DuckieDai Momentum Toolkit Python Program

physics · MIT License

Overview

Solve basic momentum, a missing final collision velocity, or the shared velocity of two objects that stick together.

Tested on a TI calculator
Downloaded 41 times
Version 1.0.0
6961 bytes
No imports

Download MOMENTUM.py Read the source How to install

Before you run it

TI-84 Plus CE Python · tested on OS 5.8.3, Python App 5.8.3.0048
TI Connect CE .py conversion to a Python AppVar in RAM; physically verified one program at a time
The selected collision is an isolated one-dimensional system and velocity signs encode direction.
Masses must be positive and divisor velocities cannot be zero when solving mass.
External impulse invalidates momentum conservation.

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Learn the math

How momentum and collisions work

The idea

Momentum is mass times velocity. It has a direction, so an object moving the other way has negative momentum.

In a collision with no outside force, the total momentum before equals the total momentum after. That one fact solves most collision problems.

The formula

p = m*v

m1*v1i + m2*v2i = m1*v1f + m2*v2f

vf = (m1*v1 + m2*v2)/(m1 + m2)

p: momentum (kg*m/s)
m: mass (kg)
v: velocity (m/s), with a sign for direction

Using the program

1 Basic momentum: solve p, m, or v from the other two.
2 Collision solver: enter both masses, both starting velocities, and one final velocity to find the other.
3 Stick together: two objects collide and move off as one.

Worked example

A 2 kg cart moving at 3 m/s hits a 4 kg cart at rest and they stick. Choose 3 and enter 2, 3, 4, and 0.

vf = (2*3 + 4*0)/(2 + 4)

The program shows Final velocity = 1.0 m/s. For the basic mode, a 2 kg object at 3 m/s gives p = 6.0 kg*m/s.

Tips and common mistakes

Pick a positive direction and keep it. Anything moving the other way gets a negative velocity.
Momentum is conserved in every collision. Kinetic energy is conserved only in elastic ones.
Objects that stick together share one final velocity.

Where this comes up

It covers the momentum and collisions unit of high school and college physics: carts on a track, a ball and a bat, objects that couple together, and recoil problems.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

"""DuckieDai Momentum for TI-84 Plus CE Python."""


def duckiedai_intro(program_name, wait=True):
    """Show the reusable DuckieDai program opening."""
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("+----------------------+")
    print("Loading...")

    if wait:
        input("Press enter to start ")
        print("\n" * 6)


def number(prompt):
    """Allow positive, negative, or zero values."""
    while True:
        try:
            value = float(input(prompt))

            if value > -1e100 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter a valid number.")


def positive_number(prompt):
    """Require a value greater than zero."""
    while True:
        try:
            value = float(input(prompt))

            if value > 0 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter a number above 0.")


def show_answer(name, value, unit):
    input("Press enter for answer ")
    print("\n" * 6)
    print("ANSWER")
    print(name + " = " + str(value))
    print(unit)


def basic_momentum():
    print("BASIC MOMENTUM")
    print()
    print("p = m*v")
    print()
    print("1. Solve momentum")
    print("2. Solve mass")
    print("3. Solve velocity")
    print()

    choice = input("Choose 1-3: ")
    print()

    # -------------------------
    # Momentum
    # -------------------------

    if choice == "1":

        mass = positive_number("Mass (kg): ")
        velocity = number("Velocity (m/s): ")

        momentum = mass * velocity

        print()
        print("Using:")
        print("p = m*v")

        show_answer(
            "p",
            momentum,
            "kg*m/s"
        )

    # -------------------------
    # Mass
    # -------------------------

    elif choice == "2":

        momentum = number("Momentum: ")
        velocity = number("Velocity (m/s): ")

        if velocity == 0:
            print()
            print("Cannot divide by")
            print("zero velocity.")

        else:
            mass = momentum / velocity

            print()
            print("Using:")
            print("p = m*v")
            print()
            print("Rearranged:")
            print("m = p/v")

            show_answer(
                "m",
                mass,
                "kg"
            )

    # -------------------------
    # Velocity
    # -------------------------

    elif choice == "3":

        momentum = number("Momentum: ")
        mass = positive_number("Mass (kg): ")

        velocity = momentum / mass

        print()
        print("Using:")
        print("p = m*v")
        print()
        print("Rearranged:")
        print("v = p/m")

        show_answer(
            "v",
            velocity,
            "m/s"
        )

    else:
        print("Invalid choice.")


def collision_solver():
    print("2-OBJECT COLLISION")
    print()
    print("Momentum before")
    print("= momentum after")
    print()
    print("m1*v1i + m2*v2i")
    print("=")
    print("m1*v1f + m2*v2f")
    print()
    print("Direction matters!")
    print("+ right / - left")
    input("Press enter for menu ")
    print("\n" * 6)
    print()
    print("Which is unknown?")
    print()
    print("1. Object 1 final v")
    print("2. Object 2 final v")
    print()

    choice = input("Choose 1 or 2: ")
    print()

    m1 = positive_number("Mass 1 (kg): ")
    m2 = positive_number("Mass 2 (kg): ")

    v1i = number("Initial v1: ")
    v2i = number("Initial v2: ")

    print()

    # ===================================
    # Solve v1 final
    # ===================================

    if choice == "1":

        v2f = number("Final v2: ")

        initial_p = (
            m1 * v1i +
            m2 * v2i
        )

        v1f = (
            initial_p -
            m2 * v2f
        ) / m1

        print()
        print("Using conservation:")
        print("Pi = Pf")
        print()
        print("m1*v1i + m2*v2i")
        print("= m1*v1f + m2*v2f")
        print()
        print("Rearranged:")
        print("v1f =")
        print("(Pi-m2*v2f)/m1")

        show_answer(
            "v1 final",
            v1f,
            "m/s"
        )

    # ===================================
    # Solve v2 final
    # ===================================

    elif choice == "2":

        v1f = number("Final v1: ")

        initial_p = (
            m1 * v1i +
            m2 * v2i
        )

        v2f = (
            initial_p -
            m1 * v1f
        ) / m2

        print()
        print("Using conservation:")
        print("Pi = Pf")
        print()
        print("m1*v1i + m2*v2i")
        print("= m1*v1f + m2*v2f")
        print()
        print("Rearranged:")
        print("v2f =")
        print("(Pi-m1*v1f)/m2")

        show_answer(
            "v2 final",
            v2f,
            "m/s"
        )

    else:
        print("Invalid choice.")


def stick_together():
    print("STICK TOGETHER")
    print("COLLISION")
    print()
    print("Objects share one")
    print("final velocity.")
    print()
    print("+ right / - left")
    print()

    m1 = positive_number("Mass 1 (kg): ")
    v1 = number("Velocity 1: ")

    m2 = positive_number("Mass 2 (kg): ")
    v2 = number("Velocity 2: ")

    final_v = (
        m1 * v1 +
        m2 * v2
    ) / (m1 + m2)

    print()
    print("Using:")
    print("m1*v1 + m2*v2")
    print("=")
    print("(m1+m2)*vf")
    print()
    print("Rearranged:")
    print("vf =")
    print("(m1*v1+m2*v2)")
    print("/(m1+m2)")

    show_answer(
        "Final velocity",
        final_v,
        "m/s"
    )


def main():
    duckiedai_intro("MOMENTUM")

    print("MOMENTUM TOOLKIT")
    print()
    print("1. Basic momentum")
    print("2. Collision solver")
    print("3. Stick together")
    print()

    choice = input("Choose 1-3: ")

    print()

    if choice == "1":
        basic_momentum()

    elif choice == "2":
        collision_solver()

    elif choice == "3":
        stick_together()

    else:
        print("Invalid choice.")

    print()
    print("DuckieDai says: done!")


# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

"""DuckieDai Momentum for TI-84 Plus CE Python."""
def duckiedai_intro(program_name, wait=True):
"""Show the reusable DuckieDai program opening."""
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 6)
def number(prompt):
"""Allow positive, negative, or zero values."""
while True:
try:
value = float(input(prompt))
if value > -1e100 and value < 1e100:
return value
except ValueError:
pass
print("Enter a valid number.")
def positive_number(prompt):
"""Require a value greater than zero."""
while True:
try:
value = float(input(prompt))
if value > 0 and value < 1e100:
return value
except ValueError:
pass
print("Enter a number above 0.")
def show_answer(name, value, unit):
input("Press enter for answer ")
print("\n" * 6)
print("ANSWER")
print(name + " = " + str(value))
print(unit)
def basic_momentum():
print("BASIC MOMENTUM")
print()
print("p = m*v")
print()
print("1. Solve momentum")
print("2. Solve mass")
print("3. Solve velocity")
print()
choice = input("Choose 1-3: ")
print()
# -------------------------
# Momentum
# -------------------------
if choice == "1":
mass = positive_number("Mass (kg): ")
velocity = number("Velocity (m/s): ")
momentum = mass * velocity
print()
print("Using:")
print("p = m*v")
show_answer(
"p",
momentum,
"kg*m/s"
)
# -------------------------
# Mass
# -------------------------
elif choice == "2":
momentum = number("Momentum: ")
velocity = number("Velocity (m/s): ")
if velocity == 0:
print()
print("Cannot divide by")
print("zero velocity.")
else:
mass = momentum / velocity
print()
print("Using:")
print("p = m*v")
print()
print("Rearranged:")
print("m = p/v")
show_answer(
"m",
mass,
"kg"
)
# -------------------------
# Velocity
# -------------------------
elif choice == "3":
momentum = number("Momentum: ")
mass = positive_number("Mass (kg): ")
velocity = momentum / mass
print()
print("Using:")
print("p = m*v")
print()
print("Rearranged:")
print("v = p/m")
show_answer(
"v",
velocity,
"m/s"
)
else:
print("Invalid choice.")
def collision_solver():
print("2-OBJECT COLLISION")
print()
print("Momentum before")
print("= momentum after")
print()
print("m1*v1i + m2*v2i")
print("=")
print("m1*v1f + m2*v2f")
print()
print("Direction matters!")
print("+ right / - left")
input("Press enter for menu ")
print("\n" * 6)
print()
print("Which is unknown?")
print()
print("1. Object 1 final v")
print("2. Object 2 final v")
print()
choice = input("Choose 1 or 2: ")
print()
m1 = positive_number("Mass 1 (kg): ")
m2 = positive_number("Mass 2 (kg): ")
v1i = number("Initial v1: ")
v2i = number("Initial v2: ")
print()
# ===================================
# Solve v1 final
# ===================================
if choice == "1":
v2f = number("Final v2: ")
initial_p = (
m1 * v1i +
m2 * v2i
)
v1f = (
initial_p -
m2 * v2f
) / m1
print()
print("Using conservation:")
print("Pi = Pf")
print()
print("m1*v1i + m2*v2i")
print("= m1*v1f + m2*v2f")
print()
print("Rearranged:")
print("v1f =")
print("(Pi-m2*v2f)/m1")
show_answer(
"v1 final",
v1f,
"m/s"
)
# ===================================
# Solve v2 final
# ===================================
elif choice == "2":
v1f = number("Final v1: ")
initial_p = (
m1 * v1i +
m2 * v2i
)
v2f = (
initial_p -
m1 * v1f
) / m2
print()
print("Using conservation:")
print("Pi = Pf")
print()
print("m1*v1i + m2*v2i")
print("= m1*v1f + m2*v2f")
print()
print("Rearranged:")
print("v2f =")
print("(Pi-m1*v1f)/m2")
show_answer(
"v2 final",
v2f,
"m/s"
)
else:
print("Invalid choice.")
def stick_together():
print("STICK TOGETHER")
print("COLLISION")
print()
print("Objects share one")
print("final velocity.")
print()
print("+ right / - left")
print()
m1 = positive_number("Mass 1 (kg): ")
v1 = number("Velocity 1: ")
m2 = positive_number("Mass 2 (kg): ")
v2 = number("Velocity 2: ")
final_v = (
m1 * v1 +
m2 * v2
) / (m1 + m2)
print()
print("Using:")
print("m1*v1 + m2*v2")
print("=")
print("(m1+m2)*vf")
print()
print("Rearranged:")
print("vf =")
print("(m1*v1+m2*v2)")
print("/(m1+m2)")
show_answer(
"Final velocity",
final_v,
"m/s"
)
def main():
duckiedai_intro("MOMENTUM")
print("MOMENTUM TOOLKIT")
print()
print("1. Basic momentum")
print("2. Collision solver")
print("3. Stick together")
print()
choice = input("Choose 1-3: ")
print()
if choice == "1":
basic_momentum()
elif choice == "2":
collision_solver()
elif choice == "3":
stick_together()
else:
print("Invalid choice.")
print()
print("DuckieDai says: done!")
# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

Filename: MOMENTUM.py
Size: 6961 bytes
SHA-256: 0614e495056cecb9cdfaa84c4d8b50a8645e78cf4e6bc4e203edf3d21f2ef0fc

Usage

Inputs

Tool mode and requested unknown
Masses and signed velocities for the selected calculation

Outputs

Momentum, velocity, or mass with the applicable formula and unit

Units: Mass uses kilograms, velocity uses metres per second, and momentum uses kilogram metres per second.

Assumptions and limitations

Assumptions

The selected collision is an isolated one-dimensional system and velocity signs encode direction.

Constraints

Masses must be positive and divisor velocities cannot be zero when solving mass.

Known failures

External impulse invalidates momentum conservation.
A one-dimensional model does not resolve multi-axis collisions.

Compatibility and review

Review status: Tested on a TI calculator
Tested on: TI-84 Plus CE Python; OS 5.8.3; Python App 5.8.3.0048; exact paginated .py transferred through TI Connect CE into RAM and tested individually
What happened: Passed: branded intro, momentum toolkit menu, basic and collision workflows, direction guidance, and answer screen ran on the physical calculator
Dependencies: No imports
Suggested calculator name: MOMENTUM — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Transfer and launch

Download the .py file, send it to your calculator with TI Connect CE as MOMENTUM or another name, then open the Python App and try the worked example on this page first.

Full installation and troubleshooting guide. Check your teacher's or exam's rules before using any program.

Version history

1.0.0 — current version, published 2026-09-23. Download this reviewed version

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