Energy Stores and Transfers Comprehensive Study Guide

Fundamental Principles and Measurement of Energy

Energy is not a physical substance that moves between objects, but rather a conceptual tool used to track a specific, critical quantity within a system, analogous to the way money is used to track wealth. It is a concept that allows us to explain what can happen in a given scenario, though it does not explain why things happen. For instance, while knowing a car has fuel tells us the car has the capacity to move, it does not dictate its destination. Without energy, such as that provided by fuel, a system or machine cannot function or perform work.

The standard scientific unit of energy is the joule ($J$). Because the joule represents a very small amount of energy, measurements are frequently expressed in kilojoules ($kJ$), where $1\,kJ = 1000\,J$. In historical and some modern contexts, the kilocalorie ($kcal$), often colloquially referred to as a calorie, is used to measure energy stored in food. The conversion factor between these units is $1\,kcal = 4.2\,kJ$. Different food types store varying amounts of energy based on their composition. For every $100\,g$ of food, the energy storage values are: bananas store $340\,kJ$, beans store $400\,kJ$, rice stores $500\,kJ$, cooked chicken stores $800\,kJ$, and chocolate stores $1500\,kJ$.

Energy Requirements for Human Biological Function and Activity

The human body requires energy from food for all internal biological processes and external physical activities. Approximately three-quarters of the energy consumed daily is allocated to basic bodily maintenance, such as breathing and keeping the body warm. Young children have additional energy requirements to support the growth and development of bones, muscles, and the brain. Even in a state of rest, such as sleeping, the body requires approximately $300\,kJ$ per hour to maintain internal organ function and body temperature.

The specific amount of energy an individual needs daily depends heavily on their level of activity. Different activities have distinct energy costs, which are typically measured in kilojoules per minute ($kJ/min$). Sitting requires $6\,kJ/min$, standing requires $7\,kJ/min$, washing and dressing involves $15\,kJ/min$, walking slowly uses $13\,kJ/min$, cycling consumes $25\,kJ/min$, playing football requires $59\,kJ/min$, and swimming uses $73\,kJ/min$. High-intensity activities, like running or playing, can deplete upwards of $3500\,kJ$ per hour. Athletes and explorers, such as those trekking to the North or South Pole, require significantly more energy to sustain physical effort and maintain body heat in extreme environments.

Energy balance is the relationship between energy intake and expenditure. For an adult, the ideal is to ingest only as much energy as is required for daily activities. If energy intake exceeds expenditure, the body stores the surplus as fat for future use. Conversely, if intake is less than required, the body draws from its fat stores, leading to weight loss.

Categorization of Energy Stores

Energy is categorized based on how it is stored. It does not exist in different forms or 'types' as independent entities, but rather as a singular quantity that can be calculated and situated within various stores. When referencing 'kinetic energy', it is more accurate to describe it as energy stored kinetically or as energy within a kinetic store.

The chemical store includes energy held in the bonds of food and fuels such as coal, oil, and wood. Fuels provide stored energy that can be released through burning to produce heat or generate electricity. Interestingly, $1\,kg$ of wood stores a similar amount of energy to $1\,kg$ of chocolate. The gravitational potential store, or Gravitational Potential Energy ($GPE$), is the energy an object possesses due to its position relative to the center of the Earth. A change in height results in a change in this store. The elastic store, or Elastic Potential Energy ($EPE$), is the energy stored when an object is compressed or stretched, such as the springs in a mattress or a pulled elastic band. Materials that return to their original shape after being deformed are defined as elastic.

The nuclear store is found within the nuclei of atoms. The Sun is a massive nuclear store where nuclear fusion occurs—a process where hydrogen atoms combine to form helium, releasing enormous amounts of energy. The kinetic store pertains to all moving objects; a fast-moving object has a larger kinetic store than a slower object of the same mass. Finally, the thermal store represents the energy related to the temperature of an object. Hotter objects have more energy in their thermal store than colder objects, and when fuels burn, they transfer energy to the thermal store of the surrounding air.

Mechanisms of Energy Transfer

Energy is transferred between stores through several distinct pathways. Forces, radiation (including light and sound), heating, and electric currents are the primary mechanisms of transfer. Unlike stores, these pathways cannot hold energy; they only facilitate its movement. For example, in a battery-powered radio, energy is transferred from a chemical store to the surroundings. The pathway involves an electric current moving energy from the battery to the radio and sound waves moving energy to the environment.

In a torch or flashlight, an electric current transfers energy from the battery to the bulb. Similarly, electric kettles use currents to transfer energy to heat water. When physical forces act on objects, such as walking upstairs or pulling a catapult, energy is transferred between stores. Radiation transfers involve energy moving through light from the Sun or a candle, or through sound waves produced by musical instruments or vocal cords. Heating is a transfer process often resulting from a temperature difference between an object and its surroundings.

Energy Dissipation, Friction, and Efficiency

In every energy transfer process where a change occurs, some energy is inevitably transferred to the surroundings, usually in a form that is no longer useful. This phenomenon is known as energy dissipation. Dissipated energy most commonly manifests as heat or sound. For instance, in a light bulb, the goal is to transfer energy as light, but the bulb also gets hot, representing wasted or dissipated energy that enters the thermal store of the air.

Dissipation frequently occurs because of friction between moving parts or air resistance against an object. When a child swings on a playground swing, friction in the swing's pivot and air resistance cause some kinetic energy to transfer to the thermal store of the surroundings, eventually causing the swing to stop unless more energy is added. Once energy is dissipated and the surroundings become slightly warmer, that energy is typically considered 'lost' to the specific application, as it can no longer be easily harnessed for work.

Dynamics of Gravitational and Kinetic Energy Systems

Gravitational Potential Energy ($GPE$) and Kinetic Energy ($KE$) are frequently exchanged in mechanical systems. $GPE$ is position-dependent; moving up two floors in a building results in double the $GPE$ gain compared to one floor. It is also mass-dependent; if a mother has twice the mass of her son, she will gain twice the $GPE$ climbing the same height. Kinetic energy is dependent on both the mass and speed of an object. If a lion and an antelope run at the same speed, the lion has more $KE$ due to its higher mass. If two lions have the same mass, the faster one possesses more $KE$.

In an 'up and down' scenario, such as throwing a ball, energy shifts between these stores. As the ball rises, its speed decreases ($KE$ decreases) and its height increases ($GPE$ increases). At the peak of its flight, the ball stops for an instant, meaning its $KE$ is zero and its $GPE$ is at a maximum. As it falls back down, $GPE$ is transferred back into $KE$. Engineers use these principles to design rollercoasters, which lift passengers to a high point (generating massive $GPE$) so they can achieve high speeds ($KE$) on the descent. Friction and air resistance on the tracks ensure that some energy is always dissipated during the ride.

Elastic Potential Energy and Material Mechanics

Elastic potential energy ($EPE$) is stored when materials are deformed through stretching or compression. A classic historical example is the bow and arrow, such as those used in ancient Assyria over $2000$ years ago, where pulling the string changes the shape of the bow, increasing its chemical-to-elastic energy storage. When a ball hits the ground, it deforms, transferring its $KE$ into $EPE$. It then resumes its shape, transferring the $EPE$ back into $KE$ to bounce upward. However, energy is dissipated via sound and internal heating during the deformation, which is why a ball never bounces back to its original release height.

Biology also utilizes elastic stores. Tendons, such as the Achilles tendon in the human calf, connect muscle to bone and stretch during walking to store and release energy. This mechanism is even more pronounced in animals like kangaroos and frogs, which utilize specialized tendons to achieve massive leaps. In modern medicine, scientists use computer models of the human body and $EPE$ to design prosthetic legs for paralympic athletes that mimic this natural energy storage and release.

Scientific Methodology and Pendulum Investigation

A pendulum consists of a mass, known as a bob, attached to a string that swings back and forth. The period of a pendulum is the time it takes to complete one full cycle (moving from one side to the other and back again). Investigating the factors that affect this period requires a testable hypothesis. For example, Aditi and Diya hypothesized that the length of the string affects the period. They predicted that a shorter string involves less height difference between the bob at the center and the end of its swing, meaning less $GPE$ is available, but the movement cycle is faster.

Aditi's plan for investigation involves varying the string length from $10\,cm$ to $50\,cm$ in increments of $5\,cm$. To increase accuracy, she measures the time for $10$ full swings and divides the result by $10$ to determine the period. Diya's plan focuses on string lengths between $30\,cm$ and $100\,cm$, taking three repeat measurements for each length to calculate an average. Both students identified string length as the independent variable (the one to change) and the period as the dependent variable (the one to measure), while controlling the mass of the bob and the distance the bob is pulled back from the center.

Questions and Discussion

1. Name three fuels. Coal, oil, and wood.

2. Give two reasons why your body needs energy when you are asleep. To keep internal organs (like the heart and lungs) functioning and to maintain a constant body temperature.

3. Calculate the number of joules in 200 kJ. Since $1\,kJ = 1000\,J$, then $200\,kJ = 200 \times 1000 = 200,000\,J$.

4. Explain why it is important for young children to take in more energy than they need for the activities they do each day. Young children require extra energy to facilitate growth and the development of bones, muscles, internal organs, and the brain.

5. Calculate the number of minutes that you would need to cycle to use up the energy in 100 g of chocolate.$100\,g$ of chocolate contains $1500\,kJ$. Cycling uses $25\,kJ/min$. Therefore: $\frac{1500\,kJ}{25\,kJ/min} = 60\text{ minutes}$.

6. Write down two sources of chemical energy. Food and fuels (such as gasoline or wood).

7. A child picks up a toy from the floor. Name the store that has gained energy. The gravitational potential store (or $GPE$).

8. Describe the way energy is stored in a stretched elastic band. It is stored elastically in an elastic store (or as $EPE$).

9. A student thinks that the Sun is a huge ball of fire that provides the energy for the Earth. Would you say that they are correct? Explain your answer. No, they are incorrect. The Sun is not a ball of fire; its energy comes from nuclear fusion (hydrogen atoms combining into helium) occurring in its core, making it a nuclear energy store.

10. Describe what is meant by 'energy is dissipated'. Energy is dissipated when it is transferred to the surroundings in a non-useful form, typically as sound or thermal energy, which results in the surroundings becoming warmer.

11. A man and his son run to the top of a hill and stop. The mass of the man is bigger than the mass of the boy.

• a. Write down who has more kinetic energy while they are both running at the same speed. Explain your answer. The man has more kinetic energy because he has a larger mass.
• b. Would it be possible for them to have the same amount of kinetic energy? Explain your answer. Yes, if the boy runs significantly faster than the man to compensate for his lower mass.
• c. When they are at the top of the hill, who has more GPE? Explain your answer. The man has more $GPE$ because he has more mass at the same height.