Students should be able to calculate the resultant of two forces that act…

The idea

A resultant force is the single force that has the same effect as all the forces acting on an object combined. When exactly two forces act along the same straight line, they may point in the same direction or in opposite directions. If they act in the same direction, add their magnitudes: 30 N right plus 20 N right gives 50 N right. If they act in opposite directions, subtract the smaller magnitude from the larger: 30 N right plus 20 N left gives 10 N right. The resultant always takes the direction of the larger force. A resultant of zero means the forces are balanced, so the object's motion does not change. Draw a free-body diagram, choose a positive direction, then combine the two values with correct signs before stating magnitude and direction.

What earns the marks

• Identify the two forces and their directions from the diagram or description before doing any arithmetic.
• Choose a positive direction and assign each force a sign, for example right positive and left negative.
• For forces in the same direction, add the magnitudes and keep that common direction.
• For forces in opposite directions, subtract the smaller magnitude from the larger and give the direction of the larger force.
• State the resultant as a magnitude with a direction, such as 10 N to the left, not just 10 N.
• Recognise that a resultant of 0 N means the two forces are balanced and the object's motion is unchanged.

Common mistakes and how to put them right

• Adding the magnitudes of forces that act in opposite directions.

  Put it right by subtracting the smaller from the larger and keeping the direction of the larger force.

• Giving a bare number such as 10 N without a direction.

  Put it right by naming the direction, for example 10 N to the right.

• Treating a resultant of 0 N as 'no forces'.

  Put it right by explaining that two equal and opposite forces still act but cancel, so the object's motion does not change.

Exam tips

• Sketch the two forces as arrows on a straight line and mark one direction as positive before calculating.
• Show the signed addition or subtraction in your working so the examiner can follow your reasoning.
• Finish with a full sentence giving magnitude and direction, and check whether the answer is sensible for the sizes given.