Resultant Forces (Oxford AQA IGCSE Combined Science Double Award)

Resultant Forces

What is a resultant force?

• When a number of forces are acting on a single object, the forces can be replaced by a single force that has the same effect on the motion of the object as all the original forces acting together

• This single force is called the resultant force

• The resultant force determines:

  • The direction in which the object will move as a result of all of the forces

  • The magnitude of the final force experienced by the object

What is a Free-Body force diagram?

• Free-body force diagrams are vector diagrams showing the multiple forces acting on a single object

• The vectors can be drawn onto a picture of the object, or the object can be represented by a dot

Free-Body force diagram of a car

• The vertical forces add together

  • In the example of the car, the normal contact force and the weight are equal in magnitude and opposite in direction

  • Therefore, the vertical forces add up to zero

  • We say the forces are balanced

• The horizontal forces add together

  • In the car example, the thrust force has a greater magnitude than the frictional force and acts in the opposite direction

  • Therefore, the net horizontal force is in the forward direction

• Taking all the forces into account, the resultant force is in the forward direction

• A non-zero resultant force will cause a change in the object's motion

• A change in the object's motion is an acceleration

  • In the example of the forward travelling car, the car will accelerate or speed up

Calculating resultant forces

• Force is a vector quantity, it has both magnitude and direction

• When adding forces together it is important to assign positive and negative values to show the direction in which the forces are acting

• If a 5 N force acts to the right and a 5 N force acts to the left on an object, then we assign one of the values as positive and one as negative

• So the resultant force acting on the object is

• The forces acting on the object are equal in magnitude and opposite in direction therefore they cancel one another out

• This is like two people pushing a box with equal force from opposite sides, the box doesn't move

• If two people push the box from the same side in the same direction, one with a 3 N force and one with a 7 N force, then the forces will add together and the box will move in the direction of the resultant force

• If two people push the box in opposite directions, one with a 7 N force to the left (negative) and one with a 3 N force to the right (positive), then the forces will add together and the box will move in the direction of the resultant force

Zero and Non-Zero resultant forces

Using scale diagrams to determine resultant force

• There are two methods that can be used to combine vectors using a scale diagram: the triangle method and the parallelogram method

• To combine vectors using the triangle method:

  • Step 1: link the vectors head-to-tail

  • Step 2: the resultant vector is formed by connecting the tail of the first vector to the head of the second vector

  • Step 3: The magnitude of the resultant vector can be found by measuring the length of the arrow

• To combine vectors using the parallelogram method:

  • Step 1: link the vectors tail-to-tail

  • Step 2: complete the resulting parallelogram

  • Step 3: the resultant vector is the diagonal of the parallelogram

  • Step 4: The magnitude of the resultant vector can be found by measuring the length of the arrow

Triangle and Parallelogram method of combining vectors