Chapter 1: Conservation and Dissipation of Energy

Knowledge Organiser

1. Calculating the Energy in an Energy Store

When the height of an object changes, its gravitational potential energy (GPE) changes as well. The relationship can be expressed mathematically as follows:
Change of gravitational potential energy store,
$riangle E_p ext{ (J)} = m ext{ (kg)} imes g ext{ (N/kg)} imes riangle h ext{ (m)}$
In simpler terms:
$E_p = mgh$
Where:

• $E_p$ is the gravitational potential energy in joules (J)
• $m$ is the mass of the object in kilograms (kg)
• $g$ is the gravitational field strength in newtons per kilogram (N/kg)
• $h$ is the change in height in meters (m)

The kinetic energy (KE) of an object, which refers to the energy it possesses due to its motion, is dependent solely on its mass and velocity. The kinetic energy can be calculated using the formula:
E_k ext{ (J)} = rac{1}{2} imes m ext{ (kg)} imes v^2 ext{ (m/s)}^2

• Where $E_k$ represents kinetic energy,
• $m$ is the mass of the object, and
• $v$ is the speed of the object in meters per second (m/s).

An object’s elastic potential energy when it is deformed (stretched or compressed) can be calculated as follows:
E_e ext{ (J)} = rac{1}{2} imes k ext{ (N/m)} imes e^2 ext{ (m)}^2

• Here, $E_e$ is the elastic potential energy,
• $k$ is the spring constant in newtons per meter (N/m), and
• $e$ is the extension or compression in meters (m).
  (Assuming that the limit of proportionality has not been exceeded.)

2. Understanding Power

Power quantifies the rate at which work is performed, or equivalently, the rate at which energy is transferred. The definition of power is:
Power,
P ext{ (W)} = rac{E ext{ (J)}}{t ext{ (s)}}
Where:

• $P$ is power in watts (W)
• $E$ is energy transferred in joules (J)
• $t$ is time in seconds (s)
  Alternatively, power can also be defined through work done as:
  P = rac{W ext{ (J)}}{t ext{ (s)}}
  Where $W$ is work done in joules (J).

3. The Concept of Systems

In physics, a system refers to either a single object or a group of objects. Within this system, energy is transferred between its stores or to the surroundings whenever a change occurs.
A closed system is defined as a system where no energy can enter or escape to its surroundings. In this case, the total energy within a closed system remains constant over time.

4. Energy Stores

Different types of energy can be categorized as follows:

• Chemical: Energy transferred during a chemical reaction; examples include energy from fuels, food, or batteries.
• Kinetic: Energy possessed by an object due to its motion; an example is a ball rolling down a hill.
• Gravitational Potential: Energy stored in an object as a result of its position in a gravitational field; for example, an object positioned above the ground.
• Elastic Potential: Energy stored in an object that is spring-like when it is either stretched or compressed, such as a stretched rubber band or compressed spring.
• Thermal: The energy attributable to the temperature of a substance, like a hot drink.

5. Energy Transfers

Energy can be transferred among different stores through various mechanisms:

• Heating: Energy transfer occurs from a warmer object to a cooler object.
• Waves: Energy can be transmitted through different wave types, including light and sound.
• Electricity: An electric current is a means of transferring energy.
• Forces (Mechanical Work): Energy is transferred when a force moves or alters the shape of an object.

Examples of Energy Transfer Processes

1. When stretching a rubber band, energy from a person's chemical store is transferred to the elastic potential store of the rubber band.
2. When a block is dropped, energy shifts from its gravitational potential store to its kinetic energy store via gravitational force.
3. Upon impact with the ground, energy from the block’s kinetic store dissipates as thermal energy and sound waves into the thermal energy store of the surroundings.
4. In electric kettles, energy from the electric current is transferred to the kettle's heating element, subsequently moving to heat the water.
5. During motion, friction converts kinetic energy into thermal energy, which is distributed between the moving object, the object in contact, and the surroundings.

6. Work Done and Energy Transfer

The amount of work done on an object translates to the energy transferred to that object. The equation governing work done is:
Work done,
$W ext{ (J)} = F ext{ (N)} imes s ext{ (m)}$
Where:

• $W$ is work done in joules (J)
• $F$ is the force applied in newtons (N)
• $s$ is the distance moved along the force's line of action in meters (m).

7. Energy Efficiency and Dissipation

Energy cannot be created or destroyed; it can solely be transferred, stored, or dissipated. Dissipation refers to energy that spreads out and becomes less useful, typically ending up in the thermal store of the surroundings.

No energy transfer is entirely efficient. Some energy ends up dissipated, often as heat through friction in machinery. Techniques to minimize this include:

• Lubrication: Reduces unwanted energy transfers due to friction.
• Streamlining: Decreases energy loss from air resistance (drag in fluids).
• Thermal Insulation: Minimizes energy waste due to thermal dissipation to surroundings.

Efficiency Calculation

Efficiency is a metric reflecting how much energy is successfully utilized. The equation for efficiency, expressed as a decimal is:
ext{Efficiency} = rac{ ext{Useful Energy Output (J)}}{ ext{Total Input Energy (J)}}
To express efficiency in percentage terms, multiply the decimal result by 100 and append the percentage symbol (%).

8. Key Terms and Definitions

Make sure to know these definitions:

• Chemical: Pertaining to energy produced or consumed in a chemical reaction.
• Closed System: A system where no energy can be exchanged with the surroundings, leading to a constant total energy state.
• Dissipated: Energy that is spread out and transferred to less useful stores.
• Efficiency: A measure of the ratio of useful energy output to total input energy.
• Elastic Potential: Energy stored in objects that can stretch or compress.
• Electrostatic: Potential energy due to electric charge interaction.
• Gravitational Potential: Energy held by an object due to its height in a gravitational field.
• Kinetic: Energy that an object possesses because of its motion.
• Lubrication: The application of a substance to minimize friction between surfaces.
• Magnetic: Energy related to magnetic fields.
• Nuclear: Energy released during nuclear reactions.
• Power: The rate of energy transfer (measured in watts).
• Streamlining: Designing objects to minimize resistance through fluids.
• System: A collection of interacting components or entities.
• Thermal: Energy associated with the temperature of a system.
• Work Done: Energy transferred when a force is applied over a distance.

Page 2: Review Questions and Answers

1. Name the five energy stores:
      - Chemical
      - Kinetic
      - Gravitational potential
      - Elastic potential
      - Thermal

2. Name four ways in which energy can be transferred:
      - Heating
      - Waves
      - Electricity
      - Mechanically (by forces)

3. What is a system?
      - An object or group of objects.

4. What is a closed system?
      - A system where no energy can be transferred to or from the surroundings. The total energy in the system remains constant.

5. What is work done?
      - Energy transferred when a force moves an object.

6. What is the unit for energy?
      - Joules (J)

7. How is one joule of work defined?
      - The work done when a force of 1 N causes an object to move 1 m in the direction of the force.

8. Describe the energy transfers when a moving car brakes and slows down:
      - Energy is transferred mechanically from the kinetic store of the car to the thermal store of its brakes; energy is then dissipated to the thermal store of the surroundings. In modern cars, energy may also transfer to the chemical store of the battery via electric current.

9. Describe the energy transfer when an electric kettle is used to heat water:
      - The electric current in a kettle transfers energy to the heating element's thermal store; energy is then transferred by heating from this thermal store to the thermal store of the water.

10. Describe the energy transfer when a ball is fired using an elastic band:
       - Energy is transferred mechanically from the elastic store of the elastic band to its kinetic store; some energy is dissipated to the thermal store of the surroundings.

11. Describe the energy transfer when a battery-powered toy car is used:
       - Energy is transferred electrically from the chemical store of the battery to the kinetic store of the toy car; some energy is dissipated to the thermal store of the surroundings.

12. Describe the energy transfer when a falling apple hits the ground:
       - Energy is transferred from the gravitational potential store to the kinetic store of the apple; upon hitting the ground, the kinetic energy is dissipated into the thermal store of the surroundings, through heating and sound waves.

13. Name the unit that represents the rate of energy transferred (in joules per second):
       - The watt (W)

14. A motor is 30% efficient. What does that mean?
       - It indicates that 30% of the input energy is usefully transferred, while 70% is dissipated.