ME101-Basic Mechanical Engineering (STATICS) FRICTION Textbook: Engineering Mechanics- STATICS and DYNAMICS 11th Ed., R. C. Hibbeler and A. Gupta Course Instructor: Miss Saman Shahid

Characteristics of Dry Friction Friction can be defined as a force of resistance acting on a body that prevents or retards slipping of the body relative to a second body or surface with which it is in contact. This force is always tangent to the surface at points of contact with other bodies.

Types of Friction Fluid Friction: it exists when the contacting surfaces are separated by a film of fluid (gas or liquid). The nature of fluid friction is studied in fluid mechanics since it depends upon knowledge of the velocity of the fluid and the fluid’s ability to resist shear forces. Dry Friction/Coulomb Friction: it occurs between the contacting surfaces of bodies when there is no lubricating fluid.

Shear Force If a coplanar force system acts on a member, then in general, a resultant internal normal force N, shear force V, and bending moment M will act at any cross-section along the member.

Theory of Dry Friction Consider the effects caused by pulling horizontally on a block of uniform weight W which is resting on a rough horizontal surface. The floor exerts a distribution of both normal force and frictional force along the contacting surface. For equilibrium, the normal forces must act upward to balance the block’s weight, and the frictional forces act to the left to prevent the applied force P from moving the block to the right. It can be seen that many microscopic irregularities exist between the two surfaces and, as a result, reactive forces ΔRn are developed at each of the protuberances (a detailed approach towards friction including the effects of temperature, density, cleanliness and atomic or molecular attraction between the contacting surfaces) These reactive forces contributes both a frictional component ΔFn and normal component ΔNn.

Equilibrium The distribution of ΔFn indicates that F always act tangent to the contacting surface, opposite to the direction of P. The normal force N is determined from the distribution of ΔNn and is directed upward to balance the block’s weight. Note that N acts a distance x to the right of the line of action of W. This location which coincides with the centroid (geometric center) of the loading diagram, is necessary in order to balance the “tipping effect” caused by P.

Impending Motion In cases where h is small or the surfaces of contact are rather “slippery”, the frictional force F may not be great enough to balance P, and consequently the block will tend to slip before it can tip.

1-Static Friction A certain maximum value Fs called the limiting static frictional force. When this value is reached, the block is in unstable equilibrium since any further increase in P will cause deformations and fractures at the points of surface contact, and consequently the block will begin to move. Experimentally, it has been determined that the limiting static frictional force Fs is directly proportional to the resultant normal force N.

2-Kinetic Friction If the magnitude of P on the block is increased so that it becomes greater than Fs, the frictional force at the contacting surfaces drops slightly to a smaller value Fk, called the kinetic frictional force. The block will not held in equilibrium (P>Fk); instead, it will begin to slide with increasing speed. At P>Fk, then P has the capacity to shear off the peaks at the contact surfaces and cause the block to “lift” somewhat out of it settled position and “ride” on top of these peaks. Once the block begins to slide, high local temperatures at the points of contact cause momentary adhesion (welding) of these points. The continued shearing of these welds is the dominant mechanism creating kinetic friction.

Variation of Frictional Force versus Applied Load Frictional force categorized in three different ways: F is a limiting static frictional force if equilibrium is maintained, F is a limiting static frictional force Fs when it reaches a maximum value needed to maintain equilibrium, F is termed a kinetic frictional force Fk when sliding occurs at the contacting surface. Notice from graph that for very large values of P or for high speeds, because of aerodynamic effects, Fk and likewise µk begin to decrease.

Types of Friction Problems They can be easily classified once free-body diagrams are drawn and the total number of unknowns are identified and compared with the total number of available equilibrium equations. There are three types: Equilibrium Impending Motion at All Points Impending Motion at Some Points

1- Equilibrium Problems in this category are strictly equilibrium problems which require the total number of unknowns to be equal to the total number of available equilibrium equations. After calculation of frictional forces, their numerical values can be checked to be sure they satisfy the inequality F<=µN; otherwise slipping will occur and the body will not remain in equilibrium. In diagram, we must determine the frictional forces at A and C to check if the equilibrium position of the two-member frame can be determined. If the bars are uniform and have known weights of 100N each. There are six unknown force components which can determined from six equilibrium equations (three for each member).

2- Impending Motion at All Points In this case, the total number of unknowns will equal the total number of available equilibrium equations plus the total number of available frictional equations (static or kinetic). Consider the problem of finding the smallest angle at which the 100N bar can be placed against the wall without slipping. Here are five unknowns. For the solution, there are three equilibrium equations and two static frictional equations which apply at both points of contact.

3- Impending Motion at Some Points In this case, the total number of unknowns will be less than the number of available equilibrium equations plus the total number of frictional equations or conditional equations for tipping. As a result, several possibilities for motion or impending motion will exist and the problem will involve a determination of the kind of motion which actually occurs. For example, consider the diagram, if we wish to find horizontal force P needed to cause movement. There are total seven unknowns. For a unique solution, we must satisfy the six equilibrium equations (three for each member) and only one of two possible frictional equations. This means that as P increases it will either cause slipping at A and no slipping at C or vice-versa.

Example Consider pushing on the uniform crate that has a weight W and sits on the rough surface. If the magnitude of P is small, the crate will remain in equilibrium. As P increases the crate will either be on the verge of slipping on the surface, or if the surface is very rough (large µ) then the resultant normal force will shift to the corner, x=b/2 and the crate will tip over. The crate has a greater chance of tipping if P is applied at a greater height h above the surface, or if the crate’s width b is smaller.

Example 8.1 The uniform crate shown has a mass of 20kg. If a force P=80N is applied to the crate, determine if it remains in equilibrium. The co-efficient of static friction is 0.3.