DuckieDai Work and Energy Python Program

physics · MIT License

Overview

Solve work, kinetic energy, speed changes from net work, force, distance, or force angle with guided formulas.

Tested on a TI calculator
Downloaded 39 times
Version 1.0.0
8680 bytes
Uses math

Download WORKNRG.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
Angles are entered in degrees and net work follows the work-energy theorem.
Mass and distance inputs must be positive where required; inverse cosine inputs must remain in range.
Some inputs yield no real speed.

Try the DuckieDai calculator screen

Follow the reviewed program's real menu, prompts, validation, calculation, and result flow before downloading.

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Simulation boundary: This preview uses a reviewed browser adapter. It does not execute the downloaded Python and does not prove TI-Python or calculator compatibility.

Learn the math

How work and kinetic energy work

The idea

Work is done when a force moves something. Only the part of the force along the direction of motion counts, which is where the cosine comes from.

The work-energy theorem says the net work done on an object equals the change in its kinetic energy.

The formula

W = F*d*cos(theta)

KE = 0.5*m*v^2

Wnet = KEf - KEi

W: work in joules (J)
F: force (N)
d: distance moved (m)
theta: angle between the force and the motion, in degrees
KE: kinetic energy (J)

Using the program

1 Calculate work and 2 Kinetic energy use the first two formulas directly.
3 Final speed and 4 Initial speed use the work-energy theorem with a net work value.
5 Solve force, 6 Solve distance, and 7 Solve angle rearrange the work formula. The menu is two screens long.

Worked example

A 10 N force pushes a box 5 m in the direction of the force. Choose 1 and enter 10, 5, and an angle of 0.

W = 10.0 x 5.0 x cos(0.0)

The program shows W = 50.0 joules.

Tips and common mistakes

Angles are entered in degrees.
A force at 90 degrees to the motion does no work. A force opposing the motion does negative work.
Some inputs have no real answer, for example a final speed when the net work removes more energy than the object has.

Where this comes up

It is the work and energy unit of high school and college physics. Once you know the work-energy theorem, many problems that look like kinematics become one-line energy calculations.

Exact reviewed bytes

Source code

Download .py

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

"""DuckieDai Work and Energy for TI-84 Plus CE Python."""

from math import cos, radians, sqrt, acos, degrees


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):
    """Ask until a valid finite number is entered."""
    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):
    """Ask until a positive finite number is entered."""
    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 main():
    duckiedai_intro("WORK & ENERGY")

    print("WORK & ENERGY")
    print()
    print("1. Calculate Work")
    print("2. Kinetic Energy")
    print("3. Final speed")
    print("   from net work")
    print("4. Initial speed")
    print("   from net work")
    input("Press enter for more ")
    print("\n" * 6)
    print("5. Solve force")
    print("6. Solve distance")
    print("7. Solve angle")
    print()

    choice = input("Choose 1-7: ")

    print()

    # ==========================================
    # 1. WORK
    # W = F*d*cos(theta)
    # ==========================================

    if choice == "1":

        force = number("Force (N): ")
        distance = positive_number("Distance (m): ")
        angle = number("Angle (degrees): ")

        work = (
            force *
            distance *
            cos(radians(angle))
        )

        print()
        print("Using:")
        print("W = F*d*cos(theta)")
        print()
        print("W = " + str(force) +
              " x " + str(distance))
        print("x cos(" + str(angle) + ")")

        show_answer(
            "W",
            work,
            "joules"
        )


    # ==========================================
    # 2. KINETIC ENERGY
    # KE = 0.5*m*v^2
    # ==========================================

    elif choice == "2":

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

        ke = (
            0.5 *
            mass *
            velocity ** 2
        )

        print()
        print("Using:")
        print("KE = 0.5*m*v^2")
        print()
        print("KE = 0.5 x " +
              str(mass) + " x")
        print(str(velocity) + "^2")

        show_answer(
            "KE",
            ke,
            "joules"
        )


    # ==========================================
    # 3. FINAL SPEED FROM NET WORK
    #
    # W = KEf - KEi
    #
    # vf = sqrt(vi^2 + 2W/m)
    # ==========================================

    elif choice == "3":

        mass = positive_number("Mass (kg): ")
        vi = number("Initial speed: ")
        work = number("Net work (J): ")

        inside = (
            vi ** 2 +
            (2 * work / mass)
        )

        if inside < 0:

            print()
            print("No real final speed.")
            print("Check the values.")
            print()
            print("Negative work may")
            print("stop the object.")

        else:

            vf = sqrt(inside)

            print()
            print("Using:")
            print("W = KEf - KEi")
            print()
            print("Rearranged:")
            print("vf=sqrt(vi^2+2W/m)")

            show_answer(
                "Final speed",
                vf,
                "m/s"
            )


    # ==========================================
    # 4. INITIAL SPEED FROM NET WORK
    #
    # vi = sqrt(vf^2 - 2W/m)
    # ==========================================

    elif choice == "4":

        mass = positive_number("Mass (kg): ")
        vf = number("Final speed: ")
        work = number("Net work (J): ")

        inside = (
            vf ** 2 -
            (2 * work / mass)
        )

        if inside < 0:

            print()
            print("No real initial speed.")
            print("Check the values.")

        else:

            vi = sqrt(inside)

            print()
            print("Using:")
            print("W = KEf - KEi")
            print()
            print("Rearranged:")
            print("vi=sqrt(vf^2-2W/m)")

            show_answer(
                "Initial speed",
                vi,
                "m/s"
            )


    # ==========================================
    # 5. SOLVE FORCE
    #
    # F = W / (d*cos(theta))
    # ==========================================

    elif choice == "5":

        work = number("Work (J): ")
        distance = positive_number("Distance (m): ")
        angle = number("Angle (degrees): ")

        c = cos(radians(angle))

        if abs(c) < 0.0000001:

            print()
            print("Cannot solve force.")
            print("cos(angle) is zero.")

        else:

            force = (
                work /
                (distance * c)
            )

            print()
            print("Using:")
            print("W = F*d*cos(theta)")
            print()
            print("Rearranged:")
            print("F=W/(d*cos(theta))")

            show_answer(
                "F",
                force,
                "newtons"
            )


    # ==========================================
    # 6. SOLVE DISTANCE
    #
    # d = W / (F*cos(theta))
    # ==========================================

    elif choice == "6":

        work = number("Work (J): ")
        force = number("Force (N): ")
        angle = number("Angle (degrees): ")

        c = cos(radians(angle))

        denominator = force * c

        if abs(denominator) < 0.0000001:

            print()
            print("Cannot solve distance.")
            print("Check force/angle.")

        else:

            distance = (
                work /
                denominator
            )

            print()
            print("Using:")
            print("W = F*d*cos(theta)")
            print()
            print("Rearranged:")
            print("d=W/(F*cos(theta))")

            show_answer(
                "d",
                distance,
                "meters"
            )


    # ==========================================
    # 7. SOLVE ANGLE
    #
    # theta = acos(W / (F*d))
    # ==========================================

    elif choice == "7":

        work = number("Work (J): ")
        force = number("Force (N): ")
        distance = positive_number("Distance (m): ")

        denominator = force * distance

        if denominator == 0:

            print()
            print("Cannot solve angle.")

        else:

            ratio = work / denominator

            if ratio < -1 or ratio > 1:

                print()
                print("No real angle.")
                print("Check the values.")

            else:

                angle = degrees(
                    acos(ratio)
                )

                print()
                print("Using:")
                print("W = F*d*cos(theta)")
                print()
                print("Rearranged:")
                print("theta=acos(W/(F*d))")

                show_answer(
                    "theta",
                    angle,
                    "degrees"
                )

    else:

        print("Invalid choice.")

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


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

"""DuckieDai Work and Energy for TI-84 Plus CE Python."""
from math import cos, radians, sqrt, acos, degrees
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):
"""Ask until a valid finite number is entered."""
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):
"""Ask until a positive finite number is entered."""
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 main():
duckiedai_intro("WORK & ENERGY")
print("WORK & ENERGY")
print()
print("1. Calculate Work")
print("2. Kinetic Energy")
print("3. Final speed")
print(" from net work")
print("4. Initial speed")
print(" from net work")
input("Press enter for more ")
print("\n" * 6)
print("5. Solve force")
print("6. Solve distance")
print("7. Solve angle")
print()
choice = input("Choose 1-7: ")
print()
# ==========================================
# 1. WORK
# W = F*d*cos(theta)
# ==========================================
if choice == "1":
force = number("Force (N): ")
distance = positive_number("Distance (m): ")
angle = number("Angle (degrees): ")
work = (
force *
distance *
cos(radians(angle))
)
print()
print("Using:")
print("W = F*d*cos(theta)")
print()
print("W = " + str(force) +
" x " + str(distance))
print("x cos(" + str(angle) + ")")
show_answer(
"W",
work,
"joules"
)
# ==========================================
# 2. KINETIC ENERGY
# KE = 0.5*m*v^2
# ==========================================
elif choice == "2":
mass = positive_number("Mass (kg): ")
velocity = number("Velocity (m/s): ")
ke = (
0.5 *
mass *
velocity ** 2
)
print()
print("Using:")
print("KE = 0.5*m*v^2")
print()
print("KE = 0.5 x " +
str(mass) + " x")
print(str(velocity) + "^2")
show_answer(
"KE",
ke,
"joules"
)
# ==========================================
# 3. FINAL SPEED FROM NET WORK
#
# W = KEf - KEi
#
# vf = sqrt(vi^2 + 2W/m)
# ==========================================
elif choice == "3":
mass = positive_number("Mass (kg): ")
vi = number("Initial speed: ")
work = number("Net work (J): ")
inside = (
vi ** 2 +
(2 * work / mass)
)
if inside < 0:
print()
print("No real final speed.")
print("Check the values.")
print()
print("Negative work may")
print("stop the object.")
else:
vf = sqrt(inside)
print()
print("Using:")
print("W = KEf - KEi")
print()
print("Rearranged:")
print("vf=sqrt(vi^2+2W/m)")
show_answer(
"Final speed",
vf,
"m/s"
)
# ==========================================
# 4. INITIAL SPEED FROM NET WORK
#
# vi = sqrt(vf^2 - 2W/m)
# ==========================================
elif choice == "4":
mass = positive_number("Mass (kg): ")
vf = number("Final speed: ")
work = number("Net work (J): ")
inside = (
vf ** 2 -
(2 * work / mass)
)
if inside < 0:
print()
print("No real initial speed.")
print("Check the values.")
else:
vi = sqrt(inside)
print()
print("Using:")
print("W = KEf - KEi")
print()
print("Rearranged:")
print("vi=sqrt(vf^2-2W/m)")
show_answer(
"Initial speed",
vi,
"m/s"
)
# ==========================================
# 5. SOLVE FORCE
#
# F = W / (d*cos(theta))
# ==========================================
elif choice == "5":
work = number("Work (J): ")
distance = positive_number("Distance (m): ")
angle = number("Angle (degrees): ")
c = cos(radians(angle))
if abs(c) < 0.0000001:
print()
print("Cannot solve force.")
print("cos(angle) is zero.")
else:
force = (
work /
(distance * c)
)
print()
print("Using:")
print("W = F*d*cos(theta)")
print()
print("Rearranged:")
print("F=W/(d*cos(theta))")
show_answer(
"F",
force,
"newtons"
)
# ==========================================
# 6. SOLVE DISTANCE
#
# d = W / (F*cos(theta))
# ==========================================
elif choice == "6":
work = number("Work (J): ")
force = number("Force (N): ")
angle = number("Angle (degrees): ")
c = cos(radians(angle))
denominator = force * c
if abs(denominator) < 0.0000001:
print()
print("Cannot solve distance.")
print("Check force/angle.")
else:
distance = (
work /
denominator
)
print()
print("Using:")
print("W = F*d*cos(theta)")
print()
print("Rearranged:")
print("d=W/(F*cos(theta))")
show_answer(
"d",
distance,
"meters"
)
# ==========================================
# 7. SOLVE ANGLE
#
# theta = acos(W / (F*d))
# ==========================================
elif choice == "7":
work = number("Work (J): ")
force = number("Force (N): ")
distance = positive_number("Distance (m): ")
denominator = force * distance
if denominator == 0:
print()
print("Cannot solve angle.")
else:
ratio = work / denominator
if ratio < -1 or ratio > 1:
print()
print("No real angle.")
print("Check the values.")
else:
angle = degrees(
acos(ratio)
)
print()
print("Using:")
print("W = F*d*cos(theta)")
print()
print("Rearranged:")
print("theta=acos(W/(F*d))")
show_answer(
"theta",
angle,
"degrees"
)
else:
print("Invalid choice.")
print()
print("DuckieDai says: done!")
# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

Filename: WORKNRG.py
Size: 8680 bytes
SHA-256: 408f33e65e1ad0b1e800702a87b5119af000d89515b73dd24da948bf5b14bf33

Usage

Inputs

Requested calculation mode
Applicable force, distance, angle, mass, work, and velocity values

Outputs

Requested work-energy quantity with derivation and labelled unit

Units: Use newtons, metres, degrees, kilograms, metres per second, and joules consistently.

Assumptions and limitations

Assumptions

Angles are entered in degrees and net work follows the work-energy theorem.

Constraints

Mass and distance inputs must be positive where required; inverse cosine inputs must remain in range.

Known failures

Some inputs yield no real speed.
Force or distance cannot be recovered when the relevant cosine or divisor is zero.

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, multi page work energy menu, selected calculation workflow, derivation, and answer screen ran on the physical calculator
Dependencies: math
Suggested calculator name: WORKNRG — 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 WORKNRG 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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