physics

# Resolution of Forces

A gymnast grabs the bar with one hand and rises from the floor as shown in the figure below. Since the bar is held only with the right hand, this hand bears the entire weight of the gymnast.

The gymnast hangs on one arm

Now he grips the bar with his other hand. The weight that was previously carried by one arm is distributed over both arms. Each arm carries half of his weight, so the arms are less strained.

The gymnast grasps the pole with both hands parallel

The force with which one arm was loaded was replaced by two forces. We say that we have resolved the force into two forces. This is the exact opposite of the process of adding forces:

when adding forces, two or more forces are replaced by a single force,

• but here we are looking for two forces, the sum of which gives us the original single force.

• From both cases, we can see that the gymnast grips the bar in two different ways during different exercises - and therefore the arms are loaded differently.

• How big is this load?

• What forces do the hands exert on the pole?

• How will the arms be loaded if the pole is gripped at an angle to the vertical?

In finding answers to the above questions, we start by resolving the forces. In this way, we will be able to determine how the force is distributed in certain directions. We will discuss the distribution of forces on:

• parallel forces,

• non-parallel forces.

## Why we resolve forces

We resolve forces for different reasons:

• To distribute the forces over several parallel carrier lines

We do this when we want to resolve one larger force into several smaller ones. Thus, each of the carrier lines will be loaded less than if the force acts over only one carrier line.

Example

The example is available to registered users free of charge.

Example

The example is available to registered users free of charge.

• To replace one force with two forces acting at an angle

We do this, for example, because we cannot pull the body in the desired direction. It can be pulled in different directions, but the body still moves in the desired direction.

Example

The example is available to registered users free of charge.

• To determine how much of the force acts in the selected directions

In this case, we are talking about force components. We resolve the force into the components in two selected directions so that the sum of the two components is equal to the original force.

Example

The example is available to registered users free of charge.

By resolving,:

• we replace a larger force with smaller parallel forces,

• we replace a force with two forces that have a more favourable direction of action,

• we determine how much or what component of the force acts in a particular direction.

The resultant of the resolved forces or components must be the same as the original force.

## Resolution of forces in parallel direction

In this case, a force is replaced by two or more equal, parallel forces. The sum of the forces must be equal to the original force.

Example

The example is available to registered users free of charge.

A force can be replaced by two half-forces that have the same direction as the original force.

## Resolution of forces in non-parallel direction

A force can be resolved into two components that subtend an angle with the original force. We will determine how much of the original force acts in the chosen directions. The force and the line (direction) on which both parts of the force will lie must be given. We call them carrier lines. Therefore, we get force components on the carrier lines.

We will look at the process using the two examples below.

Example

The example is available to registered users free of charge.

Example

The example is available to registered users free of charge.

A force can be resolved into two components acting in different directions. We must have the original force and carrier lines given. We resolve this with the parallelogram of forces. The original force is the diagonal of the parallelogram, and the components of the force are the sides of the parallelogram.

The size of the components depends on the angle at which they are inclined with the vertical. The larger the angle, the larger the force components.