Define and apply the torque of a couple in real‑world situations.
A couple consists of two equal and opposite forces that do not act along the same line. The forces are separated by a distance (the lever arm), so the system produces a turning effect.
Because the forces are equal and opposite, the net force on the system is zero, but the net torque is not.
The magnitude of the torque produced by a couple is simply the product of the force magnitude and the separation distance:
\$\tau = F \times d\$
where F is the magnitude of each force and d is the perpendicular distance between the lines of action of the forces.
Direction is given by the right‑hand rule: point your fingers along the first force, curl towards the second, and your thumb points in the direction of the torque.
When you push on a door handle, you apply a force F = 15 N at a distance d = 0.3 m from the hinge.
Because the hinge provides an equal and opposite reaction force, the two forces form a couple.
Torque produced:
\$\tau = 15\,\text{N} \times 0.3\,\text{m} = 4.5\,\text{N·m}\$
This torque turns the door clockwise (right‑hand rule).
| Device | Force (N) | Distance (m) | Torque (N·m) |
|---|---|---|---|
| Wrench on bolt | 20 | 0.15 | 3.0 |
| Door handle | 15 | 0.30 | 4.5 |
| Nut on bolt | 10 | 0.20 | 2.0 |