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