CAPÍTULO IV. Sistemas de Encofrado Horizontal
4. Sistemas de Encofrado Horizontal
4.2. Encofrados Industrializados
The picture shows crates of supplies being dropped into a remote area by parachute. What forces are acting on a crate of supplies and the parachute?
One force which acts on every object near the earth’s surface is its own weight. This is the force of gravity pulling it towards the centre of the earth. The weight of the crate acts on the crate and the weight of the parachute acts on the parachute.
The parachute is designed to make use of air resistance. A resistance force is present whenever a solid object moves through a liquid or gas. It acts in the opposite direction to the motion and depends on the speed of the object. The crate also experiences air resistance, but to a lesser extent than the parachute.
Other forces are the tensions in the guy lines attaching the crate to the parachute.
These pull upwards on the crate and downwards on the parachute.
All these forces can be shown most clearly if you draw force diagrams for the crate and the parachute.
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Force diagrams
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Force diagrams are essential for the understanding of most mechanical situations.
A force is a vector: it has a magnitude, or size, and a direction. It also has a line of action. This line often passes through a point of particular interest. Any force diagram should show clearly
L the direction of the force
L the magnitude of the force
L the line of action.
In figures 3.1 and 3.2 each force is shown by an arrow along its line of action. The air resistance has been depicted by a lot of separate arrows but this is not very satisfactory. It is much better if the combined effect can be shown by one arrow.
When you have learned more about vectors, you will see how the tensions in the guy lines can also be combined into one force if you wish. The forces on the crate and parachute can then be simplified.
Figure 3.1 Forces acting on the crate Figure 3.2 Forces acting on the parachute air resistance
weight of parachute
Figure 3.3 Forces acting on the crate Figure 3.4 Forces acting on the parachute weight of crate
air resistance on crate combined tension
air resistance on parachute
weight of parachute
combined tension air resistance
weight of crate
tensions in the cords
Forces and Newton’s laws of motion
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Centre of mass and the particle model
When you combine forces you are finding their resultant. The weights of the crate and parachute are also found by combining forces; they are the resultant of the weights of all their separate parts. Each weight acts through a point called the centre of mass or centre of gravity.
Think about balancing a pen on your finger. The diagrams show the forces acting on the pen.
So long as you place your finger under the centre of mass of the pen, as in figure 3.5, it will balance. There is a force called a reaction between your finger and the pen which balances the weight of the pen. The forces on the pen are then said to be in equilibrium. If you place your finger under another point, as in figure 3.6, the pen will fall. The pen can only be in equilibrium if the two forces have the same line of action.
If you balance the pen on two fingers, there is a reaction between each finger and the pen at the point where it touches the pen. These reactions can be combined into one resultant vertical reaction acting through the centre of mass.
The behaviour of objects which are liable to rotate under the action of forces is covered in Mechanics 2 Chapter 11. In Mechanics 1 you will only deal with situations where the resultant of the forces does not cause rotation. An object can then be modelled as a particle, that is a point mass, situated at its centre of mass.
Newton’s third law of motion
Sir Isaac Newton (1642–1727) is famous for his work on gravity and the
mechanics you learn in this course is often called Newtonian Mechanics because it is based entirely on Newton’s three laws of motion. These laws provide us with an extremely powerful model of how objects, ranging in size from specks of dust to planets and stars, behave when they are influenced by forces.
Figure 3.5 Figure 3.6
Force diagrams
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We start with Newton’s third law which says that
L When one object exerts a force on another there is always a reaction of the same kind which is equal, and opposite in direction, to the acting force.
You might have noticed that the combined tensions acting on the parachute and the crate in figures 3.3 and 3.4 are both marked with the same letter, T. The crate applies a force on the parachute through the supporting guy lines and the parachute applies an equal and opposite force on the crate. When you apply a force to a chair by sitting on it, it responds with an equal and opposite force on you. Figure 3.8 shows the forces acting when someone sits on a chair.
The reactions of the floor on the chair and on your feet act where there is contact with the floor. You can use R1, R2 and R3 to show that they have different magnitudes. There are equal and opposite forces acting on the floor, but the forces on the floor are not being considered and so do not appear here.
L
? Why is the weight of the person not shown on the force diagram for the chair?Gravitational forces obey Newton’s third law just as other forces between bodies.
According to Newton’s universal law of gravitation, the earth pulls us towards its centre and we pull the earth in the opposite direction. However, in this book we are only concerned with the gravitational force on us and not the force we exert on the earth.
All the forces you meet in mechanics apart from the gravitational force are the result of physical contact. This might be between two solids or between a solid and a liquid or gas.
Forces and Newton’s laws of motion
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Friction and normal reaction
When you push your hand along a table, the table reacts in two ways.
L Firstly there are forces which stop your hand going through the table. Such forces are always present when there is any contact between your hand and the table. They are at right angles to the surface of the table and their resultant is called the normal reaction between your hand and the table.
L There is also another force which tends to prevent your hand from sliding.
This is the friction and it acts in a direction which opposes the sliding.
Figure 3.9 shows the reaction forces acting on your hand and on the table. By Newton’s third law they are equal and opposite to each other. The frictional force is due to tiny bumps on the two surfaces (see electronmicrograph below). When you hold your hands together you will feel the normal reaction between them.
When you slide them against each other you will feel the friction.
When the friction between two surfaces is negligible, at least one of the surfaces is said to be smooth. This is a modelling assumption which you will meet frequently in this book. Oil can make surfaces smooth and ice is often modelled as a smooth surface.
Figure 3.9
friction force on hand
normal reaction on hand
normal reaction on table
friction force on table
Etched glass magnified to high resolution, showing the tiny bumps.
Force diagrams
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L When the contact between two surfaces is smooth, the only forces between them are normal reactions which act at right angles to any possible sliding.
L
? What direction is the reaction between the sweeper’s broom and the smooth ice?EXAMPLE 3.1 A TV set is standing on a small table. Draw a diagram to show the forces acting on the TV and on the table as seen from the front.
SOLUTION
The diagram shows the forces acting on the TV and on the table. They are all vertical because the weights are vertical and there are no horizontal forces acting.
Figure 3.10
resultant normal reaction of TV acting on table resultant normal reaction
of table acting on TV
resultant normal reaction of floor on
right-hand legs resultant normal
reaction of floor on left-hand legs
weight of TV
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EXAMPLE 3.2 Draw diagrams to show the forces acting on a tennis ball which is hit downwards across the court
(i) at the instant it is hit by the racket
(ii) as it crosses the net
(iii) at the instant it lands on the other side.
SOLUTION
EXERCISE 3A In this exercise draw clear diagrams to show the forces acting on the objects named in italics. Clarity is more important than realism when drawing these diagrams.
1 A gymnast hanging at rest on a bar.
2 A light bulb hanging from a ceiling.
3 A book lying at rest on a table.
4 A book at rest on a table but being pushed by a small horizontal force.
5 Two books lying on a table, one on top of the other.
6 A horizontal plank being used to bridge a stream.
7 A snooker ball on a table which can be assumed to be smooth
(i) as it lies at rest on the table
(ii) at the instant it is hit by the cue.
8 An ice hockey puck
(i) at the instant it is hit when standing on smooth ice
(ii) at the instant it is hit when standing on rough ice.
Figure 3.11
normal reaction of ground
friction force of ground air resistance (when
ball is moving quickly) weight of ball
force of racket
(i) (ii) (iii)