The force associated with a lever is a moment of a force (the turning effect of a force). The The effect of the force must be considered in relation to the direction (sense) in which it tends to turn around. We must make a distinction between a clockwise and an anticlockwise moment. Great attention must be given to the lever arm, which is always the perpendicular distance from the hinge or pivot or fulcrum to the line of action of the force. The calculation of moments is repeatedly used throughout the unit and it is important that this concept is fully understood.
A moment is expressed in units of, newton-metres (Nm), or kilonewton-metres (kNm)
Figure 1 Hopefully Figure 1 makes sense to you. As you can see the point of application and direction (line of action) of the forces are significant in respect of the moments magnitude. By keeping the forces vertical the lever arm of F3 and F4 on the dashed member is lesser than on the solid member and by moving the member further down the distance to F3 and F4 will decrease even more. When the member reaches the vertical (turning 90° downwards) the distance will be zero. F3 creates a Figure 2 Figure 2 is the same the dashed member shown in Figure 1. Here the member is placed in a horizontal position and the forces acting on the member are inclined. Remember that forces can be resolved into horizontal and vertical components. Whether we use of F3 or F4 times the perpendicular distance or the vertical components of F3 or F4 times their perpendicular distance the magnitude of the resulting moments will be the same. .The horizontal component of F4 times the horizontal distance to the hinge equals F4 times the inclined distance to the hinge. The following example will prove this statement. Figure 3As can be seen the vertical component of the 5 kN force times the perpendicular distance A see-saw is a common equipment found on playgrounds. We all know how to keep the see-saw levelled; children on either side must be of the same weight and sit from the support (fulcrum) at equidistant. If one child is heavier than the other the heavier child must move closer to the fulcrum. The see-saw works on the principle that the
When a force system, acting in the same plane, is in Since an international convention does not exist, in this course, a clockwise rotation about the center of moments will be considered as positive; a counter-clockwise rotation about the center of moments will be considered as negative. Use the following convention: (The sign convention for a moment can be the other way round. What is important is to make a distinction between a clockwise and anti-clockwise moment. This may be confusing and students should stick to the forementioned convention.)
A body is in a state of
We will now resolve a single force into a force acting at another point and a couple. This principle is often applied in beam design when we tranferred a force to a different position. If this is done then consideration must be given to the moment resulting from the transfer (i.e. force × tranferred distance). The following example will demonstrate this.
We use the principle of moments to find the answer. In our example the fulcrum is the back wheel at 2.3 metre from the centre of gravity. To keep the system in equilibrium the clockwise moment [kg x (6.0-2.3)].mass times the distance to the back wheelThe equation written mathematically 28750 = mass x 3.7 mass = 28750 / 3.7 =7.770.3 kg |