Free Body Diagrams

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Free Body Diagrams

• Chapter 1 in Text

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Free-body diagram

• An essential tool for evaluating every situation
  in biomechanics.
• The critical first step in analyzing any
  biomechanical event.
• Isolates the body (leg, arm, shoe, ball, block
  etc.) from all other objects.
• Only shows external forces acting on an object.

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Internal Forces

• Forces that act within the object or system whose
  motion is being investigated.
• Newtons 3rd Law states that forces come in equal
  and opposite pairs.
• With internal forces, the forces act on different
  parts of the same system.
• These forces cancel each other out, and therefore
  dont affect the motion of the system.
• Forces at the knee if you are looking at the
  motion of the entire leg.

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External Forces

• Only external forces can change the motion of an
  object or system.
• External forces are those forces that act on an
  object as a result of its interaction with the
  environment.
• These include friction, air resistance, gravity,
  pushing or pulling

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Static Equilibrium

• The state of an system when all the external
  forces on that system sum to zero and the system
  is not moving.
• In other words, the system is at rest, and has no
  net force acting on it.

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Constructing a Free Body Diagram of a Man pushing
a Book on a Desk
Step 1 Decide which body or combination of bodies
(system) to isolate as the free body diagram
Step 2 The body (or system) is isolated by a
diagram that represents its complete external
boundary
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Step 3 Represent all external forces acting on
the isolated body in their proper positions.
Known external forces should be represented by
vector arrows with their appropriate magnitude
and direction indicated.
Gravity acts on the CM of an object.
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Step 4 The coordinate axis should be shown on the
diagram indicating positive and negative
directions.
Note The acceleration of the body will always be
in the direction of the net force.
Friction force will always oppose the direction
of motion (velocity).
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The Man
Fy2 and Fy3 upward ground reaction
forces Fy1 body weight Fx2 and Fx3
friction force Fx4 reaction force of
book on subject
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The Book
Fy2 upward table reaction force Fy1
book weight Fx2 friction force Fx4 push
from instructor on book
If book accelerates Fx4 gt Fx2 If book -
accelerates Fx4 lt Fx2 Zero acceleration
Fx4 Fx2
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Gymnast Performing Iron Cross

• Show the complete free body diagram for
• The right hand ring
• The gymnast
• The cable
• The cable and ring

Given ax 0 ay 0
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a) The Right Hand Ring
Given ax 0 ay 0
?Fx max
?Fy may
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b) The Gymnast
Given ax 0 ay 0
?Fx max

?Fy may
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c) The Right Hand Cable
Given ax 0 ay 0
?Fx max

?Fy may
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d) Cable and Ring
Given ax 0 ay 0
?Fx max

?Fy may
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Down Hill Skier
Show the complete free body diagram for the skier
and skis system
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Given ax lt 0 ay 0
?Fx max

?Fy may
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Pushing Book on Table

• Draw the complete FBD of
• The book
• The table

Given ax gt 0 ay 0
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a) The Book
Given ax gt 0 ay 0
Fx2
mg
Fx1
Fy1
?Fx max Fx2 Fx1 max gt 0 Fx2 gt Fx1
?Fy may Fy1 mg may 0 Fy1 mg
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b) The Table
Given ax 0 ay 0
?Fx max Fx1 Fx2 Fx3 max 0 Fx1 Fx2
Fx3
?Fy may Fy2 Fy3 Fy1 mg may 0 Fy2
Fy3 Fy1 mg
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Hammer Thrower

• Draw the complete FBD of
• The athlete
• ax lt 0 ay 0
• The hammer
• ax gt 0 ay lt 0

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a) The Athlete
Given ax lt 0 ay 0
?Fx max Fx2 Fx1 max lt 0 Fx2 lt Fx1
?Fy may Fy1 mg may 0 Fy1 mg
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b) The Hammer
Given ax gt0 ay lt 0
?Fx max Fx1 max gt 0 Fx1 gt 0
?Fy may mg may lt 0 0 gt mg