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Wavy Edges

Due to problems in the manufacture of tinplate coils, the edge of the strip can be slightly longer than the centre. This causes a 'wave' on the wall of the coil but can be rectified by differentially stretching the strip to make the edges flat. Students are required to apply Pythagoras' theorem to find the radius...

Tin Can Design

Tin cans come in a variety of shapes and sizes. In this activity students consider the net of a tin can, the formula for the total surface area and the formula for the volume of the can. The first problem requires students to express the total surface area as a function of r by eliminating h. The second problem...

Reduction Mill

The reduction mill reduces the thickness of a strip of steel using a series of rollers, each roller making the steel slightly thinner. The percentage reduction is constant on each pair of rollers. The mathematics used to calculate the actual reduction is similar to that used when calculating compound interest....

Drinks Cans

Drinks cans are made by stamping out circular discs from a sheet of tin. Given the dimensions of the sheet of tin and the diameter of the circle stamped out, students are required to calculate the wastage and to investigate whether there is a more efficient method. The problem requires students to be able to...

Coil Feed Line

This problem features a coil of tinplate being stored on a mandrel. In the first problem, students are presented with the diameter of the mandrel, the height from the floor, the width of the coil and the density of the steel. The problem is to calculate the maximum coil weight. A worked solution is included with...

UTOPIAE - CPD for Advanced Higher Physics/Maths teachers

UTOPIAE presents two...

Rocket performance in Bloodhound SSC

This detailed exemplar explores the rocket engine performance in the BLOODHOUND SSC engineering project. It requires student knowledge of physics, chemistry and mathematics when applied in mechanical engineering.

​The resource explains the history of the BLOODHOUND project, the dynamics of...

Formula One Race Strategy

This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within Formula One racing. Here students learn about the models which are used to develop race strategy, since every F1 team must decide how much fuel their cars will start each race with, and the laps on which they will...

Dropped Load Assessment in Nuclear Industry

This resource, from Mathematics for Engineering Exemplars, introduces mathematical models for the risk assessment of dropped load, which are used to analyse the safety of structures within nuclear power stations. Here students learn about the formulae which engineers use to calculate the maximum dynamic stress and...

Wind Turbine Power Calculations

This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the field of mechanical and electrical engineering in the power industry. When planning a wind farm it is important to know the expected power and energy output of each wind turbine to be able to calculate its...

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