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XE 121
Engineering Concepts
Lecture 2
Force, matter, mechanical
systems
Dr Nicolas D. D. Miché
[email protected]
University of Brighton – School of Computing Engineering and Mathematics
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Force, matter, mechanical systems
Fundamentals
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Force is a Vector. The SI unit for force is the Newton
(N). One Newton of force is equal to 1 kg * m/s2.
Force is a quantitative description of the interaction
between two physical bodies, such as an object and
its environment. Force is proportional to acceleration.
In calculus terms, force is the derivative of
momentum with respect to time.
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Mass. A measure of the amount of matter contained
in or constituting a physical body. In classical
mechanics, the mass of an object is related to the
force required to accelerate it and hence is related to
its inertia, and is essential to Newton's laws of
motion. Objects that have mass interact with each
other through the force of gravity.
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Acceleration, Acceleration is the rate of change of
velocity as a function of time. It is a Vector. In
calculus terms, acceleration is the second
derivative of position with respect to time or,
alternately, the first derivative of the velocity with
respect to time. The SI units for acceleration are
m / s2 (meters per second squared or meters per
second per second).
m
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Moments/Torque
 F ,O  M F ,O  F  r
+
F
r
A
O
M F ,O
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Expressed as Magnitude:
  r  F sin   F  d
More torque with a spanner?
More torque with a screwdriver?
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Example: net torque on a
cylinder
T1 = 5 N
R1 = 1 m
T2 = 15 N
R2 = 0.5 m
Calculate the net torque on this system of forces
according to the coordinate system shown
Quiz XE121-L2-1
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Measurement of torque: Dynamometer
Distance
Distance
Force (perpendicular)
Load cell (force
measurement)
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Water (or Froude) dynamometer
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Load
Cell
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Friction
Static Dry Friction
Friction forces occur in the opposite direction to forces tending to move two
objects in contact
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If you press a textbook flat against a vertical wall;
what is the direction of the friction force exerted by the wall on
the book?
Quiz XE121-L2-4
• A - downward
• B - upward
• C - out from the wall
• D - into the wall
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The static frictional force cannot exceed a certain magnitude, called the limiting
static friction.
Fmax ≥ P → Equilibrium
Fmax < P → Slippage
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The maximum frictional force between two surfaces is proportional to the normal
contact force
Fmax    N
With
μ = μs static coefficient of friction when non-slip
μ = μk static coefficient of friction for slippage
The angle α of the resultant R is specified by
tan α = F/N
At Fmax, α reaches a max value of φs such as
tan s  s
The limit conditions of friction can
be represented within a cone of
friction
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A
B
30º
Quiz XE121-L2-2
30º
Which is the easier way to move the sled?
• A - pushing from behind, slightly downwards
• B - pulling with a rope, slightly upwards
• C - either
Quiz XE121-L2-3
Why is that?
•Answer in a few words
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Slippage / non-slippage
Non-slip condition
Plane intersecting
tan   s
Direction
of potential
sliding
F  ( Fmax  s  N )
Maximum static friction
Plane intersecting
tan   s
F  ( Fmax  s  N )
Slippage
Plane intersecting
Direction
of potential
sliding
Direction of
tan   s
F  Fmax  k  N 
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Some typical coefficients of friction
μs
μk
Steel on Steel (dry)
0.6
0.4
Steel on Steel (grease)
0.1
0.05
Brake pad on Cast iron
0.4
0.3
Teflon on Steel
0.04
0.04
Dry
0.8
0.5
Wet
0.4
Icy
0.1
Tyre on Road
Synovial joints in humans
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0.01
0.003
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Simple experimental determination of friction coefficients
A block of material A remains static
on a ramp of material B
The y component of the weight of
the block (mg cosθ) results in an
opposite normal contact force n
The x component of the weight of
the block (mg sinθ) is opposed by
the friction force f
The incline angle is increased until
the block is on the edge of slipping.
At this point the friction force has
reached its maximum.
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Therefore, friction coefficient
A/B
f
   tan 
n
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XE 121 – Engineering Concepts – Mechanical Part
Next week
•Mechanical links, static equilibrium
Dr Nicolas D. D. Miché
[email protected]
University of Brighton – School of Computing Engineering and Mathematics
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