Forces and Motion

Always balanced rule

Practical Activity for 16-19 IOP RESOURCES

In this activity students see that a ruler supported by two fingers remains balanced when they slide their fingers towards its centre. You can use it to introduce the co-efficient of friction.

Apparatus and Materials

  • A metre rule


Ask students to:

  1. Use the index finger of each hand to support a meter rule at either end. Gently slide their fingers closer together until they meet at the midpoint – the rule should remain horizontal and balanced throughout.
  2. Then, support the meter rule with one finger close to the 10 cm mark and the other finger close to the 70 cm mark. Note which one of the downward forces they feel on their fingers is larger. Then slide their fingers closer together and note which finger moves first.
  3. Repeat step 2 with one finger at the 30 cm mark and the other at the 90 cm mark.

Discussion prompts

  • Which finger experiences the greater contact force due to the rule?
  • Which finger experiences the greater frictional force when you try to move it?
  • Can you draw a force diagram for the rule? What is the direction of the resultant force?

Teaching notes

For many students it will seem counter-intuitive that the ruler remains horizontal as the fingers are moved inwards. When the two fingers are moved towards one another, first one sticks and the other slips. Then the second finger sticks and the first slips.

The finger that slips is the one further from the midpoint of the rule. You can feel that the (downward) contact force on this finger is less than the contact force on the other. This can be explained by considering moments about the midpoint of the rule. The diagram below illustrates step 2 in the procedure, force A is further from the midpoint than force B and since the rule is balanced, A must be less than B.

The finger that slips is the one further from the midpoint which indicates that this finger experiences less friction than the one that sticks. So the horizontal forces on the rule are unbalanced (FB is greater than FA) and the rule is pushed sideways (to the left, in the diagram).

This experiment shows that the frictional force between two objects is greater when the contact force between them is greater. This can be used to introduce the idea of the coefficient of friction µ, where

µ = frictional force / contact force

that is, the frictional force is proportional to the contact force (and depends on the nature of the surfaces in contact).

Learning outcome

Students recognise that frictional forces are proportional to the contact force and identify the co-efficient of friction as the constant of proportionality.

This experiment was safety-tested in March 2020.

is a special case of Force
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