Find out how to model a battery mathematically
A look at a fluid mechanics technique called the Steady Flow
Investigate the effects of the half-lifes of the isotopes of cobalt
on the mass of a mystery lump of the element.
Show that even a very powerful spaceship would eventually run out
of overtaking power
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.
Explore the energy of this incredibly energetic particle which struck Earth on October 15th 1991
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?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
When a mixture of gases burn, will the volume change?
A think about the physics of a motorbike riding upside down
A look at different crystal lattice structures, and how they relate
to structural properties
What is an AC voltage? How much power does an AC power source
Derive an equation which describes satellite dynamics.
Can you match up the entries from this table of units?
Look at the units in the expression for the energy levels of the electrons in a hydrogen atom according to the Bohr model.
Dip your toe into the world of quantum mechanics by looking at the
Schrodinger equation for hydrogen atoms
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?
Derive Euler's buckling formula from first principles.
This article, including exercises, gives a thorough grounding in
the topic of AC/DC circuits.
A series of activities to build up intuition on the mathematics of
At what positions and speeds can the bomb be dropped to destroy the
As a capacitor discharges, its charge changes continuously. Find
the differential equation governing this variation.
A preview of some of the beam deflection mechanics you will look at
in the first year of an engineering degree
Follow in the steps of Newton and find the path that the earth
follows around the sun.
Find the equation from which to calculate the resistance of an
infinite network of resistances.
A look at power generation using wind turbines.
Can you work out which of the equations models a bouncing bomb?
Will you be able to hit the target?
How do these modelling assumption affect the solutions?
Explore the mathematics behind the famous Wheatstone Bridge
Prove that you can make any type of logic gate using just NAND
See how the motion of the simple pendulum is not-so-simple after
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?
In this question we push the pH formula to its theoretical limits.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Can you work out how to produce the right amount of chemical in a
Investigate the mathematics behind blood buffers and derive the
form of a titration curve.
At what temperature is the pH of water exactly 7?
Put your complex numbers and calculus to the test with this
Use the logarithm to work out these pH values
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
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 meaning of the scalar and vector cross products and see how the two are related.
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.
Can you work out what this procedure is doing?
Doug has just finished the first year of his undergraduate
engineering course at Cambridge University. Here he gives his
perspectives on engineering.
What does the empirical formula of this mixture of iron oxides tell
you about its consituents?
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?