Download Forces in Mechanical Systems

Forces in Mechanical
Systems
1.1
Objectives
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Define force and describe how forces are
measured.
Describe what happens when forces on an
object are balanced and when they are
unbalanced.
Explain the meaning of Newton’s first law of
motion.
Define scalar, vector, weight, mass and torque.
Determine the resultant force on an object when
two or more forces act on it.
Solve problems involving force, lever arm, and
torque.
Force
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A push or a pull
In Mechanical Systems forces change an
object’s motion.
Forces can be transmitted to a variety of
mechanical parts
Bicycle
Measuring Forces
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Metric System
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Based on powers of 10
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The SI base units
for seven basic
quantities:
Quantity
Unit
Symbol
Length ( l )
meter
m
Mass ( m )
kilogram kg
Time ( t )
second
s
Electric Current ( I )
ampere
A
Temperature ( T )
Kelvin
K
Amount of Substance
(n)
mole
mol
Luminous intensity
candela
cd
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Derived units – unit made from a
combination of base units.
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SI unit of speed is m/s (length / time)
Acceleration is m/s2 (speed / time)
Force is the Newton (N) which is actually
kg m/s2
Comparison of English and SI Units
Length
Time
Mass
Force
English
foot (ft)
second (s)
slug
pound (lb)
SI
meter (m)
second (s)
kilogram (kg)
Newton (N)
Weight and Mass Conversions
1 pound = 16 ounces
1 kilogram weighs 9.80 N or 2.2 lb
1 pound = 4.45 newtons
1 slug weighs 32.2 lb
1 kilogram = 1000 grams
1 slug = 14.59 kg
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Force can be
measured with a
spring scale.
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Spring stretch is
directly proportional to
force
Weight is the force
due to gravity.
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Make sure units match before
calculations are run on values.
Force is a Vector
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The effect of force on an object depends
on two things
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magnitude
direction
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Vector is a quantity that must be
described by both magnitude and
direction.
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1
Force is a vector quantity.
Displacement, velocity, acceleration, and
momentum are also vector quantities1.
We will cover these later.
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Scalars – quantities described by
magnitude only.
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Temperature
elapsed time
Pressure
mass
How to Represent Forces
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Vector drawing –
arrows are
proportional to
magnitude and point
in the direction of the
vector. (Figs 1.4 and
1.5, p. 9)
Balanced and Unbalanced Forces
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Net force – the sum of all forces acting on
an object
Fnet = F = F1 + F2 ……
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Balanced forces – when the net force on
an object is equal to zero.
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Motion of object stays the same – called
equilibrium.
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Speed and direction stays the same.
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Unbalanced forces – when the net force
on an object is not equal to zero.
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Motion of the object changes
Falling objects and terminal velocity
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Figure 1.7a
Fgravity > Fdrag
Figure 1.7b
Fgravity = Fdrag
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Terminal velocity –
final velocity reached
when gravity and drag
are balanced.
Newton’s First Law of Motion
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An object at rest remains at rest, acted
upon by an unbalanced force. Likewise an
object in motion will keep its velocity,
unless an unbalanced force acts on it.
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Sometimes called the law of inertia.
Example 1-1
 A yo-yo weighing 0.25
lb hangs motionless
at the end of a string.
Draw the forces
acting on the yo-yo.
Adding Forces That Act Along a
Line
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Forces are added to find net force (Fnet) on
an object.
Easy if in the same direction.
Sign can be used to indicate direction
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Forces in the up or to the right directions are
in the positive.
Forces in the downward or the left directions
are negative.
Example 1-2 Tug-of-War Problem
 Five people compete in a tug-of-war.
Three people on the left side each pull
with 230 N of force. Two people on the
right side each pull with 300 N of force.
Who will win the tug-of-war?
Adding Forces That Do Not Act
Along a Line
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Forces can’t be added
if they do not act
along a straight line.
Example in Figure
1.11
To solve we use a
graphing method
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Vectors are drawn
“head-to-tail.”
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Step 1: Draw first vector
Step 2: Draw second vector
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Step 3: Draw the resultant
force
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Resultant force – single vector
representing the sum of two
or more vectors.
Step 4: Determine the
magnitude and direction of the
resultant.
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“Head-to-tail”
Pythagorean Theorem for
right triangles
Step 5: Make some conclusions
Weight and Mass Aren’t the Same
Thing!
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Unbalanced force acts on object at rest, it
Since the amount
will move.
of inertia depends
on the amount of
matter, two books
have twice the
inertia.
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Two books have twice the mass, and
require twice the force to get them to
move.
Torque and Rotation
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Torque – a quantity that causes rotation in
mechanical systems.
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The effect of a force applied on a body at
some distance from the axis of rotation.
Can be:
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Clockwise (cw)
Or, counterclockwise (ccw)
Line of action – line along the applied force that extends in both directions.
Torque = applied force x lever arm
=FL
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What are the English units for torque?
SI units?
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Gear
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Teeth
Shaft
Teeth of one gear mesh with another gear.
Driving gear
 Driven gear
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Example 1-3 Calculation of Torque
Applied by a Torque Wrench
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A torque wrench has a lever arm of 1.5 ft.
A force of 40 lb is applied to the end of
the wrench to tighten a bolt. Find the
torque applied to the bolt in a.) lb·ft and
b.) N·m.
Example 1-4 Torques in a BeltDriven System
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The motor pulley in a belt-driven system has a radius of
5 cm (0.05 m). The large pulley attached to the shaft of
a machine has a radius of 20 cm (0.20 m). The dragging
or pulling force of the belt is 40 N. Assume that the belt
doesn’t slip as the motor and belt drive the load pulley.
What is the torque applied to each pulley?
Opposing Torques
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Opposing torques, like forces, can be in
equilibrium. (torques cancel each other
out)
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If system at rest, it stays at rest.
If in motion, it continues to rotate.
If unbalanced, the net torque will cause a
change in the rotational speed.
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It speeds up or slows down.
Example 1-5 Truck Scales Involve
Opposing Torques
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A 48 000 lb truck sits on the platform of truck-weighing
scales. The truck weight acts on a 0.5 ft lever arm about
the pivot point. A 1000 lb balancing weight is hung on
the opposite side of the pivot point, 20 ft away. Find:
(a.) Torque of truck about pivot point. (b.) Torque of
balance weight about the pivot point. (c.) Whether or
not the torques are balanced.