Archimedes' Lever
![[left][size=100][/size][size=100][/size][size=100]Photo by: José San Martín-Universidad Rey Juan Carlos[/size][/left]](https://www.geogebra.org/resource/hrnerqy4/Dz5GKE2t1waqNcJA/material-hrnerqy4.png)
Photo by: José San Martín-Universidad Rey Juan Carlos
The background and importance of the topic
Activity description
![[size=100]Fig. 1 Simple example of the lever concept
Image source: José San Martín-Universidad Rey Juan Carlos[/size]](https://www.geogebra.org/resource/gck6hqhw/guHJYrgSG5qQMXxe/material-gck6hqhw.png)
![[size=100][left]Fig. 2 Detail of elements involved in the law of the lever.
Image source: https://es.wikipedia.org/wiki/Palanca[/left][/size]](https://www.geogebra.org/resource/azgmpwez/GDkr2ImpvP8Afu5p/material-azgmpwez.png)
Fig. 2 Detail of elements involved in the law of the lever. Image source: https://es.wikipedia.org/wiki/Palanca
The activity solution
![[size=100][left]Fig. 3 Detail of the different parts that make up the System.
Image source: José San Martín-Universidad Rey Juan Carlos[/left][/size]](https://www.geogebra.org/resource/c5nz424e/0MGKyGAgU6rAZYkm/material-c5nz424e.png)
Fig. 3 Detail of the different parts that make up the System. Image source: José San Martín-Universidad Rey Juan Carlos
- At one end we have the basket, where the objects to be lifted can be placed. It is the resistance point R according to the terminology we have used to enunciate the law of the lever.
- On the opposite tip of the lever, we have the point where we will apply our force, that is, the point P according to the terminology we have been using so far. It has been designed so that it resembles a hand (cartoon style), for illustrative purposes.
- Finally, we have the arm itself. It has 7 slots that allow anchoring the arm to the support through a peg-shaped axis, positioning the axis in any of the mentioned 7 slots. According to the chosen slot, we can change the distances between the support and the basket (Br, according to the terminology used), as well as between the support and the hand (Bp, according to the terminology followed so far).
![[size=100][left]Fig. 4 Example STL file generated
Image source: José San Martín-Universidad Rey Juan Carlos[/left][/size]](https://www.geogebra.org/resource/x2sdmevf/mxB7Z8pTW5uebZU1/material-x2sdmevf.png)
Fig. 4 Example STL file generated Image source: José San Martín-Universidad Rey Juan Carlos
Activity solution
a. List of required materials
- STL files for printing.
- Access to a 3D printer.
- After we print all the components, we will obtain the following ones:
- Arm-lever (Fig.3-In green): It is the largest elongated piece that we can see in green
- Balancing support (Fig.3-In blue): it is the system support, and it is advisable to anchor it to a surface
- Axis (Fig.3-In red): This is the axis that serves as a union between the two previous parts
- Different weights to place in the basket, such as:
- Objects of a similar volume, but of different materials, such as, for example, plastic, wood and metal.
- Objects of the same material, but different volumes, representing for example animals that have different weight, such as a mouse, a horse and an elephant.
- A set of coins that we place in the basket successively, so that the more coins there are, the more force we must apply for lifting them, or we must move the lever’s axis.
b. Preparation of the Activity
![[size=100][left]Fig. 5 Image of Archimedes lever at rest.
Image source: José San Martín-Universidad Rey Juan Carlos[/left][/size]](https://www.geogebra.org/resource/g7taqwwq/Z1nF722i1KAEQzaY/material-g7taqwwq.png)
Fig. 5 Image of Archimedes lever at rest. Image source: José San Martín-Universidad Rey Juan Carlos
![[size=100][left]Fig. 6 Different lever configurations
Image source: José San Martín-Universidad Rey Juan Carlos[/left][/size]](https://www.geogebra.org/resource/mfwhcgsz/37XSVa62GvAAcYaQ/material-mfwhcgsz.png)
Fig. 6 Different lever configurations Image source: José San Martín-Universidad Rey Juan Carlos
c. Activity development
The basic activity (and the proposed complementary or enrichment actions, point 3.4) contribute to foster the acquisition of knowledge including observing and exploring the children's environment, developing creativity and initiating children in the knowledge of sciences, among other issues. The Objectives could include:
- Understand that a machine/mechanism can help us do tasks that we cannot do alone.
- Intuitively understand what a lever is.
- Understand that larger animals weigh more (mouse < horse < elephant). Secondarily, they understand that the different materials from which objects are made also contribute to them having different weights.
- Introduce the concept of a simple mechanism or machine.
- Identify an example that children may know, such as a scale that tilts to where it weighs the most, or a seesaw for children to play in the playground.
- Ask the children what the heaviest thing they can lift.
- Ask next, if anyone believes that they are capable of lifting, for example, something as big as an adult, the whole Earth, etc.
- Ask the children if they know what a lever is, without further comment. Let them verbalize different options, explaining their operation, even if they are wrong, before making the formal explanation of the lever.
- Ask if anybody knows how ancient Greece was, if they have seen it in any series or movie (for example, it is possible that someone has seen the Disney movie Hercules or some similar reference). Prepare an image, such as the one shown in Figure 7. Enunciate the phrase "Give me a foothold and I will lift up the world" and ask if you understand what you mean by it, making a simple explanation.
- Once the activity has begun with the questions described in the Participation/Involvement phase, students are presented with 3 possible weights to lift. Each one can be of different material, for example, plastic, wood and metal, but, on the other hand, they could have a similar volume.
- The weights of different materials are presented to the children, explaining that the animals weigh some more than others, having them check this by themselves.
- The shaft is placed in an intermediate position of the lever holes, between the axis assembly and the balancing support. The weights are placed in the basket successively and the hand is pressed in each case, checking that it is easier for us to lift them, but that it costs a little more to lift the elephant than the mouse.
- The position of the shaft and the weights that we put in the basket are varied, so that the children check that the effort changes, and that the lever helps in this task. Additionally, you can play with questions about in which position of the axis it is more difficult to lift the weights, whether the axis is closer to the hand or the basket. Or with questions like “is it more difficult to lift a mouse with the shaft in the position closest to the hand or the elephant with the shaft in the position farthest from the hand? The main idea is to leave it to the children to experiment with all the options and come up to their own conclusions.
A video demostration
Enhancing the Activity
- You can play with the materials. For example, you can talk about coins with materials simulating gold, silver and bronze.
- You can represent an Earth and put it in the basket so that they associate the image with the famous phrase of Archimedes.
- It is possible to use the lever for explaining the concept of forces and torques for high school students.
- You can modify how the lever is used, turning it, for example, into a catapult
- You can use smaller versions of the system (smaller models for 3D printers are included in the materials provided), or the large system divided into smaller parts that are then assembled (those models are also included).
The knowledge test
Where did Archimedes come from?
How could you lift a heavy weight more easily?
Archimedean lever is an example of
Special needs’ learners
Alternative activity
Conducting a Workshop
- see the possibilities of using 3D printers and CAD tools as motivating tools in sciences and art classes.
- use digital interactive learning resources created in GeoGebra.
- critically evaluate the quality and applicability of the digital learning resource.