Tug-of-War Vector Addition

A tug-of-war setup demonstrates how forces act as vectors. People or teams pulling on a central ring or rope represent individual force vectors. If the pulls are balanced, the ring stays still; if unbalanced, the ring moves in the direction of the resultant force.

1. Tie a rope to a central ring or mark a central point on the ground.
2. Organize students or teams to pull on the rope from different directions.
3. Begin with two teams pulling in opposite directions with equal strength; note that the ring remains in place (unless unevenly matched).
4. Allow one team to pull harder or add a third team at an angle; observe that the ring shifts in the direction of the stronger or combined pull.
5. Discuss how each team’s pull represents a vector with both magnitude (force) and direction.
6. Show how the observed motion matches the vector sum (the resultant force).

• None

• Use three or more teams pulling at different angles to illustrate vector addition in two dimensions.
• Have observers sketch arrows representing the forces and compare the drawn vector sum with the ring’s motion.
• Film the center point of the rope for replay analysis to show how the motion matches the vector sum.
• Use spring scales on each rope to measure the pulling forces and calculate the expected resultant.

• Ensure the ground is clear and dry to prevent slipping.
• Use a rope thick enough to avoid rope burns; gloves are recommended.
• Keep the pulling moderate; avoid sudden jerks that could cause falls.
• Supervise closely to prevent accidents from unbalanced pulls.

• Why does the ring stay still when two equal forces pull in opposite directions? (Because the forces cancel, resulting in no net force.)
• What happens when a third team pulls at an angle? (The resultant force points in a new direction, and the ring moves accordingly.)
• How is the motion of the ring related to the vector sum of all the forces? (The ring always moves in the direction of the resultant force.)
• How can you predict the direction of motion before pulling? (By adding the force vectors graphically or by calculating their horizontal and vertical components.)