Statics Chaper 5 Friction

Intro Two surfaces are in contact – forces tangent to the contact surfaces – known as friction forces – always exist if a surface has a tendency to slide on another surface, or two surfaces are actually in sliding contact Two main types of friction Dry friction Fluid friction (not discussed in this chapter)

Laws of Dry Friction Firgure 5-1b N and F represent the rectangular components of the reaction- component N is normal to the contact surface known as normal force – Component F is tangent to the contact surface and is called the friction force Friction force always acts in the direction opposite to the directions of motion When the force P reaches a value large enough to overcome the static friction force – block will start to slide Once block is in motion – friction force drops abruptly to a lower value and remains constant at this value Figure 5-1 c

Laws of Dry Friction Static Friction force -Experimental evidence indicates that the maximum static friction force denoted by Fm – is proportional to the normal force and is independent of the size of the contact area Fm=UsN – Us is the constant called coefficient of static friction Kinetic friction force – after sliding occurs – friction force is reduced to a smaller value denoted by Fk – value of Fk is also proportional to the normal force and is independent of the size of the contact area and the velocity of motion Fk=UkN – Uk is the constant called the coefficient of kinetic friction Angles of Friction – instead of using the normal and the tangential components N and F of the reaction – it is sometimes convenient to use the reaction force R itself Formalu – 5-3 page 195 The angle is known as the angle of static friction or angle of kinetic friction

Problems Involving Dry Friction If a body is not in motion the static friction force acting on the body is just enough to maintain the body in equilibrium. The maximum static friction force that can be developed in the contact surface is Fm=UsN If a body is sliding, the kinetic friction force acting on the body is Fk=UkN in the direction opposite to that of the slding motion of the body Friction forces is always tend to slow down or stop motion – never generate motion Tipping about a Point Two distinct possibilities of motion – slipping and tipping Figures 5-3 page 196 -197

Wedges Wedges are small blocks with small angles between two of their faces Can be used to apply large forces, raise heavy loads, or make small adjustments in positioning heavy machines Mechanical Advantage – for a machine is defined in general as the ratio of the output force to the input force Formula 5-5 page 204

Square Threaded Screws Screws are used to as fastener and for transforming couples into axial forces Square threaded screws are used in jacks presses and other mechanisms Figure 5-5 Lead angle Square thread can be regarded as an incline wrapped around a cylinder Horizontal distance of the incline is equal to 2pie r, where r is the mean radius of the thread L=np L= vertical rise of the screw , n number of threads p is the pitch Formula page 209 -5-7

Square Threaded Screws Moment required for loading – friction force is independent of the contact area – contact between the threads may be simulated by the contact between a block and incline Formula 5-8 page 210 Self Locking – screw is self locking if the load W remains in place when the loading couple is released – friction force alone is enough to support the load Releasing moment – to lower the load for a self locking screw a moment M’ in the opposite direction must be applied – this application causes equivalent force P’ acting in the direction opposite Formula page 210-211

Belt Friction Flexible is wrapped around a cylindrical drum the tensions on the two sides of belt may differ substantially without causing the belt to slip on the drum Maximum ration between the two tensions before slipping occurs – this ration is important in the design of belt drives, brand brakes, hoisting rigs, and many other machines Maximum Ration of Belt Tensions Forces acting on the belt include belt tension Th and Tl on the two sides of the belt Ration of two tension Th/Tl is maximum when the be3lt is on verge of slipping Formula 5-11 page 213

Rolling Resistance Refers to the resistance from the supporting surface to a rolling wheel that will gradually cause the wheel to slow down. Rolling resistance ins not due to tangential friction forces Figure 5-10 – consider a wheel under a load W rolling on a horizontal surface – due to the load and rolling action of the wheel – the wheel and the supporting surface undergo some deformation – as a result the reaction is distributed over an area rather than at a single contact point Coefficient of Rolling Resistance – wheel is rolling at constant speed the forces acting on the wheel are in equilibrium Formula 5-13 page 219

Rolling Resistance The rolling resistance is proportional to the weight. Thus a wheel of heavier weight would require a greater force to keep it rolling at a constant speed In general rolling resistance is much smaller than sliding resistance . This is the reason for using wheels on vehicles and ball bearings in machines Tests indicate that the coefficient of rolling resistance varies only slightly with the wheel radius r. Neglecting this variation we see that the rolling resistance varies inversely with the radius r of the wheel. This explains why the rolling resistance on a bigger wheel is less.