Resultant Forces and Free Body Diagrams

By adding up all of the forces acting on an object, you can calculate the resultant force. This is the overall force acting on an object.

Free body diagrams are simple diagrams that show all of the forces acting on an object. The body or object is typically shown as a dot or a box, as you can see below.

Although free body diagrams do not need to be drawn to scale, they can be useful if they are. It is also important to label all the arrows on the diagram, so you are aware of the forces acting on the object.

Free Body Diagram of a Resting Object

The forces acting on the book are weight and the reaction force, which are balanced.

As you can see in the diagram above, the two arrows are the same size. This tells us that the forces acting on the book are equal (but opposite). The length of the arrow indicates the magnitude of the force. When forces are balanced, the resultant force is zero.

Free Body Diagram of a Moving Object

Let’s look at the forces acting on an aeroplane as it flies through the sky. We can create a free body diagram to show all the forces acting on the plane.

  • The force to the left is air resistance (otherwise known as drag)
  • The force to the right is thrust
  • Upwards force is lift
  • Downwards force is weight

As all forces are vectors, each force acting on the aeroplane has a magnitude and a direction. The magnitude can be shown by the length of the arrow and the direction can be shown by where the arrow is pointing. The magnitudes of the forces are expressed in newtons.

Because we have four forces acting in different directions, some of them will cancel out, which we can calculate and find the resultant force. We can separate the horizontal and vertical forces when calculating the resultant force, as this is easier.

Calculating the resultant force

With the vertical forces, there is 90,000 N upwards and 90,000 N downwards. When we subtract one from the other, these forces cancel out, meaning we have 0 newtons overall in vertical forces.

For the horizontal forces, we have 130,000 N to the left and 90,000 N to the right. When we subtract the smaller number from the larger number, we have a resultant force of 40,000 N to the right. Even when taking into account the vertical and horizontal forces, the overall force is still 40,000 N to the right.

When the resultant force is not 0, then the object will accelerate. The velocity will only change if there is a non-zero resultant force acting on the object.

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