Welcome to Physics 8463: Energy Stores and Changes!
Welcome! In this chapter, we are going to explore one of the most important ideas in all of science: Energy. We’ll learn how energy is stored, how it moves from one place to another, and how we can calculate exactly how much energy is involved in different situations. Think of energy like "nature’s currency"—it’s what objects use to "pay" for movement, heat, or changing shape!
1. Energy Stores and Systems
Before we dive into the math, we need to understand where energy lives. Scientists use the word System to describe a specific object or a group of objects they are studying. If you are heating a cup of tea, the "system" is the tea and the cup.
What happens when a system changes?
Whenever something happens (like a ball being thrown or a kettle boiling), energy is shifted between different stores. Here are some common situations mentioned in your syllabus:
- An object projected upwards: As a ball travels up, energy is transferred from its kinetic store to its gravitational potential store.
- A moving object hitting an obstacle: The kinetic energy of the moving object is transferred to other stores, such as the thermal store of the surroundings (heat) and the elastic potential store of the object if it dents.
- An object accelerated by a constant force: Work is done on the object, and energy is transferred into its kinetic store.
- A vehicle slowing down: Brakes use friction to transfer energy from the car's kinetic store to the thermal store of the brakes and the air.
- Bringing water to a boil in a kettle: Energy is transferred electrically to the thermal store of the heating element, and then by heating to the thermal store of the water.
Quick Review: Three ways to change energy
1. Heating (like a stove).
2. Work done by forces (like pushing a box).
3. Work done when a current flows (like using a battery or a plug).
Key Takeaway: A system is just the objects you are looking at. Energy isn't "used up"; it just moves from one store to another.
2. Kinetic Energy (\(E_k\))
If an object is moving, it has energy in its kinetic store. The faster it moves and the heavier it is, the more kinetic energy it has.
The Formula:
\(kinetic \space energy = 0.5 \times mass \times (speed)^2\)
\(E_k = \frac{1}{2} m v^2\)
- \(E_k\) = kinetic energy in joules (J)
- \(m\) = mass in kilograms (kg)
- \(v\) = speed in metres per second (m/s)
Common Mistake to Avoid: Don't forget to square the speed (\(v^2\)) before multiplying by the other numbers! Only the speed is squared, not the mass.
Memory Aid: Think of "Kicking Everything"—if you can kick it and it moves, it has Kinetic energy!
3. Elastic Potential Energy (\(E_e\))
When you stretch or squash an object (like a spring or a rubber band), you are storing energy in its elastic potential store.
The Formula:
\(elastic \space potential \space energy = 0.5 \times spring \space constant \times (extension)^2\)
\(E_e = \frac{1}{2} k e^2\)
- \(E_e\) = elastic potential energy in joules (J)
- \(k\) = spring constant in newtons per metre (N/m) (this tells you how stiff the spring is)
- \(e\) = extension in metres (m) (how much further it stretched compared to its original length)
Did you know? This formula only works as long as the spring doesn't permanently deform. This limit is called the limit of proportionality.
4. Gravitational Potential Energy (\(E_p\))
When you lift an object up in a gravitational field, it gains energy in its gravitational potential store. The higher it goes, the more energy it stores.
The Formula:
\(g.p.e. = mass \times gravitational \space field \space strength \times height\)
\(E_p = m g h\)
- \(E_p\) = GPE in joules (J)
- \(m\) = mass in kilograms (kg)
- \(g\) = gravitational field strength in N/kg (On Earth, this is usually 9.8 N/kg, and it will be given to you in the exam)
- \(h\) = height in metres (m)
Key Takeaway: Kinetic is for movement, Elastic is for stretching, and Gravitational is for height.
5. Internal Energy and Specific Heat Capacity
Everything has internal energy. This is the total energy stored inside the particles of a system. When we heat something up, we increase the energy of its particles, which increases the temperature.
Specific Heat Capacity (SHC)
The Specific Heat Capacity of a substance is the amount of energy required to raise the temperature of one kilogram of the substance by one degree Celsius.
The Formula:
\(change \space in \space thermal \space energy = mass \times specific \space heat \space capacity \times temperature \space change\)
\(\Delta E = m c \Delta\theta\)
- \(\Delta E\) = change in thermal energy in joules (J)
- \(m\) = mass in kilograms (kg)
- \(c\) = specific heat capacity in J/kg °C
- \(\Delta\theta\) (delta theta) = temperature change in °C
Analogy: Imagine heating a swimming pool vs. a cup of tea. The pool has a huge mass, so even if you use the same heater, its temperature change will be much smaller than the tea's!
Don't worry if this seems tricky... You will often do a Required Practical to find the specific heat capacity of a block of metal. It involves measuring the energy put in and the temperature rise.
6. Power
In Physics, Power isn't about how strong you are—it’s about how fast you can transfer energy!
Definition:
Power is the rate at which energy is transferred or the rate at which work is done.
The Formulas:
\(P = \frac{E}{t}\) (Power = Energy transferred ÷ Time)
\(P = \frac{W}{t}\) (Power = Work done ÷ Time)
- \(P\) = Power in watts (W)
- \(E\) or \(W\) = Energy or Work in joules (J)
- \(t\) = Time in seconds (s)
Important Point: An energy transfer of 1 joule per second is equal to a power of 1 watt.
Example: If two motors lift the same heavy weight to the same height, they both do the same amount of Work. However, the motor that does it faster has more Power.
Quick Review Box:
- Energy is measured in Joules (J).
- Power is measured in Watts (W).
- Time must always be in Seconds (s) for these formulas!
Key Takeaway: Power is just "Energy divided by Time." The faster the energy moves, the higher the Power!