DEVIL PHYSICS
THE BADDEST CLASS ON CAMPUS
PRE-DP PHYSICS
GIANCOLI LESSON 9-4 TO 9-5
APPLICATION TO MUSCLES AND JOINTS
STABILITY AND BALANCE
Objectives
 Apply the concepts learned in static
equilibrium to problems involving the
muscles and joints of the human body
 Calculate the force required by muscles to
perform different functions
 Understand the physics behind why humans
are susceptible to lower back pain
 Know the meaning of stable equilibrium,
unstable equilibrium and neutral equilibrium
Introductory Video:
How the Body Works - Muscles
Muscles and Joints
 Muscles attached to two different bones
 Attachment points called insertions
 Bones attached at joints
 Muscles can only contract and relax
 Muscles are normally paired to extend
(extensor muscles) and to contract (flexor
muscles)
Example Problem
 What force must be applied: (a) to hold a 15-kg
dumbbell at your side, (b) to hold it at a 45° angle to
your body, and (c) at a 90° angle to your body?
Neglect the mass of the arm. The person is 1.8m tall.
Example Problem
 What force must be applied: (a) to hold a 15-kg
dumbbell at your side, (b) to hold it at a 45° angle to
your body, and (c) at a 90° angle to your body?
Neglect the mass of the arm. The person is 1.8m tall.
(a) With the dumbbell at your side, tension in your
arm and shoulder support the weight of the
dumbbell. There is no torque generated.
Farm  mdb g  147 N
Example Problem
(b) With the dumbbell at a 45° angle, there is a
moment arm for both the insertion and the arm,
but less than that for an arm at 90°.
 62.2  43.1 
Farm .05cos 45  mdb g 
1.8cos 45
100


Farm  1012 N
Example Problem
(c) With the dumbbell at a 90° angle, the moment
arm for both the insertion and the arm is at a
maximum.
Will the force at 90° be greater than, less than, or the
same as the force at 45°?
Example Problem
(c) With the dumbbell at a 90° angle, the moment
arm for both the insertion and the arm is at a
maximum. The force is the same as at 45°.
 62.2  43.1 
Farm .05  mdb g 
1.8
100


Farm  1012 N
Lower Back Pain
 Using the diagrams below, calculate the
magnitude and direction of the force on
the fifth lumbar vertebra.
Lower Back Pain
 Using the diagram on the right, calculate
the magnitude and direction of the force
on the fifth lumbar vertebra.
 First we need to find the force of the
muscles using Στ.
18°
FM
12°
30°
60°
Lower Back Pain
 Using the diagram on the right, calculate
the magnitude and direction of the force
on the fifth lumbar vertebra.
 First we need to find the force of the muscles
using Στ.
 Find the perpendicular components of the weights
60°
wx 
sin 60 
wx

wx   wx sin 60 CW 
wx
Lower Back Pain
 Using the diagram on the right, calculate
the magnitude and direction of the force
on the fifth lumbar vertebra.
 First we need to find the force of the muscles
using Στ.
 Find the perpendicular components of the weights
 Now find the perpendicular component of FM
18°
FM
FM 
sin 12 
FM
12°
30°
60°

FM   FM sin 12 CCW 

wx   wx sin 60 CW 

Lower Back Pain
 Using the diagram on the right, calculate
the magnitude and direction of the force
on the fifth lumbar vertebra.
 First we need to find the force of the muscles
using Στ.
  rF
0.48FM sin 12  0.36w3 sin 60  0.48w2 sin 60  0.72w1 sin 60
0.10FM  0.14w  0.050w  0.044w

0.237 w
FM 
 2.37 w
0.10
FM   FM sin 12 CCW 
wx   wx sin 60 CW 
Lower Back Pain
 Using the diagram on the right, calculate
the magnitude and direction of the force
on the fifth lumbar vertebra.
 Now we need to find Fv by finding its
components.
 First find vertical and horizontal components of FM
sin 18 
FM-x
FM  y
FM
FM  y  FM sin 18
FM-y
18°
FM 12°
30°
60°
FM  x
cos 18 
FM

FM  x  FM cos 18
FM  2.37w
Lower Back Pain
 Using the diagram on the right, calculate
the magnitude and direction of the force
on the fifth lumbar vertebra.
 Now we need to find Fv by finding its
components.
 First find vertical and horizontal components of FM
FM-x
FM  y  FM sin 18
FM  y  0.732 w
FM  x  FM cos 18
FM  x  2.25w
FM-y
18°
FM 12°
30°
60°
FM  2.34w
Lower Back Pain
 Using the diagram on the right, calculate
the magnitude and direction of the force
on the fifth lumbar vertebra.
 Now we need to find Fv by finding its
components.
 Now find vertical and horizontal components of FV
through ΣFx and ΣFy
FM-x
FM-y
FV-x
FV-y
18°
FM 12°
30°
60°
FM  y  0.732w
FY
FM  x  2.25w
Lower Back Pain
 Using the diagram on the right, calculate
the magnitude and direction of the force
on the fifth lumbar vertebra.
 Now we need to find Fv by finding its
components.
 Now find vertical and horizontal components of FV
through ΣFx and ΣFy
FV-x
Fx  0
FV  x  FM  x  2.25w
Fy  0
FV  y  FM  y  w1  w2  w3
FV  y  1.38w
FV-y
FY
FM  y  0.732w
FM  x  2.25w
Lower Back Pain
 Using the diagram on the right, calculate
the magnitude and direction of the force
on the fifth lumbar vertebra.
 Now we need to find Fv by finding its
components.
 Pythagorize and Tangentiate
FV 
FV  x   FV  y 
2
FV  2.64w
tan  
  tan
FV-y
FV  y
FY
FV  x
1
FV  y
FV  x
FV-x
2
FV  x  2.25w
 31.5
FV  y  1.38w
Lower Back Pain
 This is why you should lift with your legs and your back
straight. While the vertebra and discs still have to support the
weight, it drastically reduces required back muscle force.
wx
FM-x
FM-y
FV-x
FV-y
60°
FY
18°
FM 12°
30°
60°
60°
wx
Personal Testimony
Stability and Balance
 A body in static equilibrium will not move if
left undisturbed
 What happens if it is disturbed?
 Depends on Balance and Stability
 Stable Equilibrium – body returns to its original
position
 Unstable Equilibrium – body continues to move in
the direction of displacement and may accelerate
 Neutral Equilibrium – body stays in its displaced
position
Stability and Balance
 Stable equilibrium
Stability and Balance
 Unstable equilibrium
Stability and Balance
 Neutral equilibrium
Stability and Balance
 Three Cases
Stability and Balance
 Instability occurs when the center of gravity is
no longer above its base of support
 Potential for instability increases as the
distance between CG and base increases
 Potential for instability increases as the size
of the base decreases
Stability and Balance
 General Rule: Stability can be increased if
you can lower the center of gravity and/or
increase the size of the base of support
Stability and Balance
 Reading Activity Question:
Tilt the boxes and truck
backward until the center
of mass is over the axle of
the hand truck. The hand
truck is then supporting all
of the weight of the boxes
and itself.
Stability and Balance
 Which is more stable, a human or a dog?
Stability and Balance
 Which is more stable, a human or a dog?
 Does this imply that most humans are
unbalanced? You be the judge.
Σary Review
 Can you apply the concepts learned in static
equilibrium to problems involving the
muscles and joints of the human body?
 Can you calculate the force required by
muscles to perform different functions?
 Do you understand the physics behind why
humans are susceptible to lower back pain?
 Do you know the meaning of stable
equilibrium, unstable equilibrium and neutral
equilibrium?
QUESTIONS
Homework
#34-42 (skip #41)
Muscles of the Body