Static Friction
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Transcript Static Friction
King Fahd University of
Petroleum & Minerals
Mechanical Engineering
Dynamics ME 201
BY
Dr. Meyassar N. Al-Haddad
Lecture # 11
Sir Isaac Newton
1642-1727
Proposed fundamental
laws that are the basis
of modern mechanics
3 laws of motion
law of gravitation
Newton’s laws
Law of inertia a body in motion will stay in motion and a body at rest will
stay at rest unless acted upon by a net external force.
Law of force-acceleration A particle acted upon by an unbalanced force F
experiences an acceleration a that has the same direction as the force
and a magnitude that is directly proportional to the force
F ma
Law of action-reaction for every action, there is an equal and opposite
reaction
mg = FN
Law of gravitation - all bodies are attracted to one another with a force
proportional to the product of their masses and inversely proportional
to the square of the distance between them.
m1m2
F G 2
r
13.2 The Equation of Motion
F ma
• Free-Body diagram
(Force Diagram)
• Kinetic diagram
(acceleration Diagram)
13.3 Equation of Motion for a System of
Particles
F ma
Fi f i mi a i
Internal forces cancel each other
F m a
F ma
i
i i
G
13.4 Equations of Motion: Rectangular
Coordinates
• When the net force is
projected to separate
coordinate axes the
Newton’s second law
still holds
F ma
F i F j F k m( a i a
x
y
z
F
F
F
x
max
y
ma y
z
maz
x
y
j az k)
Free Body Diagram Method
•Draw each object separately
•Draw all the forces acting on that object
•Get x and y components of all the forces to
calculate the net force
•Apply Newton’s second law to get
acceleration
•Use the acceleration in any motion analysis
and establish a Kinetic Diagram
ma
Normal & Frictional Force
Action-Reaction forces
- mg = FN
F
mg
Ff
FN
Static Friction ( ms )
The coefficient of static friction
is material dependent.
Friction
• Static friction – parallel force on the
surface when there is no relative motion
between the 2 objects
• Static friction force can vary from zero to
Maximum
Static Dynamic
Ff = msFN Ff = mkFN
Applied external force
Kinetic Friction ( mk )
• Kinetic friction – parallel force on the
surface when there is relative motion
between the 2 objects
• Kinetic friction force is always the same
F f μ k FN
Static
• is material dependent.
Friction
• The coefficient of Kinetic friction
Ff = msFN
Dynamic
Ff = mkFN
Applied external force
Spring Force
• Spring force
Fs ks
s
• k : spring stiffness (N/m)
• s : stretched or
compressed length
s l lo
lo
l
Example 13-4
•
•
•
•
m = 2 kg
y = 1m
smooth
a=?
ma
mg Fs sin ma
S 12 0.752 0.75 0.5m
1 1
θ tan
53.13
0.75
Nc Fs cos θ ks cos θ 3x 0.5x cos 53 0.9 N
Nc Fs cos 0
ag
ks
sin θ 9.21m/s 2
m
Problem
mg
y
x
N
mk N
a=?
F
y
0;
N mg cos 0
N 40 9.81 cos 20 0
N 369 N
F
x
max
mk N mg sin ma
0.25(369) 40 9.81 sin 20 40ax
ax 5.66 m / s 2
Example 13-5
m A= 3 kg
m B= 5 kg
From rest
vB= ? In 2 second
o aB t
Block B
Same
should be ٍSame
Fy may
Block A
Fy may
2s A s B l
196.2 T 5aB
2 A B 0
981 2T 3a A
2a A aB 0
Problem
VA = ?
ac
0 = 2ac + aA
2Sc + SA = L
aA = -2ac
F 0: N 200 * 9.81cos 30 0 N 1699 N
F ma : 0.5N 2T mg sin 30 200a
y
x
c
c
F
mg
y
maA 125 * 9.81 T 125aA
maA
T 1226.25 125aA (2)
(2) (1)
849.5 2(1226.25 125aA) 981 200ac
622 200ac 250aA
200ac 500ac
ac 0.888(m / s 2 ) aA 1.777(m / s 2 ) T 1004 N
VA 2a A s 4.62(m / s)
Review
•
•
•
•
Example 13.1
Example 13.2
Example 13.3
Example 13.4