Energy Conservation
A mechanics module showing how gravitational potential energy transforms into kinetic energy in an ideal system.
Available module · Mechanics / Energy · Port 8508Learning objectives
By the end of this module, the learner should be able to:
- calculate kinetic energy from mass and velocity;
- calculate gravitational potential energy from mass, gravity, and height;
- explain conservation of mechanical energy from first principles;
- describe how potential energy decreases while kinetic energy increases during a fall;
- interpret total mechanical energy as a constant in an ideal falling-object model;
- connect energy accounting to real engineering systems.
First-principles explanation
Energy is the capacity to do work. A raised object stores gravitational potential energy because work has been done against the gravitational field to lift it. If the object is released, gravity does work on it as it falls.
In an ideal model with no air resistance and no friction, the energy is not destroyed. Instead, gravitational potential energy is converted into kinetic energy. At the initial height, potential energy is maximum and kinetic energy is zero. As height decreases, potential energy decreases by the same amount that kinetic energy increases.
Core equations
- Ek is kinetic energy, measured in joules (J).
- Ep is gravitational potential energy, measured in joules (J).
- m is mass, measured in kilograms (kg).
- v is velocity, measured in metres per second (m/s).
- g is gravitational field strength, measured in metres per second squared (m/s²).
- h is height above the chosen datum, measured in metres (m).
Worked example
Problem: A 2 kg object is held 5 m above the ground. Take gravitational field strength as 9.81 m/s². Find the gravitational potential energy stored at that height.
Known values:
- m = 2 kg
- h = 5 m
- g = 9.81 m/s²
Calculation:
Ep = mgh = 2 x 9.81 x 5 = 98.1 J
Answer: The object stores 98.1 J of gravitational potential energy. In an ideal fall to ground level, this becomes 98.1 J of kinetic energy.
Interactive simulator
The Energy Conservation simulator lets the learner adjust mass, initial height, and gravity, then observe potential energy, kinetic energy, and total mechanical energy during an ideal fall.
Local launch command:
python -m streamlit run simulations/energy_conservation/streamlit_web_app.py --server.port 8508
Engineering meaning
Energy conservation is a foundation for checking whether a mechanical design is physically plausible. Engineers use the same balance when analysing lifts, braking systems, falling masses, roller-coaster sections, impact tests, pendulums, storage systems, and energy-transfer mechanisms.
The ideal model gives a reference case. Real systems can then be compared against it to estimate losses caused by air resistance, friction, heating, sound, deformation, or rotation.
Assumptions and limits
- The falling object is treated as a point mass.
- Air resistance is ignored.
- Friction is ignored.
- Gravity is treated as constant over the height range.
- Energy transforms only between gravitational potential energy and kinetic energy.
- Rotational motion, deformation, heat transfer, and sound are not included.
Challenge questions
- What happens to stored potential energy if the height is doubled?
- Why does kinetic energy increase as height decreases?
- Why does total mechanical energy remain constant only in the ideal model?
- Where does energy go in a real system with air resistance?
- How could an engineer use the ideal result as a benchmark for an actual machine?