CAPÍTULO V. Medidas de Protección Aplicables a Trabajos con Encofrados Horizontales
2. Medidas de Protección Colectiva
2.2. Redes de Seguridad
M1 3
Historical note
Isaac Newton was born in Lincolnshire in 1642. He was not an outstanding scholar either as a schoolboy or as a university student, yet later in life he made remarkable contributions in dynamics, optics, astronomy, chemistry, music theory and theology. He became Member of Parliament for Cambridge University and later Warden of the Royal Mint. His tomb in Westminster Abbey reads ‘Let mortals rejoice that there existed such and so great an Ornament to the Human Race’.
Reviewing a mathematical model: air resistance
In mechanics you express the real world as mathematical models. The process of modelling involves the cycle shown in Figure 3.25 and this is used in the example that follows.
Figure 3.25
Forces and Newton’s laws of motion
60
M1 3
L
? Why does a leaf or a feather or a piece of paper fall more slowly than other objects?Model 1: The model you have used so far for falling objects has assumed no air resistance and this is clearly unrealistic in many circumstances. There are several possible models for air resistance but it is usually better when modelling to try simple models first. Having rejected the first model you could try a second one as follows.
Model 2: Air resistance is constant and the same for all objects.
Assume an object of mass m falls vertically through the air.
The equation of motion is mg R ma a g R
m
The model predicts that a heavy object will have a greater acceleration than a lighter one because R
m is smaller for larger m.
This seems to agree with our experience of dropping a piece of paper and a book, for example. The heavier book has a greater acceleration.
L
? However, think again about air resistance. Is there a property of the object other than its mass which might affect its motion as it falls? How do people and animals maximise or minimise the force of the air?Try dropping two identical sheets of paper from a horizontal position, but fold one of them. The folded one lands first even though they have the same mass.
This contradicts the prediction of model 2. A large surface at right angles to the motion seems to increase the resistance.
Figure 3.26
Reviewing a mathematical model: air resistance
M1 3
Model 3: Air resistance is proportional to the area perpendicular to the motion.
Assume the air resistance is kA where k is constant and A is the area of the surface perpendicular to the motion.
The equation of motion is now mg kA ma a g kA
m
According to this model, the acceleration depends on the ratio of the area to the mass.
EXPERIMENT
Testing the new model
For this experiment you will need some rigid corrugated card such as that used for packing or in grocery boxes (cereal box card is too thin), scissors and tape.
Cut out ten equal squares of side 8 cm. Stick two together by binding the edges with tape to make them smooth. Then stick three and four together in the same way so that you have four blocks A to D of different thickness as shown in the diagram.
Cut out ten larger squares with 12 cm sides. Stick them together in the same way to make four blocks E to H.
Observe what happens when you hold one or two blocks horizontally at a height of about 2 m and let them fall. You do not need to measure anything in this experiment, unless you want to record the area and mass of each block, but write down your observations in an orderly fashion.
1 Drop each one separately. Could its acceleration be constant?
2 Compare A with B and C with D. Make sure you drop each pair from the same height and at the same instant of time. Do they take the same time to fall? Predict what will happen with other combinations and test your predictions.
Figure 3.27
Figure 3.28
Forces and Newton’s laws of motion
I Every object continues in a state of rest or uniform motion in a straight line unless it is acted on by a resultant external force.
II Resultant force mass acceleration or F ma.
III When one object exerts a force on another there is always a reaction which is equal, and opposite in direction, to the acting force.
L Force is a vector; mass is a scalar.
L The weight of an object is the force of gravity pulling it towards the centre of the earth. Weight = mg vertically downwards.
2 S.I. units
1 newton (N) is the force required to give a mass of 1 kg an acceleration of 1 m s–2.
A force of 1000 newtons (N) = 1 kilonewton (kN).
3 Experiment in a similar way with E to H.
4 Now compare A with E, B with F, C with G and D with H. Compare also the two blocks whose dimensions are all in the same ratio, i.e. B and G.
L
? Do your results suggest that model 3 might be better than model 2?If you want to be more certain, the next step would be to make accurate measurements. Nevertheless, this model explains why small animals can be relatively unscathed after falling through heights which would cause serious injury to human beings.
L
? All the above models ignore one important aspect of air resistance. What is that?Key points
M1 3
4 Types of force
L Forces due to contact between surfaces
L A smooth light pulley
5 Commonly used modelling terms
L inextensible does not vary in length
L light negligible mass
L negligible small enough to ignore
L particle negligible dimensions
L smooth negligible friction
L uniform the same throughout
6 Reviewing a model
tension
thrust or compression (rod only)
L Forces in a joining rod or string
normal reaction
friction
direction of possible sliding
L Forces on a wheeled vehicle
tensions on both sides are equal
forces act on the objects attached at the ends
Applying Newton’s second law along a line