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Broad Topics > STEM problem type > Individual

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Battery Modelling

Stage: 5 Challenge Level: Challenge Level:1

Find out how to model a battery mathematically

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Keep Your Momentum Going

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Cobalt Decay

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Go Spaceship Go

Stage: 5 Challenge Level: Challenge Level:1

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

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Striking Gold

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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The Ultra Particle

Stage: 5 Challenge Level: Challenge Level:1

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

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Constantly Changing

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Drug Stabiliser

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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The Not-so-simple Pendulum 1

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Lennard Jones Potential

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Eudiometry

Stage: 5 Challenge Level: Challenge Level:1

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

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Motorbike Momentum

Stage: 5 Challenge Level: Challenge Level:1

A think about the physics of a motorbike riding upside down

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Pack Man

Stage: 5 Challenge Level: Challenge Level:1

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

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Pumping the Power

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Sweeping Satellite

Stage: 5 Challenge Level: Challenge Level:1

Derive an equation which describes satellite dynamics.

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New Units for Old

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Levels of Bohr

Stage: 5 Challenge Level: Challenge Level:1

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

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The Real Hydrogen Atom

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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The Not-so-simple Pendulum 2

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Whoosh

Stage: 5 Challenge Level: Challenge Level:1

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

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Euler's Buckling Formula

Stage: 5 Challenge Level: Challenge Level:1

Derive Euler's buckling formula from first principles.

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AC/DC Circuits

Stage: 5

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

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Building up Friction

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Dam Busters 1

Stage: 5 Challenge Level: Challenge Level:1

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

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Differential Electricity

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Beam Me Up

Stage: 5 Challenge Level: Challenge Level:1

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

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Not Another NAND!

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Resistance

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Turbo Turbines

Stage: 5 Challenge Level: Challenge Level:1

A look at power generation using wind turbines.

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Impedance Can Be Complex!

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Model Solutions

Stage: 5 Challenge Level: Challenge Level:1

How do these modelling assumption affect the solutions?

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The Wheatstone Bridge

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the mathematics behind the famous Wheatstone Bridge circuit.

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Dam Busters 2

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Earth Orbit

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Blood Buffers

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Catalyse That!

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Approximately Certain

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Over-booking

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Mixing Ph

Stage: 5 Challenge Level: Challenge Level:1

Use the logarithm to work out these pH values

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Reaction Rates

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Extreme Dissociation

Stage: 5 Challenge Level: Challenge Level:1

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

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More Realistic Electric Kettle

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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Ph Temperature

Stage: 5 Challenge Level: Challenge Level:1

At what temperature is the pH of water exactly 7?

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Cross with the Scalar Product

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the meaning of the scalar and vector cross products and see how the two are related.

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Maximum Flow

Stage: 5 Challenge Level: Challenge Level:1

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

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Air Routes

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

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Mystery Procedure

Stage: 4 Challenge Level: Challenge Level:1

Can you work out what this procedure is doing?

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Reductant Ratios

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What does the empirical formula of this mixture of iron oxides tell you about its consituents?

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Is Your DNA Unique?

Stage: 5 Challenge Level: Challenge Level:1

Use combinatoric probabilities to work out the probability that you are genetically unique!

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Who Is an Engineer? A Quick Perspective After One Year of a University Engineering Course

Stage: 5

Doug has just finished the first year of his undergraduate engineering course at Cambridge University. Here he gives his perspectives on engineering.