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The Bouncing Ball

Where the Energy Goes When a Ball Hits the Floor

Big Question: How does a moving ball turn impact into deformation, then turn some of that stored energy back into upward motion?

Quick Answer

Before impact, the falling ball has kinetic energy. During the collision, the ball and floor deform. Some kinetic energy becomes elastic potential energy in the deformed ball and surface.

As the ball recovers its shape, elastic forces push it upward and convert part of that stored energy back into kinetic energy.

The collision is not perfectly elastic. Energy is transferred into heat, sound, vibrations and internal molecular motion. Therefore the ball leaves the floor with less mechanical energy than it had just before impact and usually rises to a lower height than the release point.

gravitational energy → kinetic energy → deformation energy → rebound kinetic energy + heat + sound + vibration.

What You Will Learn

• Why a ball deforms during impact.
• What elastic deformation means.
• How energy changes form during a bounce.
• Why a ball does not rebound to its original height.
• Why different balls bounce differently.
• How floor material changes rebound.
• Why temperature can affect rubber.
• What coefficient of restitution means.
• Why sound is evidence of energy transfer.
• How to measure rebound fairly.

Part 1 — Before the Drop: Gravitational Potential Energy

Hold a ball above the floor. Because of its position in Earth’s gravitational field, the ball–Earth system has gravitational potential energy.

Release the ball and gravity accelerates it downward. Potential energy decreases while kinetic energy increases.

Part 2 — Just Before Impact: Maximum Speed

Ignoring air resistance, the ball reaches its greatest downward speed immediately before contact with the floor.

Its energy is mostly kinetic at that instant.

Part 3 — The Collision Takes Time

Contact is not a mathematical instant. The bottom of the ball touches first. The ball compresses over a short but measurable time.

During this contact interval, large forces change the ball’s momentum.

Part 4 — The Ball Stores Energy by Deforming

As the ball flattens, molecules and polymer chains in its material are displaced from their preferred arrangements. The material resists this deformation.

Energy is stored in the deformed structure, similar in principle to stretching a spring.

moving ball → compressed ball = kinetic energy temporarily stored as elastic strain energy.

Part 5 — The Floor Also Deforms

No real floor is infinitely rigid. Wood flexes, carpet compresses and even concrete deforms by tiny amounts.

The collision therefore involves two materials. A soft floor can absorb more energy and return less to the ball.

Part 6 — Recovery Creates the Rebound

After maximum compression, elastic forces drive the ball back toward its original shape. While the ball remains in contact with the floor, those forces accelerate its centre of mass upward.

When contact ends, the ball leaves the floor with upward velocity.

Part 7 — Why the Ball Does Not Return to the Same Height

If every joule of mechanical energy were returned, the ball could rise to its original height in an idealised system.

Real materials are not perfectly elastic. Internal friction converts some organised mechanical energy into disorganised thermal motion. The floor vibrates. Air vibrates and carries sound. The ball can wobble or spin.

So the rebound begins with less mechanical energy.

Part 8 — Sound Is an Energy Receipt

The “thump” of impact is evidence that some energy left the ball–floor mechanical motion as sound waves.

The sound energy is usually small compared with the total, but it is useful because your ears can detect one path of energy transfer directly.

Part 9 — Heat Is Harder to Notice

Repeatedly deform rubber and it can warm slightly. Internal molecular rearrangements and friction dissipate energy as heat.

A single bounce produces a tiny temperature rise that is difficult to feel, but many rapid deformations can make the effect measurable.

Part 10 — Different Balls Store and Return Energy Differently

• A superball can return a large fraction of impact energy.
• A tennis ball combines a rubber shell with pressurised gas.
• A basketball uses an inflated bladder and elastic shell.
• A clay ball deforms plastically and may barely rebound.
• A steel ball can rebound well from a hard surface despite appearing rigid.

Bounce therefore depends on material structure, geometry and the surface struck.

Part 11 — Pressure Inside Inflated Balls Matters

In an inflated ball, impact compresses the gas as well as deforming the shell. Higher internal pressure can change stiffness, contact time and rebound behaviour.

This is why sports balls have specified inflation ranges.

Part 12 — Temperature Changes Rubber

Rubber is a polymer. Its molecular mobility depends on temperature.

A cold rubber ball can become less able to deform and recover in the same way as a warmer ball, changing bounce height. Exact behaviour depends on the rubber formulation and temperature range.

Part 13 — Coefficient of Restitution

Physicists describe collision elasticity using the coefficient of restitution.

For a simple vertical bounce, it can be related to drop height H and rebound height h:

e ≈ √(h/H)

A value near 1 means a highly elastic collision. A smaller value means more kinetic energy is lost from the relative rebound motion.

It is not a universal number for a ball alone; it depends on both colliding materials and conditions.

Follow One Bounce

1. Ball is held above floor.
2. Gravitational potential energy is available.
3. Ball falls and gains kinetic energy.
4. Bottom contacts floor.
5. Ball and floor deform.
6. Kinetic energy becomes elastic strain and internal energy.
7. Maximum compression occurs.
8. Elastic recovery pushes upward.
9. Ball leaves floor.
10. Some energy remains as heat, sound and vibration.
11. Ball rises to a lower height.
12. The cycle repeats with less mechanical energy each time.

A Text Diagram You Can Draw Anywhere

HIGH BALL
 gravitational energy
       ↓
FALLING BALL
 kinetic energy
       ↓
IMPACT
 ball flattens
       ↓
ELASTIC STORAGE + HEAT + SOUND
       ↓
RECOVERY
 upward push
       ↓
REBOUND
 less mechanical energy
       ↓
LOWER HEIGHT

Think Like a Scientist — Measure Rebound Height

1. Tape a vertical measuring scale to a wall.
2. Release the ball without pushing it.
3. Use the same drop height each trial.
4. Film in slow motion.
5. Measure the first rebound height.
6. Repeat at least five times.
7. Compare different balls on the same floor.
8. Then compare one ball on different surfaces.

Change only one variable at a time.

How Do We Know?

High-speed cameras measure deformation and contact time. Force sensors measure collision force. Infrared instruments can detect heating. Microphones record sound. Rebound height gives a simple estimate of collision elasticity.

A strong explanation should account for all these receipts at once.

Observation vs Inference

• Observation: the ball rebounds lower than release height.
• Observation: high-speed video shows flattening during impact.
• Observation: impact makes sound.
• Inference: deformation stores energy temporarily.
• Inference: some mechanical energy is dissipated into internal energy and other modes.

Common Misconceptions and Repairs

Misconception	Better model
The floor throws the ball upward.	Contact forces arise as ball and floor deform; elastic recovery accelerates the ball.
The ball keeps all its energy.	Total energy is conserved, but mechanical energy spreads into heat, sound and vibration.
A hard ball does not deform.	All real materials deform under sufficient force, even if the change is tiny.
Higher bounce means more energy was created.	Higher bounce means a larger fraction of impact energy returned to mechanical motion.
Coefficient of restitution belongs only to the ball.	It characterises the collision pair and conditions.
No bounce means no energy.	Energy can be dissipated through permanent deformation, heat and sound.

Checkpoint Questions

1. What energy does a raised ball have?
2. What happens to that energy while falling?
3. Why does the ball flatten during impact?
4. What is elastic deformation?
5. What pushes the ball upward?
6. Why is rebound height lower?
7. Where does missing mechanical energy go?
8. Why does floor material matter?
9. Why can temperature change rubber bounce?
10. What does coefficient of restitution describe?

Apply It — Three Floors

• A: concrete.
• B: thick carpet.
• C: sprung wooden sports floor.

Predict how the same ball may rebound differently and identify which surface properties must be measured before making a precise claim.

Answer Key

Open after attempting the application

Concrete usually deforms little and can return a large fraction of energy to a suitable elastic ball. Thick carpet deforms strongly and dissipates more energy, often reducing rebound. A sprung floor can store and return energy too, so the exact bounce depends on timing, stiffness and damping. “Harder floor = always higher bounce” is a useful trend, not a universal law.

Can You Explain WHY?

• Why must the ball deform before it can rebound?
• Why can sound prove that energy left the visible motion?
• Why does a carpet reduce bounce?
• Why can a steel ball still deform?
• Why does rebound height reveal collision elasticity?
• Why is energy conserved even when the ball eventually stops?

Singapore Everyday Connection

Basketball courts, table-tennis balls, footballs and playground balls make collision physics visible every day. Compare the same ball on concrete, rubber flooring and grass. Record rebound height rather than judging by sound alone.

Primary Science / PSLE Bridge

• forces change motion;
• gravity acts on objects;
• energy can change form;
• materials can deform;
• fair tests control variables;
• observations can be measured quantitatively.

Go Beyond Primary Science

Primary idea	Higher-resolution science
Ball flattens	Stress and strain
Ball springs back	Elastic modulus and viscoelasticity
Bounce loses height	Damping and hysteresis
Impact changes momentum	Impulse
Different collisions rebound differently	Coefficient of restitution
Rubber changes with temperature	Polymer dynamics and glass transition

Deep Science Window — Rubber Is Viscoelastic

Rubber behaves partly like an elastic solid and partly like a dissipative material. Polymer chains stretch and rearrange during deformation. Some energy is returned; some becomes heat.

This combination is called viscoelasticity and explains why real stress–strain cycles show hysteresis rather than perfect recovery.

Evidence Boundaries

• Bounce ≠ perfectly elastic collision.
• Energy loss from motion ≠ energy destroyed.
• Hard-looking material ≠ zero deformation.
• Rebound height ≠ property of ball alone.
• Hooke’s law ≠ exact model for all ball deformation.
• Higher pressure ≠ unlimited bounce. Sports balls have safe operating ranges.

Manual Summary — KNOW → CONNECT → EXPLAIN → APPLY → CHECK

KNOW: kinetic energy, gravitational potential energy, deformation, elasticity, rebound, dissipation and restitution.

CONNECT: fall → impact → deformation → elastic recovery → rebound + heat/sound.

EXPLAIN: the bounce is powered by recovery from deformation, not by energy appearing at the floor.

APPLY: sports balls, springs, shoes, vehicle suspension and protective materials.

CHECK: does the explanation account for both rebound and the lower final height?

Where to Go Next

• The Physical World
• eduKate Learning Manual: Paper Fibres
• eduKate Learning Manual: Spider Silk

Research Sources and Further Reading

• OpenStax College Physics — Inelastic Collisions and Bouncing-Ball Experiment
• OpenStax Physics — Elasticity, Stress and Strain
• OpenStax Physics — Work and Energy

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