Lesson 2 of 6 · Kinetic and potential energy
Track energy in motion and position
8 minute lesson · 3 checks along the way
Your goal for this lessonCalculate a simple exchange between kinetic and gravitational potential energy while stating the reference frame and height convention.
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Motion is measured relative to something
A tool resting inside an orbiting spacecraft is stationary relative to the cabin but moving rapidly relative to Earth. Its therefore depends on the used to measure its velocity. For a nonrotating object treated as a particle at ordinary spacecraft speeds, translational kinetic energy is K = ½mv². Use mass in kilograms and speed in meters per second to obtain joules.
Doubling speed quadruples this kinetic energy at unchanged mass. Doubling mass at unchanged speed doubles it. Direction does not make kinetic energy negative: the speed is squared. A body moving left and an identical body moving right at the same speed have equal kinetic energies in that frame. Their momenta point in opposite directions, a distinction that will matter when we study collisions.
Potential energy belongs to an interaction
describes the configuration of interacting masses. Near Earth’s surface, a small upward displacement h gives a change approximately mgh, where g is local gravitational acceleration. Speaking of a lifted object’s potential energy is convenient shorthand for the object–Earth system. Gravity has not created energy from nothing; lifting with a crane transfers energy into that system while other parts of the equipment consume energy.
Choose a reference height and keep it consistent. Calling the floor zero potential energy is a convention, not a claim that all energy vanishes there. Changes between heights remain the same if the zero moves. The mgh approximation assumes gravity is effectively constant across the height change; it must not be extended unchanged across a journey from Earth to the Moon.
Check 1 of 3
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Work through a decision
Predict a fall with stated assumptions
Imagine a 2-kilogram test mass released from rest 5 meters above a floor. Treat Earth as fixed for this small experiment, use g = 10 m/s², and neglect air resistance. Set gravitational potential energy to zero at the floor. Initially it is 2 × 10 × 5 = 100 , while the mass’s kinetic energy is zero. Follow the motion only until just before contact.
As the mass falls, gravitational potential energy decreases and kinetic energy increases. Just above the floor, K = 100 joules. Substituting into ½ × 2 × v² = 100 gives v = 10 m/s. This predicts the impact speed in the model, not the bounce or damage. Those outcomes require additional information about deformation, contact forces, and energy transferred during the collision.
Check 2 of 3
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Separate what a photograph can show
The recovery photograph from SpaceX Crew-3 shows Dragon Endurance suspended on lifting equipment after returning to Earth. A still image reveals its support and position within the recovery operation; it does not supply a timed motion record. The capsule could have little kinetic energy relative to the recovery ship while the ship and capsule together move relative to the surrounding water or Earth.
Estimating a small increase in gravitational potential energy during the hoist would require the lifted mass and the change in vertical height. Estimating kinetic energy would instead require speed in a stated frame. Neither can be obtained from the capsule’s scorched appearance. The photograph helps you select a physical situation, while measurements and explicit assumptions make an energy calculation meaningful.
Dragon Endurance during recovery after SpaceX Crew-3 splashed down on May 6, 2022, photographed by Aubrey Gemignani. This is the actual recovered capsule, with lifting cables, weathered exterior, and heat shield visible. The photograph does not supply a measured hoisting distance or speed.
Look closely
Use the lifting cables to identify the support. Why can a capsule’s height and scorched surface not tell you its kinetic energy during recovery?
See what to notice
Kinetic energy requires mass and speed in a specified frame. Height relates to gravitational potential energy, while surface condition reflects earlier history. A timed position record and an appropriate mass measurement would support the recovery-motion calculation.
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