The two component forces together have the same effect as the single force.

The idea

The two components are not an approximation: together they have exactly the same effect on the object as the single force they came from. That is why you may replace a force by its components, work with them separately, and still be describing the same physics. It also works in reverse. Given two perpendicular forces, draw them as the sides of a rectangle from a common starting point, complete the rectangle, and the diagonal from that point is the single force equivalent to both. Measure the diagonal and convert it with the stated scale to get the magnitude, then measure the angle from a stated reference direction to get the direction. The components can never simply be added as numbers.

What earns the marks

• Stating that the two perpendicular components together have the same effect as the original single force.
• Constructing the original force as the diagonal of the rectangle drawn on the two components.
• Measuring that diagonal and converting it to a force using the stated scale.
• Giving the direction as an angle measured from a stated reference line.

Common mistakes and how to put them right

• Adding the two component magnitudes arithmetically to get the original force.

• Drawing the single force as one side of the rectangle rather than as the diagonal.

• Omitting the angle, so the answer is not a complete vector.

• Measuring the diagonal but forgetting to apply the scale.

• Measuring the angle from an unstated or inconsistent reference direction.

Exam tips

• Say which direction your angle is measured from, for example 'above the horizontal', or the direction mark cannot be awarded.
• Use a set square or the corner of a ruler to keep the rectangle's angles at 90 degrees.
• Check that your diagonal is longer than either side; if it is not, the drawing is wrong.