Physics 001.001.017 Efficiency of Mechanical Work

Alignment

Learning Intentions

By the end of the lesson, students will be able to:

• Explain that mechanical energy transfers and transformations are never perfectly efficient.
• Describe how friction, air resistance and deformation transform some mechanical energy into thermal energy.
• Recognise that energy is conserved, but the amount of useable energy decreases when energy spreads to the environment as heat.
• Distinguish between total energy and useable energy.

Success Criteria

By the end of the lesson, students have successfully:

• Identified where heat loss occurs in a mechanical system.
• Explained why heat loss reduces the amount of useable energy available for further work.
• Used energy flow diagrams to represent useful and wasted energy pathways.
• Applied the idea of degraded energy to examples such as a bouncing ball, car braking and pendulum motion.

Syllabus Reference

• Unit 1: Thermal, Nuclear and Electrical Physics, Topic 1: Heating Processes
• Explain how energy transfers and transformations in mechanical systems always result in some heat loss to the environment, so that the amount of useable energy is reduced.

Phenomenon

A basketball is dropped from a height. It bounces several times, but each bounce is lower than the one before. Eventually, it comes to rest.

The ball did not “lose” energy in the sense that energy disappeared. Instead, some of its mechanical energy was transformed into thermal energy and sound. The ball, floor and surrounding air became slightly warmer, although the temperature increase is usually too small to notice without sensitive equipment.

This demonstrates a key idea in thermodynamics: energy is conserved, but not all energy remains useable for doing mechanical work.

Key Idea

Energy transfers and transformations in mechanical systems always result in some energy spreading into the environment as thermal energy. This reduces the amount of useable energy available to continue doing mechanical work.

Concept

Mechanical systems involve energy stores such as kinetic energy and gravitational potential energy.

For example:

• a moving car has kinetic energy
• a raised object has gravitational potential energy
• a compressed spring has elastic potential energy

In an ideal system with no friction, air resistance, sound or deformation, mechanical energy would be conserved within the system.

In real systems, non-conservative forces act. These include:

• friction
• air resistance
• drag
• internal resistance
• deformation
• rolling resistance

These forces transform some mechanical energy into thermal energy. The energy still exists, but it becomes more spread out and less useful for doing organised mechanical work.

For a mechanical system:

where the “wasted” energy is usually transferred to the environment as heat and sound.

Convention

Energy is not destroyed. Instead, it is transformed or transferred.

A useful way to describe this is:

However, the useable mechanical energy decreases:

The “missing” mechanical energy has usually become thermal energy of the surroundings:

A more complete representation is:

Useable energy means energy that can be readily transformed into useful work.

Degraded energy means energy that has spread into the surroundings as thermal energy and is no longer easily available for useful mechanical work.

Misconceptions

Common misconceptions students have regarding the concept when applying to various situations and solving problems. It could be a conceptual, mathematical or logical misconception.

• Energy is “lost” or destroyed when an object slows down.
• Heat loss means energy has disappeared from the universe.
• Thermal energy is always useless, rather than less useable in a particular context.
• If an object stops moving, it must have no energy left.
• Friction only opposes motion and does not involve an energy transformation.

Further Reading

• Conservation of energy
• First law of thermodynamics
• Mechanical energy
• Friction and drag
• Efficiency
• Second law of thermodynamics, qualitatively

Explicit Instruction

Begin with the bouncing ball demonstration.

Ask students:

“Why does the ball not return to its original height?”

Guide students to the idea that:

• the ball starts with gravitational potential energy
• gravitational potential energy transforms into kinetic energy as it falls
• kinetic energy transforms back into gravitational potential energy as it rises
• each bounce transfers some energy to the ball, floor and air as heat and sound
• less mechanical energy remains after each bounce

The important point is that total energy is conserved, but useable mechanical energy decreases.

A mechanical system often transforms energy between kinetic energy and potential energy:

In an ideal falling and rising system:

In a real system:

decreases over time because some energy is transferred to the environment.

So:

The energy transferred as heat is usually not easily recovered to do useful mechanical work again. This is why the amount of useable energy is reduced.

Worked Examples

Worked Example 1

A ball is dropped from a height. It initially has of gravitational potential energy. After one bounce, it rises to a height where it has only of gravitational potential energy.

How much energy was transferred to the surroundings?

Solution:

Therefore, was transferred to the surroundings, mainly as heat and sound.

Explanation:

The energy was not destroyed. The ball has less useable mechanical energy because some energy has been transferred to the ball, floor and air as thermal energy and sound.

Worked Example 2

A cyclist travelling along a flat road stops pedalling. The bicycle gradually slows down.

Explain why the bicycle slows down in terms of energy transfers.

Solution:

The cyclist and bicycle initially have kinetic energy.

As the bicycle moves, friction and air resistance act on the system.

These forces transform kinetic energy into:

• thermal energy in the tyres, road, bearings and air
• sound energy
• internal energy due to slight deformation of materials

As kinetic energy decreases, the bicycle slows down.

The total energy is conserved, but the useable mechanical energy of the cyclist-bicycle system decreases because some energy is transferred to the environment as heat.

Worked Example 3

A car’s brakes are used to slow the car down. The car’s kinetic energy decreases by .

Assume is transferred as thermal energy to the brake pads, wheels and surrounding air. The rest is transferred as sound and deformation.

Calculate the energy transferred by sound and deformation.

Solution:

Therefore, was transferred by sound and deformation.

Explanation:

The car’s kinetic energy was transformed into other forms of energy. Most became thermal energy, which is why brakes become hot during use.

Check for Understanding

Check 1

A pendulum is pulled to one side and released. Over time, the pendulum swings lower and lower until it stops.

Question:

Where has the pendulum’s mechanical energy gone?

Expected answer:

The mechanical energy has been transformed into thermal energy and sound due to air resistance and friction at the pivot. The energy is still conserved, but it has become less useable for doing mechanical work.

Check 2

True or false:

“When a moving object stops because of friction, its energy has been used up.”

Expected answer:

False.

The energy has not been used up or destroyed. The object’s kinetic energy has been transformed into thermal energy of the object and surroundings.

Check 3

A toy car is released from the top of a ramp. It reaches the bottom with less kinetic energy than expected from its initial gravitational potential energy.

Question:

Explain why.

Expected answer:

Some gravitational potential energy was transformed into thermal energy and sound due to friction between the wheels and axles, friction between the wheels and ramp, air resistance, and deformation. Therefore, less energy remained as useable kinetic energy.

Investigation (Alternative to Explicit)

Hypothesis

If a ball is dropped from a greater height, then more energy will be transferred to the surroundings during the bounce because the ball has more initial gravitational potential energy.

Data Collection

Equipment:

• ball
• metre ruler or measuring tape
• clamp stand or wall scale
• phone camera for slow-motion recording
• flat hard surface

Method:

1. Drop the ball from a known height, such as .
2. Record the bounce using slow-motion video.
3. Measure the maximum height reached after the first bounce.
4. Repeat at least three times.
5. Repeat for other drop heights, such as , and .
6. Record results in a table.

Suggested table:

Trial	Drop height in	Bounce height in	Initial energy in	Final useable energy in	Energy transferred in

Analysis

Students calculate:

Students then compare the initial mechanical energy with the mechanical energy available after the bounce.

The percentage of mechanical energy retained can be calculated using:

Evaluation

Students should evaluate:

• accuracy of height measurements
• effect of parallax error
• consistency of release method
• whether the ball was spinning
• whether the surface changed during the experiment
• whether slow-motion video improved precision
• whether repeated trials reduced random error

Students should conclude that the ball does not return to its original height because some mechanical energy is transformed into thermal energy and sound during the collision with the floor.

Problems

The following problems are designed to develop qualitative and quantitative understanding of heat loss and reduced useable energy in mechanical systems.

1. A ball is dropped with of gravitational potential energy. After bouncing, it has of gravitational potential energy at the top of its rebound.

   a. How much energy was transferred to the environment?

   b. Name two forms this energy may have taken.

2. A skateboarder rolls along a flat path and gradually slows down.

   Explain why the skateboarder slows down even though energy is conserved.

3. A car’s brakes reduce its kinetic energy from to .

   a. Calculate the decrease in kinetic energy.

   b. Explain where this energy goes.

4. A pendulum has of mechanical energy at the start. After several swings, it has of mechanical energy.

   Calculate the energy transferred to the surroundings.

5. A student says, “Friction wastes energy, so energy is not conserved.”

   Write a response that corrects this misconception.

6. Draw an energy flow diagram for a cyclist braking to stop. Include:

   • initial kinetic energy
   • useful or intended energy transfer
   • heat loss
   • sound
   • environment

7. A toy car starts with of gravitational potential energy at the top of a ramp. At the bottom, it has of kinetic energy.

   a. How much energy was transferred to the environment?

   b. Explain why this energy is less useable.

8. Explain why no real mechanical machine can be efficient.

Followup

Self-check

Students should be able to answer the following questions:

• Can I explain why a bouncing ball reaches a lower height after each bounce?
• Can I identify the useful and wasted energy transfers in a mechanical system?
• Can I explain why heat loss does not break the law of conservation of energy?
• Can I distinguish between energy being conserved and useable energy being reduced?
• Can I explain why friction and air resistance cause mechanical systems to become less efficient?

Next Topic

Describe the concept of efficiency.

This lesson leads naturally into calculating efficiency using:

Students will use this relationship to quantify how much input energy becomes useful output energy and how much is transferred to the environment.