Look at the calculus behind the simple act of a car going over a step.

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

This is the area of the advanced stemNRICH site devoted to the core applied mathematics underlying the sciences.

Ever wondered what it would be like to vaporise a diamond? Find out inside...

How fast would you have to throw a ball upwards so that it would never land?

Which line graph, equations and physical processes go together?

Get some practice using big and small numbers in chemistry.

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

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

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

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Find out why water is one of the most amazing compounds in the universe and why it is essential for life. - UNDER DEVELOPMENT

This is the technology section of stemNRICH - Core.

Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?

Can you work out the natural time scale for the universe?

Where will the spaceman go when he falls through these strange planetary systems?

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

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

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

A look at the fluid mechanics questions that are raised by the Stonehenge 'bluestones'.

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

Explore the Lorentz force law for charges moving in different ways.

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

Problems which make you think about the kinetic ideas underlying the ideal gas laws.

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

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.

How high will a ball taking a million seconds to fall travel?

engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering

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

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

Can you arrange a set of charged particles so that none of them start to move when released from rest?

An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.

Explore how can changing the axes for a plot of an equation can lead to different shaped graphs emerging

Work out the numerical values for these physical quantities.

Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.

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

Which units would you choose best to fit these situations?

When you change the units, do the numbers get bigger or smaller?

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

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

Work in groups to try to create the best approximations to these physical quantities.

A think about the physics of a motorbike riding upside down