In posts 18.6 and 18.7, we saw that a simple pendulum, consisting of a small object hanging by a light string of length L, will swing backwards and forwards with a frequency of f = (1/2π)(g/L)1/2 where g is the magnitude of the earth’s gravitational field (post 16.16). This statement about frequency is equivalent to… Continue reading 18.8 Natural frequency and resonance

In post 18.6, we saw how the motion of a simple pendulum could be explained by it conserving mechanical energy. This explanation shows that the pendulum is an example of a simple harmonic oscillator – a system that does not dissipate mechanical energy and so continues to oscillate indefinitely. But this explanation involved a lot… Continue reading 18.7 The simple pendulum

Before you read this, I suggest you read posts 16.21 and 17.38. This post is very mathematical, so you might want to stop reading after the paragraph on “models” – if you decide to do this, it might be worth reading the final two paragraphs. A pendulum is an object, like that shown in the… Continue reading 18.6 The pendulum: a simple harmonic oscillator

Before you read this, I suggest you read posts 18.1 and 18.3. To calculate pH values, we need to understand more about the pH scale, for measuring acidity and alkalinity, that was in introduced in post 18.1. The definition of pH is that pH = – log10[H+]. In this definition, [H+] represents the molar concentration… Continue reading 18.5 Calculating pH values

Some people believe that children shouldn’t be allowed to use calculators in mathematics and science classes in schools – I disagree. Scientists use calculators for many of the routine and tedious calculations that they frequently have to perform. So, if schools are teaching children how to do science, they should teach them to use calculators… Continue reading 18.4 Calculators in schools

Before you read this, I suggest you read post 18.2. If x, y and z are numbers related by x = yz we say that z is the logarithm of x to the base y. This is a lot of words to explain a simple idea that is usually written x = logyz   or x… Continue reading 18.3 Logarithms

We have met examples of this topic in several previous posts, especially post 16.7. Now I want to write about it in more detail. If we want to write a number a multiplied by itself 5 times, we could write a × a × a × a × a but this is very tedious –… Continue reading 18.2 Powers of numbers

Before you read this post, I suggest you read posts 17.49 and 17.50. Acidity and alkalinity are important for many biological processes. Azaleas will only grow well in acid soils. Saliva is alkaline but your stomach contents are acid. Healthy urine is acidic but infected urine can be alkaline. The previous paragraph raises several questions… Continue reading 18.1 pH

Before you read this, I suggest you read post 17.49. In post 17.49, we saw that an acid is something that acts as a source of hydrogen ions; something that reacts with hydrogen ions is called a base. A base that can dissolve in water is called an alkali. An alkaline solution is a solution… Continue reading 17.50 Alkalis

Before you read this, I suggest you read posts 16.30, 16.33, 16.39 and 17.48. In 2017 there was an alarming increase in attacks in London in which victims had acid thrown in their faces. One way in which these attacks could be reduced might be to make it illegal for people to carry acids in… Continue reading 17.49 Acids