Balancing a beam
Science can reveal simple patterns with considerable predictive power. This is of huge practical value. Knowing what affects the turning of a balanced beam leads to understanding such a pattern.
For each student group
Beam with regular markings, simple
Wooden prism block
Metal 'loads', square and identical
Health & Safety and Technical notes
These items of apparatus are available from educational suppliers as part of a "lever kit".
The square metal loads should have approximately the same diagonal length as the width of the beam.
a Place the wooden prism block underneath the centre of the wooden beam. The block acts as a pivot.
b Rest a paper clip on the beam and move it closer to or further from the pivot to balance the beam as well as you can. You won't be able to get the beam to balance exactly. When it is very close to being balanced then it tips one way as easily as the other. Fix the paper clip under the beam with a little Sellotape.
c Place one square load, 1 unit of length along the beam from the pivot, placing the diagonal of the square along the line of the first distance mark on the beam.
d Balance this, roughly, with one square load on the other side of the pivot. Make a written record of the number of square loads and their distances from the pivot.
e Add a square load on top of one of the others, to make a pile of two on one side of the pivot. Move the single square load on the other side so that the beam is roughly balanced again. Make a record of the numbers of loads and their distances.
f Add another load to make a pile of three. Move the single load again, to roughly balance the beam.
g You will find it useful to put your records into a table. A table is easier to make and use than a long list.
h Make the pile of square loads four high and five high. Move the single load each time so that the beam is roughly balanced. Record all of your results.
There is a pattern in the result. Try to spot it.
i OPTIONAL: Put two loads at two positions on one side of the pivot and try to balance them with one load on the other. Repeat a few times, at different distances and try to spot the pattern in these results.
1 The pattern in the results can be described in several ways.
A student who says words to the effect that, 'doubling the load on one side requires the distance on the other side to be doubled' has spotted the pattern. One who says that, 'the product of load and distance is the same on both sides of the beam when it is balanced' has
provided a more general description that can be used to make predictions. In other words, the beam balances when the anti-clockwise moment equals the clockwise moment.
Different students will require different amounts of support in this. The most able will not only identify a pattern but will see for themselves that they can use it to make predictions of load position in order to achieve balance. Others will not see a pattern at all unless it is directly pointed out to them. It is worth explaining that the pattern is important because of its predictive power, which can be applied in many practical situations.
2 Students' application of the predictive power of their new learning can be tested by moving the multiple loads to two marks from the pivot, and asking them to say where the single load must be placed for balance.
3 The number of loads here provides a 'measurement' of weight, or force.
The product of the force and its distance from the pivot is a measure of its turning effect, and is called the moment of the force.
For balance, the sum of the 'clockwise' moments is the same as the sum of the 'anticlockwise' moments. Large forces on one side of the fulcrum can be balanced by smaller forces on the other, provided that the smaller force is further from the fulcrum.
4 To illustrate the turning effect of a force, demonstrate with the classroom door. Try pushing it at the edge, then close to the hinge, then at intermediate positions. Compare the effects. You could try pushing near the hinge while a pupil pushes (from the other side) farther out. If you do this then take care that fingers cannot be trapped if the door closes.
5 An interesting variation is to replace the variable load by a weak spring such as an expendable steel spring.
To do this, place the pivot near the edge of the table. Tie the upper end of the spring to the beam with thread, one space from the pivot. Attach the lower end of the spring to an anchoring mass resting on the ground. The spring should be a little bit stretched. Adjust the tension by altering the length of cord used in securing the spring to the lever or the anchor.
Again there is a clockwise turning effect, or moment, and an anticlockwise moment, which should be the same for balance to be achieved. You can use this system to 'measure' the force exerted by the stretched spring, in terms of weight of the loads. Weight = mass x gravitational field strength (w=mg).
6 Why is a weak spring needed? If the lever is only a short distance above the table, it can only tilt a little and the pull of the string will be practically constant. To ensure such constancy, the stretch of the spring must be large compared with the change when the lever tilts.
This experiment was safety-checked in August 2007Source: www.nuffieldfoundation.org