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Things are roughened up and friction is now added to the approximate simple pendulum
How do you choose your planting levels to minimise the total loss at harvest time?
A series of activities to build up intuition on the mathematics of friction.
Show that even a very powerful spaceship would eventually run out of overtaking power
Investigate the mathematics behind blood buffers and derive the form of a titration curve.
See how the motion of the simple pendulum is not-so-simple after all.
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?
A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?
Draw graphs of the sine and modulus functions and explain the humps.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Can you make matrices which will fix one lucky vector and crush another to zero?
What does the empirical formula of this mixture of iron oxides tell you about its consituents?
Dip your toe into the world of quantum mechanics by looking at the Schrodinger equation for hydrogen atoms
Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.
Explore the distribution of molecular masses for various hydrocarbons
Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.
Explore the energy of this incredibly energetic particle which struck Earth on October 15th 1991
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.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Investigate why the Lennard-Jones potential gives a good approximate explanation for the behaviour of atoms at close ranges
Use vectors and matrices to explore the symmetries of crystals.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
How does the half-life of a drug affect the build up of medication in the body over time?
Think about the bond angles occurring in a simple tetrahedral molecule and ammonia.
Which of these infinitely deep vessels will eventually full up?
Can you draw the height-time chart as this complicated vessel fills with water?
Can you find the maximum value of the curve defined by this expression?
In this question we push the pH formula to its theoretical limits.
Can you match up the entries from this table of units?
Can you work out how to produce the right amount of chemical in a temperature-dependent reaction?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Prove that you can make any type of logic gate using just NAND gates.
Follow in the steps of Newton and find the path that the earth follows around the sun.
Can you think like a computer and work out what this flow diagram does?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
Find the equation from which to calculate the resistance of an infinite network of resistances.
Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.
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.
A short introduction to complex numbers written primarily for students aged 14 to 19.
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?
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.