Download Force in Mechanical Systems

Force in Mechanical
Systems
Overview
Force in Mechanical Systems
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What is a force?
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Created by a push/pull
How is a force transmitted?
•
For example by:
• Chains and sprockets
• Belts and wheels
• Spur gears
• Rods
Force in Mechanical Systems
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How is force measured?
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Using a device such as a
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English
Metric (SI)
• beam balance,
• spring balance
What are the units of force?
> pound (lb)
> Newton (N)
What are balanced forces?
• All forces acting on a body cancel each other out,
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resulting in no net (or zero) force
The body remains in a state of constant motion
(or rest)
Newton’s 1st Law
• Law of Inertia
What is equilibrium?
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The result of
balanced forces on
a body
• If the body is at rest,
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it remains at rest
If the body is in
motion, that motion
does not change
What are unbalanced forces?
• All forces acting do not cancel out, resulting in a
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net (non-zero) force.
The body changes its speed, direction or shape
Newton’s 2nd Law
How are forces described?
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Forces are quantities that are described in
terms of 2 parameters:
• Magnitude of the force (ex. 10 lbs, 100N)
• Direction of the force (ex. Left, up, north)
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Any quantity that is described thus is called a
VECTOR quantity
• Ex. 10 lbs NE, or 50N left
• Examples of other vectors
• Velocity
• Acceleration
• Momentum
If not a VECTOR, then?
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A quantity that is described by its
magnitude only is called a SCALAR
quantity
Examples of scalars
• Temperature
• Mass
• Pressure
How are forces represented?
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Drawn as an arrow
• Arrow length is magnitude
• Ex.
10 ft.lb
• Arrow heading is direction
• NE
• Ex. 10 ft.lb NE
Force (vector) arithmetic – in
line
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Adding forces acting on a line
• If the forces are acting in the same direction –
ADD to get the total force (resultant) on the
body
• Ex. 5N right + 10N right = 15 N right
• If the forces are acting in the opposite
direction – SUBTRACT to get the total force
on the body
• Ex. Tug of war
• 500N to right
1000N
1500N
Adding forces acting at a right
angle (20N right and 10 N up)
• Cannot add arithmetically to find the total force
(resultant)
• Use graph paper
• Draw the 1st force (A) scaled appropriately with an
arrow head to show direction (ex. 1 square = 2N)
• at the head of the arrow draw the 2nd force (B) at
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C
B
A
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right angles to the 1st using the same scale as the
1st.
connect the tail of the 1st force with the head of the
2nd force to represent the resultant (or total) force
(C).
measure this resultant using the same scale and
measure the heading of the resultant (angle
between A and C) with a protractor.
Practice
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Use the graph paper to draw the 2 vectors
(40lb right and 30lb up) and the resultant.
• Use a scale such as 1 cm = 5lb
• Draw the 40lb (A)
• Draw the 30lb (B) starting from the tip of A
• Connect the start and finish points = resultant (C)
• Measure the resultant length (C) using the scale
C
A
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above
Measure the resultant angle using a protractor
B
Weight vs Mass?
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Weight is a representation of the effect of gravity
on an object – vector quantity
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Weight is the gravitational force with units of pounds (lbs)
or Newtons (N)
Mass is the amount of matter a body contains
with units of pounds mass (lbm) or kilograms (kg)
– scalar quantity
At the same location on earth, the greater the
mass the greater the weight.
Conversion
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1 kg = 2.2 lb (so: 220 lbs = 100 kg)
What is torque?
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Torque is a forcelike quantity in the
rotational mechanical system, or a turning
force resulting from applying a force at some
distance from the axis of rotation of the
body
Torque examples:
• wrenches, gears, flywheels or screws, rope starter
on chainsaw
Torque
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Can be clockwise (cw) or counterclockwise
(ccw)
Formula for calculating torque
• Torque = applied force times length of the lever
•
arm
T = F x L, where
• F = force, in lbs or newtons
• L = lever arm length, in feet or meters
• T = applied torque, in lb-ft or N.m
Examples of torque in action
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Gears
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Driving gear teeth mesh with…
Driven gear teeth
Radius of the gear is the lever arm
Wrench (torque or crescent)
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A force is applied at a distance
(moment arm) from the axis of
rotation (pivot point).
Opposing torque
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If the clockwise and counterclockwise
torques cancel each other out, then
the system is in equilibrium and its
rotational state does not change.
If the opposing torques do not cancel
each other out, then the net torque
will cause a change in the rotational
speed of the system.
Practice
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A torque wrench has a lever arm of 1.5
ft. A force of 40 lbs is applied at the end
of the wrench to tighten the bolt. What is
the torque in lb-ft?
Torque = force x lever arm
• Torque = 40 x 1.5 = 60 lb-ft