File size: 4,928 Bytes
148c2e2 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 |
import streamlit as st
import numpy as np
from abc import ABC, abstractmethod
import matplotlib.pyplot as plt
class RhinoDisplacement(ABC):
@abstractmethod
def displacement(self, time):
pass
class AcceleratingRhino(RhinoDisplacement):
def __init__(self, acceleration):
self.acceleration = acceleration
def displacement(self, time):
return 0.5 * self.acceleration * time**2
class RhinoMeetingTime(ABC):
@abstractmethod
def calculate_meeting_time(self, acceleration, speed, distance):
pass
class CalculateMeetingTime(RhinoMeetingTime):
def calculate_meeting_time(self, acceleration, speed, distance):
a = 0.5 * acceleration
b = speed
c = -distance
discriminant = b**2 - 4 * a * c
if discriminant < 0:
return None
time = (-b + np.sqrt(discriminant)) / (2 * a)
return time
class RhinoDisplacementPlot(ABC):
@abstractmethod
def plot_displacement(self):
pass
class DisplacementVisualization(RhinoDisplacementPlot):
def __init__(self, accelerating_rhino, constant_speed_rhino, meeting_time):
self.accelerating_rhino = accelerating_rhino
self.constant_speed_rhino = constant_speed_rhino
self.meeting_time = meeting_time
def plot_displacement(self):
fig, ax = plt.subplots()
times = np.linspace(0, self.meeting_time, 100)
disp_acc = [self.accelerating_rhino.displacement(t) for t in times]
disp_const = [self.constant_speed_rhino.displacement(t) for t in times]
ax.plot(times, disp_acc, label='Accelerating Rhino')
ax.plot(times, disp_const, label='Constant Speed Rhino')
ax.annotate('Accelerating rhino = 400 m', (self.meeting_time, disp_acc[-1]),
textcoords="offset points", xytext=(0, 10), ha='center')
ax.annotate('Constant speed Rhino = 1200 m', (self.meeting_time, disp_const[-1]),
textcoords="offset points", xytext=(0, 10), ha='center')
ax.set_xlabel('Time (s)')
ax.set_ylabel('Displacement (m)')
ax.legend()
return fig
def main():
st.title("Rhino Meeting Displacement Calculator")
st.image("rhinos_0.png", caption='Rhinos Charging Towards One Another 0')
acceleration = st.number_input("Acceleration of the first rhino (m/s^2)", value=1/8)
speed = st.number_input("Speed of the second rhino (m/s)", value=15)
distance = st.number_input("Initial distance between the rhinos (m)", value=1600)
if st.button("Generate Rhinos Charging Towards One Another Motion Graph Problem"):
st.write("Two rhinos initially 1600 m apart, begin running directly toward one another at the same time. One rhino uniformly accelerates from rest at 1/8 m.s^2, while the other rhino runs with a constant speed of 15 m/s. What is the net displacement of each rhino when they meet?")
if st.button("Formulations Required For Solving Problem"):
st.latex(r'Accelerating rhino: s_1(t) = \frac{1}{2}at^2')
st.latex(r'Constant speed rhino: s_2(t) = vt')
st.latex(r'Total Distance Covered by both rhinos: 1600 meters')
st.latex(r'Utilize form ax^2 + bx + c = 0')
st.latex(r'a = \frac{1}{2}\frac{1}{16}t^2')
st.latex(r'b = 15 m/s')
st.latex(r'\frac{1}{16}t^2 + 15t = 1600')
st.latex(r'c= -1600')
st.latex(r'\Delta = b^2 - 4ac = 15^2 - 4\frac{1}{16}1600 = 225 + 400 = 625')
st.latex(r'Solve for t: t = \frac{-15+-\sqrt(625)}{\frac{1}{8}} = \frac{-15 +- 25}{\frac{1}{8}}')
st.latex(r'Positive solution: t = \frac{10}{\frac{1}{8}} = 80 seconds')
st.latex(r'Accelerating rhino s_1(t) = s_1(80) = \frac{1}{2}\frac{1}{8}80^2 = \frac{1}{16}6400 = 400 meters')
st.latex(r'Constant speed rhino s_2(t) = s_2(80) = 15 * 80 = 1200 meters')
if st.button("Calculate"):
calc_meeting_time = CalculateMeetingTime()
time = calc_meeting_time.calculate_meeting_time(acceleration, speed, distance)
if time is not None:
accelerating_rhino = AcceleratingRhino(acceleration)
constant_speed_rhino = ConstantSpeedRhino(speed)
disp_acc = accelerating_rhino.displacement(time)
disp_const = constant_speed_rhino.displacement(time)
st.write(f"Time to meet: {time:.2f} seconds")
st.write(f"Displacement of accelerating rhino: {disp_acc:.2f} meters")
st.write(f"Displacement of constant speed rhino: {disp_const:.2f} meters")
visualization = DisplacementVisualization(accelerating_rhino, constant_speed_rhino, time)
fig = visualization.plot_displacement()
st.pyplot(fig)
else:
st.write("The rhinos will never meet under these conditions.")
st.image("rhinos_1.png", caption='Rhinos Charging Towards One Another 1')
if __name__ == "__main__":
main() |