Learn Work, Energy, and Power | Forces and Energy

To understand how physics describes motion and interactions, you need to know how work, energy, and power are defined and calculated:

Work is done when a force causes an object to move in the direction of the force.

Formula: W = F * d * cos(θ)
- W: work (in joules, J);
- F: force (in newtons, N);
- d: displacement (in meters, m);
- θ: angle between the force and displacement vectors.

Kinetic Energy (KE) is the energy of motion.

Formula: KE = 0.5 * m * v**2
- m: mass (in kilograms, kg);
- v: velocity (in meters per second, m/s).

Potential Energy (PE), in the context of gravity, is the stored energy due to an object's position.

Formula: PE = m * g * h
- g: acceleration due to gravity (9.81 m/s²);
- h: height above the reference point (in meters, m).

Power measures how quickly work is done or energy is transferred.

Formula: P = W / t
- P: power (in watts, W);
- t: time taken (in seconds, s).


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# Calculate work done, kinetic and potential energy for a moving object

import numpy as np

# Given values
force = 50      # Newtons
distance = 10   # Meters
theta = 0       # Degrees (force and displacement in same direction)

# Work done
work = force * distance * np.cos(np.deg2rad(theta))
print(f"Work done: {work} J")

# Object properties
mass = 2        # kg
initial_velocity = 0    # m/s
final_velocity = 5      # m/s
height_initial = 0      # m
height_final = 3        # m
g = 9.81                # m/s^2

# Change in kinetic energy
KE_initial = 0.5 * mass * initial_velocity**2
KE_final = 0.5 * mass * final_velocity**2
delta_KE = KE_final - KE_initial
print(f"Change in kinetic energy: {delta_KE} J")

# Change in potential energy
PE_initial = mass * g * height_initial
PE_final = mass * g * height_final
delta_PE = PE_final - PE_initial
print(f"Change in potential energy: {delta_PE} J")

This code models energy transformations in a stepwise manner:

It first calculates work using the formula, taking into account the direction of force and displacement;
For kinetic energy, it computes both the initial and final values using the object's mass and velocity, then finds the change by subtraction;
For potential energy, it calculates the initial and final gravitational potential energies based on height, and determines the change;
The results show how energy is transferred: work done on the object can increase its kinetic or potential energy, depending on how force is applied and the object's motion or position.


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# Plotting energy changes over time for an object moving under gravity

import matplotlib.pyplot as plt

mass = 1.0    # kg
g = 9.81      # m/s^2
h0 = 10       # Initial height (m)
v0 = 0        # Initial velocity (m/s)
time = np.linspace(0, 1.5, 100)

# Calculate position and velocity over time (free fall)
y = h0 - 0.5 * g * time**2
y = np.maximum(y, 0)
v = -g * time
v[y == 0] = 0

# Kinetic and Potential Energy over time
KE = 0.5 * mass * v**2
PE = mass * g * y

plt.plot(time, KE, label="Kinetic Energy")
plt.plot(time, PE, label="Potential Energy")
plt.plot(time, KE + PE, label="Total Energy", linestyle='--')
plt.xlabel("Time (s)")
plt.ylabel("Energy (Joules)")
plt.title("Energy Changes During Free Fall")
plt.legend()
plt.show()

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