Inclined Plane

4 Key excerpts on "Inclined Plane"

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  eBook - ePub

  The Logic of Machines and Structures

  • Paul Sandori(Author)
  • 2016(Publication Date)
  • Dover Publications

    (Publisher)

  CHAPTER THREE

  The Inclined Plane

  “A mystery is not a mystery”

  The Law of the Inclined Plane — The Triangle of Forces — The Parallelogram Law — The Algebra of Arrows — More Simple Machines — Principles and Limitations — Example

  THE LAW OF THE Inclined Plane

  The contraption seen in Fig. 3.1 is a typical perpetual motion machine. The principle of operation is simple: a heavy chain is fitted around the wheels of the machine in such a way that the right part of the chain is always longer, and therefore heavier, than the left part. The inventor assumed that this imbalance would make the chain move and keep it going around indefinitely. Such inventions started to appear in the twelfth century and multiplied rapidly despite the fact that none of them ever worked, including the example here. The search for perpetual motion was always fruitless—but the profound insight that such motion is impossible led to valuable discoveries. One of them was the law of the Inclined Plane, discovered by Simon Stevin.

  The problem facing Stevin was this: a body placed on an Inclined Plane (which is simply a ramp) somehow appears lighter than when it is sitting on a horizontal plane. For example, body D in Fig. 3.2 can be supported on the ramp AB by a considerably smaller body E. This makes the ramp a simple machine no less wonderful than the lever. Under ideal circumstances (no friction), a pull slightly greater than the weight of body E will move the load up the ramp. Thus with the help of the ramp we can raise a heavy load which, unaided, we could not lift.

  How much force do we have to use to lift a given load up a ramp of known slope? While the law of the lever goes back to at least the days of Aristotle, the Inclined Plane defeated most writers before Stevin.

  Stevin reasoned as follows: imagine a chain of equally spaced identical spheres draped over a triangle where side AB is twice the length of side BC (Fig. 3.3

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  How Things Work

  The Physics of Everyday Life

  • Louis A. Bloomfield(Author)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  Ramps and Inclined Planes show up in many devices, where they reduce the forces needed to perform otherwise difficult tasks. They also change the character of certain activ- ities. Skiing wouldn’t be very much fun if the only slopes available were horizontal or vertical. By choosing ski slopes of various grades, you can select the ramp forces that set 2000 N 5 m 5 m 200 N (a) (b) m 0 N 50 m Fig. 1.3.5 To lift a piano weighing 2000 N, you can either (a) push it straight up or (b) push it along a ramp. To keep the piano moving at a constant velocity, you must make sure it experiences a net force of zero. If you lift it straight up the ladder in (a), you must exert an upward lifting force of 2000 N to balance the piano’s downward weight. If you push it up the ramp shown in (b), you will only have to push the piano uphill with a force of 200 N to give the piano a net force of zero. Chapter Summary and Important Laws and Equations 31 you in motion. Gentle slopes leave only small ramp forces and small accelerations; steep slopes produce large ramp forces and large accelerations. Finally, our observation about mechanical advantage is this: mechanical advantage allows you to do the same work, but you must make a trade-off—you must choose whether you want a large force or a large distance. The product of the two parts, force times dis- tance, remains the same. Check Your Understanding #6: Access Ramps Ramps for handicap entrances to buildings are often quite long and may even involve several sharp turns. A shorter, straighter ramp would seem much more convenient. What consideration leads the engineers designing these ramps to make them so long? Answer: The engineers must limit the amount of force needed to propel a wheelchair steadily up the ramp. The steeper the ramp, the more force is required. Why: A person traveling in a wheelchair on a level surface experiences little horizontal force and can move at constant velocity with very little effort.

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  Mechanical Engineering Science

  In SI Units

  • J. L. Gwyther, W. D. Brown, G. Williams(Authors)
  • 2014(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  6 Friction and the Inclined Plane All surfaces, even although they may appear smooth to the naked eye, consist of a very large number of irregular shapes which, when magnified under a microscope, cause the surfaces to appear rough. If two such surfaces are brought into contact with each other, and a force is applied tending to make one surface slide over the other, it will be found that the 'rough' surfaces resist motion. This resistance is known as 'friction', and the force which must be applied to overcome the resistance is known as the 'force of friction'. If we make an experiment with two rough surfaces which are dry (that is, no form of lubrication is applied) we shall find that the force required to start one surface sliding over the other is greater than that required to keep the surface sliding at a constant velocity. The resistance to the force required to start motion is called 'static friction,' whereas the smaller resistance to the force required to maintain motion at a steady speed is called 'kinetic friction'. Limiting friction Suppose a rectangular block of material is resting on a flat, horizontal surface, and the two surfaces in contact are smooth to the eye but rough when viewed under a microscope. If a small force P is applied F 4 Block »P ////////////^ 'surface'//////// Figure 6.1 Besisted motion Friction and the Inclined Plane 59 to the block its movement will be resisted by the force of friction F, (figure 6.1). If no movement takes place the force P will be balanced by an equal and opposite force F. Further, the weight W of the block, acting vertically downwards, will be resisted by the flat surface. Thus, a reaction B will act upwards from the flat surface as in figure 6.2. F-4 * P ////////////A//////////// Figure 6.2 Condition for equilibrium, block stationary. These four forces will be in equilibrium, and so, if no movement of the block occurs, we can say R = W and F = P Now let the force P be increased slowly.

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  Engineering Science N2 Student's Book

  TVET FIRST

  • MJJ van Rensburg(Author)
  • 2016(Publication Date)
  • Troupant

    (Publisher)

  This is because the amount of force needed is reduced, but the object has to be moved through a longer distance. However, the amount of work done to move an object up an Inclined Plane is the same as the work needed to lift the object vertically. Pushing a car up an incline can be very difficult, but if you forget to set the handbrake a car will sometimes go down a slope all by itself. The question we will answer in this section is: what are the forces that make movement up or down an incline difficult or easy? Inclined Plane: a flat surface that is at an angle to the horizontal; a tilted surface; also called a slope or an incline normal force frictional force force parallel to plane ( W sin θ ) force perpendicular to plane ( W cos θ ) weight ( W ) θ θ Figure 4.29: An object lying on an Inclined Plane 104 If an object is placed on an Inclined Plane (as shown in Figure 4.29], there are three forces acting on it: • The normal force exerted by the plane onto the object. • The force due to gravity (the object’s weight, ‘ W ’ or ‘ mg ’) which acts vertically downwards. • The frictional force, which opposes motion and acts parallel to the plane and opposite to the direction of motion. Note According to the syllabus, the frictional force should be ignored in this unit. The examples in this section therefore do not take the effect of friction into account. Frictional force will be dealt with in Module 6. When a mass is at rest on an Inclined Plane, the effect of the gravitational force will be twofold: • A force acting perpendicular to the plane ( W cos θ or mg cos θ). • A force acting parallel to the plane ( W sin θ or mg sin θ). The perpendicular gravitational force balances the normal force and the parallel gravitational force accelerates the object down the Inclined Plane. Because the normal force and the perpendicular gravitational force are balanced, the net force on the object is the parallel component of the gravitational force (if we ignore the frictional force).

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