Who's First?

What is the best order for players to stand in a game of Tug of War?

This article uses friction and normal force concepts to explain how people should be ordered in a game of Tug of War. The easiest way to explain this concept is to start with the answer and work backward. The order that players should stand in depends on each player's height. To find out why, let's look at the physics of Tug of War. First, we must set the stage. The game will occur on flat, equal ground and each team will have players of the same physical attributes (shoes included). If Team 1 has a tall player, Team 2 will also have a tall player, and so on. Every aspect of the competition will be equal for both teams other than the order they stand in.

For a team to win in tug of war, they must have a greater friction force on the ground than the other team. The friction force is horizontal and resists motion. A greater friction force will allow a team to pull the rope in the their direction without losing footing while pulling the other team in the same direction. So with the understanding that the team with a greater friction force will win, we should consider the composition of the friction force. Friction is proportional to two physical variables. The first is a friction coefficient which describes the "roughness" between the two surfaces. Under our simplified circumstance, both teams have the same shoes and are on the same ground so that both teams will have an equal friction coefficient. This leaves only one variable, normal force, which is directly proportional to the friction.

So we've concluded that to win in Tug of War, a team should try to increase their net normal force, increasing the friction. The normal force will be equal to the net downward force. If gravity pulls me down by 100 Newtons and a rope pushes me down another 10 Newtons, the normal force will be 110 Newtons. Let's look at the two scenarios to find out how each one works. In Figure 1A, the players are lined up from shortest at the front to tallest at the back. In this configuration, the players at the back are pulling upward on the rope which pulls up on and "lifts" the shorter people at the front. As a result, the players at the front will also have less of a normal force, decreasing the total friction. On the other hand, Figure 1B has the tallest players in the front and the shortest in the back. In this configuration, the players in the back can be pulling down, which increases the downward force of the taller players in the front. This is because the rope being pulled down, which also pull down on the people at the front. As a result, the net normal force, and friction will increase for this team. This verifies that the team that stands from tallest at the front to shortest at the back will win the game.

Figure 1A

Figure 1B