Before you read this, I suggest you read post 19.21. The picture shows an object (in yellow) with two convex curved surfaces. This object is made of a material whose refractive index in air, n, is greater than 1; we will suppose that this material is glass but it could be any transparent material with… Continue reading 22.1 Refraction at curved surfaces – lenses

Before you read this, I suggest you read post 21.23. In post 21.23 we met the idea that the sequence of bases in mRNA determined the sequence of amino acids in a protein. The question then is – what sequence of bases will code a given amino acid sequence? We shall see that the experiments… Continue reading 21.24 The genetic code

In post 21.11, we saw that genes are made of DNA and that genetic information is code in the sequence of its bases; more details on the importance of this base sequence were given in post 21.12. But this raises a fundamental question. How does a DNA sequence determine who we are? How does my… Continue reading 21.23 Implementing genetic information

Before you read this, I suggest you read post 21.21. If you’ve read post 2.21, you may wonder why anyone would be interested in torsion of a cylinder. The reason is that long, thin cylinders (rods) are used as shafts to transfer rotational motion in many different types of machines. The drivetrain of a car… Continue reading 21.22 Rotating shaft

Before you read this, I suggest you read post 20.19. Torsion is the deformation you apply when you start to remove a screw-top from a bottle. In the picture above, torsion is applied to a cylinder, with a fixed base, so that A moves to A’. O is the centre of the top face of… Continue reading 21.21 Torsion

Before you read this, I suggest you read posts 21.17 and 21.19. This post is a continuation of post 21.19. I am going to use the ideas in post 21.19 to develop the equations stated, without proof, in post 21.17, that allow us to calculate the deflection and maximum stress in two examples of beams:… Continue reading 21.20 More about beams

Before you read this, I suggest you read post 21.17. In post 21.17, we saw that beams can support a load because they are bent by it. I also gave some rules for calculating the deflection of some simple beams and the maximum stress in them. But I didn’t explain how these rules are derived.… Continue reading 21.19 Bending a beam

In post 20.15, we saw how to calculate the forces that could maintain a system in equilibrium. We developed equations, by equating the vector sum of the forces acting on the system and the vector sum of the torques acting on the system, that could be solved to find the forces. But suppose the equations… Continue reading 21.18 Statically indeterminate systems

A door, or a window, fills a hole in a wall. The wall above the hole is supported by a horizontal beam, called a lintel. Gravity exerts a force Mg on the mass, M, of the wall above the beam, where g is the acceleration due to gravity, as explained in post 16.16. Note that… Continue reading 21.17 Beams

This post is about equilibrium in statics – the title could cause confusion because the word “equilibrium” is used in science in several different contexts. In post 21.15 we saw that statics describes a system that is not moving in the frame of reference of an observer – it is in equilibrium. We also saw… Continue reading 21.16 Equilibrium