17.12. Twice as much isn’t twice as big

Author:	Freek Pols
Time:	5 minutes
Level:	Grade 4
Concepts:	Force, Newton's third law

Fig. 17.22 The basic setup.

Introduction

Students often think that when you have related quantities and you increase one, the other will also increase. More of A results in more of B. In a series of experiments, Tsakmaki and Koumaras [2016] attempted to dispel this students’ misconception. Using the context of the Magdeburg hemispheres, we explore whether twice as much is really twice as much with regards to Newton’s third law. You can direct this demonstrations towards various goals, depending on what you want to achieve.

Equipment

• 4 stands

• 2 pulleys

• 2 stand clamps

• 2 strings

• 1 spring scale

• 8 mass blocks

Preparation

Assemble the setup as shown in Figure 17.22 beforehand.

Procedure

Ask the students to predict the outcome of the historical experiment with the Magdeburg hemispheres. Von Guericke put two large hemispheres together and vacuumed them. One side was tied with a rope to a tree, the other side was tied to four horses. The horses couldn’t pull the hemispheres apart. Would it be possible if the tree was replaced by four horses? Explain.

Have a student read the value on the spring scale in Figure 17.22. Explain that you will replace the stand with mass blocks. In the context of the Magdeburg hemispheres experiment, you replace the tree with four horses. Ask the students to predict if the force read on the spring scale will increase, decrease, or stay the same, and whether they think the hemispheres would possible separate now.

Replace the stand with the equivalent mass blocks, as shown in Figure 17.23. Have the student read the value on the spring scale again. Discuss with them the result. Here, twice as much weight attached to the string does not imply a twice as big force exerted…

Fig. 17.23 The modified setup; the result is the same.

Physics background

Newton’s third law states that in equilibrium, there are always two forces that are equal in magnitude but opposite in direction. In situation 1 (Figure 17.22), the string attached to the stand prevents the block from falling. There is no acceleration, change of direction, or deformation, so the forces are equal. This means the tension in the string (and thus what you read on the spring scale) is equal to the gravitational force acting on the mass blocks.

The same reasoning applies to situation 2 (Figure 17.23): the mass at the left (which were already there) stay put. Thus the tension did not change.

References

TK16

Paraskevi Tsakmaki and Panagiotis Koumaras. When more of a doesn’t result in more of b: physics experiments with a surprising outcome. School Science Review, 98(383):94–100, 2016.