17.4. Tug-of-War

Can one girl be stronger than four boys?

Author:	Freek Pols
Time:	5 minutes
Age group:	15 - 18
Concepts:	Forces, components of forces, analyzing forces

Introduction

Can one girl be stronger than four boys? Sure! if she is clever…

Equipment

• 4 boys

• 1 girl

• 1 strong rope

Fig. 17.7 The young lady will always be stronger

Preparation

Ask four strong boys and one girl as volunteers.

Procedure

Ask the four boys whether they are, together, stronger than the girl. Let the four boys take up the rope, two on each end and encourage them to pull hard and keep the rope stretched horizontal. Then ask the young lady to use her finger to push the rope downward in the middle (see Figure 17.7). The boys will not succeed in keeping the rope tight and horizontal.

Ask the students in the class to explain why the boys cannot keep the rope tight and horizontal. Make a simple drawing on the board and demonstrate that a vertical force of 50 N exerted by the girl requires each boy to exert a force of more than 700 N when the angle between the rope and horizontal is 1°. This is a surprisingly large force to compensate the small vertical force exerted by the finger.

Tip

Another version of this demonstration was published by Vollebregt and Hooyman [2007]. They connected two ropes on either side of a crate of beer and told the boys to pull so hard that the ropes would be horizontal. Impossible!

Fig. 17.8 The rope cannot be pulled horizontal in this case.

Physics background

The boys exert a horizontal force. While the rope is horizontal, this force does not have a vertical component. When the rope is pressed downward by the finger, there will be a vertical component of the force of the boys, however, it is small:

\[2\cdot F_{\text{boys on rope}} \cdot sin(\theta) = -F_{\text{lady on rope}}\]

\[\Rightarrow F_{\text{boys on rope}} = \frac{-F_{\text{lady on rope}}}{2·sin(\theta)} \]

Angle \(\theta\) is the angle between rope and the horizontal and is very small, thus the vertical component of the force of the boys is very small. Therefore, minimal force is needed to bend the rope downwards.

Follow-up

Use photographs of cable car and power line set-ups to calculate the tension in the cables. See for instance this Dutch national exam question.

References

VH07

M. Vollebregt and C. Hooyman. De rol van de docent bij probleem-stellend onderwijs, op weg naar een andere lesaanpak. NVOX, 2007.