Force Table Vector Addition

Using a force table with pulleys and hanging masses, students create one or more known forces on a central ring and determine the equilibrant that brings the system to equilibrium.

1. Set the force table so 0°, 90°, 180°, and 270° align with +x, +y, −x, and −y. Install the central pin and check that pulleys spin freely.
2. Measure and record each empty hanger’s mass. Add masses as needed; convert total mass into force by multiplying the mass (in kilograms) by the acceleration due to gravity (9.8 m/s²).
3. Plan the setup on paper first: choose one or more forces (magnitudes and angles), resolve each into x and y components, and compute the resultant. The equilibrant has the same magnitude but points in the opposite direction.
4. Without hanging any masses yet, determine the angle and mass needed to realize the equilibrant force.
5. Hang the chosen masses for the original force(s) at their angles. Keep the central pin in place while strings are tensioned.
6. Add a third string at the equilibrant angle with the calculated mass to balance the system.
7. Test equilibrium by carefully removing the central pin. If the ring stays centered with no drift, the forces are in equilibrium; if it moves, refine angles or masses and retest.
8. Repeat for two-force and three-force cases, recording all masses, angles, components, and observations.

Experiment 1: Force Table and Vector Addition of Forces - MRC Pahayahay:

Experiment 04 Vectors on the Force Table - Brandon Fleming:

📄 Vector Addition of Forces Lab - Marus Allen et. al: https://phys.libretexts.org/Courses/Prince_Georges_Community_College/PHY-2020%3A_General_Physics_I_Lab/01%3A_Vector_Addition_of_Forces_Lab

• Graphical method: construct a head-to-tail vector diagram to predict the equilibrant, then verify on the table.
• Component check: sum measured forces’ x and y components to confirm they are approximately zero at equilibrium.
• Sensitivity study: vary one angle or mass slightly to show how small errors affect the ring position.
• Four equal forces at 0°, 90°, 180°, 270° to illustrate symmetry and cancellation.

• Keep the central pin installed whenever masses are being added or adjusted.
• Do not exceed pulley or hanger limits; distribute masses so strings run straight and do not rub hardware.
• Keep fingers, hair, and clothing clear of pulleys and hanging masses; stand to the side when removing the pin.
• Verify each hanger’s mass value and secure knots to prevent sudden drops.

• What is the difference between the resultant and the equilibrant? (The resultant is the vector sum of applied forces; the equilibrant is equal in size and opposite in direction, so together they cancel out.)
• Why is the tension in each horizontal string equal to the weight of its hanging mass? (Because the string transmits the same pull as the downward pull of the mass due to gravity, assuming frictionless pulleys.)
• How can you predict the equilibrant’s angle and magnitude using components? (By adding up the horizontal and vertical parts of each force, then reversing the direction of the resultant to find the equilibrant.)
• If the ring drifts after removing the pin, what sources of error are most likely? (Angle misreads, wrong mass totals, pulley friction, strings not radial, or the table not leveled.)
• Why must you plan and calculate before hanging masses? (To avoid unsafe drops and to minimize trial-and-error by setting the correct equilibrant from the start.)