This project is an exploration of basic mechanical principles through hands-on experimentation and measurement.

Participants will learn about everyday forces, and how we can interact with them through measurement or redirection. They will construct their own scientific measuring device (the dynamometer) and build a pulley system of their own design.

Throughout the process, scientific collaboration will be achieved through the collation of measurements and the sharing of ideas and creations.

Get ready to awaken your inner scientist with this project that will revolutionize your understanding of the world around you!

Physics, Measurement, Math

**TIP**: Scroll down to read tips for educators.

While we’ll never be able to move objects with our minds or play mind tricks on people we don’t like, forces are acting all around us every day and shape the world we live in and how we interact with it.

In this activity, you will explore everyday forces and learn how we can manipulate and measure them. In doing so, you will learn what a force is in the context of mechanical physics, and how essential they are to understanding the physical world.

You will also learn how physicists conduct experiments to test their ideas and investigate new concepts. You will find out the importance of taking careful measurements, and the factors you should consider when designing instruments to measure physical quantities for use in science.

You will demonstrate the importance of scientific collaboration when exploring new ideas and trying to understand how things work, and even participate in some healthy competition with your scientific colleagues.

You can find a more detailed discussion of the resources needed in the ‘Tips for Educators’ section.

*Dynamometer:*

- Laser-cut dynamometer flat pack sheet (send-out)
- Glue/tape
- Rubber bands of differing material/size
- Standard weights (see ‘Tips for Educators’)
- Marker pen
- Notepad and pencil

Pulley:

- Laser-cut pulley flat pack sheet (send-out)
- Glue/tape
- String
- Creative means for hanging your pulley

So how do real forces work?

Think of a force as a push or a pull from one object to another. Forces can come in many different forms. They can involve direct contact between the objects (like when you push on a door) or can act from a distance (like a magnet pulling a metal paperclip). They can be big or small, and will always act in a certain direction. We measure their size in Newtons (N), which are named after a very famous physicist, Isaac Newton, who laid the foundations for the physics we know today.

To keep track of all these details, physicists like to draw diagrams of the situation, labelling forces with arrows.

**For example**, have a look at Figure 1 below, where Jerry and Sally are fighting over their shopping trolley. Sally is pulling harder than Jerry, so her blue force arrow is long and to the left. Jerry is pulling weaker than Sally, so his red force arrow is short and to the right.

In this project, we’ll be looking more closely at forces that we experience every day.

One such force, that affects us all and everything around us, is gravity.

In fact, the force of gravity acts between any objects that have mass, and results in what we call weight. Here on Earth, it always acts downwards and pulls us towards the ground.

**Common Misconception:**

Often in everyday speech, the words “**mass**” and “**weight**” get mixed up, but in physics these terms have very specific definitions.

**Mass** refers to the amount of matter an object has, or more simply the amount of ‘stuff’ that you can physically touch and feel. Mass is measured in kilograms (kg).

**Weight** is another name for the force of gravity and is measured in Newtons (N), just like any other force.

*Weight Force (N)=Mass (kg)×10 (1)*

**Extra for Math Experts:**

Upon seeing Equation 1, a good physicist would ask, “so where does that times 10 come from?”

You might have seen it before – it’s the acceleration due to gravity on Earth usually given the symbol g. This is how fast every object on the planet would speed up when falling if there was no air getting in the way. Both a feather and a bowling ball would fall at the same rate in a vacuum!

The full formula for Equation 1 is really: F = mg. We can use this formula to find the downward weight force of any object on the surface of the Earth.

You have the power to manipulate a force!

The pulley is a device that can be used to change the direction of a force. This allows you to redirect forces if the pulley is placed correctly.

Pulleys utilise another everyday force called tension. This is the pull that a rope will give when it is tight. Pulleys can be positioned so that the pull from multiple parts of the rope all help to lift against the weight force of an object. This reduces the force needed to lift the object and you can check this with your dynamometer.

Try starting with the basic system in Figure 4 below and once you understand how the pulleys can be combined, try making your own machines to lift heavier weights with little input force.

**1. Construct your dynamometer.**

All you need for this is the laser-cut dynamometer flat pack sheet. Assembly can be done in a few easy steps – watch our helpful video for step-by-step instructions on this website.

**2. Calibrate your instrument.**

Every scientific measuring instrument needs a scale. For your dynamometer, you’ll be making this scale yourself. First, choose the smallest of your standard weights and hang it from the hook. Write the weight force (which you can calculate using Equation 1 below) on the scale at the mark the dynamometer comes to rest.

*Weight Force (N) = Mass (kg) × 10*

**3. Establish a scale.**

Next, choose another of your standard weight and calculate its weight force via Equation 1. Write this on your dynamometer scale.

Now you can use the interval between the two different standard weights to fill out the rest of your scale. The distance between the two entries on the scale corresponds to the difference in weight force between your two standard weights.

You can now move that distance up and down the scale to fill it all out. Try to divide the difference by the number of ticks between the two entries to find out what each tick corresponds to – this forms your scale.

**4. Test for the best rubber band material (optional).**

*Difference = 5N – 2N = 3N*

*Distance = 30 ticks*

*3N ÷ 30 ticks = 0.1N per tick*

When making your dynamometers, try testing out a different rubber band material for each one made. You could try using thick vs thin, big vs small, different rubber types and different brands. You could even double loop a thin rubber band – be creative. For each different material the scale you make will be different, this could help you find the best material to use for measuring classroom items.

You can now move that distance up and down the scale to fill it all out. Try to divide the difference by the number of ticks between the two entries to find out what each tick corresponds to – this forms your scale.

**5. Build a library of materials (optional).**

For those who have tested different materials in the previous step, write down interesting properties and record these in a table online.

This will allow us to collate a library of different materials and find out which materials are best. We will be looking for which material can measure the biggest weight and which materials allow the best precision – produce a scale with the smallest intervals of measurement.

**6. Measure your house/classroom.**

Once you’re happy with the construction of your dynamometer and its material, you can now start measuring the objects around your house/classroom. As you do this, make note of each measurement, and investigate the limits of your dynamometer. What’s the biggest weight its scale can go to? How about the smallest? How accurate can it measure the smallest intervals?

**7. Catalogue your data.**

When you measure a new object, enter its details in the table online. Make sure to check to see if your item has already been entered first. Together with all the participants, we will build a catalogue of household/classroom items and their weights as measured by you!

**1. Construct the pulley**

This time use the smaller laser cut pulley flat pack sheet to construct a pulley. Again, you can watch a step-by-step instructions video on this website.

*Quick tip:* Glue the 3 wheels together.

**2. Build a simple mass-pulley system**

It’s best to start small. Putting together a pulley system can be a bit tricky and might need a few hands to help. First, try constructing the simple system in the diagram here.

**3. Design your own machine.**

Be creative! First, draw a diagram of your design in the scientific style used above. Remember to begin with an end to attach to your weight, which will pull downwards. Pulleys then must alternate top to bottom and end with a dynamometer to measure the reduction in force from your pulley system. Label the components and draw in force arrows to show the transfer of force along the pulleys and to your dynamometer.

**4. National Weight-lifting competition**

Upload a photo of your design and record the biggest weight measured. Then find the ranking of your pulley system on a leader board of all the participants across NZ!

Watch our dynamometer assembly video:

Watch our dynamometer calibration video:

Watch our pulley assembly video:

Watch a demonstration of the pulley system:

Here are some suggestions and ideas that you might want to consider when planning your approach to this project. There is also some advice around how the experiment could be simplified for younger learners.

- Describe how forces work in an everyday context and explore basic mechanical principles.
- Understand how forces can be measured with a dynamometer and how pulleys can be used to redirect them.
- Investigate the importance of careful calibration for production of scientific measuring devices.
- Design a mechanical pulley system using scientific techniques.
- Discuss the importance of collaboration when gathering data and exploring scientific concepts.
- Collaborate with other schools to share results, discuss ideas and collate data.

*How science works?*

- Designing experiments to measure physical quantities and further investigate the ideas proposed.
- Gather and tabulate measured data.
- Formulate and revise scientific explanations using logic and evidence.
- Acknowledge that each one of us has the power to investigate and evaluate evidence by our own. Promote critical thinking.

* *

*Science in history and cultural awareness*

- Discuss and explore how modern science is an endeavour resulting from the contribution, collaboration and cross-pollination of all cultures.
- Discuss the contributions and approaches of Māori culture in techniques of measurement.

* *

*The tools of science*

- Physical theories, concepts, and models as a way of explaining the natural world.
- Features of an accurate measuring device and methods for calibration.
- The importance and limitations of the measurement process as a way of collecting data about the physical world.

* *

*Mathematics as a language for doing science*

- Number – fractions and decimals

Identifying physical intervals and applying known values to produce a scale for measurement.

- Unit conversions and relationships

Using and manipulating units of measurement so that values are compatible with physical relationships. Applying appropriate relationships between physical quantities.

- Measurement

Constructing and calibrating a measuring device. Carrying out a physical measurement.

Finding Standard Weights:

The ideal calibration for the dynamometer would be a set of standard masses fit with a hook and slot, but this is by no means a common classroom item. We’ve come up with a few suggestions for what you could use – but you can try anything that is convenient for you (and gives a reasonably accurate scale).

- Canned food items with labelled mass, e.g.: tin of tomatoes, beans, etc.
- Unopened packets of baking goods with labelled mass, e.g.: bag of sugar or flour

Any items with a labelled mass will work, and you will need a minimum of 2 items with different masses. The range of your dynamometer will depend on the type of rubber band used, but would typically be no more than a kg. Good standard weights would be anywhere between 0.01-0.5kg (10-500g).

You could also fill a small container with a measured amount of a powdered item (flour, sugar, sand, etc.) with a known density to produce a desired mass (mass = density x volume).

This website has a very comprehensive list of densities: https://www.engineeringtoolbox.com/density-materials-d_1652.html

Hanging your pulley systems:

The most straightforward method is to hang pulleys from pins in a pinboard, but bear in mind that this will only bear a limited amount of applied force. Another option that we’ve found works well from home is to use parallel coat hangers fixed to a door handle/frame or curtain rails. It then helps to tie loops of string to hook the pulleys and dynamometer onto and keep them fixed in place as in Figure 7 to the right.

*Figure 7: Pulley fixed with a loop and knot*

For younger learners who might not be comfortable with using mathematical equations (yet!), there are a few things you could do differently to streamline the project and focus on building fun contraptions.

**Simplifying units:**

In this guide, learners use the SI units for force (Newtons – N) when calibrating their dynamometer. This means that they will need to calculate the weight force in N from their known mass in kg, via the weight force equation (1) – or more simply multiplying by 10. Unit conversion and use of SI units is an important skill in physics and in this case also helps to highlight the difference between weight and mass. However, you could use the unit kilogram-force (kgf) instead. This is a gravitational unit for force where 1 kg of mass produces 1 kgf of weight force, so Equation 1 is already incorporated into the units and there’s no calculation involved.

**Hands-on Calibration:**

The method outlined here involved measuring only two standard weights and resolving the scale of the dynamometer analytically, but there are many ways to achieve sufficient calibration for classroom use. Another more practical method could be to measure many different known masses, and enter each weight force value on the scale. The interval of tick marks could then be estimated based on a large sample of entries rather than calculated.

There will always be significant uncertainty that comes from the limitations of preparing instruments for scientific measurement at home. This could be doorway for discussion of uncertainties in scientific experiments with more advanced classes. Here are some considerations:

- Inevitably, you will need to do some considerable rounding when estimating the intervals of your scale for the dynamometer, for it to be readable.
- Zero error could be an issue. It won’t always be apparent where the dynamometer naturally comes to rest at, as the mass of the hook is very small. It is best to extrapolate where the zero mark should be based on the intervals of standard masses, rather than ‘force’ a zero by judgement.
- Your scale will have a smallest interval that is readable – this limits the precision of the device.
- The rubber band will wear out over time – this means that the scale might change after extensive use or over extension.
- In a pulley system, all components need to be clear of obstacles for the measurement of force to be accurate. This means the string and pulleys need to be clear and should ideally run coplanar (none of them should ‘stick out’).

Use of the dynamometer and the design of pulley systems provide a great opportunity to introduce free body diagrams if your learners are at that level.

If you want to go even further with the theory, a discussion of Newton’s laws would fit in well with the concepts covered here.

You could highlight the importance of careful design for scientific experiments and ask learners to draw a technical diagram of their pulley systems before constructing.

Emphasise the power that comes with the reduction factor of forces applied to a multi-pulley system. Explain that each section of the string ‘takes’ an equal amount of the weight force of your object.

Suggest and discuss alternative devices for weight measurement (scales) and lifting loads (levers).

Discuss the importance and advantages of collaboration in science and encourage learners to engage and contribute online – we’d love to hear from you!

Have fun!

- View this really good site for quickly checking theory.
- View our Head Scientist’s website entry on the dynamometer and pulley.
- If you have any questions/comments or requests, feel free to get in touch with Rhia Hewett, Dr Rodrigo Martinez Gazoni, or any of the BIG SCIENCE! team.

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