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 reactioncomponent 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.