# stemNRICH - The Physical World

### Welcome to the Physical World collection of stemNRICH resources.

In these resources, maths is used as a tool to explore some aspect of the physical sciences.  Some might be best used in the maths lesson, with reference made to the science.  Others could be taught as cross-curricular topics.

Stage 3 is roughly 11-14 years and Stage 4 roughly 14-16 years. The stars indicate how easily most learners can get into the problem, although most problems contain enough depth to challenge and stimulate all.

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### Problems with teacher support

The following problems contain detailed teacher support concerning how we might use the task in schools.  However, since these problems are intended to be rich mathematical activities they can be used effectively in many ways and at many levels of sophistication, both in the classroom and by individuals.

### Playground Snapshot

##### Stage: 2 and 3 Challenge Level:

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

### Observing the Sun and the Moon

##### Stage: 2 and 3 Challenge Level:

How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

### Troublesome Triangles

##### Stage: 2 and 3 Challenge Level:

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple simulation game to investigate the properties of such systems.

### Avalanche!

##### Stage: 2 and 3 Challenge Level:

Investigate how avalanches occur and how they can be controlled

### Helicopters

##### Stage: 2, 3 and 4 Challenge Level:

Design and test a paper helicopter. What is the best design?

### Make Your Own Solar System

##### Stage: 2, 3 and 4 Challenge Level:

Making a scale model of the solar system

### Does This Sound about Right?

##### Stage: 3 Challenge Level:

Examine these estimates. Do they sound about right?

### Pinhole Camera

##### Stage: 3 Challenge Level:

Make your own pinhole camera for safe observation of the sun, and find out how it works.

### Temperature

##### Stage: 3 Challenge Level:

Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?

### Reaction Timer

##### Stage: 3 Challenge Level:

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

### Programming: Moiré Patterns

##### Stage: 3 and 4

We need computer programmers! Logo is a great entry-level programming language - and you can create stunning graphics while you learn.

### stemNRICH - The Physical World

##### Stage: 3 and 4 Challenge Level:

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

### Global Warming

##### Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

### Far Horizon

##### Stage: 4 Challenge Level:

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

### Perfect Eclipse

##### Stage: 4 Challenge Level:

Use trigonometry to determine whether solar eclipses on earth can be perfect.

### Guessing the Graph

##### Stage: 4 Challenge Level:

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

### Big and Small Numbers in Chemistry

##### Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

### Big and Small Numbers in Physics

##### Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

### How Do You React?

##### Stage: 4 Challenge Level:

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

### Bigger or Smaller?

##### Stage: 4 Challenge Level:

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

### Electric Kettle

##### Stage: 4 Challenge Level:

Explore the relationship between resistance and temperature

##### Stage: 4 Challenge Level:

Which units would you choose best to fit these situations?

### Carbon Footprints

##### Stage: 4 Challenge Level:

Is it really greener to go on the bus, or to buy local?

### Investigating the Dilution Series

##### Stage: 4 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

### 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.

### Big and Small Numbers in the Physical World

##### Stage: 4 Challenge Level:

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

### A Question of Scale

##### Stage: 4 Challenge Level:

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?

### Speed-time Problems at the Olympics

##### Stage: 4 Challenge Level:

Have you ever wondered what it would be like to race against Usain Bolt?

### 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.

### Alternative Record Book

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

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

### chemNRICH

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

chemNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of chemistry, designed to help develop the mathematics required to get the most from your study of chemistry at A-level and university.

### physNRICH

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

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

### Approximately Certain

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

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

### Construct the Solar System

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

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

### Heavy Hydrocarbons

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

Explore the distribution of molecular masses for various hydrocarbons

### Problems without specific teacher support

The following problems are without specific teacher notes. These are often problems which would be difficult to fit into a typical curriculum area at school or are very open ended. They will be interesting for students interested in the general subject area to explore alone or for teachers to explore for ideas to bring to their own classrooms.