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Forces & Moments

Forces

A force can be defined as any push or pull exerted on a body. The S.I. unit of force is the Newton, one Newton being the force required to produce in a mass of one kilogram an acceleration of one meter per second. When considering a force the following points regarding the force must be known:

  1. The magnitude of the force.
  2. The direction in which the force is applied.
  3. The point at which the force is applied.

The resultant force. When two or more forces are acting at a point, their combined effect can be represented by one force which will have the same effect as the component forces. Such a force is referred to as the ‘resultant force’, and the process of finding it is called the ‘resolution of the component forces’.

The resolution of forces. When resolving forces it will be appreciated that force acting towards a point will have the same effect as equal force acting away from the point, so long as both forces act in the same direction and in the same straight line. Thus a force of 10 New tons (N) pushing to the right on a certain point can be substituted for a force of 10 New tons (N) pulling to the right from the same point.

  • Resolving two forces which act in the same straight line: If both forces act in the same straight line and in the same direction the resultant is their sum, but if the forces act in opposite directions the resultant is the difference of the two forces and acts in the direction of the larger of the two forces.
  • Resolving two forces which do not act in the same straight line: When the two forces do not act in the same straight line, their resultant can be found by completing a parallelogram of forces.
  • Resolving two forces which act in parallel directions: When two forces act in parallel directions, their combined effect can be represented by one force whose magnitude is equal to the algebraic sum of the two component forces, and which will act through a point about which their moments are equal.

Moments of forces

The moment of a force is a measure of the turning effect of the force about a point. The turning effect will depend upon the following:

  1. The magnitude of the force.
  2. The length of the lever upon which the force acts, the lever being the perpendicular distance between the line of action of the force and the point about which the moment is being taken.

The magnitude of the moment is the product of the force and the length of the lever. Thus, if the force is measured in Newtons and the length of the lever in meters, the moment found will be expressed in Newton-meters (Nm).

Resultant moment. When two or more forces are acting about a point their combined effect can be represented by one imaginary moment called the ‘Resultant Moment’. The process of finding the resultant moment is referred to as the ‘Resolution of the Component Moments’.

Resolution of moments. To calculate the resultant moment about a point, find the sum of the moments to produce rotation in a clockwise direction about the point, and the sum of the moments to produce rotation in an anticlockwise direction. Take the lesser of these two moments from the greater and the difference will be the magnitude of the resultant. The direction in which it acts will be that of the greater of the two component moments.

Mass

In the S.I. system of units it is most important to distinguish between the mass of a body and its weight. Mass is the fundamental measure of the quantity of matter in a body and is expressed in terms of the kilogram and the tonne, whilst the weight of a body is the force exerted on it by the Earth’s gravitational force and is measured in terms of the Newton (N) and kilo-Newton (kN).

Moments of mass

If the force of gravity is considered constant then the weight of bodies is proportional to their mass and the resultant moment of two or more weights about a point can be expressed in terms of their mass moments.

 

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