Advanced problems in the mathematical sciences.
This is the area of the advanced stemNRICH site devoted to the core applied mathematics underlying the sciences.
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
An introduction to a useful tool to check the validity of an equation.
An article about the kind of maths a first year undergraduate in
physics, engineering and other physical sciences courses might
encounter. The aim is to highlight the link between particular
maths. . . .
At what positions and speeds can the bomb be dropped to destroy the
Find out how to model a battery mathematically
A look at a fluid mechanics technique called the Steady Flow
Which parts of these framework bridges are in tension and which parts are in compression?
Put your complex numbers and calculus to the test with this
This is the technology section of stemNRICH - Core.
Look at the calculus behind the simple act of a car going over a
Can you match up the entries from this table of units?
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
Given the equation for the path followed by the back wheel of a
bike, can you solve to find the equation followed by the front
Explore the power of aeroplanes, spaceships and horses.
Have you got the Mach knack? Discover the mathematics behind
exceeding the sound barrier.
What is an AC voltage? How much power does an AC power source
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Things are roughened up and friction is now added to the
approximate simple pendulum
A look at the fluid mechanics questions that are raised by the
How do these modelling assumption affect the solutions?
See how the motion of the simple pendulum is not-so-simple after
Was it possible that this dangerous driving penalty was issued in
Show that even a very powerful spaceship would eventually run out
of overtaking power
In this short problem we investigate the tensions and compressions
in a framework made from springs and ropes.
Can you work out which of the equations models a bouncing bomb?
Will you be able to hit the target?
This article, including exercises, gives a thorough grounding in
the topic of AC/DC circuits.
What is a random pattern?
This short question asks if you can work out the most precarious
way to balance four tiles.
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 voltages and currents in this interesting circuit configuration.
In an extension to the Stonehenge problem, consider the mechanical
possibilities for an arrangement of frictional rollers.
Prove that you can make any type of logic gate using just NAND
A look at power generation using wind turbines.
Derive Euler's buckling formula from first principles.
Explore the mathematics behind the famous Wheatstone Bridge
As a capacitor discharges, its charge changes continuously. Find
the differential equation governing this variation.
A series of activities to build up intuition on the mathematics of
A preview of some of the beam deflection mechanics you will look at
in the first year of an engineering degree
Doug has just finished the first year of his undergraduate
engineering course at Cambridge University. Here he gives his
perspectives on engineering.
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
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?
Can you work out what this procedure is doing?
Can you set the logic gates so that this machine can decide how many bulbs have been switched on?
What will happen when you switch on these circular circuits?
Can you think like a computer and work out what this flow diagram