Force vectors

When adding vector quantities remember that the directions have to be taken into account.

The result of adding vectors together is called the resultant.

When adding two vectors together:

  • the greatest (maximum) resultant is equal to their sum - this happens when forces act in the same direction
  • the smallest (minimum) resultant is equal to their difference - this happens when forces act in opposite directions
  • the resultant can have any value between these limits depending on the angle between the two vectors

In problems, vectors may be added together by scale diagram or mathematically.

Question
An object is pulled to the right by a force of 100 newtons at angle of 60 degrees above horizontal. It is also pulled to the right by a force of 100 newtons at angle of 60 degrees below horizontal.

Two forces of value 100 N act on the object shown below.

Find the resultant force on the object.

A force of 100N at an angle of 60 degrees to horizontal line coming from the square object. The force of 100 N comes back to the horizontal line at the same 60 degree angle.

Length of vectors consistent with scale.

By scale drawing:

Scale 1 cm = 10 N

Size of resultant force = 100 N

Direction of resultant displacement = 60° to either force