GCSE
Physics
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Introduction to GCSE Physics (AQA) -
1.1 Energy Stores, Transfers and Power -
1.2 Conservation and Dissipation of Energy -
1.3 National and Global Energy Resources -
2.1 Current, Potential Difference and Resistance -
2.2 Series and Parallel Circuits -
2.3 Domestic Uses and Safety -
2.4 Energy Transfers -
2.5 Static Electricity -
3.1 Changes of State and the Particle Model -
3.2 Internal Energy and Energy Transfers -
3.3 Particle Model and Pressure -
4.1 Atoms and Isotopes -
4.2 Atoms and Nuclear Radiation -
4.3 Hazards and Uses of Radioactive Emissions and of Background Radiation -
4.4 Nuclear Fission and Fusion -
5.1 Forces and their Interactions -
5.2 Work Done and Energy Transfer -
5.3 Forces and Elasticity -
5.4 Moments, Levers and Gears -
5.5 Pressure and Pressure Differences in Fluids -
5.6 Forces and Motion -
5.6.1 Describing Motion Along a Line -
5.6.2 Distance and Displacement -
5.6.3 Speed -
5.6.4 Velocity -
5.6.5 The Distance–Time Relationship -
5.6.6 Acceleration -
5.6.7 Forces, Accelerations and Newton's Laws of Motion -
5.6.8 Newton's First Law -
5.6.9 Newton's Second Law -
5.6.10 Newton's Third Law -
5.6.11 Forces and Braking -
5.6.12 Stopping Distance -
5.6.13 Reaction Time -
5.6.14 Factors Affecting Braking Distance
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5.7 Momentum [HT] -
6.1 Waves in Air, Fluids and Solids -
6.2 Electromagnetic Waves -
6.3 Black Body Radiation -
7.1 Permanent and Induced Magnetism, Magnetic Forces and Fields -
7.2 The Motor Effect -
7.3 Induced Potential, Transformers and the National Grid [HT] -
8.1 Solar System; Stability of Orbital Motions; Satellites -
8.2 Red-Shift -
9.1 Required Practicals -
9.1.1 Required Practical Activity 1 -
9.1.2 Required Practical Activity 2 -
9.1.3 Required Practical Activity 3 -
9.1.4 Required Practical Activity 4 -
9.1.5 Required Practical Activity 5 -
9.1.6 Required Practical Activity 6 -
9.1.7 Required Practical Activity 7 -
9.1.8 Required Practical Activity 8 -
9.1.9 Required Practical Activity 9 -
9.1.10 Required Practical Activity 10
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1. Energy
1.1.2 Calculating Energy Transfers
In this lesson, you will explore different types of energy transfers and learn how to calculate them. This includes the energy of moving objects, objects lifted off the ground, and energy stored in springs.
Calculating Kinetic Energy
Any object that is moving has energy in its kinetic energy store. However, how do we know exactly how much kinetic energy is stored in a moving object? There are two variables that allow us to calculate how much kinetic energy a moving object has:
- The speed at which the object is moving.
- The mass of the moving object.
If either the speed or mass of a moving object increases, the kinetic energy it stores also increases. We can calculate the kinetic energy of a moving object using the formula shown in Equation 2 below.
\(E_k=\frac{1}{2}mv^2\)
or
\(\text{kinetic energy} = 0.5 \times \text{mass} \times \text{speed}^{2}\)
\(E_k=\frac{1}{2}mv^2\) is the same as \(E_k=0.5\times m\times v^2\). These are just two different ways of writing the same equation.Note
The kinetic energy formula has three components:
- \(E_{k}\) is the kinetic energy stored in the object. \(E_{k}\) has units of joules (J).
- \(m\) is the mass of the object. \(m\) must always have units of kilograms (kg) when used in the kinetic energy formula.
- \(v\) is the speed of the object. \(v\) must always have units of metres per second (m/s) when used in the kinetic energy formula.
Imagine that you have been asked to calculate the kinetic energy of a toy car which has a mass of 2 kg and is moving at a speed of 5 m/s. To calculate the toy car’s kinetic energy, you will need to use the kinetic energy formula you have just learned about: \(E_k=0.5\times m\times v^2\) Then substitute the variables with the values given to you in the question: \(E_k=0.5\times 2\times (5)^2\) Finally, carry out the calculations to get the kinetic energy of the toy car: \(E_k=0.5\times 2\times (5)^2\) \(E_k=0.5\times 2\times 25\) \(E_k=25\,\text{J}\) Therefore, we just calculated that the toy car has a kinetic energy of 25 J.Example
Sometimes, you may already be given the kinetic energy of an object and you are asked to work out one of the other variables which could be either the mass or the speed of the object. Imagine a 3 kg dog is running and has 6 J of kinetic energy stored. You are asked to calculate the speed at which the dog is running. The first thing you will need to do is to use the kinetic energy formula and rearrange it to make speed the subject of the equation: \(E_k=0.5\times m\times v^2\) \(\frac{E_k}{0.5\times m} = v^2\) Then substitute the variables with the values given to you in the questions: \(\frac{6}{0.5\times 3} = v^2\) Finally, carry out the calculations to get the speed of the dog: \(\frac{6}{0.5\times 3} = v^2\) \(v^2 = 4\) \(v=2 \, \text{m/s}\) Therefore, the dog is running at 2 m/s.Example
Calculating Gravitational Potential Energy
To raise any object above ground level (e.g. a child lifting a ball off the ground), a force must be applied upwards. This force does work, causing energy to be transferred from one energy store (e.g. the chemical energy store in the child’s arms), to the gravitational potential energy stores of the object being lifted.
The reason work has to be done (or energy needs to be transferred) when we lift an object is because of the Earth’s gravitational field. When an object is in a gravitational field, a gravitational force or gravity pulls the object towards the centre of the gravitational field (e.g. the centre of the Earth). This is why work has to be done to lift objects on Earth, because the gravitational force pulling the object down has to be overcome.
There are three things that the amount of gravitational potential energy stored in an object raised above ground level depends on:
- The mass of the object raised above ground level.
- The height the object has been raised to.
- The strength of the gravitational field the object is in.
The larger the mass of an object, the higher up the object is lifted, or the stronger the gravitational field strength the object is in, the more work needs to be done to lift the object. Therefore, more energy is transferred to the object’s gravitational potential energy stores. We can calculate the gravitational potential energy of an object using the formula shown in Equation 3 below.
\(E_p=mgh\)
or
\(\text{gravitational potential energy} = \text{mass}\times\text{gravitational field strength}\times\text{height}\)
The gravitational potential energy formula has four components:
- \(E_p\) is the gravitational potential energy stored in the object. \(E_p\) has units of joules (J).
- \(m\) is the mass of the object. \(m\) must always have units of kilograms (kg) when used in the gravitational potential energy formula.
- \(g\) is the gravitational field strength of the gravitational field the object is in. \(g\) has units of newtons per kilogram (N/kg).
- \(h\) is height the object has been readied above ground level. \(h\) must always have units of meters (m) when used in the gravitational potential energy formula.
Imagine that you are asked to calculate the gravitational potential energy of a 5 kg box raised to a height of 2 m above the ground by a rope. The gravitational field strength on Earth is close to 9.8 N/kg. First you will need the formula used to calculate gravitational potential energy which you have just learned about: \(E_p = m \times g \times h\) Then substitute the variables with the values given to you in the question: \(E_p = 5 \times 9.8 \times 2\) Finally, carry out the calculations to get the gravitational potential energy of the box: \(E_p = 5 \times 9.8 \times 2\) \(E_p = 98 \text{J}\) Therefore, the gravitational potential energy of the box raised above ground level is 98 J.Example
Calculating Elastic Potential Energy
To stretch or compress an object, a force has to be exerted on the object (e.g. when stretching a rubber band with your fingers). This force does work, causing energy to be transferred from one energy store (e.g. the chemical energy store in your fingers) to the object’s elastic potential energy stores and changing the shape of the object in the process (e.g. the rubber band becomes longer when stretched).
However, not all objects that are stretched or compressed store the energy from the work done to change their shape as elastic potential energy. Only elastic objects, which return to their original shape after stretching or compression do. We say that when an object changes shape from stretching or compressing that the object has been deformed. Inelastic objects are objects that do not return to their original shape after being deformed from stretching or compressing.
There is one constant and one variable that allow us to calculate how much elastic potential energy a spring has:
- The spring constant, which is a constant specific to springs.
- The extension which is the length by which the spring has been stretched.
Every type of elastic object has its own elasticity constant that helps us calculate the elastic potential energy stored in the object. In this lesson, we will only focus on the elastic potential energy in a spring and the spring constant. The more a spring is stretched or extended, the more work has to be done. This means that the more energy is stored in a spring’s elastic potential energy stores, the greater the extension of the spring is. We can calculate the elastic potential energy of a stretched spring using the formula shown in Equation 4 below.
\(E_e=\frac{1}{2}ke^2\)
or
\(\text{elastic potential energy} = 0.5\times\text{spring constant}\times\text{extension}\)
The elastic potential energy formula has three components:
- \(E_e\) is the elastic potential energy stored in the spring. \(E_e\) has units of joules (J).
- \(k\) is the spring constant. \(k\) has units of newtons per meter (N/m).
- \(e\) is the extension of the spring. \(e\) must always have units of metres (m) when used in the elastic potential energy formula.
Imagine you are asked to calculate the elastic potential energy of a spring with a spring constant of 10 N/m which has been stretched by 0.2 m. First you will need the formula used to calculate elastic potential energy which you have just learned about: \(E_e = 0.5 \times k \times e^2\) Then substitute the variable and constant with the values given to you in the question: \(E_e = 0.5 \times 10 \times (0.2)^2\) Finally, carry out the calculations to get the elastic potential energy of the stretched spring: \(E_e = 0.5 \times 10 \times (0.2)^2\) \(E_e = 0.5 \times 10 \times 0.04\) \(E_e = 0.2 \text{J}\) Therefore, the elastic potential energy of the stretched spring is 0.2 J.Example
You should keep in mind that if a spring is extended too much, it will exceed its limit of proportionality. Once the limit of proportionality has been exceeded, the spring’s elastic potential energy cannot be calculated with the elastic potential energy equation that you have learned about in this lesson.
You will learn more about limits of proportionality in a later lesson.Note
Calculating Kinetic Energy
- The amount of kinetic energy stored in a moving object depends on two things: the mass of the object and the speed of the object.
- The faster an object moves or the larger the mass of the object, the more kinetic energy it stores.
- The kinetic energy stored by a moving object can be calculated using the equation: \(E_{k} = \frac{1}{2} m v^{2}\)
- \(E_{k}\) is the kinetic energy of the object and is measured in joules (J).
- \(m\) is the mass of the object and is measured in kilograms (kg).
- \(v\) is the speed of the object and is measured in metres per second (m/s).
Calculating Gravitational Potential Energy
- To raise an object above ground level work must be done which results in energy transferred into the object’s gravitational energy stores.
- Work has to be done to raise an object above ground level because of the Earth’s gravitational field pulling the object down.
- The amount of gravitational potential energy stored in an object raised above ground level depends on three things: the mass of the object, the height the object has been raised to, and the strength of the gravitational field the object is in.
- The gravitational potential energy gained by an object raised above ground level can be calculated using the equation: \(E_{p} = mgh\)
- \(E_{p}\) is the gravitational potential energy of the object and is measured in joules (J).
- \(m\) is the mass of the object and is measured in kilograms (kg).
- \(g\) is the gravitational field strength and is measured in newtons per kilogram (N/kg).
- \(h\)is the height of the object and is measured in meters (m).
Calculating Elastic Potential Energy
- Stretching or compressing an object can transfer energy to the object’s elastic potential energy stores.
- Deformation is the change in the shape of an object from being stretched or compressed.
- Elastic objects are objects that return to their original shape after being deformed from stretching or compressing and store elastic potential energy.
- Inelastic objects are objects that do not return to their original shape after being deformed from stretching or compressing and do not store elastic potential energy.
- The amount of elastic potential energy stored in a stretched spring can be calculated using the equation: \(E_{e} = \frac{1}{2} k e^{2}\)
- is the elastic potential energy and is measured in joules (J).
- is the spring constant and is measured in newtons per metre (N/m).
- is the extension of the spring and is measured in meters (m).
- The elastic potential energy equation for a spring cannot be used once the spring’s limit of proportionality has been exceeded.