Extension 2: Mechanical Advantage


In lesson 9, students used the Force Machine to explore the properties of levers and the Law of the Lever. However, students may not realize that they use levers every day. This lesson focuses on a very common lever system – the ordinary pair of scissors, and uses scissors to develop the concept of Mechanical Advantage, which follows directly from the Law of the Lever.


For the class

  • Chart paper for large drawings of scissors.
  • Pegboard model of scissors, made from two links joined with a pivot, and a large pair of scissors.

For each pair of students

  • A pair of scissors (if possible, there should be a variety of scissor types within the class).
  • A ruler graduated in millimeters.
  • A small piece of cardboard, thick enough so it is moderately hard to cut.
  • Worksheets 1 and 2, available as downloads below.


1.      Is a scissors a lever? Demonstrate a pegboard model of a scissors “cutting” something. Then compare this model to real scissors. See a video of this. 

  • Outcome: A scissors is a pair of 1st class levers.

2.      The scissors problem: Distribute scissors and small pieces of cardboard. Students try cutting the cardboard at different positions on the blades. They discuss how their findings relate to what was learned with the Force Machine.  Here is a video

  • Outcome: Moving the cardboard closer to the pivot makes it easier to cut

3.      Scissors and the Law of the Lever:  Demonstrate how to measure the input arm and output arm of a scissors, then show how the Law of the Lever uses these measurements on a scissors to compare input and output forces. This video is preparation for Mechanical Advantage. 

  • Outcome: The law of the Lever explains why cutting is easier close to the pivot and more difficult far from the pivot.

4.      What is Mechanical Advantage? The ratio of input arm to output arm lets you know how hard something will be to cut.  This ratio is called Mechanical Advantage.  It is explained in this video.  

  • Outcome: Mechanical Advantage = (Input arm) / (Output arm).

5.      Mechanical Advantage for a scissors used two ways: Students measure and record the length of the input arm and the output arm when cutting close to the pivot (Worksheet 1) and when cutting far from the pivot (Worksheet 2). They calculate the Mechanical Advantage of the scissors when cutting at each of the positions, using the lengths of the input arm and output arm. The ratio (input arm) / (output arm) is important, because it also tells you the ratio between the force you supply at the input, and how much force comes out at the output.

  • Outcome:  Mechanical Advantage = Output force / Input force.

6.      Discussion of data from scissors measurements. Students compare the Mechanical advantages they calculated for different scissors and different points of cutting.

7.      Extensions.  Students measure other everyday mechanisms and calculate their Mechanical Advantages. Especially interesting are tools with long handles such as bolt cutters, pliers, wrecking bars and lopping shears.


1. Measurements: Students differ in the way they make measurements, so it is hard to compare their results. Here are videos of questions that should be answered consistently:

  • Where is the pivot?
  • How long is the input arm?
  • How long is the output arm?

2. Use of worksheets:

  • How do you do the experiment?

Worksheet 1

L10 Worksheet 1.bmp

Worksheet 2

L10 Worksheet 2.bmp

City Technology, The City College of New York, NAC Building 6/207, New York, NY 10031 Tel. 212 650 8389 Fax. 212 650 6268 Email: citytechnology@ccny.cuny.edu