A number of forces acting on an object may be replaced by a single force…

The idea

When several forces act on an object, their combined effect is represented by a single resultant force. This has the same effect as all original forces acting together. To find it, add forces acting in the same direction and subtract those in opposite directions. For example, if a box is pushed right with 10 N and left with 4 N, the resultant is 6 N to the right. If forces are balanced, the resultant is zero and the object remains at rest or moves at constant velocity. If unbalanced, the resultant causes acceleration. For forces at an angle, a scale diagram can be used to find the resultant (HT only). Understanding resultant force is essential for explaining motion.

What earns the marks

• The resultant force is a single force that has the same effect as all the original forces acting together.
• Forces acting in the same direction are added; forces acting in opposite directions are subtracted.
• The direction of the resultant force is the direction of the larger force when two forces act along the same line.
• If the resultant force is zero, the forces are balanced and the object's motion does not change (it stays at rest or moves at constant velocity).
• If the resultant force is not zero, the object accelerates in the direction of the resultant force.
• For forces at an angle, the resultant can be found using a scale diagram (HT only).
• The resultant force is a vector quantity, having both magnitude and direction.

Common mistakes and how to put them right

• Adding all forces together regardless of direction.

  Put it right: Assign positive and negative directions before adding.

• Forgetting to state the direction of the resultant force.

  Put it right: Include the direction (e.g., 'to the right' or 'upwards').

• Assuming that if forces are balanced, the object must be stationary.

  Put it right: Balanced forces mean no change in motion, not necessarily no motion.

• Confusing resultant force with the sum of all forces without considering direction.

  Put it right: Treat forces as vectors.

Exam tips

• When calculating resultant force, draw a free-body diagram to visualise the forces and their directions.
• If forces are at an angle, use a carefully drawn scale diagram to find the magnitude and direction of the resultant force (HT only).
• For multiple forces along a line, choose a positive direction and assign signs to each force before adding.
• Always check whether the question asks for magnitude only or magnitude and direction.