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Changes in energy stores

Energy stores and systems

In this chapter you will learn:

  1. How to define an Energy System and Energy Stores?

  2. What are different types of Energy Stores?

  3. How to calculate Kinetic Energy, Elastic Potential Energy and Gravitational Potential Energy?

  4. How to calculate change in Thermal Energy?

  5. The law of conservation of Energy.

  6. Transfer of energy between Energy Stores.

  7. Pathways for transfer of energy.

What is a system?

A system is an object or a group of objects. Therefore, we can say that an Energy System consists of either a single object or a group of objects. It is important to note that whenever a system changes, there are changes in the way energy is stored within that system.

System, energy and energy stores

Before we look at different types of energy stores, we should understand a few related terms and concepts.

  • Energy can be defined as capacity for doing work.

  • Within a system, energy can be stored, and transferred in different ways. An energy store refers to a particular way in which energy is stored.

  • Energy cannot be created or destroyed. Energy can only be transferred (shifted) from one energy store to another. This is called the law of conservation of energy.

  • When energy is transferred (shifted) from one energy store to another, work is done.

  • Energy is measured in Joules. This is the same for all of the different energy stores.

Types of energy stores

There are eight energy stores: Magnetic, Thermal (Internal), Chemical, Kinetic, Electrostatic, Elastic Potential, Gravitational Potential and Nuclear.

Kinetic energy store

Any object that is moving has energy in its kinetic energy store. The energy in the kinetic energy store of an object depends on it's mass (m) and it's speed (v).

The kinetic energy of a moving object can be calculated using the following equation:

kinetic energy = 0.5 × mass × (speed)2

Equation for kinetic energy

The units used in the equation above are as follows:

  • kinetic energy, Ek, is measured in joules, J

  • mass, m, is measured in kilograms, kg

  • speed, v, is measured in meters per second, m/s

Following are a few important observations from the above equation:

  1. Kinetic energy of an object is directly proportional to its mass.

  2. Kinetic energy of an object is directly proportional to the square of its speed.

  3. If an object is not moving at all, its speed will be 0; therefore, it will have no energy in its Kinetic energy store, irrespective of its mass.

Note: You will be required to apply this knowledge to answer questions in your physics exam.

How does kinetic energy change with the change in mass?

If you increase (or decrease) the mass by a given factor, keeping the speed constant, the kinetic energy will increase (or decrease) by the same factor. Say, you increase the mass by a factor of 3, the kinetic energy will also increase by a factor of 3.

The following table shows the change in kinetic energy when the mass is increased by a factor of 3 (assuming a constant speed of 5 m/s):

Table 1: Change in kinetic energy with change in mass
Mass (in Kgs) Kinetic energy (in Jules) Comments
2 25
6 (increased by a factor of 3) 75 Kinetic energy also increased by a factor of 3

How does kinetic energy change with the change in speed?

If you increase (or decrease) the speed by a given factor, keeping the mass constant, the kinetic energy will increase (or decrease) by the square of the same factor. Say, you increase the speed by a factor of 3, the kinetic energy will increase by a factor of 9 (32 = 9).

The following table shows the change in kinetic energy when the speed is increased by a factor of 3 (assuming a constant mass of 2 Kg):

Table 2: Change in kinetic energy with change in speed
Speed (in m/s) Kinetic energy (in Jules) Comments
5 25
15 (increased by a factor of 3) 225 Kinetic energy increased by a factor of 9

Worked example:

Question 1

The speed of an object is 6 m/s. The mass of the object is 50 kg.

Calculate the kinetic energy of the rocket just after being launched.

Answer:

kinetic energy = 0.5 × mass × (speed)2

Equation for calculating kinetic energy of a moving object

kinetic energy = 0.5 × 50 × 62

kinetic energy = 0.5 × 50 × 36

kinetic energy = 900 J

Magnetic energy store

Energy is stored when two magnetic objects are attracting or repelling, for as long as their magnetic poles remain apart. Examples of this energy store can be seen in fridge magnets and compasses.

Internal (thermal) energy store

Energy is stored in a hot object, for as long as the object remains hot. More hot an object is, the more thermal energy the material contains. This is the total kinetic and potential energy of the particles in an object. Depending on how hot an object is, it's particles vibrate faster or slower, which means they have different amounts of kinetic energy. In hotter objects, the particles vibrate faster because they have more internal energy.

The change in the Thermal energy of a system as its temperature changes can be calculated using the following equation:

change in thermal energy = mass × specific heat capicity × temperature change

Equation for calculating change in thermal energy

The units used in the equation above are as follows:

  • change in thermal energy, ΔE, is measured in joules, J

  • mass, m, is measured in kilograms, kg

  • specific heat capacity, c, is measured in joules per kilogram per degree Celsius, J/kg °C

  • temperature change, Δθ, is measured in degree Celsius, °C

Following are a few important observations from the above equation:

  1. Change in thermal energy of an object is directly proportional to its mass.

  2. Change in thermal energy is directly proportional to the specific heat capacity of the material.

  3. Change in thermal energy is directly proportional to the change in temperature.

  4. The greater the mass, more energy is required to change the temperature by the same amount, for a given material. For example, if you want to change the temperature of 10 Kgs of a material by 1°C, you would require twice the amount of energy required to change the temperature of 5 Kgs of the same material by 1°C.

  5. Specific heat capacity is usually different for different materials.

  6. If there is no change in temperature, there will not be any change in thermal energy.

Worked example:

Question 1

An object of mass 5 Kg is being heated.

Starting temperature of the object is 20 °C

Specific heat capacity of the object is 510 J/kg °C

Calculate the energy required to raise the temperature of the object to 40 °C?

Answer:

change in thermal energy = mass × specific heat capacity × temperature change

ΔE = 5 × 510 × 20

ΔE = 51,000 J

Chemical energy store

Chemical energy is stored in chemical bonds which exist between molecules, in things such as food, fuel, batteries, muscles and electrical cells. The energy could be stored for as long as the food or fuel exist.

Electrostatic energy store

The energy stored when repelling charges have been moved closer together or attracting charges have been pulled farther together. The energy can be stored for as long as the separated charges exist, which is usually minutes or hours. This energy can be seen generally in thunderclouds.

Elastic potential energy store

In some materials, energy is stored when they are in a stretched or compressed state. This is called elastic potential energy. This energy is released when the stretched or compressed object returns to its orginal state. In other words, energy is stored in a stretched band or spring, for as long as these objects are stretched. Elastic potential energy increases with the increase in length of a stretched spring.

The elastic potential energy of an object can be calculated using the following equation:

elastic potential energy = 0.5 × spring constant × (extension)2

Equation for elastic potential energy

(assuming the elastic limit of proportionality has not been exceeded)

The units used in the equation above are as follows:

  • elastic potential energy, Ek, is measured in joules, J

  • spring constant, k, is measured in newtons per metre, N/m

  • extension, e, is measured in metres, m

Gravitational potential energy store

Lifted objects store energy in gravitational potential energy store.

The amount of energy in a gravitational potential energy store depends upon the mass of the object (m), its height (h) and the gravitational field strength (g).

The gravitational potential energy of an object can be calculated using the following equation:

gravitational potential energy = mass × gravitational field strength × height

Formula for calculating gravitational potential energy

The units used in the equation above are as follows:

  • gravitational potential energy, Ep, is measured in joules, J

  • mass, m, is measured in kilograms, kg

  • gravitational field strength, g, is measured in newtons per kilogram, N/kg

  • height, h, is measured in meters, m

Worked example:

Question 1

How much gravitational potential energy does a 200 g object gain when it is lifted up 4 m onto a shelf?

gravitational field strength = 10 N/kg

Answer:

gravitational potential energy = mass × gravitational field strength × height

gravitational potential energy = 0.2 × 10 × 4

gravitational potential energy = 8 J

Nuclear energy store

This energy is stored in the nucleus of an atom. This energy can be released during nuclear fission or radioactive decay. The energy could be stored for seconds or for many years, depending on the atom.

Energy Transfers

Energy can be transferred (shifted) from one energy store to another in different ways. It does this by going along a process called pathway. The following are four types of energy transfer:

Energy can be transferred by heating, by radiation, electrically and mechanically.

  • Mechanically: A force moving an object through a distance or change its shape e.g. pushing, pulling, stretching or compressing.

  • Electrically: Electric energy is transferred when a moving electrical charge is doing work against a resistance.

  • Heating: The transfer of heat goes from the hot object to a colder object.

  • Radiation: Energy transferred as a wave. The Sun emits visible light, infrared and ultraviolet radiation which is received by the Earth.

Energy dissipation

When an energy transfer takes place some energy is dissipated.

Whenever energy is transferred from one form to another, some energy is wasted in the form of heat, light or sound.

Examples of dissipation

  • In a light bulb, a thin wire is heated until it glows, with a significant amount of energy being lost as heat.

  • In a tumble dryer, the energy is transferred into thermal energy that helps to dry clothes but some energy is dissipated as sound waves.

  • In a radio set some energy is dissipated in the form of infrared radiation when the electrical work is transferred into useful sound.

  • In a mechanical systems some energy is dissipated when two surface rub together. the energy is wasted because of the friction between two surfaces.

The conservation of energy

The law of conservation of energy states that energy neither be created nor destroyed - only transferred (shifted) from one energy store to another. Therefore, energy can only be stored, transferred (shifted) usefully from one store to another, or dissipated. The total amount of energy stored in various energy stores of a system remains the same before and after the transfer. The following examples demonstrate how conservation of energy works.

Examples of conservation of energy

  • Burning gasoline to power cars is an energy conversion process. The chemical energy in gasoline is converted to thermal energy, which is then converted to mechanical energy that makes the car move.

  • When an object of certain mass falls from a height, the speed of the object continuously increases, which means the amount of energy in it's kinetic energy store increases. However, because of the loss of altitude, it's gravitational potential energy decreases. Some of the gravitational potential energy is also transferred to the internal (thermal) energy store of the air particles that come in contact with the falling object.

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