Balanced forces

1. Forces on an object are balanced when they cancel each other out completely, so the resultant force is zero.
2. An object with balanced forces acting on it is in equilibrium.
3. Balancing is a special case, because the forces must match in both size and direction.
   1. For two forces to balance, they must be equal in size, act in opposite directions and act along the same line.
   2. For several forces to balance, the total force in each direction must equal the total force in the opposite direction.
4. A zero resultant force means the object does not accelerate, so its velocity stays the same.
   1. A stationary object with balanced forces stays stationary.
   2. A moving object with balanced forces keeps moving at a constant speed in a straight line.
5. Balanced forces therefore tell you that the velocity is not changing, not that the object is at rest.

Drawing balanced free body diagrams

1. A free body diagram for balanced forces shows each force on the object as a labelled arrow, with balancing forces drawn as arrows of equal length pointing in opposite directions.
2. Draw the object as a box or a dot, and draw only the forces acting on that object.
3. Consider the vertical forces and the horizontal forces separately.
   1. The upward arrows must have the same total length as the downward arrows.
   2. The arrows pointing one way along the horizontal must have the same total length as the arrows pointing the other way.
4. If a situation has no horizontal forces, such as an object hanging still, the diagram shows only vertical arrows.

Balanced forces on stationary objects

1. A book on a shelf has its weight acting downwards and an equal normal contact force from the shelf acting upwards.
2. A hanging basket outside a café has its weight acting downwards and an equal tension from its chain acting upwards.
3. A boat floating still in a harbour has its weight acting downwards and an equal upthrust from the water acting upwards.
4. Two teams in a tug of war that is not moving pull on the rope with equal forces in opposite directions, so the rope stays still.
5. In each case the arrows on the free body diagram are equal and opposite, so the object stays at rest.

Balanced forces on moving objects

1. A car at a steady speed on a straight, level road has a forward driving force balanced by backward air resistance and friction, and its weight balanced by the normal contact force from the road.
2. A skydiver at terminal velocity has her weight balanced by an equal upward air resistance, so she falls at a constant speed.
3. A lift rising at a steady speed has its weight balanced by an equal upward tension in its cable.
4. A plane cruising at a constant height and speed has its weight balanced by an upward lift force and its thrust balanced by air resistance.
5. In each case the object keeps moving, but its velocity does not change, because the resultant force is zero.