Force vs. Position Graph

3 Key excerpts on "Force vs. Position Graph"

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  eBook - ePub

  Introduction to Sports Biomechanics

  Analysing Human Movement Patterns

  • Roger Bartlett(Author)
  • 2007(Publication Date)
  • Routledge

    (Publisher)

  Figure 5.1 .

  The effects of a force are not altered by moving it along its line of action. Its effects on rotation – though not on linear motion – are changed if the force is moved parallel to the original direction and away from its line of action. A torque, also known as a

  Figure 5.1 Directional quality of force.

  moment of force or a turning effect, is then introduced; this is an effect tending to rotate the object (see below). A quantitative analyst should exercise care when solving systems of forces graphically and would usually adopt a vector approach (see Appendix 4.1 ).

  The SI unit of force is the newton (N) and the symbol for a force vector is F . One newton is the force that when applied to a mass of one kilogram (1 kg), causes that mass to accelerate at 1 m/s2 in the direction of the force application. A sports performer experiences forces both internal to and external to the body. Internal forces are generated by the muscles and transmitted by tendons, bones, ligaments and cartilage; these will be considered in Chapter 6 . The main external forces, the combined effect of which determines the overall motion of the body, are as follows.

  Weight

  Weight is a familiar force (Figure 5.1 ) attributable to the gravitational pull of the Earth. It acts vertically downwards through the centre of gravity of an object towards the centre of the Earth. The centre of gravity (G in Figure 5.1 ) is an imaginary point at which the weight of an object can be considered to act. For the human performer, there is little difference between the positions of the centre of mass (see later) and the centre of gravity. The former is the term preferred in most modern sports biomechanics literature and will be used in the rest of this book. One reason for this preference is that the centre of gravity is a meaningless concept in weightless environments, such as space shuttles. An athlete with a mass of 50 kg has a weight (G ) of about 490 N at sea level, at which the standard value of gravitational acceleration, g , is assumed to be 9.81 m/s2

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  eBook - ePub

  Foundations of Mechanical Engineering

  • A. D. Johnson(Author)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  Figure 4.10(b) the force in the rope.

  Fig. 4.9 (a) Weight suspended by a rope; (b) vector representing rope tension.

  Although the forces are equal in magnitude, their directions differ and this can be shown in the notation: force W ab has the vector running from a to b and force F ba has the force running from b to a.

  Forces and force systems may be represented and analysed using this method.

  Fig. 4.10

  4.4 Equilibrium

  The suspended block in Figure 4.9(a) is hanging on the end of a rope and is stationary. The force applied by the weight of the block on the rope is precisely reacted to by the opposing force within the rope. Since the applied force and the reaction force are exactly equal the system can be said to be in equilibrium (in balance). This state can be confirmed since the block does not move up or down. A slight imbalance in any of the forces and the block would rise or fall. The state of equilibrium occurs naturally and has many examples. For example, a chair pushes upwards with the same force as a seated person pushes down.

  Thus far equilibrium has only been treated in terms of static forces. However, it should be noted that equilibrium can also exist in moving objects.

  A locomotive, pulling carriages and travelling at a constant speed, is in equilibrium since the force developed by the locomotive is exactly equal to the resisting force applied by the carriages. Carriage resistance is due to frictional and air resistances. If the locomotive were to increase its power output, thus increasing the force applied to the rails, between an imbalance the applied and resisting forces would exist and the whole train would increase its velocity.

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  eBook - ePub

  The Really Useful Science Book

  A Framework of Knowledge for Primary Teachers

  • Steve Farrow, Amy Strachan(Authors)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  Similarly, the force supplied or produced by a moving object will be proportional to its mass. Imagine the start of a snooker game. The cue ball is pushed towards the group of red balls and strikes them, scattering them around the table. What might the result be if the cue ball were to be replaced by a table-tennis ball or a sponge rubber ball accelerating at the same rate? In either case, the mass of the replacement cue ball is much smaller than that of the regular cue ball, and the correspondingly smaller force delivered by such small masses would have little impact (literally) on the triangular pack of red balls. This relationship can be summarized as:

  force is proportional to mass, or F (is proportional to) m (2)

  This can also be investigated with a sand tray, but this time with spheres of similar size but different masses being dropped – for example, a pea, a marble, a ball bearing – into the sand, from the same height. Again, the larger ‘craters’ left by spheres of larger mass should confirm the effect.

  The two effects described in equations (1) and (2) can be combined as:

  Force = mass × acceleration, or (F = ma) (3)

  Conversely, if the force acting on an object remains constant, the acceleration of the object produced by the force will be inversely proportional to the mass of the object. In other words, if the mass of the object doubles, the acceleration will be halved, providing the force remains constant. In the trolley experiment shown above, the second law predicts that, if the mass of the trolley was 100 g, and it moved 1 m along the ramp in the first second of travel, an increase in the mass of the trolley to 200 g would result in it travelling only 0.5 m in the first second, under the effect of the same force: when the mass doubles, the acceleration is halved.

  So, acceleration is inversely proportional to mass, or:

  (4)

  And, as F (is proportional to) a (from equation (1), above):

  (5)

  CONCEPT CONFUSION

  Children often think that, for something to be moving, one force has to be bigger than another. However, it is important to highlight that, when an object is moving steadily, or not at all, the forces are balanced. If forces are unbalanced (one force is bigger than the opposing force), acceleration or deceleration will occur.

  Gravity

  This last equation can also be exemplified by a consideration of objects falling – being pulled towards the Earth – under the effect of gravity. All finite objects are made of matter, and the amount of matter in an object is known as its mass, measured in grams. There is a force of attraction, known as the gravitational force, between all objects, and again it was Newton who realized that the force of attraction between two objects was a function of the mass and the distance apart of the two objects. The larger the masses of the two objects, and the closer together they are, the greater will be the gravitational attraction between them. Between objects of small mass, the gravitational force is so small as to be almost negligible. Objects of larger mass (such as the Earth), however, do exert a pull (a gravitational force) on small objects in their vicinity, and it is this pull, continuously exerted by the mass of the Earth, that tends to return any airborne objects to the Earth’s surface. In practice, of course, this means that objects ‘fall’ to Earth under the effect of the gravitational force. Although we do not feel the ‘pull’ of gravity ourselves (partly because our systems have evolved under gravity, so that we tend not to notice it), we can feel the effect of gravity every time we lift an object – a heavy bag of shopping, for example. The force of gravity is ‘pulling’ the mass of the shopping back towards the centre of the Earth, and we need to apply a lifting force to overcome its effect. More force is needed to lift a heavy bag of shopping than a light one, because the heavy bag ‘weighs’ more. What is the difference between mass and weight?

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