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动力 动力臂 阻力 阻力臂
或
F₁ L₁ F₂ L₂
其中#xff0c;F₁为动力#xff0c;L₁为动力臂#xff1b;F₂为阻力#xff0c;L₂为阻力臂。
核心含义…python中学物理实验模拟杠杆平衡条件 杠杆原理平衡条件
动力 × 动力臂 阻力 × 阻力臂
或
F₁ × L₁ F₂ × L₂
其中F₁为动力L₁为动力臂F₂为阻力L₂为阻力臂。
核心含义
省力 如果 L₁ L₂动力臂大于阻力臂那么 F₁ F₂。这意味着我们可以用较小的动力克服较大的阻力但代价是动力作用点移动的距离会比阻力作用点移动的距离更大省力费距离。例如撬棍撬石头、开瓶器开瓶盖。费力 如果 L₁ L₂动力臂小于阻力臂那么 F₁ F₂。这意味着我们需要用较大的动力克服较小的阻力但好处是动力作用点移动的距离比阻力作用点移动的距离更小费力省距离。例如镊子夹东西、钓鱼竿钓鱼。等臂 如果 L₁ L₂动力臂等于阻力臂那么 F₁ F₂。这时杠杆既不省力也不费力但可以改变力的方向或方便操作。例如天平、跷跷板当两边重量相等时。
杠杆原理的本质
杠杆原理是能量守恒定律在简单机械中的具体体现。虽然它可以改变力的大小放大或缩小但遵循“功的原理”动力 × 动力作用点移动距离 阻力 × 阻力作用点移动距离。省力必然费距离费力必然省距离不能省功。 根据支点位置杠杆通常分为三类
第一类杠杆支点在中间
例子 跷跷板、剪刀、天平、撬棍、钳子夹持端、手推车的抬起动作支点是轮轴。
特点 可以省力当 L₁ L₂可以费力当 L₁ L₂也可以等臂当 L₁ L₂还可以改变用力方向。
第二类杠杆阻力点在中间
例子 独轮手推车阻力是货物重力在中间、核桃夹夹核桃的部位在中间、开瓶器瓶盖在中间、船桨水对桨的阻力在中间。 特点 总是省力因为 L₁ 总是大于 L₂但费距离。动力方向与阻力方向通常相同向下。
第三类杠杆动力点在中间
例子 镊子、筷子、钓鱼竿手持端在中间、人的前臂肘关节是支点肱二头肌发力点在中间手拿东西是阻力点、铲子手握的地方在中间。
特点 总是费力因为 L₁ 总是小于 L₂但省距离动力作用点移动一小段距离阻力作用点会移动较大距离。可以放大移动的速度或距离常用于需要精细操作或速度放大的场合。
运行效果截图 源码如下
import tkinter as tk
from tkinter import ttk
import mathclass LeverSimulator:def __init__(self):self.root tk.Tk()self.root.title(杠杆原理模拟器 - 三类杠杆演示)self.root.geometry(1200x960)self.root.configure(bglightblue)# 杠杆参数self.canvas_width 1100self.canvas_height 400self.fulcrum_y 200 # 支点Y坐标# 杠杆类型和参数self.lever_type tk.StringVar(valuefirst) # first, second, third# 力和力臂参数self.power_force tk.StringVar(value20) # 动力self.resistance_force tk.StringVar(value40) # 阻力self.power_arm tk.StringVar(value150) # 动力臂self.resistance_arm tk.StringVar(value75) # 阻力臂# 动画控制self.is_animating Falseself.lever_angle 0self.animation_speed 0.05# 预设示例self.examples {first: [(剪刀, {power: 15, resistance: 30, power_arm: 120, resistance_arm: 60}),(跷跷板, {power: 25, resistance: 50, power_arm: 200, resistance_arm: 100}),(天平, {power: 10, resistance: 10, power_arm: 150, resistance_arm: 150})],second: [(开瓶器, {power: 20, resistance: 60, power_arm: 150, resistance_arm: 50}),(胡桃钳, {power: 25, resistance: 100, power_arm: 180, resistance_arm: 45}),(手推车, {power: 30, resistance: 120, power_arm: 160, resistance_arm: 40})],third: [(镊子, {power: 40, resistance: 10, power_arm: 30, resistance_arm: 120}),(筷子, {power: 30, resistance: 12, power_arm: 50, resistance_arm: 150}),(钓鱼竿, {power: 50, resistance: 15, power_arm: 40, resistance_arm: 160})]}self.setup_ui()self.update_lever()def setup_ui(self):# 主标题title_label tk.Label(self.root, text杠杆原理模拟器 - 三类杠杆演示, font(Arial, 18, bold), bglightblue, fgdarkblue)title_label.pack(pady10)# 控制面板control_frame tk.LabelFrame(self.root, text控制参数, font(Arial, 12), bglightblue)control_frame.pack(pady5, padx10, fillx)# 杠杆类型选择type_frame tk.Frame(control_frame, bglightblue)type_frame.pack(pady10)tk.Label(type_frame, text杠杆类型:, bglightblue, font(Arial, 12, bold)).pack(sideleft, padx10)type_radio1 tk.Radiobutton(type_frame, text第一类杠杆\n(支点在中间), variableself.lever_type, valuefirst,bglightblue, font(Arial, 10),commandself.change_lever_type, justifycenter)type_radio1.pack(sideleft, padx15)type_radio2 tk.Radiobutton(type_frame, text第二类杠杆\n(阻力点在中间), variableself.lever_type, valuesecond,bglightblue, font(Arial, 10),commandself.change_lever_type, justifycenter)type_radio2.pack(sideleft, padx15)type_radio3 tk.Radiobutton(type_frame, text第三类杠杆\n(动力点在中间), variableself.lever_type, valuethird,bglightblue, font(Arial, 10),commandself.change_lever_type, justifycenter)type_radio3.pack(sideleft, padx15)# 参数设置和示例选择param_main_frame tk.Frame(control_frame, bglightblue)param_main_frame.pack(pady10)# 参数输入区域param_frame tk.LabelFrame(param_main_frame, text参数设置, font(Arial, 11), bglightblue)param_frame.pack(sideleft, padx20)# 动力tk.Label(param_frame, text动力 F1 (N):, bglightblue, font(Arial, 10)).grid(row0, column0, stickyw, padx5, pady5)power_entry tk.Entry(param_frame, textvariableself.power_force, width10)power_entry.grid(row0, column1, padx5, pady5)power_entry.bind(KeyRelease, lambda e: self.update_lever())# 动力臂tk.Label(param_frame, text动力臂 L1 (cm):, bglightblue, font(Arial, 10)).grid(row1, column0, stickyw, padx5, pady5)power_arm_entry tk.Entry(param_frame, textvariableself.power_arm, width10)power_arm_entry.grid(row1, column1, padx5, pady5)power_arm_entry.bind(KeyRelease, lambda e: self.update_lever())# 阻力tk.Label(param_frame, text阻力 F2 (N):, bglightblue, font(Arial, 10)).grid(row2, column0, stickyw, padx5, pady5)resistance_entry tk.Entry(param_frame, textvariableself.resistance_force, width10)resistance_entry.grid(row2, column1, padx5, pady5)resistance_entry.bind(KeyRelease, lambda e: self.update_lever())# 阻力臂tk.Label(param_frame, text阻力臂 L2 (cm):, bglightblue, font(Arial, 10)).grid(row3, column0, stickyw, padx5, pady5)resistance_arm_entry tk.Entry(param_frame, textvariableself.resistance_arm, width10)resistance_arm_entry.grid(row3, column1, padx5, pady5)resistance_arm_entry.bind(KeyRelease, lambda e: self.update_lever())# 示例选择区域example_frame tk.LabelFrame(param_main_frame, text典型示例, font(Arial, 11), bglightblue)example_frame.pack(sideleft, padx20)self.example_listbox tk.Listbox(example_frame, height6, width20, font(Arial, 10))self.example_listbox.pack(padx5, pady5)self.example_listbox.bind(ListboxSelect, self.load_example)# 控制按钮button_frame tk.Frame(control_frame, bglightblue)button_frame.pack(pady10)tk.Button(button_frame, text开始动画, commandself.start_animation,font(Arial, 11), bglightgreen, width12).pack(sideleft, padx8)tk.Button(button_frame, text停止动画, commandself.stop_animation,font(Arial, 11), bglightcoral, width12).pack(sideleft, padx8)tk.Button(button_frame, text重置参数, commandself.reset_lever,font(Arial, 11), bglightyellow, width12).pack(sideleft, padx8)# 画布self.canvas tk.Canvas(self.root, widthself.canvas_width, heightself.canvas_height, bgwhite, reliefsunken, bd2)self.canvas.pack(pady10)# 信息显示区域info_frame tk.LabelFrame(self.root, text计算结果与分析, font(Arial, 12), bglightblue)info_frame.pack(pady5, padx10, fillx)# 分两列显示信息info_left_frame tk.Frame(info_frame, bglightblue)info_left_frame.pack(sideleft, fillboth, expandTrue)info_right_frame tk.Frame(info_frame, bglightblue)info_right_frame.pack(sideright, fillboth, expandTrue)self.moment_label tk.Label(info_left_frame, text, bglightblue, font(Arial, 11), fgdarkgreen)self.moment_label.pack(anchorw, padx10, pady2)self.balance_label tk.Label(info_left_frame, text, bglightblue, font(Arial, 12, bold))self.balance_label.pack(anchorw, padx10, pady2)self.advantage_label tk.Label(info_right_frame, text, bglightblue, font(Arial, 11), fgdarkblue)self.advantage_label.pack(anchorw, padx10, pady2)self.type_description tk.Label(info_right_frame, text, bglightblue, font(Arial, 10), fgpurple)self.type_description.pack(anchorw, padx10, pady2)def change_lever_type(self):改变杠杆类型self.update_example_list()self.reset_to_default()self.update_lever()def update_example_list(self):更新示例列表self.example_listbox.delete(0, tk.END)lever_type self.lever_type.get()for name, params in self.examples[lever_type]:self.example_listbox.insert(tk.END, name)def load_example(self, event):加载选中的示例selection self.example_listbox.curselection()if selection:lever_type self.lever_type.get()example_name, params self.examples[lever_type][selection[0]]self.power_force.set(params[power])self.resistance_force.set(params[resistance])self.power_arm.set(params[power_arm])self.resistance_arm.set(params[resistance_arm])self.update_lever()def reset_to_default(self):重置为默认参数defaults {first: {power: 20, resistance: 40, power_arm: 150, resistance_arm: 75},second: {power: 20, resistance: 60, power_arm: 150, resistance_arm: 50},third: {power: 40, resistance: 10, power_arm: 30, resistance_arm: 120}}lever_type self.lever_type.get()params defaults[lever_type]self.power_force.set(params[power])self.resistance_force.set(params[resistance])self.power_arm.set(params[power_arm])self.resistance_arm.set(params[resistance_arm])def calculate_positions(self):计算各点位置try:power_arm float(self.power_arm.get())resistance_arm float(self.resistance_arm.get())lever_type self.lever_type.get()center_x self.canvas_width // 2if lever_type first:# 第一类杠杆支点在中间fulcrum_x center_xpower_x fulcrum_x - power_armresistance_x fulcrum_x resistance_armelif lever_type second:# 第二类杠杆阻力点在中间power_x center_x - (power_arm - resistance_arm) // 2resistance_x power_x resistance_armfulcrum_x power_x power_armelse: # third# 第三类杠杆动力点在中间fulcrum_x center_x - (power_arm resistance_arm) // 2power_x fulcrum_x power_armresistance_x fulcrum_x power_arm resistance_armreturn fulcrum_x, power_x, resistance_xexcept ValueError:return self.canvas_width//2, self.canvas_width//2-100, self.canvas_width//2100def calculate_lever_angle(self):计算杠杆倾斜角度try:power_force float(self.power_force.get())resistance_force float(self.resistance_force.get())power_arm float(self.power_arm.get())resistance_arm float(self.resistance_arm.get())# 计算力矩power_moment power_force * power_armresistance_moment resistance_force * resistance_arm# 计算力矩差moment_diff power_moment - resistance_momentmax_angle math.pi / 8 # 最大倾斜角度22.5度if abs(moment_diff) 0.1:return 0else:# 根据力矩差计算角度max_moment max(power_moment, resistance_moment, 1)angle (moment_diff / max_moment) * max_anglereturn max(-max_angle, min(max_angle, angle))except ValueError:return 0def draw_lever(self):绘制杠杆系统self.canvas.delete(all)# 绘制背景网格self.draw_grid()# 计算各点位置fulcrum_x, power_x, resistance_x self.calculate_positions()# 计算倾斜后的Y坐标lever_length max(abs(power_x - fulcrum_x), abs(resistance_x - fulcrum_x)) * 2# 动力点位置power_angle math.atan2(0, power_x - fulcrum_x) self.lever_anglepower_y self.fulcrum_y - (power_x - fulcrum_x) * math.tan(self.lever_angle)# 阻力点位置resistance_angle math.atan2(0, resistance_x - fulcrum_x) self.lever_angleresistance_y self.fulcrum_y - (resistance_x - fulcrum_x) * math.tan(self.lever_angle)# 杠杆两端点left_most min(power_x, resistance_x, fulcrum_x) - 50right_most max(power_x, resistance_x, fulcrum_x) 50left_y self.fulcrum_y - (left_most - fulcrum_x) * math.tan(self.lever_angle)right_y self.fulcrum_y - (right_most - fulcrum_x) * math.tan(self.lever_angle)# 绘制杠杆self.canvas.create_line(left_most, left_y, right_most, right_y, width8, fillbrown, capstyleround)# 绘制支点self.draw_fulcrum(fulcrum_x, self.fulcrum_y)# 绘制力self.draw_forces(power_x, power_y, resistance_x, resistance_y)# 绘制力臂标注self.draw_arms(fulcrum_x, power_x, resistance_x)# 绘制标示点self.canvas.create_oval(power_x-6, power_y-6, power_x6, power_y6, fillblue, outlinedarkblue, width2)self.canvas.create_oval(resistance_x-6, resistance_y-6, resistance_x6, resistance_y6, fillred, outlinedarkred, width2)# 添加类型说明self.draw_type_explanation(fulcrum_x, power_x, resistance_x)def draw_grid(self):绘制背景网格for i in range(0, self.canvas_width, 50):self.canvas.create_line(i, 0, i, self.canvas_height, filllightgray, width1)for i in range(0, self.canvas_height, 50):self.canvas.create_line(0, i, self.canvas_width, i, filllightgray, width1)def draw_fulcrum(self, fulcrum_x, fulcrum_y):绘制支点# 支点三角形self.canvas.create_polygon(fulcrum_x-20, fulcrum_y15,fulcrum_x20, fulcrum_y15,fulcrum_x, fulcrum_y-5,fillgray, outlineblack, width2)# 支点标记self.canvas.create_text(fulcrum_x, fulcrum_y35, text支点, fillblack, font(Arial, 10, bold))def draw_forces(self, power_x, power_y, resistance_x, resistance_y):绘制力箭头try:power_force float(self.power_force.get())resistance_force float(self.resistance_force.get())arrow_scale 2.5# 动力箭头power_arrow_length power_force * arrow_scaleif self.lever_type.get() second:# 第二类杠杆动力向上self.canvas.create_line(power_x, power_y, power_x, power_y - power_arrow_length,width4, fillblue, arrowtk.LAST, arrowshape(10,12,4))text_y power_y - power_arrow_length - 15else:# 其他情况动力向下self.canvas.create_line(power_x, power_y, power_x, power_y power_arrow_length,width4, fillblue, arrowtk.LAST, arrowshape(10,12,4))text_y power_y power_arrow_length 15self.canvas.create_text(power_x, text_y, textf动力F1{power_force}N, fillblue, font(Arial, 10, bold))# 阻力箭头总是向下resistance_arrow_length resistance_force * arrow_scaleself.canvas.create_line(resistance_x, resistance_y, resistance_x, resistance_y resistance_arrow_length,width4, fillred, arrowtk.LAST, arrowshape(10,12,4))self.canvas.create_text(resistance_x, resistance_y resistance_arrow_length 15, textf阻力F2{resistance_force}N, fillred, font(Arial, 10, bold))except ValueError:passdef draw_arms(self, fulcrum_x, power_x, resistance_x):绘制力臂标注try:power_arm float(self.power_arm.get())resistance_arm float(self.resistance_arm.get())arm_y self.fulcrum_y - 60# 动力臂self.canvas.create_line(fulcrum_x, arm_y, power_x, arm_y,width3, fillblue, arrowtk.BOTH, arrowshape(8,10,3))self.canvas.create_text((fulcrum_x power_x)/2, arm_y-20, textf动力臂L1{power_arm}cm, fillblue, font(Arial, 10, bold))# 阻力臂self.canvas.create_line(fulcrum_x, arm_y-15, resistance_x, arm_y-15,width3, fillred, arrowtk.BOTH, arrowshape(8,10,3))self.canvas.create_text((fulcrum_x resistance_x)/2, arm_y-35, textf阻力臂L2{resistance_arm}cm, fillred, font(Arial, 10, bold))except ValueError:passdef draw_type_explanation(self, fulcrum_x, power_x, resistance_x):绘制杠杆类型说明positions [(支点, fulcrum_x, black),(动力点, power_x, blue),(阻力点, resistance_x, red)]# 按X坐标排序positions.sort(keylambda x: x[1])explanation_y 50explanation_text f从左到右{positions[0][0]} → {positions[1][0]} → {positions[2][0]}self.canvas.create_text(self.canvas_width//2, explanation_y, textexplanation_text, filldarkgreen, font(Arial, 12, bold))def update_info(self):更新信息显示try:power_force float(self.power_force.get())resistance_force float(self.resistance_force.get())power_arm float(self.power_arm.get())resistance_arm float(self.resistance_arm.get())power_moment power_force * power_armresistance_moment resistance_force * resistance_arm# 力矩信息moment_text f动力矩: M1 F1 × L1 {power_force} × {power_arm} {power_moment:.1f} N·cm\nmoment_text f阻力矩: M2 F2 × L2 {resistance_force} × {resistance_arm} {resistance_moment:.1f} N·cmself.moment_label.config(textmoment_text)# 平衡状态diff abs(power_moment - resistance_moment)if diff 0.1:self.balance_label.config(text✓ 杠杆平衡 (M1 M2), fggreen)elif power_moment resistance_moment:self.balance_label.config(textf↺ 逆时针转动 (M1 M2), fgorange)else:self.balance_label.config(textf↻ 顺时针转动 (M2 M1), fgorange)# 机械效益分析mechanical_advantage resistance_force / power_force if power_force ! 0 else 0if mechanical_advantage 1:advantage_text f机械效益: {mechanical_advantage:.2f} 1 (省力杠杆)elif mechanical_advantage 1:advantage_text f机械效益: {mechanical_advantage:.2f} 1 (费力杠杆)else:advantage_text f机械效益: {mechanical_advantage:.2f} 1 (等臂杠杆)self.advantage_label.config(textadvantage_text)# 类型描述lever_type self.lever_type.get()descriptions {first: 第一类杠杆支点在中间可以是省力、费力或等臂杠杆,second: 第二类杠杆阻力点在中间一定是省力杠杆, third: 第三类杠杆动力点在中间一定是费力杠杆}self.type_description.config(textdescriptions[lever_type])except ValueError:self.moment_label.config(text请输入有效的数值)self.balance_label.config(text)self.advantage_label.config(text)self.type_description.config(text)def update_lever(self):更新杠杆显示target_angle self.calculate_lever_angle()if not self.is_animating:self.lever_angle target_angleself.draw_lever()self.update_info()def start_animation(self):开始动画self.is_animating Trueself.animate()def stop_animation(self):停止动画self.is_animating Falsedef animate(self):动画循环if self.is_animating:target_angle self.calculate_lever_angle()angle_diff target_angle - self.lever_angleif abs(angle_diff) 0.001:self.lever_angle angle_diff * self.animation_speedelse:self.lever_angle target_angleself.draw_lever()self.root.after(50, self.animate)def reset_lever(self):重置杠杆self.stop_animation()self.lever_angle 0self.reset_to_default()self.update_lever()def run(self):运行程序self.update_example_list()self.root.mainloop()# 运行程序
if __name__ __main__:simulator LeverSimulator()simulator.run()OK!
