Resolving forces - Higher

Two forces can be added together to find a resultant force. A single force can be resolved (broken down) into two component forces at right angles to each other.

In the diagram of a toy trailer below, when a child pulls on the handle, some of the 5 newton (N) force pulls the trailer upwards away from the ground and some of the force pulls it to the right.

A toy trailer has a handle in a position as if it is being pulled, with an arrow on the end of the handle.

A force can be represented by a vector quantity that has both magnitude and direction. Vector diagrams can be used to resolve the pulling force into a horizontal component acting to the right, and a vertical component acting upwards.

Vector diagrams

Draw a right-angled triangle to scale, in which each side represents a force. Try to choose a simple scale, for example 1 cm = 1 N. For the toy trailer example above, draw:

  • a line representing the 5 N force at 37°
  • a horizontal line ending directly below the end of the first line
  • a vertical line between ends of the two lines
  • arrow heads to show the direction in which each force acts

Measure the lengths of the horizontal and vertical lines. Use the scale for the first line to convert these lengths to the corresponding forces.

A right angled triangle with small arrows on the three sides of the triangle.The child's pulling force can be resolved into a 4 N force to the right, and a 3 N force upwards

An alternative way of drawing the resolved forces is shown here. The effect of the child's pulling force can be achieved exactly the same by pulling horizontally and vertically. The two component forces together have the same effect as the single force.

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