Resultant forces

Usually several forces act on an object at once. The resultant force is the single force that has the same effect as all of them together.

For forces in a line:

• Add forces that act in the same direction.
• Subtract forces that act in opposite directions.

Example: a car's engine gives a driving force of 2000 N forwards. Friction and air resistance add up to 500 N backwards.

Resultant force = 2000 − 500 = 1500 N forwards

If the forces are balanced, the resultant is zero. A still object stays still, and a moving object keeps moving at the same speed in the same direction.

A free-body diagram shows all the forces acting on one object.

• Draw the object as a box or a dot.
• Draw each force as an arrow starting at the object.
• Make each arrow's length match the size of the force, and point it in the force's direction.
• Label each arrow with the force's name and size.

Example: for a book resting on a table, draw two arrows of equal length: weight pointing down, and the normal contact force from the table pointing up. They are balanced, so the resultant is zero.

To find the resultant of two forces at an angle, use a scale drawing:

1. Choose a scale, such as 1 cm = 1 N.
2. Draw the first force as an arrow to scale.
3. Draw the second force from the tip of the first (tip to tail).
4. Draw a line from the start of the first arrow to the tip of the second. This is the resultant.
5. Measure its length and convert back to newtons; measure its angle with a protractor.

Example: 3 N east and 4 N north give a resultant of 5 N, at about 37° east of north.

Resolving is the reverse: one force can be split into two components at right angles that have the same effect.

If the force arrows drawn tip to tail make a closed shape, the resultant is zero and the object is in equilibrium.