Can you stop the tray from tipping? Learn about the law of the lever to beat your opponent in this simple game.
We encounter various types of lever in our everyday lives: opening a drink with a bottle opener, cutting paper with scissors, taking the lid off a paint pot using a screwdriver, and – the simplest of all – playing on a seesaw in the park. Yet, the principle of levers is sometimes so natural to us that we do not pay any attention to how it actually works.
In this easy game, pairs of students aged 11–19 take it in turns to add wooden blocks or objects to a tray balanced on a pivot. By competing to keep the tray level, students learn about the physics of levers – simple machines that make work easier by reducing the force needed to move a load. They can understand the moment of a force and the balance law of a lever (Haverlíková, 2011).
Competitive students will strive to understand the basic principles so they can beat their opponents, and a practical game will enrich the learning process and contribute to a creative atmosphere in the classroom. The activity, including time for explanations and questions, will take around 1.5 hours.
Prior to the activity, introduce your students to the physical principles behind the lever. There are four basic elements to consider when using a lever:
When you use a lever, you apply a turning force (the moment) around the pivot to move the load. Moments reduce the effort needed to move the load by increasing the distance over which it is acting. This explains why less force is needed to open a door by pushing at the side furthest from the hinge than at the side closest to the hinge. When you push at the hinge side of the door, you must apply more force because the distance is smaller.
A moment can be calculated using the following equation:
M = F x d
where:
M = moment of the force (Nm)
F = applied force (N)
d = perpendicular distance between the pivot and the point where the force is applied (m)
Once students understand the physical principles behind the lever, they can consider how to use physics to win the game.
Working in pairs, each team will need:
See figure 1 for example materials.
Before your students go head-to-head in the game, they can apply their knowledge of levers to answer the following questions:
If you start off with a balanced tray, what would happen when you add an object to the tray?
Depending on the weight of the object and where it is placed on the tray, there can be no visible effect, or the tray can rotate, tilt or fall over.
An object is added to the balanced tray, making it tilt. Why? Where would the object need to be placed to cause the most tilting?
When an object is placed at a distance from the pivot, a moment is established, causing the tray to tilt. The moment of a force is directly proportional to the distance between the body and the pivot (M = F x d), so if the same object is placed further from the pivot, the tray will tilt more. If the object is placed at a distance too far from the pivot, the tray will tip and touch the table. The effect also depends on the weight (F) of the object.
An example is shown in figure 2. If a load acting on the tray with a force of 0.6 N is placed at a distance of 0.1 m from the pivot, the moment may be calculated as follows:
M = F x d
= 0.6 N x 0.1 m
= 0.06 Nm
The resulting moment of force would make the tray tilt.
If we put the same load further from the pivot, e.g. 0.2 m away, the moment of force would increase to 0.12 Nm, which would cause the tray to tilt further or to touch the table.
Where should you place an object so that an empty or balanced tray remains balanced?
When an object is placed on the pivot, the moment of force is equal to zero (d = 0) so there is no visible effect on the tray.
Your opponent places an object on the tray, causing it to tilt. Where should you place your object to rebalance the tray?
To keep the tray balanced, you must follow the physical principles related to the moment of a force. When an object is in equilibrium, the total anticlockwise moments should be equal to the total clockwise moments (F_{1} x d_{1} = F_{2} x d_{2}).
There are a few possibilities:
In figure 3, the object that acts on the tray with a force of 0.3 N is two times lighter that the object opposite, which acts on the tray with a force of 0.6 N. If we want to balance the moment of force, the lighter object must be placed at a distance two times greater.
M_{1}= F_{1} x d_{1} M_{2} = F_{2} x d_{2}
= 0.3 N x 0.2 m = 0.6 N x 0.1 m
= 0.06 Nm = 0.06 Nm
If you keep the position of an object the same but vary the weight of the object, what is the effect on the moment?
Placing a heavier object on the tray will cause the tray to tilt more. This is because the moment (M) is directly proportional to the applied force (F) and the perpendicular distance (d).
After your students have considered the questions, they are ready to play the game.
If neither student causes the tray to fall, and there are no more objects left in their pile, the students gain one point each.
These rules can be varied, as agreed between the teacher and students.
Note: to increase the friction to stop the objects gliding off the tray when it tips, place a piece of paper on the tray.
To encourage the students to think about the physical principles of levers and moments during the game, ask them some of the following questions:
You could repeat the pre-game questions to see if the activity has strengthened students’ understanding of the topic.
You can increase the difficulty of the game by making some changes:
The activity was produced by Science on Stage Slovakia at the science centre SteelPark in Košice, Slovakia. Science on Stage^{w1} is the network for European science, technology, engineering and mathematics (STEM) teachers, which was initially launched in 1999 by EIROforum, the publisher of Science in School. The non-profit association Science on Stage brings together science teachers from across Europe to exchange teaching ideas and best practice with enthusiastic colleagues from 25 countries.