Application of Friction in Engineering Mechanics

Application of Friction:

1. Ladder Friction: The ladder is a device for climbing or scaling roofs or walls. It consists of two long uprights of wood, iron or rope connected by several cross pieces called rungs. These runs serve as steps:

Consider a ladder AB resting on the rough ground and leaning against a wall, as shown in the figure:

As the upper end of the ladder tends to slip downwards, therefore the direction of the force of friction between the ladder and the wall Fw will be upwards as shown in the figure. Similarly, the lower end, of the ladder tends to slip away from the wall, therefore the direction of the force of friction between the ladder and the floor Ff will be towards the wall as shown in the figure:

Since the system is in equilibrium, therefore the algebraic sum of the horizontal and vertical components of the forces must also be equal to zero.

2. Wedge Friction: A wedge is usually of a triangular or trapezoidal cross-section. It is generally used for slight adjustments in the position of the body i,e. for tightening fits or keys for shafts. Sometimes, a wedge is also used for lifting heavy weights as shown below figure:

It will be interesting to know that the problems on wedges are the problems of equilibrium on inclined planes. Thus these problems may be solved either by the equilibrium method or by applying Lami’s theorem. Now consider a wedge ABC, which is used to lift the body DEFG.

3. Screw Friction: The screws, bolts, studs, nuts, etc are widely used in various machines and structures for fastenings. These fastenings have threads which are made by cutting a continuous helical groove on a cylindrical surface. If the threads are cut on the outer surface of a solid rod, these are known as external threads. But of the threads are cut on the internal surface of a hollow rod. These are known as internal threads.

The screw threads are mainly of two types. V-threads and square threads. The V-threads are stronger and other more frictional resistance to motion than square threads. Moreover, the V-threads have the advantage of preventing the nut from slackening pieces together. Square threads are used in screw jacks, vice screws etc, which are used for lifting heavy loads. The following terms are important for the study of screws:

i. Helix: It is the curve traced by a particle while describing a circular path at a uniform speed and advancing in the axial direction at a uniform rate. Or in other words, it is the curve traced by a particle while moving along a screw thread.

ii. Pitch: It is the distance from one point of a thread to the corresponding point on the next thread. It measured parallel to the axis of the screw.

iv. Depth of thread: It is the distance between the top and bottom surfaces of a thread also known as the crest and root of the thread.

v. Single-threaded screw: If the lead of the screw is equal to its pitch, it is known as a single-threaded screw.

vi. Multi-threaded screw: If more than one thread is cut in one lead distance of a screw, it is known as a multi-threaded screw in a double-threaded screw, two threads are cut in one lead length. In such cases, all the threads run independently along the length of the rod. Mathematically,