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Broad Topics > STEM problem type > Individual

### Battery Modelling

##### Stage: 5 Challenge Level:

Find out how to model a battery mathematically

### Levels of Bohr

##### Stage: 5 Challenge Level:

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

### The Ultra Particle

##### Stage: 5 Challenge Level:

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

##### Stage: 5 Challenge Level:

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

### Motorbike Momentum

##### Stage: 5 Challenge Level:

A think about the physics of a motorbike riding upside down

### Pack Man

##### Stage: 5 Challenge Level:

A look at different crystal lattice structures, and how they relate to structural properties

### Go Spaceship Go

##### Stage: 5 Challenge Level:

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

### The Not-so-simple Pendulum 2

##### Stage: 5 Challenge Level:

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

### Striking Gold

##### Stage: 5 Challenge Level:

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.

### Constantly Changing

##### Stage: 4 Challenge Level:

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

### Lennard Jones Potential

##### Stage: 5 Challenge Level:

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

### The Real Hydrogen Atom

##### Stage: 5 Challenge Level:

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

### Eudiometry

##### Stage: 5 Challenge Level:

When a mixture of gases burn, will the volume change?

### Sweeping Satellite

##### Stage: 5 Challenge Level:

Derive an equation which describes satellite dynamics.

### Pumping the Power

##### Stage: 5 Challenge Level:

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

### The Not-so-simple Pendulum 1

##### Stage: 5 Challenge Level:

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

### Drug Stabiliser

##### Stage: 5 Challenge Level:

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

### New Units for Old

##### Stage: 5 Challenge Level:

Can you match up the entries from this table of units?

### Cobalt Decay

##### Stage: 5 Challenge Level:

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

### Earth Orbit

##### Stage: 5 Challenge Level:

Follow in the steps of Newton and find the path that the earth follows around the sun.

### Whoosh

##### Stage: 5 Challenge Level:

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

### Crystal Symmetry

##### Stage: 5 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals.

### Electric Kettle

##### Stage: 4 Challenge Level:

Explore the relationship between resistance and temperature

### Approximately Certain

##### Stage: 4 and 5 Challenge Level:

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

### Resistance

##### Stage: 5 Challenge Level:

Find the equation from which to calculate the resistance of an infinite network of resistances.

### Reaction Rates

##### Stage: 5 Challenge Level:

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

### Debt Race

##### Stage: 5 Challenge Level:

Who will be the first investor to pay off their debt?

### Dam Busters 1

##### Stage: 5 Challenge Level:

At what positions and speeds can the bomb be dropped to destroy the dam?

### Dam Busters 2

##### Stage: 5 Challenge Level:

Can you work out which of the equations models a bouncing bomb? Will you be able to hit the target?

### Not Another NAND!

##### Stage: 4 and 5 Challenge Level:

Prove that you can make any type of logic gate using just NAND gates.

### Heavy Hydrocarbons

##### Stage: 4 and 5 Challenge Level:

Explore the distribution of molecular masses for various hydrocarbons

### AC/DC Circuits

##### Stage: 5

This article, including exercises, gives a thorough grounding in the topic of AC/DC circuits.

### Euler's Buckling Formula

##### Stage: 5 Challenge Level:

Derive Euler's buckling formula from first principles.

### Beam Me Up

##### Stage: 5 Challenge Level:

A preview of some of the beam deflection mechanics you will look at in the first year of an engineering degree

### Over-booking

##### Stage: 5 Challenge Level:

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?

### Blood Buffers

##### Stage: 5 Challenge Level:

Investigate the mathematics behind blood buffers and derive the form of a titration curve.

### Fix Me or Crush Me

##### Stage: 5 Challenge Level:

Can you make matrices which will fix one lucky vector and crush another to zero?

### Turbo Turbines

##### Stage: 5 Challenge Level:

A look at power generation using wind turbines.

### Why Multiply When You're about to Divide?

##### Stage: 5 Challenge Level:

A brief introduction to PCR and restriction mapping, with relevant calculations...

### Molecular Sequencer

##### Stage: 4 and 5 Challenge Level:

Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.

### Model Solutions

##### Stage: 5 Challenge Level:

How do these modelling assumption affect the solutions?

### Extreme Dissociation

##### Stage: 5 Challenge Level:

In this question we push the pH formula to its theoretical limits.

### Ph Temperature

##### Stage: 5 Challenge Level:

At what temperature is the pH of water exactly 7?

### Mixing Ph

##### Stage: 5 Challenge Level:

Use the logarithm to work out these pH values

### Catalyse That!

##### Stage: 5 Challenge Level:

Can you work out how to produce the right amount of chemical in a temperature-dependent reaction?

### Building up Friction

##### Stage: 5 Challenge Level:

A series of activities to build up intuition on the mathematics of friction.

### Differential Electricity

##### Stage: 5 Challenge Level:

As a capacitor discharges, its charge changes continuously. Find the differential equation governing this variation.

### The Wheatstone Bridge

##### Stage: 5 Challenge Level:

Explore the mathematics behind the famous Wheatstone Bridge circuit.

### Impedance Can Be Complex!

##### Stage: 5 Challenge Level:

Put your complex numbers and calculus to the test with this impedance calculation.