Interactive physics simulator
Energy
Explore the capacity to do work. Analyze how energy transforms from kinetic to potential, travels through system pathways, and exhibits mass-energy equivalence.
Interactive Energy Lab
Analyze the conservation and transfer of energy inside real-time interactive physics systems.
Live Telemetry
- Source Output
- 0.0 W
- Converter Efficiency
- 100%
- Load Output
- 0.0 W
- Energy Forms
- None
- Kinetic Energy (KE)
- 0.0 J
- Potential Energy (PE)
- 0.0 J
- Total Energy (E)
- 0.0 J
- Velocity (v)
- 0.0 m/s
- Rest Mass (m)
- 0.0 mg
- Energy equivalent (E)
- 0.0 J
- TNT Equivalent
- 0.0 tons
- Households Powered
- 0.0 yrs
Understanding Energy
In physics, energy is defined as the scalar capacity or ability of a system to perform mechanical work. Energy resides in multiple forms, but it is never created or destroyed. It simply transfers between bodies or transforms between physical forms.
The SI unit of energy is the Joule (J), defined as:
According to the Law of Conservation of Energy, the total energy of an isolated system remains perfectly constant:
Key Concept: Energy Forms
Energy is categorized into two macroscopic groupings: Kinetic Energy (KE) (associated with macroscopic motion) and Potential Energy (PE) (stored energy due to fields, gravity, elastic deformation, chemical bonds, or atomic spacing). Toggling the simulator shows how solar radiant photons transform into electrical flow, which is then converted into thermal or mechanical action.
Mechanical Energy Conservation
In a conservative system without friction, the total mechanical energy is conserved:
As a coaster descends, height decreases (PE drops), causing speed to increase (KE gains). Non-conservative forces like friction do negative work, converting mechanical energy into heat.
Solved Examples
A solar panel absorbs E_{light} = 1500 Joules of radiant energy from the sun. If it converts E_{electrical} = 225 Joules into electrical energy, calculate the efficiency of the solar panel and the amount of energy dissipated as heat.
- Identify the given values: Input energy E_{input} = 1500 J, Useful output energy E_{useful} = 225 J.
- Recall the efficiency formula: Efficiency = (E_{useful} / E_{input}) · 100%.
- Substitute values: Efficiency = (225 / 1500) · 100% = 0.15 · 100% = 15%.
- Recall energy conservation: E_{input} = E_{useful} + E_{lost}.
- Calculate dissipated heat energy: E_{lost} = 1500 J - 225 J = 1275 Joules.
- Explain the outcome: Only 15% of solar energy becomes electricity. The remaining 85% (1275 J) is transformed into thermal energy, heating the panel itself.
Answer: Efficiency = 15%, Heat Energy Dissipated = 1275 J
A roller coaster cart of mass m = 400 kg starts from rest at the top of a hill of height h = 25 meters. Friction is negligible. Calculate the gravitational potential energy at the top, the kinetic energy at the bottom of the hill (h = 0 m), and the speed of the cart at the bottom. (Use gravity acceleration g = 9.8 m/s²).
- Identify the variables: Mass m = 400 kg, height h = 25 m, gravity g = 9.8 m/s².
- Calculate Gravitational Potential Energy (PE): PE = m · g · h = 400 · 9.8 · 25 = 98,000 Joules (or 98 kJ).
- Apply Conservation of Mechanical Energy: Since there is no friction, the mechanical energy remains constant. At the top, speed v = 0, so KE_{top} = 0. Total mechanical energy E = PE + KE = 98,000 + 0 = 98,000 J.
- Calculate Kinetic Energy (KE) at the bottom: At the bottom (h = 0 m), PE_{bottom} = 0. Therefore, all potential energy is converted to kinetic energy: KE_{bottom} = 98,000 Joules.
- Solve for speed v: KE = 1/2 · m · v² ⇒ 98,000 = 1/2 · 400 · v² ⇒ 98,000 = 200 · v².
- v² = 98,000 / 200 = 490 ⇒ v = √490 ≈ 22.14 m/s.
Answer: PE at Top = 98,000 J, KE at Bottom = 98,000 J, Speed v ≈ 22.14 m/s
An electron of mass m_{e} = 9.11 × 10^{-31} kg and a positron of the same mass collide and undergo matter-antimatter annihilation, converting their combined rest mass entirely into radiant energy. Calculate the total energy released in Joules and electronvolts (1 eV = 1.6 × 10^{-19} J). (Use speed of light c = 3.0 × 10^8 m/s).
- Identify the given values: electron mass = positron mass = 9.11 × 10^{-31} kg, c = 3.0 × 10^8 m/s.
- Calculate the total annihilated mass: Δm = 2 · m_{e} = 2 · (9.11 × 10^{-31} kg) = 1.822 × 10^{-30} kg.
- Recall Einstein's mass-energy formula: E = Δm · c².
- Calculate energy in Joules: E = (1.822 × 10^{-30}) · (3.0 × 10^8)² = 1.822 × 10^{-30} · (9.0 × 10^{16}) = 1.6398 × 10^{-13} Joules.
- Convert energy to electronvolts (eV): E_{eV} = (1.6398 × 10^{-13} J) / (1.6 × 10^{-19} J/eV) ≈ 1,024,875 eV = 1.025 MeV (Mega-electronvolts).
Answer: Energy E ≈ 1.64 × 10^{-13} J (or 1.025 MeV)
Common Mistakes
- Believing energy is "consumed" or destroyed. When a battery "dies" or a moving car stops, the energy is not destroyed; it has simply dissipated as low-grade thermal energy into the environment.
- Confusing energy with power. Energy represents the total work capacity (measured in Joules), whereas power is the rate of energy transfer or consumption per unit time (P = W/t, measured in Watts).
- Treating mass and energy as separate entities. Rest mass is stored energy (E=mc2). In nuclear interactions or annihilation, mass transforms directly into radiant energy.
Mass-Energy Equivalence
Albert Einstein established that mass can be converted directly into energy according to:
where c ≈ 3.0 × 108 m/s is the speed of light. Because c2 is extremely large (9 × 1016 m2/s2), a tiny amount of mass holds an immense quantity of energy, which is released during nuclear fusion, fission, or antimatter collision.
Practice Questions
1. A athlete of mass 60 kg increases their running speed from 2 m/s to 6 m/s. Calculate the change in their kinetic energy.
The initial kinetic energy is KE_{initial} = 1/2 · m · v_{initial}² = 0.5 · 60 · 2² = 120 J. The final kinetic energy is KE_{final} = 1/2 · m · v_{final}² = 0.5 · 60 · 6² = 1080 J. The change in kinetic energy is ΔKE = KE_{final} - KE_{initial} = 1080 J - 120 J = 960 Joules.
2. Explain how the law of conservation of energy is maintained when a pendulum swings back and forth in a room with air resistance.
As the pendulum swings, air resistance performs negative work, converting macroscopic mechanical energy (kinetic and potential energy) into microscopic thermal energy (heat). While the pendulum eventually slows to a halt, the energy is not destroyed; it is transferred to the bob and the surrounding air molecules as heat, keeping the total energy of the closed room constant.
3. A hydroelectric power station utilizes falling water from a vertical height of 50 m at a flow rate of 2000 kg/s. If the station operates at 85% efficiency, how much electrical power does it generate? (Use g = 9.8 m/s²).
In one second, potential energy of falling water is PE = m · g · h = 2000 kg · 9.8 m/s² · 50 m = 980,000 J (which corresponds to an input power of 980 kW). The electrical power generated is P_{elect} = Input Power · Efficiency = 980 kW · 0.85 = 833 kW (Kilowatts).
4. Why is E = mc² called mass-energy equivalence?
It shows that mass and energy are not separate, independent quantities, but rather different manifestations of the same physical property. A body at rest has a rest energy proportional to its mass, and mass can be destroyed to release radiant/thermal energy (as in nuclear fusion/fission and matter-antimatter annihilation).
FAQ
Frequently Asked Questions
What is energy in physics?
Energy is defined as the capacity or ability to do work. It is a scalar quantity that exists in many forms and is measured in Joules (J) in the SI system.
What is the Law of Conservation of Energy?
The Law of Conservation of Energy states that energy cannot be created or destroyed; it can only be transformed from one form to another. The total energy of an isolated system remains constant.
What are the main forms of energy?
The main forms of energy include Kinetic Energy (energy of motion), Potential Energy (stored energy due to position/configuration), Thermal Energy (heat), Chemical Energy (stored in molecular bonds), Electrical Energy (moving charges), Radiant/Light Energy (electromagnetic waves), and Nuclear Energy (stored in atomic nuclei).
What is the SI unit of energy?
The SI unit of energy is the Joule (J). One Joule is equivalent to one Newton-meter (1 N·m) or one kilogram-meter squared per second squared (1 kg·m²/s²).
What are some common non-SI units of energy?
Common alternative units of energy include the calorie (cal) for heat, the kilowatt-hour (kWh) for electrical energy consumption, the electronvolt (eV) for subatomic particles, and the British thermal unit (BTU) or Foot-pound (ft·lb) in the US customary system.
What is the difference between Kinetic and Potential energy?
Kinetic Energy is the energy an object possesses due to its motion (e.g., a rolling ball), whereas Potential Energy is stored energy due to an object's position, state, or configuration (e.g., a stretched rubber band or a book on a shelf).
What is Mechanical Energy?
Mechanical Energy is the sum of the macroscopic Kinetic Energy (KE) and Potential Energy (PE) in a system. In a conservative system (no friction or air resistance), the total mechanical energy (E = KE + PE) is conserved.
What is Einstein's mass-energy equivalence?
Einstein's mass-energy equivalence is stated by the famous equation E = mc2, where E is energy, m is mass, and c is the speed of light in vacuum. It shows that mass and energy are two forms of the same physical entity, and mass can be converted into energy (as in nuclear fusion/fission and matter-antimatter annihilation).
How much energy is stored in 1 gram of matter?
According to E = mc2, 1 gram (10-3 kg) of matter contains approximately 9 × 1013 Joules of energy (about 90 trillion Joules, equivalent to 21.5 kilotons of TNT or the energy output of a small nuclear bomb).
What is energy transformation?
Energy transformation is the process of changing energy from one form to another. For example, a solar panel converts radiant light energy into electrical energy, and an electric motor converts electrical energy into mechanical kinetic energy.
What is efficiency in energy systems?
Efficiency is the ratio of useful energy output to the total energy input, usually expressed as a percentage: Efficiency = (Useful Energy Output / Total Energy Input) × 100%. No real machine is 100% efficient because some energy is always lost as thermal energy due to friction or resistance.
Why does friction degrade mechanical energy?
Friction is a non-conservative force that does negative work on moving parts, converting macroscopic mechanical energy (kinetic energy) into microscopic thermal energy (heat). This increases the random motion of atoms, making that energy less available to do useful mechanical work.