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