chapter 4 equilibrium of rigid body & friction. rigid body definition of a rigid body: a rigid...
TRANSCRIPT
![Page 1: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/1.jpg)
CHAPTER 4
Equilibrium of Rigid Body & Friction
![Page 2: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/2.jpg)
Rigid BodyDefinition of a rigid body:• A rigid body is defined as a body on which the
distance between two points never changes whatever be the force applied on it.
• Or you may say the body which does not deform under the influence of forces is known as a rigid body.
• But, in real life, there would be some force under which the body starts to deform. For example, a bridge does not deform under the weight of a single man but it may deform under the load of a truck or ten trucks. However, the deformation is small.
![Page 3: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/3.jpg)
Condition for rigid body equilibrium• General equation of equilibrium for a rigid body
F=0
M=0• Equilibrium in two dimension
Fx=0
Fy=0
M=0• Equilibrium in three dimension
Fx=0
Fy=0
Fz=0
M=0
![Page 4: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/4.jpg)
Free Body Diagram (2D)• Support Reactions
– there are various types of reaction that occur at supports and point
– As a general rules, • If a support prevents the translation of a body in a
given direction, then a force is developed on the body in that direction. Likewise , if rotation is prevented , a couple moment is exerted on the body
Example :
(i) Prevents the beam from translating in the vertical direction
Prevents the beam from translating in the vertical
direction, the roller can only exert a force on the
beam
![Page 5: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/5.jpg)
The pin passes through a hole in the beam and two leaves which are
fixed to the ground. The pin can prevent
translation of the beam in any direction
This support prevent both translation and rotation of the beam, and so to do this a force and couple
moment must be developed on the beam at
its point of connection.
![Page 6: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/6.jpg)
![Page 7: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/7.jpg)
![Page 8: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/8.jpg)
• External and Internal Forces – Internal Forces – not represented on Free
Body Diagram– External Forces – do represented on Free
Body Diagram
• Weight and the center of Gravity– When the body is uniform or made of
homogeneous material , the centre of gravity will be located at the body’s geometric centre or centroid
– the body nonhomogeneous or has an unusual shape, then the location of its center of gravity will be given
W=mg
![Page 9: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/9.jpg)
• Idealized Model
![Page 10: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/10.jpg)
APPLICATIONS
A 200 kg platform is suspended off an oil rig. How do we determine the force reactions at the joints and the forces in the cables?
How are the idealized model and the free body diagram used to do this? Which diagram above is the idealized model?
![Page 11: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/11.jpg)
1. Draw an outlined shape. Imagine the body to be isolated or cut “free” from its constraints and draw its outlined shape.
2. Show all the external forces and couple moments. These typically include: a) applied loads, b)
support reactions, and, c) the weight of the body.
Idealized model Free body diagram
Example 4.1Draw the free body diagram of the uniform beam shown in figure below. The beam has a mass of 100kg
![Page 12: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/12.jpg)
Example 4.4• The link shown in Figure below is pin-connected at A
and rests against a smooth support at B. Compute the horizontal and vertical components of reaction at the pin A.
![Page 13: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/13.jpg)
Determine support reaction for beam• In determining of support reactions, the
unknown reactions acted on the beam must be identified. This can be done by referring to Table of support reaction.
• By using the Equation of Equilibrium, the support reactions can be solved.
For the point load:• the distance is taken from the point of
force to moment about point.
For distributed load (DL), • the distance is taken from the centroid of
DL to the moment about point.
![Page 14: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/14.jpg)
• A point load is self-explanatory: a load that is applied at one point
• A distributed load/uniform load, on the other hand, is applied along an edge
![Page 15: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/15.jpg)
Practical cases • In buildings, point loads on beams is subjected to
loads from other beams or columns and uniformly distributed loads are due to floors, walls and partitions and the weights of the beams themselves
Example 1
![Page 16: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/16.jpg)
Constraint for rigid body• Type of constraint
– Redundant constraint• When a body has redundant supports, that is
more supports than are necessary to hold it in equilibrium, it become statically indeterminate (more unknown loadings on the body than equations of equilibrium).
![Page 17: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/17.jpg)
– Improper constraint• Resulting in stability• axis is perpendicular to the plane of the forces
and therefore appears as a point, Hence, when all the reactive forces are concurrent at this point, the body is improperly constrained
![Page 18: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/18.jpg)
Equilibrium of rigid body in 3 DimensionFree body diagram of Support Reactions• The magnitude of forces, F = • Force’s orientation defined by the coordinate
direction angles , and
222zyx FFF
![Page 19: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/19.jpg)
A single bearing or hinge can prevent rotation by providing a resistive couple moment. However, it is usually preferred to use two or more properly aligned bearings or hinges. Thus, in these cases, only force reactions are generated and there are no moment reactions created.
Example 4.3
![Page 20: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/20.jpg)
Equation of equilibrium• Vector Equations of Equilibrium ,
F = 0, vector sum of all the external forces acting on the body
Mo = 0, is the sum of couple moments and the moments of all the forces about any point O located
either on or off the body• Scalar Equations of Equilibrium
If applies the external forces and couple moments in Cartesian Vector.
F = Fxi + Fyj + Fzk = 0
Mo = Mxi + Myj + Mzk = 0 • Since the i, j and k components are independent from one
another, the above equations are satisfied provided
Fx = 0 , Fy = 0 and Fz = 0
Mx = 0 , My = 0 and Mz = 0
![Page 21: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/21.jpg)
Example 4.14• The homogeneous plate shown in figure below has a
mass of 100kg and is subjected to a force and couple moment along it edges. If it is supported in the horizontal plane by means of a roller at A, a ball and socket joint at B and a cord at C, determine the components of reaction at the supports.
![Page 22: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/22.jpg)
Equations of Equilibrium:
Fx = 0; Bx = 0
Fy = 0; By = 0 and
Fz = 0; Az + Bz + Tc - 300N - 981 N = 0
Moment at axis equation (right hand rules=define direction of moment):
Mx = 0; Tc ( 2m) - 981 ( 1m) + Bz (2m) = 0
My = 0; 300 N (1.5m) + 981N ( 1.5m) – Bz (3m) - Az(3m) – 200N.m = 0
The components of force at B can be eliminated if the x’, y’ and z’ axes are used. We obtain
Mx’ = 0; 981 N (1m) + 300 N (2m) - Az ( 2m)= 0
My’ = 0; -300 N (1.5m) - 981N (1.5m) – 200 N.m+Tc (3m) = 0
Results
Az = 790 N Bz = -217 N, negative sign indicates that Bz acts downward
Tc = 707 N
![Page 23: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/23.jpg)
Pulleys system
![Page 24: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/24.jpg)
![Page 25: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/25.jpg)
Example 4.7• Determine the tension T in the cable of the pulley
system shown in Figure
The most solution would be as follows:Fy = 0 5T = 1500 NT = 300 N
![Page 26: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/26.jpg)
∑Fy = 0
T3 = 4T
T3 = 1200 N
∑Fy = 0
T + T4 = 1500 N
T = 300 N
∑Fy = 0
T2 = 2T
T2 = 600 N
![Page 27: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/27.jpg)
Friction
![Page 28: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/28.jpg)
Friction
![Page 29: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/29.jpg)
• What is Friction?– Friction is defined as a force of resistance acting on a
body which prevents or retards slipping of the body relative to a second body
• Friction Law for dry surface• Motion or impending motion of two forces in contact
causes a reaction force known friction force.• This friction force is :
– Parallel to a flat surface or tangent to a curved surface– Opposite in direction to the motion or impending
motion– Dependent on the force pressing the surfaces together– Generally independent of the area of surface of contact – Independent of velocity, except for extreme cases not
to be considered in this module– Dependent on the nature of the contacting surface
![Page 30: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/30.jpg)
Friction• How to define friction?
– Friction laws for dry surface• On Horizontal plane
• On Inclined plane
![Page 31: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/31.jpg)
Friction laws for dry surface on horizontal plane– Condition 1: No applied load (Not moving)
• No friction
Weight(W)
Normal force(N)
F
![Page 32: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/32.jpg)
– Condition 2 : applied load P pushed the block and the block has impending motion• F acted as a reacting force an not be great enough to
balance P and subsequently the block will tend to slip. • In other words P will slowly increases until the block is
on verge sliding, F can be to max value (Fmax) but the block still in equilibrium
– At this state F is know as static friction force, FS
Weight(W)
Normal force(N)
F
P Fs=μsN
Coefficient of static friction
Notes: if F=P, F< Fs, the equation of FS can not be use to determine the friction since the friction force not achieved the maximum value
![Page 33: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/33.jpg)
– Condition 3 : when the block is start moving (motion)• F will reduced fastly because of the momentum
influence– At this state F is know as kinetic friction force, Fk
– At this condition Fk is less than Fs
Weight(W)
Normal force(N)
Fk
P Fk=μkN
![Page 34: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/34.jpg)
– Condition 4 : the block is sliding/overturning• When P is increased (P > Fk) until it make the block
sliding/overtuning at point B. Moment at B = zero.
+ ΣMB =P(h)-W(a)
Weight(W)
Normal force(N)
Fk
P
• Total moment at B is +ve = the block is not sliding/overturning.• Total moment at B is -ve = the block is sliding/overtuning.
![Page 35: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/35.jpg)
• Resultant force– Experimentally Those limiting static frictional force Fs
and Fk is directly proportional to the resultant normal force (Fs) and to the magnitude of the resultant normal force (Fk)
– Defining the angle of static friction, фs
Φ
W
N F
P
R Φs
W
N Fs
P
R
tan Φs =Fs /N
= μs N / N
= μs
Φs = tan-1μs
![Page 36: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/36.jpg)
– Defining the angle of kinetic friction, фk
Φ
W
NF
P
R
W
N
Fk
P
RΦk
tan Φk =Fk /N
= μk N / N
= μk
Φk = tan-1μk
![Page 37: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/37.jpg)
Example 4.18• The 70N force shown in figure causes impending motion to
the right. The block is not moving due to this force. Determine the static coefficient of friction, μs. Given the mass of block is 40kg.
Solution;
Draw the free body diagram of block.
W = mg = 40(9.81)
= 392.4N
W = N
70N
70NW
Ncc Fs 18.04.392
70
N
Fs
![Page 38: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/38.jpg)
W=mg
=20000(9.81)
=196.2kN
Example 4.19• The mass of block is 20000 kg is subjected to the applied
load as shown in figure. Determine the friction force if μs = 0.5.
Solution;
Draw the free diagram of block.
80kN
Ө=20º
80 cos 20º =75.2kNӨ=20º
80 sin 20º =27.4kN80kN
NF
![Page 39: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/39.jpg)
ΣFy ↑=ΣFy↓
27.4 + N = 196.2 or can be write as 27.4 + N – 196.2 =0
N = 168.8 kN
Fx = 0 , 75.2 – F = 0
75.2 kN= F
• The friction force, Fs = μs N = 0.5(168.8) = 84.4kN.
• The value of Fs then compare to the F. Show that F < Fs. The block is not moving yet. The equation of Fs can not be used to determine the friction since the friction forces not achieved the maximum value.
• The friction force is F = 75.2kN.
![Page 40: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/40.jpg)
Example• Te uniform crate shown in Figure has a mass of 20kg. If a
force P=80 N is applied to the crate, determine if it remains in equilibrium. The coefficient of static friction is μs = 0.3
![Page 41: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/41.jpg)
Solution• Free body diagram
As shown in Figure, the resultant normal force Nc must act a distance x, from the counteract the tipping effect cause by P. there are three unknowns F, Nc and x, which can be determined strictly from three equations of equilibrium
![Page 42: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/42.jpg)
mmmx
NN
NF
solving
xNMo
NFy
FF
c
c
c
X
08.900908.0
236
3.69
0)()2.0(30cos80)4.0(30sin80;0
02.19630cos80;0
030cos80;0
00
0
0
![Page 43: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/43.jpg)
Friction laws for dry surfaces on an inclined plane• Condition 1 : the block is not moving (no friction)
N can be determined using
ΣFx = 0,
F = W sin θ and
ΣFy = 0,
N = W cos θ.
The block tends to move down on the inclined plane. The friction force acted in the opposite direction.
F< Fs
![Page 44: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/44.jpg)
• Condition 2 : the block is in the verge of impending motion
N can be determined using ΣFx = 0,
F = W sin θ and
ΣFy = 0,
N = W cos θ.
F = Fs, F = μs N
![Page 45: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/45.jpg)
• Condition 3 : the block is moving
N can be determined using ΣFy = 0, N = W cos θ.
Fk = μk N
Fk = μk N= μk W cos θ
![Page 46: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/46.jpg)
• Condition 4 : the block is sliding/overtuning
When P is increased (P > Fk) until it make the block sliding/overtuning at point A.
+ ΣMA = - W sin θ(h) + W cos θ(a)
![Page 47: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/47.jpg)
Example 4.20• A 100N force acts as shown on a 300N block placed on an
inclined plane. The coefficients of friction between the block and plane are μs=0.25 and μk=0.2. determine whether the block is in equilibrium and find the value of the friction force.
• Free body diagram
![Page 48: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/48.jpg)
Σfy = 0; - 240 + N = 0
N= 240N
Fs = μs N = 0.25(240) = 60N
Σfx = 0
100 - 180 – F = 0
F = -80N (the friction force is acted opposite direction, thus directed up and to the right)
F = 80N ( )
F > Fs , 80N > 60N, the block is moving down due to this condition. Use μk to determine the actual friction force.
The block is not in equilibrium condition.
The friction force; Fk = μk N = 0.2(240) = 48N
![Page 49: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/49.jpg)
Tips Solving problems in dry friction1) The first step is to draw a free body diagram of the body,
labeling and directing all forces involved at each surface of contact.
2) The resultant, R exerted by a surface on a free body can be resolved into a normal component N and a tangential component F. F known as a friction force. When a body is in contact with a fixed surface, the direction of the friction force, F is opposite to that of the actual or impending motion or applied load of the body.
3) No motion will occur as long as F does not exceed the maximum value of Fs = μs N where μs is the coefficient of static friction.
4) Motion will occur if a value of F larger than Fs is required to maintain equilibrium. As motion takes place, the actual force drops to Fk = μk N where μk is the coefficient of kinetic friction.
![Page 50: CHAPTER 4 Equilibrium of Rigid Body & Friction. Rigid Body Definition of a rigid body: A rigid body is defined as a body on which the distance between](https://reader036.vdocuments.mx/reader036/viewer/2022081504/56649d825503460f94a674da/html5/thumbnails/50.jpg)
Example 4.23• The static coefficient μs is 0.4 between the point A and rough
surfaces meanwhile there are no friction occurred between point B and contact surfaces. Indentify whether the wood is in equilibrium or not. Assumed the weight of wood acts at the centre of A-B.
Smooth surface
Rough surface
w