Download Levers Lecture

LEVERS
Some “rigid” structure that is hinged
at one point and has two forces
applied at other points.
5/24/2017
Dr. Sasho MacKenzie - HK 376
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Lever Terms
• The hinge or pivot point is known as the
fulcrum ( ).
• One of the forces is the resistance force
(FR) and opposes the intended movement.
• The other force is the applied force (FA)
and that causes or tends to cause the lever to
move.
5/24/2017
Dr. Sasho MacKenzie - HK 376
2
Lever Arms (Moment Arms)
• There are two lever arms for every lever. One
associated with each force.
• The resistance lever arm (dR) is the perpendicular
distance from the line of action of the resistance
force to the fulcrum.
• The applied lever arm (dA) is the perpendicular
distance from the line of action of the applied
force to the fulcrum.
FA
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dA
dR
FR
Dr. Sasho MacKenzie - HK 376
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Levers: What are they for?
• Oars, vaulting poles, golf clubs, and wheels are all
levers, but the most important levers in
kinesiology are bones and the muscles that move
them.
Levers can do two things
1. Increase Force
2. Increase Speed
5/24/2017
Dr. Sasho MacKenzie - HK 376
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Levers can Increase Force
A lever can increase the effect produced by a
muscular force. In other words, a smaller muscular
force may balance out a greater resistance force.
Weight of head 50 N
dA = 5 cm
dR = 2 cm
FA
dA
FR
Trapezius
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dR
The force of the trapezius to hold
the skull in equilibrium is given by:
FA x 5 cm = 50 N x 2 cm
FA = 20 N
Dr. Sasho MacKenzie - HK 376
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Levers can Increase Speed
A lever can increase the speed of an object. A relatively
slow hand speed can result in a very high clubhead speed
10 cm
In this golf example, the right hand is the
applied force and moves 10 cm in the last
phase of the swing, while the clubhead
travels 100 cm. The left wrist is the fulcrum.
100 cm
Both of these distances are covered
in the same period of time. Hence
the clubhead speed is 10 times that
of the right hand.
5/24/2017
Dr. Sasho MacKenzie - HK 376
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Mechanical Advantage
Mechanical advantage or leverage is the ratio of how much
force you get out relative to how much you put in.
The ratio of the applied force lever arm (dA) to the resistance
force lever arm (dR).
M.A. = dA
dR
FA
M.A. = dA = 2 =
dR
1
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dR = 1
dA = 2
FR
2
Dr. Sasho MacKenzie - HK 376
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First Class Levers
The fulcrum lies between the points of applied force and
resistance force.
Examples: See-Saw, scissors, pliers
FA
dA
dR
FR
First class levers can be used to gain a mechanical advantage
by increasing the length of the applied lever arm (dA).
First class levers can also be used to increase the speed of
movement by decreasing the length of the applied lever arm (dA).
5/24/2017
Dr. Sasho MacKenzie - HK 376
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Second Class Levers
The fulcrum lies at one end, and the applied lever arm is
greater than the resistance lever arm.
Examples: Bottle opener, wheel barrow, nut cracker
dR
FR
FA
dA
Second class levers can only be used to increase the effect of
an applied force.
5/24/2017
Dr. Sasho MacKenzie - HK 376
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Third Class Levers
The fulcrum lies at one end, and the resistance lever is
greater than the applied lever arm .
Examples: Tweezers and Tongs
dA
FR
FA
dR
Third class levers can only be used to increase the speed of
movement of the load.
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Lever Arm is Moment Arm
FA
A
A
FR = mg
FA
dA
A
dR
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FR = mg
The brachioradialis is a 3rd class
lever because the resistance lever
arm is greater than the applied
lever arm.
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Calf Raise Example
Vertical Joint
Reaction Force ?
Vertical Component of
Achilles Tendon Force?
B
A
*Assume Static Equilibrium
C
0.15 m
0.05 m
1.
2.
3.
4.
Determine unknown forces.
What class of lever?
Does it increase speed or force?
What is the M.A.?
1000 N
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Levers can Increase Speed
A lever can increase the effective speed of a muscular
contraction. A muscle contracting at 1m/s may
displace the distal end of a bone at a rate of 10 m/s.
In this kicking example, the
quadriceps shorten by 10 cm, while
the point of the foot in contact with
the ball travels 100 cm.
L = 100 cm
L = 10 cm
FA
FR
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Both of these distances are covered
in the same period of time. Hence
the foot speed is 10 times that of the
muscle contraction.
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