Physics Interactive

The Currency of the Universe

Energy is what allows us to run, machines to work, and lightbulbs to glow. It is the ability to do work, cause change, or make things happen.

The Universal Currency

Think of energy like money; you can spend it in different ways, but the total amount remains the same.

The Unit of Measure

We measure energy in Joules (J).

Fun fact: One Joule is roughly the energy needed to lift a small apple one meter into the air!

Transformative Nature

Energy never simply disappears. It just puts on a new disguise, transforming from one type into another.

Abstract Energy

Energy makes everything in our universe possible.

Kinetic Energy (KE)

The energy of motion.

Kinetic Energy is the energy an object possesses due to its motion. If it is moving, it has kinetic energy.

The amount of kinetic energy depends on two factors: mass ($m$) and speed/velocity ($v$).

KE = ½ m v²

  • m = mass in kilograms (kg)
  • v = velocity in meters per second (m/s)
  • KE = Kinetic Energy in Joules (J)

Because speed is squared in the formula, doubling your speed actually quadruples your kinetic energy!

Cheetah running
A sprinting cheetah has incredible kinetic energy because it is moving at top speed, even if its mass isn't as large as an elephant's.

KE Calculator

Kinetic Energy:
400 J

Potential Energy (PE)

Stored power waiting to be released.

Gravitational Potential

Energy stored due to an object's height above the ground.

The higher you lift an object, and the heavier the object is, the more gravitational potential energy (GPE) it stores. Think of a roller coaster paused at the very top of a massive drop.

PE = mgh

m = mass, g = gravity (9.8 m/s²), h = height

Quick Calc

Result
98 J

Elastic Potential

Energy stored when an object is stretched, compressed, or bent.

A pulled rubber band, a drawn archery bow, or a compressed spring all contain high amounts of elastic potential energy just waiting to be released.

Archery

The Mighty Flea

A common flea can jump over 100 times its own height! It achieves this by storing elastic potential energy in a special pad made of a protein called resilin in its legs, releasing it like a tiny, powerful spring.

The Ultimate Rule

"Energy can neither be created nor destroyed;
it can only be transferred or changed from one form to another."

— The Law of Conservation of Energy

Falling Object Simulator

Mechanical Energy (ME) = Constant
100m 50m 0m
1kg

Drag slider to drop the object

Potential Energy (PE) 980 J
Kinetic Energy (KE) 0 J
Total Mechanical Energy 980 J

As the object falls, it loses height (losing PE) but gains speed (gaining KE). The total mechanical energy in a perfect system remains exactly the same!

Want to explore more? Try the University of Colorado's interactive Energy Skate Park!

Open Energy Skate Park Simulator

Energy in the Real World

Reflecting on the Impacts of Science.

The Scenario

Pumped-Storage Hydroelectricity

A local government is considering building a "pumped-storage hydroelectric dam" in a nearby mountain valley to solve their town's power shortage.

  • At night, when power is cheap, they use electricity to pump water up a mountain into a reservoir (storing Gravitational Potential Energy).
  • During the day, when everyone needs power, they let the water fall back down through turbines (turning to Kinetic, then Electrical Energy) to generate electricity.
Hydroelectric Dam

Functional Energy Literacy

What is a Watt?

We don't just use Joules in real life. When you look at an appliance, you see its power consumption in Watts (W) or Kilowatt-hours (kWh).

1 Watt = 1 Joule per second (1 J/s)

Reading the Label

Energy rating labels use color codes (green to red) and letter grades (A to G) to tell consumers how efficiently a fridge or TV uses electrical energy. Understanding these helps families save money and protect our planet!

Knowledge Check & Tasks

Test your skills based on Criterion A (Calculations) & Criterion D (Impacts).

Formulas: KE = ½mv² PE = mgh g = 9.8 m/s²

Criterion A: Knowing and Understanding

Level 1-2: Emerging (Recall and Simple Application)

Q1: In your own words, state the difference between kinetic energy and gravitational potential energy.

Answer: Kinetic energy is the energy an object has because it is actively moving. Gravitational potential energy is stored energy an object has due to its height above the ground.

Q2: A 5 kg bowling ball is resting on a shelf that is 2 meters high. Calculate the gravitational potential energy of the bowling ball.

Answer:
PE = m × g × h
PE = 5 kg × 9.8 m/s² × 2 m
PE = 98 Joules

Q3: A 50 kg student is running at a velocity of 4 m/s. Calculate the student's kinetic energy.

Answer:
KE = ½ × m × v²
KE = 0.5 × 50 kg × (4 m/s)²
KE = 25 × 16
KE = 400 Joules
Level 3-4: Developing (Applying Knowledge)

Q1: An archer pulls back a bowstring and releases an arrow. Outline the specific energy transformations taking place.

Answer: The archer does work to pull the string, storing Elastic Potential Energy in the bent bow. Upon release, this stored energy rapidly transforms into the Kinetic Energy of the flying arrow.

Q2: A cheetah has a kinetic energy of 2800 J while sprinting at a velocity of 20 m/s. Calculate the mass of the cheetah.

Answer:
KE = ½ × m × v²
2800 = 0.5 × m × (20)²
2800 = 0.5 × m × 400
2800 = 200 × m
m = 2800 ÷ 200
Mass = 14 kg

Q3: A drone has 1470 J of gravitational potential energy while hovering in the air. If the drone has a mass of 3 kg, calculate how high it is flying.

Answer:
PE = m × g × h
1470 = 3 × 9.8 × h
1470 = 29.4 × h
h = 1470 ÷ 29.4
Height = 50 meters
Level 5-6: Proficient (Complex Situations)

Q1: A 60 kg skateboarder is standing at the top of a frictionless halfpipe that is 4 meters deep.

  • A) Calculate their maximum potential energy at the top.
  • B) Using the Law of Conservation of Energy, determine their kinetic energy the exact moment they reach the bottom of the halfpipe.
  • C) Calculate the skateboarder's velocity at the bottom of the halfpipe.
Answers:
A) PE = mgh = 60 × 9.8 × 4 = 2,352 J
B) Because it's frictionless, Mechanical Energy is conserved. All PE turns into KE. KE = 2,352 J
C) KE = ½mv²
2352 = 0.5 × 60 × v²
2352 = 30 × v²
v² = 78.4
Velocity = √78.4 ≈ 8.85 m/s
Level 7-8: Mastery (Evaluating Unfamiliar Situations)

Q1: A 1000 kg roller coaster car drops from a 50-meter-tall hill. It travels through the track and comes to a stop at the top of a second hill, which is only 40 meters tall.

  • A) Calculate the mechanical energy the car lost between the first and second hill.
  • B) Explain, using scientific reasoning, where this "lost" energy went and why the second hill can never be taller than the first.
Answers:
A) Initial Energy (Top of Hill 1) = PE = 1000 × 9.8 × 50 = 490,000 J.
Final Energy (Top of Hill 2) = PE = 1000 × 9.8 × 40 = 392,000 J.
Lost Energy = 490,000 - 392,000 = 98,000 J lost.

B) The energy was not destroyed; it was transformed into thermal energy (heat) and sound energy due to friction between the wheels and the track, and air resistance. The second hill can never be taller than the first because the coaster will inevitably lose some mechanical energy to the environment. It won't have enough kinetic energy left to climb higher than its starting point without an external motor doing work.

Criterion D: Reflecting on the Impacts of Science (Pumped Hydro)

Refer back to the "Pumped Hydro" tab for the context scenario to answer these questions.

Criterion D Task Discussion Points

Scientific Solution

How it works: Excess electrical energy at night does work to pump water uphill, converting electrical energy into Gravitational Potential Energy. During peak daytime demand, water flows down, converting PE to Kinetic Energy, spinning turbines to generate Electrical Energy.

Energy Loss: While Mechanical Energy is ideally conserved, real-world pumping and turbine spinning involves friction. Some energy is lost to the environment as thermal energy, meaning you get less electricity out during the day than you used to pump the water up at night.

Implications & Trade-offs

  • Economic (Positive): Provides reliable power during peak hours preventing blackouts. Creates local jobs for construction and maintenance. Can sell expensive daytime power while using cheap nighttime power.
  • Environmental (Negative): Flooding a mountain valley destroys local terrestrial habitats, displaces wildlife, and alters downstream water flow and aquatic ecosystems.
  • Evaluation: Is the destruction worth it? (Students must justify their stance based on the need for clean, reliable energy storage vs local ecological damage).

"Energy is the ultimate currency of the universe."