Prove that you can make any type of logic gate using just NAND gates.

Can you think like a computer and work out what this flow diagram does?

Show that even a very powerful spaceship would eventually run out of overtaking power

Can you work out which of the equations models a bouncing bomb? Will you be able to hit the target?

A preview of some of the beam deflection mechanics you will look at in the first year of an engineering degree

A series of activities to build up intuition on the mathematics of friction.

A look at a fluid mechanics technique called the Steady Flow Momentum Equation.

Explore the mathematics behind the famous Wheatstone Bridge circuit.

As a capacitor discharges, its charge changes continuously. Find the differential equation governing this variation.

Put your complex numbers and calculus to the test with this impedance calculation.

This article, including exercises, gives a thorough grounding in the topic of AC/DC circuits.

Derive Euler's buckling formula from first principles.

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

Investigate some of the issues raised by Geiger and Marsden's famous scattering experiment in which they fired alpha particles at a sheet of gold.

Investigate why the Lennard-Jones potential gives a good approximate explanation for the behaviour of atoms at close ranges

How does the half-life of a drug affect the build up of medication in the body over time?

A think about the physics of a motorbike riding upside down

Explore the energy of this incredibly energetic particle which struck Earth on October 15th 1991

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

Look at the units in the expression for the energy levels of the electrons in a hydrogen atom according to the Bohr model.

What is an AC voltage? How much power does an AC power source supply?

A look at different crystal lattice structures, and how they relate to structural properties

Dip your toe into the world of quantum mechanics by looking at the Schrodinger equation for hydrogen atoms

Doug has just finished the first year of his undergraduate engineering course at Cambridge University. Here he gives his perspectives on engineering.

Things are roughened up and friction is now added to the approximate simple pendulum

A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?

See how the motion of the simple pendulum is not-so-simple after all.

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

At what positions and speeds can the bomb be dropped to destroy the dam?

Follow in the steps of Newton and find the path that the earth follows around the sun.

Can you work out how to produce the right amount of chemical in a temperature-dependent reaction?

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

Find the equation from which to calculate the resistance of an infinite network of resistances.

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

Investigate the mathematics behind blood buffers and derive the form of a titration curve.

Explore the relationship between resistance and temperature

How would you design the tiering of seats in a stadium so that all spectators have a good view?

In this question we push the pH formula to its theoretical limits.