Understand the principles of statics Graphical vectors Triangle of forces theorem Parallelogram of forces theorem Concept of equilibrium cs/Forces.htm

When there are three forces acting on a body and they are in equilibrium, we use the triangle law to solve such problems: When the triangle law is applied to three forces in equilibrium, the resulting triangle will be a closed figure, ie all the vectors will be head-to-tail. Such a vector diagram implies that the resultant force is zero. If three forces acting at a point are in equilibrium, they can be represented in magnitude and direction by the sides of a triangle taken in order.

Example 1 An undercarriage leg of mass of 40 kg is suspended from the undercarriage of an aircraft. The mass is pulled sideways by a horizontal force of 231 N until the mass makes an angle of 30° with the vertical. The mass is now stationary. Determine the magnitude of the force in the undercarriage. Force in the undercarriage Horizontal Force Weight

First draw a diagram showing all the forces acting on the mass. This is called a force diagram or a free body diagram. Now we represent the three forces by means of a triangle. The mass is stationary, so the forces are in equilibrium and the sides of the triangle must all be head-to-tail Weight is obtained by multiplying the mass by N F (in the undercarriage) 400N

231N F (in the undercarriage) 400N

Student Question An undercarriage leg of mass of 50 kg is suspended from the undercarriage of an aircraft. The mass is pulled sideways by a horizontal force of 250 N until the mass makes an angle of 26.5° with the vertical. The mass is now stationary. Determine the magnitude of the force in the undercarriage. 500N 250N F (in the undercarriage)

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Scalars and Vectors A scalar quantity only has size or magnitude. It is completely specified by a number of appropriate units. For example: distance, speed, mass, energy, work, volume,... A vector quantity has size and direction. For example: displacement, velocity, force(weight), acceleration, momentum,... Scalars are added arithmetically (i.e. just add the numbers, so long as the units are the same). E.g. 2kg + 4kg = 6kg.

Vectors are added geometrically, which takes into account their directions as well as their sizes. This is described shortly using forces as an example. A familiar force is that produced by gravity - the weight of an object is defined as the force of gravity acting on the object, so weight is a vector. Like all forces, weight is measured in newton's, N. We see later that: Weight = m x g (m = mass in kg; g =10m/s 2, and is called the 'acceleration due to gravity') For example, a person of mass 70kg has a weight of 70 x 10 = 700N (acting straight downwards).

Drawing a scale diagram to find the resultant When forces do not act on the same straight line, we can still find their resultant by using the 'Parallelogram Rule'. This can be done by drawing a scale diagram or sometimes by calculation Example Two forces of 40N and 60 N act at 60 0 to each other at a point as represented below: What is their resultant force?

Procedure: (The following diagrams are not actually drawn to scale - but you could do so as a check.) 1. Choose a scale: Suppose we let 2cm represent 10N. Then an 8cm line represents the 40N force and a 12cm line represents the 60N force. Draw these lines with a 60 0 angle between them:

2. Complete the parallelogram: 3. Draw the diagonal from the point of application of the forces: The diagonal label R represents the resultant force - measure this and convert its length to newton's: Diagonal R = 17.4cm, so the resultant force R = (17.4/2cm) x 10 = 87N

4. Measure a suitable angle: The angle A = Thus, the resultant of the two original forces is a force of size 87N acting at 23 0 to the 60N force.

Example Two forces of 50N and 60N act at a point on an aircraft fuselage and at right angles (90 0 ) to each other. The 60N acts horizontally to the right. Find the resultant force (a) graphically (i.e. by drawing a scale diagram), and (b) by calculation. (a) Scale: 2cm represents 10N (the diagram below is not actually drawn to scale - you could do so as a check) Diagonal R = 15.6cm, so resultant force R = (15.6/2cm) x 10 = 78N. Also, angle A = So the resultant force has a size or magnitude of 78N acting at 40 0 to the 60N force.

Student Question Two forces of 30N and 40N act at a point on an aircraft fuselage and at right angles (90 0 ) to each other. The 40N acts horizontally to the right. Find the resultant force (a) graphically (i.e. by drawing a scale diagram), and (b) by calculation.

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Example A bell crank is pulled with a force of 280N acting along its handle, as represented below. How much force is acting directly to the right, pulling the roller along the ground, and how much is trying to lift it straight upwards?

To obtain a diagram representing the original force and the desired components, we can draw: an arrowed line to represent the 280N applied force horizontal and vertical lines through the point where the 280N force acts (any lengths, but not too short) lines from the end of the 280N force perpendicular to the two lines just drawn arrowed lines to represent the required components

F 1 is the vertical component of the 280N. F 2 is the horizontal component, which is pulling the roller along the ground. The above could be drawn to scale and the components found from the scale diagram. However, we can also calculate them

Student Question A bell crank is pulled with a force of 300N acting along its handle, as represented below. How much force is acting directly to the right, pulling the roller along the ground, and how much is trying to lift it straight upwards? 300N

Basic Principles of moments When we open a door, we apply a force to produce a turning effect. Looking top down on a door: The turning effect or moment or torque of a force depends on the size of the force and how far it is applied from the hinge (the hinge may also be referred to as the pivot or fulcrum)

Definition Example

Student Question Question 1 Calculate the moment of the following flap movements on an aircraft. Question 2 Calculate the moment after the distance has changes 10Nm Force 3m 10Nm Force 2m

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