9-1 Physics/Energy systems

A Brief Introduction to Energy
Energy is a concept that was initially created by scientists in the 19th century to explore why a certain steam engine could perform better than other steam engines. This was because some steam engines could change more than other steam engines. Energy is simply the maximum amount of change possible in an object or group of objects. Today, energy is a crucial economic, social and political topic as resources are used, such as coal, to give certain objects more energy so they can do useful things for us, like for example, power our television or computer (in order for you to read this!).

Energy stores and systems
A system is simply an object or group of objects. Think about the solar system; it is a collection of planets that orbit around the sun (all of which are objects). We study energy through looking at systems. Usually, systems are either open or closed. In an open system, matter and energy can be exchanged between objects in the system and the environment surrounding the system. For example, our planet, Earth, would be an open system since electromagnetic radiation from the sun keeps us warm. On the other hand, the Universe would be a closed system, as there is no environment outside the Universe with which matter and energy can be exchanged.

Energy is stored in objects in different forms, known as energy stores. All energy stores either relate to movement in a system or the position of an object in a system.

Energy stores that relate to movement in a system: Energy stores that relate to the positions in a system:
 * Kinetic energy (The movement of the object)
 * Thermal energy (The movement of particles which is the temperature of an object (how hot it is))
 * Electrical energy (The motion of charged particles)
 * Electromagnetic radiation (The motion of particles of light)
 * Gravitational potential energy (The amount of energy based on your position in space).
 * Elastic potential energy (The amount of energy stored when you pull an elastic band back)
 * Chemical potential energy (The amount of energy stored in chemical bonds)
 * Magnetic potential energy (The amount of energy when you put two magnets together, either they push each other away or join together)

Changes in energy when a system changes
When a system changes, energy must have been transferred from one store to another and or between objects. For example, if you had held up a pencil with you arm and dropped it, energy would be transferred from the gravitational potential energy store of the object to kinetic energy, causing the pencil to fall to the ground. Provided you understand and know each energy store, describing energy changes in a system is very simple.

Instead of simply describing energy changes, mathematics allows us to show, by magnitude (size), how much energy is being transferred. When dealing with math in physics, a very important thing to do is to understand your units of measurement. The unit of energy is always joules.

Energy store equations
Energy store equations are very simple: all you need to do is to work out when energy store your working with, what values you have and what value you are finding:

$$E_k = \dfrac{1}{2}mv^2$$

$$E_k$$Kinetic Energy (measured in joules, $$\text{J}$$)

$$m$$ mass (kilograms, $$\text{Kg}$$)

$$v$$ speed (metres per second, $$\text{m/s}$$)

If you wanted to measure the amount of kinetic energy in a car, you would measure the speed, how fast the object is travelling, of the car (with a speed gun for instance) and measure the mass (heaviness) of the car with some weighing scales (to get its mass not weight!). You could then plug in the values into the above equation and find the kinetic energy of the car.

$$E_e = \dfrac{1}{2}ke^2$$

$$E_e$$Elastic Potential Energy ($$\text{J}$$)

$$k$$ Spring constant (Newtons per meter, $$\text{N/m}$$)

$$e$$ extension (metres, $$\text{m}$$)

All we need to know to work out the amount of elastic potential energy a pulled back rubber band has, is the extension which is the distance it has been pulled back and the spring constant which is a certain value that depends on the object.

$$E_p = mgh$$

$$E_p$$Gravitational Potential Energy ($$\text{J}$$)

$$m$$ mass ($$\text{Kg}$$)

$$g$$ gravitational field strength (Newtons per kilogram, $$\text{N/Kg}$$)

$$h$$ height (metres, $$\text{m}$$)

If you wanted to know the amount of gravitational potential energy an object is when it is raised on Earth for example, you would find the object's mass and the height that it is raised, the distance between the Earth and the object, as well as the gravitational field strength which is how powerful the field of gravity is in that area. On Earth the gravitational field strength is approximately 9.8N/Kg

What is the difference between mass and weight?
Mass is the amount of material in an object whilst weight is the force of gravity applied to that object.

$$w = mg$$ As such, $$E_p = mw$$

If we substitute the units into the equation for weight, we can find what units weight is measured in:

$$\text{Kg} \times \text{N/Kg} = \text{N}$$

Thermal Energy & Specific heat capacity
$$\Delta E = m c \Delta \theta$$

$$\Delta E$$ Change in thermal energy ($$\text{J}$$)

$$m$$ mass ($$\text{Kg}$$)

$$c$$ specific heat capacity ($$\text{J/Kg°C}$$)

$$\Delta \theta$$ Change in temperature ($$\text{°C}$$)

This equation allows us to know the amount of energy stored in or released from a system as its temperature changes.

The specific heat capacity of a substance is the amount of energy required to raise the temperature of 1 kilogram of the substance by 1 degree celsius. We can work out the units by rearranging the above equation and then substituting units like we did to find the unit of weight:

$$\Delta \theta = \dfrac{\Delta E}{mc} \Longrightarrow \dfrac{\text{J}}{\text{Kg} \times \text{°C}}$$

** REQUIRED PRACTICAL 1 GOES HERE**

Power
Power is the rate of energy transfer.

$$P = \dfrac{\Delta E}{\Delta t}$$

$$\Delta E$$ Energy transferred, change in energy, ($$\text{J}$$)

$$\Delta t$$ Time taken, change in time, (seconds, $$\text{s}$$)

$$P$$ Power (watts, $$\text{w}$$)

Although power is measured in watts, it can also be thought of as measured in Joules per second if we substitute in the units into the equation. This means that:

$$\text{J/s} = \text{w}$$

This means that 1 Joule per second is equivalent to 1 Watt.