vEnd IfIf Image6.Left > 3240 And Form13.Option1.Value = True ThenForm13.Text1.Text = Val(Form8.Text2.Text) / vvEnd IfIf Image9.Left > 6120 And Form13.Option1.Value = True ThenForm13.Text3.Text = Val(Form9.Text2.Text) / vvEnd IfIf Image6.Left > 3240 And Form13.Option2.Value = True ThenForm13.Text1.Text = vvEnd IfIf Image9.Left > 6120 And Form13.Option2.Value = True ThenForm13.Text3.Text = vvEnd IfElseIf Val(Form8.Text1.Text) < Val(Form9.Text1.Text) Then ‘M1<M2时If Image6.Left < 3600 + (10 - Val(Form8.Text2.Text)) * 120 And Image9.Left < 4801 ThenImage6.Left = Image6.Left + vvdd = TrueEnd IfIf Image6.Left > 3540 + (10 - Val(Form8.Text2.Text)) * 120 Thendd = FalseEnd IfIf Image6.Left > 960 And Image9.Left > 4801 ThenImage6.Left = Image6.Left + vv * (1 - 0.437473235 - 0.517202515 * Val(Form9.Text1.Text) / Val(Form8.Text1.Text))End IfIf Image9.Left < 7560 + (10 - Val(Form9.Text2.Text)) * 120 And dd = False Then Image9.Left = Image9.Left + vv * (0.517202515 + 0.437473235 * Val(Form8.Text1.Text) / Val(Form9.Text1.Text))End IfIf Image6.Left < 3240 And Form13.Option1.Value = True ThenForm13.Text1.Text = Val(Form8.Text2.Text) / vvEnd IfIf Image9.Left > 6120 And Form13.Option1.Value = True ThenForm13.Text3.Text = Val(Form9.Text2.Text) / vv * (0.517202515 + 0.437473235 * Val(Form8.Text1.Text) / Val(Form9.Text1.Text))Form13.Text2.Text = Val(Form8.Text2.Text) / (vv * (1 - 0.437473235 - 0.517202515 * Val(Form9.Text1.Text) / Val(Form8.Text1.Text)))End IfIf Image6.Left < 3240 And Form13.Option2.Value = True ThenForm13.Text1.Text = vvEnd IfIf Image9.Left > 6120 And Form13.Option2.Value = True ThenForm13.Text3.Text = vv * (0.517202515 + 0.437473235 * Val(Form8.Text1.Text) / Val(Form9.Text1.Text))Form13.Text2.Text = vv * (1 - 0.437473235 - 0.517202515 * Val(Form9.Text1.Text) / Val(Form8.Text1.Text))End IfElse ‘M1>M2时If Image6.Left < 3600 + (10 - Val(Form8.Text2.Text)) * 120 ThenImage6.Left = Image6.Left + vEnd IfIf Image6.Left < 6200 + (10 - Val(Form8.Text2.Text)) * 120 + (10 - Val(Form9.Text2.Text)) * 120 ThenImage6.Left = Image6.Left + vv * (1 - 0.437473235 - 0.517202515 * Val(Form9.Text1.Text) / Val(Form8.Text1.Text))End IfIf Image9.Left < 7560 + (10 - Val(Form9.Text2.Text)) * 120 And Image6.Left > 3600 + (10 - Val(Form8.Text2.Text)) * 120 ThenImage9.Left = Image9.Left + vv * (0.517202515 + 0.437473235 * Val(Form8.Text1.Text) / Val(Form9.Text1.Text))End IfEnd IfIf Image6.Left > 3240 And Form13.Option1.Value = True ThenForm13.Text1.Text = Val(Form8.Text2.Text) / vvEnd IfIf Image6.Left > 6120 And Form13.Option1.Value = True ThenForm13.Text2.Text = Val(Form8.Text2.Text) / (vv * (1 - 0.437473235 - 0.517202515 * Val(Form9.Text1.Text) / Val(Form8.Text1.Text)))End IfIf Image9.Left > 6120 And Form13.Option1.Value = True ThenForm13.Text3.Text = Val(Form9.Text2.Text) / (vv * (0.517202515 + 0.437473235* Val(Form8.Text1.Text) / Val(Form9.Text1.Text)))End IfIf Image6.Left > 3240 And Form13.Option2.Value = True ThenForm13.Text1.Text = vvEnd IfIf Image6.Left > 6120 And Form13.Option2.Value = True ThenForm13.Text2.Text = vv * (1 - 0.437473235 - 0.517202515 * Val(Form9.Text1.Text) / Val(Form8.Text1.Text))End IfIf Image9.Left > 6120 And Form13.Option2.Value = True ThenForm13.Text3.Text = vv * (0.517202515 + 0.437473235 * Val(Form8.Text1.Text) / Val(Form9.Text1.Text))End IfElse ‘完全非弹性碰撞If Image6.Left < 3600 + (10 - Val(Form8.Text2.Text)) * 120 ThenImage6.Left = Image6.Left + vvEnd IfIf Image6.Left < 6350 + (10 - Val(Form8.Text2.Text)) * 120 + (10 - Val(Form9.Text2.Text)) * 120 ThenImage6.Left = Image6.Left + vv * Val(Form8.Text1.Text) / (Val(Form8.Text1.Text) + Val(Form9.Text1.Text))End IfIf Image9.Left < 7560 + (10 - Val(Form9.Text2.Text)) * 120 And Image6.Left > 3600 + (10 - Val(Form8.Text2.Text)) * 120 ThenImage9.Left = Image9.Left + vv * Val(Form8.Text1.Text) / (Val(Form8.Text1.Text) + Val(Form9.Text1.Text))End IfIf Image6.Left > 3240 And Form13.Option1.Value = True ThenForm13.Text1.Text = Val(Form8.Text2.Text) / vvEnd IfIf Image9.Left > 6120 And Form13.Option1.Value = True ThenForm13.Text3.Text = Val(Form9.Text2.Text) / (vv * Val(Form8.Text1.Text) / (Val(Form8.Text1.Text) + Val(Form9.Text1.Text)))Form13.Text2.Text = Val(Form8.Text2.Text) / (vv * Val(Form8.Text1.Text) / (Val(Form8.Text1.Text) + Val(Form9.Text1.Text)))End IfIf Image6.Left > 3240 And Form13.Option2.Value = True ThenForm13.Text1.Text = vvEnd IfIf Image9.Left > 6120 And Form13.Option2.Value = True ThenForm13.Text3.Text = vv * Val(Form8.Text1.Text) / (Val(Form8.Text1.Text) + Val(Form9.Text1.Text))Form13.Text2.Text = vv * Val(Form8.Text1.Text) / (Val(Form8.Text1.Text) +Val(Form9.Text1.Text))End IfEnd IfEnd SubPrivate Sub yq_Click() ‘仪器帮助窗口显示Form7.ShowEnd SubPrivate Sub yuanli_Click() ‘实验原理窗口显示Form4.ShowEnd SubForm3:（实验目的）Form4:（实验原理）Form5:（数据处理）Private Sub Command4_Click() ‘调用外部计算器程序Dim cal As Stringcal = Shell("C:\WINDOWS\System32\calc.exe", 1)End SubForm6:（实验步骤）Private Sub Command1_Click()Form2.Image9.Left = 4800Form6.HideForm2.flage = Falsemand1.Enabled = True ‘保证使用者在看了实验步骤以后在开始实验End SubPrivate Sub Command2_Click() ‘开始非完全弹性碰撞Form2.Image9.Left = 4800Form6.HideForm2.flage = Truemand1.Enabled = TrueEnd SubPrivate Sub Command3_Click() ‘开始完全非弹性碰撞Form2.Image9.Left = 7440Form6.HideForm2.flage = FalseEnd SubForm7:（仪器介绍）Form8:(滑块1属性设置)Private Sub Command1_Click()Dim t As IntegerIf Val(Text2.Text) < 11 Then ‘设置滑块1挡片长度Form2.Image6.Width = Val(Text2.Text) * 120Else: Form2.Image6.Width = 1200End IfIf IsNumeric(Text1.Text) And IsNumeric(Text2.Text) Then ‘判断是否输入数字Form8.HideElset = MsgBox("请正确输入数据！", 16, "数据输入错误")End IfEnd SubPrivate Sub Option1_GotFocus() ‘设置相应单位Label3.Caption = "kg"Label5.Caption = "m"End SubPrivate Sub Option2_GotFocus()Label3.Caption = "g"Label5.Caption = "cm"End SubPrivate Sub Text2_Change() ‘数据控制在10以内Dim f As IntegerIf Val(Text2.Text) > 10 Thenf = MsgBox("请输入10以内整数！", 16, "数据输入错误")End IfEnd SubForm9:（滑块2属性设置）（和滑块1的类似）Private Sub Command1_Click()If Val(Text2.Text) < 11 ThenForm2.Image9.Width = Val(Text2.Text) * 120Else: Form2.Image9.Width = 1200End IfIf IsNumeric(Text1.Text) And IsNumeric(Text2.Text) ThenForm9.HideElset = MsgBox("请正确输入数据！", 16, "数据输入错误")End IfEnd SubPrivate Sub Option1_Click()Label3.Caption = "g"Label5.Caption = "cm"End SubPrivate Sub Option2_Click()Label3.Caption = "kg"Label5.Caption = "m"End SubPrivate Sub Text2_Change()Dim f As IntegerIf Val(Text2.Text) > 10 Thenf = MsgBox("请输入10以内整数！", 16, "数据输入错误") End IfEnd SubForm10:（调平旋钮）Private Sub Image1_Click() ‘右粗调If Form12.Image2.Left > 1140 ThenForm12.Image2.Left = Form12.Image2.Left - 20ElseForm12.Image2.Left = Form12.Image2.Left + 20End IfEnd SubPrivate Sub Image2_Click() ‘右微调If Form12.Image2.Left > 1140 ThenForm12.Image2.Left = Form12.Image2.Left - 5ElseForm12.Image2.Left = Form12.Image2.Left + 5End IfEnd SubPrivate Sub Image3_Click() ‘左粗调If Form12.Image2.Left > 1140 ThenForm12.Image2.Left = Form12.Image2.Left + 20ElseForm12.Image2.Left = Form12.Image2.Left - 20End IfEnd SubForm12：（水平）Private Sub Form_Load() ‘随机确定水平位置Form12.Image2.Left = Form12.Image2.Left + Int(1001 * Rnd(1)) - 400 End SubForm13:（计时器窗口）Private Sub form13_load() ‘初始化Text1.Text = ""Text2.Text = ""Text3.Text = ""End SubPrivate Sub Option1_Click() ‘测时间档Label1.Caption = "T1a:"Label2.Caption = "T1b:"Label3.Caption = "T2b:"Label8.Caption = "s"Label9.Caption = "s"Label10.Caption = "s"End SubPrivate Sub Option2_Click() ‘测速度档Label1.Caption = "V1a:"Label2.Caption = "V1b:"Label3.Caption = "V2b:"Label8.Caption = "cm/s"Label9.Caption = "cm/s"Label10.Caption = "cm/s"End SubPrivate Sub Option3_Click() ‘测加速度档Label1.Caption = " a10:"Label2.Caption = " a1:"Label3.Caption = " a2:"Label8.Caption = "cm/s2"Label9.Caption = "cm/s2"Label10.Caption = "cm/s2"If Form12.Image2.Left - 1080 > 0 ThenForm13.Text1.Text = (Form12.Image2.Left - 1080) / 1080Form13.Text2.Text = (Form12.Image2.Left - 1080) / 1080Form13.Text3.Text = (Form12.Image2.Left - 1080) / 1080ElseIf Form12.Image2.Left - 1080 < 0 ThenForm13.Text1.Text = (1080 - Form12.Image2.Left) / 1080Form13.Text2.Text = (1080 - Form12.Image2.Left) / 1080Form13.Text3.Text = (1080 - Form12.Image2.Left) / 1080Else: Form13.Text1.Text = 0Form13.Text2.Text = 0Form13.Text3.Text = 0End IfEnd Sub【参考文献】[ 1 ] 《Visual Basic 程序设计教程》周霭如、官士鸿等编著清华大学出版社[ 2 ] 《Visual Basic6.0应用与提高》尹利民科学出版社【英文】The high school physics imitates to really imitate the experiment Ni Ya-feiTeacher Guide:LiZheng【Abstract】 Along with the development of the calculator ,the application of the calculator goes deep into the each realm ,usage Visual basic 6.0 creation the high school physics imitates a realm that true emulation experiment is among them .Hitting the experiment is a classic experiment that high school physics experiment the inside. Usage VB at compute the on board doing this experiment ,is a convenient path.【key phrase】 Imitate the true emulation; Hit;Visual basic 6.0;Form。