Work, Energy, and Simple Machines · Lesson 6 of 13
Potential Energy
“A stretched band looks still, but it is quietly saving trouble for later.”
• Explain how deformation can store potential energy. • Describe potential energy in systems of interacting objects. • Trace the conversion of potential energy into kinetic energy. • Distinguish energy stored by position from energy of motion. • Use springs, magnets, charges and gravity as connected examples.
A stretched slingshot can remain motionless in your hand, yet the moment it is released, its object shoots forward. A bent bow can launch an arrow, and a compressed spring can push a toy cart. None of these objects is moving while held in the deformed state, so their stored energy is not kinetic. Their capacity to do work comes from configuration.
Energy Stored Through Deformation
Stretching a rubber band or compressing a spring requires an external force acting through a distance. The external force does work to overcome internal forces in the object. That work is stored as potential energy in the deformed configuration. When the external force is removed, internal forces restore the original shape and can do work on another object.
In a bow, the archer’s work bends the arms of the bow and stretches the string. On release, the bow transfers stored energy to the arrow. The arrow gains kinetic energy while the bow returns toward its original shape. A spring produces the same pattern: work done during compression becomes stored energy, which can later become motion.
Elastic potential energy is energy stored when an elastic object is stretched, compressed or bent away from its original shape.
Problem
Explain the energy changes when a moving hand compresses a spring against a toy cart and then releases it.
- 1.The hand applies a force through a distance and does positive work on the spring.
- 2.The spring changes shape and stores elastic potential energy.
- 3.While held compressed, the spring and cart can be motionless even though energy is stored.
- 4.After release, the spring applies a force to the cart through a distance.
- 5.The spring’s potential energy decreases while the cart’s kinetic energy increases.
Energy Stored Through Relative Position
Potential energy can also be stored by changing the arrangement of interacting objects. Unlike magnetic poles attract. Separating them requires an external force and work. When released, they move together and gain kinetic energy. The stored energy belongs to the system of magnets and depends on their relative positions, not on either magnet in isolation.
Electric charges provide another example. A system of charges separated or arranged against their electric interaction can store energy. When released, electric forces can accelerate the charges and convert stored potential energy into kinetic energy.
A ball and Earth also form an interacting system. Lifting the ball requires work against gravitational attraction. If released, the ball and Earth move toward each other, although Earth’s motion is too small to notice because its mass is enormous. The system’s stored gravitational potential energy decreases while kinetic energy increases.
Potential energy is energy stored by an object because of deformation or by a system because of the relative positions of interacting objects.
| System or Object | How Energy Is Stored | What Happens When Released |
|---|---|---|
| Stretched rubber band | Changed shape | Band can launch an object |
| Compressed spring | Changed shape | Spring can push a cart |
| Separated unlike magnetic poles | Relative position against attraction | Magnets move together |
| Interacting electric charges | Relative arrangement of charges | Charges accelerate |
| Raised ball and Earth | Greater separation in the gravitational system | Ball falls and gains speed |
Problem
Two unlike magnetic poles are slowly pulled apart and then released. Describe work and energy during both stages.
- 1.Magnetic attraction acts to pull the magnets together.
- 2.The external force moves them apart against this attraction and does positive work on the system.
- 3.The work increases the system’s magnetic potential energy.
- 4.After release, magnetic forces pull the magnets toward each other.
- 5.Potential energy decreases while the magnets gain kinetic energy.
Problem
Why does an arrow leave a bow even though it was initially at rest?
- 1.The archer does work while pulling the string and bending the bow.
- 2.That work is stored as elastic potential energy in the deformed bow.
- 3.When released, the bow exerts a force on the arrow through a distance.
- 4.The stored energy is transferred to the arrow as kinetic energy.
- 5.The arrow therefore moves even though it initially had no kinetic energy.
Potential Energy Belongs to a Configuration
Potential energy should not be imagined as a substance hidden inside every object. It describes the capacity for work that arises from a particular configuration. A spring’s deformation is a configuration of its parts; magnetic, electric and gravitational potential energies depend on the positions of interacting objects. Changing the chosen system can therefore change how the energy account is described.
Stored Energy and the Amount of Deformation
A greater deformation generally requires more work and stores more elastic potential energy. Pulling a slingshot farther requires the hand to exert force through a greater distance, and the band also becomes harder to stretch. On release, the more strongly deformed band can usually give the projectile more kinetic energy. The exact relation for a spring is not needed here; the essential idea is that additional work creates a configuration with greater capacity to do work later.
Problem
The same elastic launcher is stretched by a small amount for one trial and by a larger amount for another. Predict the motion when the same light object is released.
- 1.The larger stretch requires work over a greater deformation.
- 2.More elastic potential energy is stored in the more deformed launcher.
- 3.On release, more energy can be transferred to the object as kinetic energy.
- 4.Under otherwise similar conditions, the object is expected to leave faster and travel farther.
- 5.Air resistance and the launch direction can affect the measured distance, so trials should be repeated.
A motionless object has zero kinetic energy in the chosen reference frame, but it may still possess potential energy because of deformation or position.
Quiz
Which description best matches Elastic Potential Energy?
Which description best matches Potential Energy?
Which term matches this description: Elastic potential energy is energy stored when an elastic object is stretched, compressed or bent away from its original shape.
Which term matches this description: Potential energy is energy stored by an object because of deformation or by a system because of the relative positions of interacting objects.
Which statement is a key takeaway from this lesson?
Practice Problems
- Explain how work is stored when a rubber band is stretched.
- Describe the energy changes when a compressed spring is released against a block.
- Why is magnetic potential energy described for a system of magnets?
- Give one example of potential energy due to deformation and one due to relative position.
Key Takeaways
• Deformation can store potential energy. • Relative positions of interacting objects can also store potential energy. • External work creates the stored configuration. • Internal forces can later convert potential energy into kinetic energy. • A motionless system may still have the capacity to do work.