Static Equilibrium. - Rice Universityphys101/ClassNotes/Static_Equilibrium.pdf · Static...
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PHYS101 Static Equilibrium – slide 1
PHYS101 - Static Equilibrium.
Dr. Suess
November 28, 2007
Static Equilibrium of a Rigid Body.
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 2
• The term equilibrium implies a body is at rest
Static Equilibrium of a Rigid Body.
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 2
• The term equilibrium implies a body is at rest or the center of
mass of the body moves with a constant velocity.
Static Equilibrium of a Rigid Body.
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 2
• The term equilibrium implies a body is at rest or the center of
mass of the body moves with a constant velocity.
• We now wish to focus specifically on bodies that are at rest
Static Equilibrium of a Rigid Body.
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 2
• The term equilibrium implies a body is at rest or the center of
mass of the body moves with a constant velocity.
• We now wish to focus specifically on bodies that are at rest
(hence the term “static” equilibrium).
Static Equilibrium of a Rigid Body.
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 2
• The term equilibrium implies a body is at rest or the center of
mass of the body moves with a constant velocity.
• We now wish to focus specifically on bodies that are at rest
(hence the term “static” equilibrium).
• Static equilibrium is of special interest to civil and mechanical
engineers.
Static Equilibrium of a Rigid Body.
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 2
• The term equilibrium implies a body is at rest or the center of
mass of the body moves with a constant velocity.
• We now wish to focus specifically on bodies that are at rest
(hence the term “static” equilibrium).
• Static equilibrium is of special interest to civil and mechanical
engineers. Why?
Static Equilibrium of a Rigid Body.
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 2
• The term equilibrium implies a body is at rest or the center of
mass of the body moves with a constant velocity.
• We now wish to focus specifically on bodies that are at rest
(hence the term “static” equilibrium).
• Static equilibrium is of special interest to civil and mechanical
engineers. Why?
◦ Structures such as bridges and buildings rely on a very sound
understanding of static equilibrium.
Static Equilibrium of a Rigid Body.
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 2
• The term equilibrium implies a body is at rest or the center of
mass of the body moves with a constant velocity.
• We now wish to focus specifically on bodies that are at rest
(hence the term “static” equilibrium).
• Static equilibrium is of special interest to civil and mechanical
engineers. Why?
◦ Structures such as bridges and buildings rely on a very sound
understanding of static equilibrium.
• So, what are the conditions which must be satisfied for a
complex, rigid body to be at static equilibrium under the action ofseveral forces?
Static Equilibrium of a Rigid Body.
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 2
• The term equilibrium implies a body is at rest or the center of
mass of the body moves with a constant velocity.
• We now wish to focus specifically on bodies that are at rest
(hence the term “static” equilibrium).
• Static equilibrium is of special interest to civil and mechanical
engineers. Why?
◦ Structures such as bridges and buildings rely on a very sound
understanding of static equilibrium.
• So, what are the conditions which must be satisfied for a
complex, rigid body to be at static equilibrium under the action ofseveral forces?
◦ Consider translational equilibrium and rotational equilibrium
separately.
Static Equilibrium of a Rigid Body.
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 2
• The term equilibrium implies a body is at rest or the center of
mass of the body moves with a constant velocity.
• We now wish to focus specifically on bodies that are at rest
(hence the term “static” equilibrium).
• Static equilibrium is of special interest to civil and mechanical
engineers. Why?
◦ Structures such as bridges and buildings rely on a very sound
understanding of static equilibrium.
• So, what are the conditions which must be satisfied for a
complex, rigid body to be at static equilibrium under the action ofseveral forces?
◦ Consider translational equilibrium and rotational equilibrium
separately. Remember, a rigid body can rotate even if the net
force on the body is zero!
Translational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 3
• Translational equilibrium occurs when the linear acceleration of
the center-of-mass of the body is zero.
Translational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 3
• Translational equilibrium occurs when the linear acceleration of
the center-of-mass of the body is zero. Think Newton’s 2nd law.
Translational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 3
• Translational equilibrium occurs when the linear acceleration of
the center-of-mass of the body is zero. Think Newton’s 2nd law.
∑~Fext = M ~acm
Translational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 3
• Translational equilibrium occurs when the linear acceleration of
the center-of-mass of the body is zero. Think Newton’s 2nd law.
∑~Fext = M ~acm = 0
Translational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 3
• Translational equilibrium occurs when the linear acceleration of
the center-of-mass of the body is zero. Think Newton’s 2nd law.
∑~Fext = M ~acm = 0
• For translational equilibrium, the net force on the rigid body mustbe zero.
Translational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 3
• Translational equilibrium occurs when the linear acceleration of
the center-of-mass of the body is zero. Think Newton’s 2nd law.
∑~Fext = M ~acm = 0
• For translational equilibrium, the net force on the rigid body mustbe zero.
• This will ensure translational equilibrium.
Translational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 3
• Translational equilibrium occurs when the linear acceleration of
the center-of-mass of the body is zero. Think Newton’s 2nd law.
∑~Fext = M ~acm = 0
• For translational equilibrium, the net force on the rigid body mustbe zero.
• This will ensure translational equilibrium. NOT rotational
equilibrium !
Rotational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 4
• Rotational equilibrium occurs when the angular acceleration of
the rigid body is zero.
Rotational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 4
• Rotational equilibrium occurs when the angular acceleration of
the rigid body is zero. Think Newton’s 2nd law for rotation.
Rotational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 4
• Rotational equilibrium occurs when the angular acceleration of
the rigid body is zero. Think Newton’s 2nd law for rotation.
∑~τext = I ~α
Rotational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 4
• Rotational equilibrium occurs when the angular acceleration of
the rigid body is zero. Think Newton’s 2nd law for rotation.
∑~τext = I ~α = 0
Rotational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 4
• Rotational equilibrium occurs when the angular acceleration of
the rigid body is zero. Think Newton’s 2nd law for rotation.
∑~τext = I ~α = 0
• For rotational equilibrium, the net torque on a rigid body must bezero.
Rotational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 4
• Rotational equilibrium occurs when the angular acceleration of
the rigid body is zero. Think Newton’s 2nd law for rotation.
∑~τext = I ~α = 0
• For rotational equilibrium, the net torque on a rigid body must bezero.
• This will ensure rotational equilibrium.
Rotational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 4
• Rotational equilibrium occurs when the angular acceleration of
the rigid body is zero. Think Newton’s 2nd law for rotation.
∑~τext = I ~α = 0
• For rotational equilibrium, the net torque on a rigid body must bezero.
• This will ensure rotational equilibrium.
◦ For a rigid body to be in static equilibrium under the action of
two forces, the two forces must be of equal magnitude and
applied in opposite directions.
Rotational Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 4
• Rotational equilibrium occurs when the angular acceleration of
the rigid body is zero. Think Newton’s 2nd law for rotation.
∑~τext = I ~α = 0
• For rotational equilibrium, the net torque on a rigid body must bezero.
• This will ensure rotational equilibrium.
◦ For a rigid body to be in static equilibrium under the action of
two forces, the two forces must be of equal magnitude and
applied in opposite directions. In addition, the forces must
have the same line of action.
Lines of Action (Two Forces)?
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 5
For the rigid body shown above, the external forces applied to the
body are equal and opposite.
Lines of Action (Two Forces)?
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 5
F
F
Lines of action are different.
The rigid object will rotate clockwise.
For the rigid body shown above, the external forces applied to the
body are equal and opposite.
Lines of Action (Two Forces)?
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 5
F
F
Lines of action are different.
The rigid object will rotate clockwise.
For the rigid body shown above, the external forces applied to the
body are equal and opposite. The body will rotate clockwise about
its center of mass; therefore, the body is not in static equilibrium.
Lines of Action (Two Forces)?
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 5
Now consider the case when the external forces applied to the
body are equal and opposite and lie on the same line of action.
Lines of Action (Two Forces)?
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 5
FF
Lines of action are the same.
The rigid object will NOT rotate clockwise.
Now consider the case when the external forces applied to the
body are equal and opposite and lie on the same line of action.
Lines of Action (Two Forces)?
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 5
FF
Lines of action are the same.
The rigid object will NOT rotate clockwise.
Now consider the case when the external forces applied to the
body are equal and opposite and lie on the same line of action.
The body will NOT rotate; therefore, the body is in static equilib-
rium.
Lines of Action (Three Forces)?
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 6
If three external forces applied to a body are concurrent (their lines
of action must intersect at a common point), the body can be in
static equilibrium as illustrated above.
Lines of Action (Three Forces)?
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 6
F
Concurrent lines of action.
FF
3
1
2
If three external forces applied to a body are concurrent (their lines
of action must intersect at a common point), the body can be in
static equilibrium as illustrated above.
Lines of Action (Three Forces)?
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 6
F
Concurrent lines of action.
FF
3
1
2
If three external forces applied to a body are concurrent (their lines
of action must intersect at a common point), the body can be in
static equilibrium as illustrated above. To ensure the body is in
static equilibrium, the sum of the forces (and the torques) must
add up to zero.
Lines of Action (Three Forces)?
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 6
F
Concurrent lines of action.
FF
3
1
2
If three external forces applied to a body are concurrent (their lines
of action must intersect at a common point), the body can be in
static equilibrium as illustrated above. To ensure the body is in
static equilibrium, the sum of the forces (and the torques) must
add up to zero. This condition of concurrent lines of action is notmentioned in your textbook
Lines of Action (Three Forces)?
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 6
F
Concurrent lines of action.
FF
3
1
2
If three external forces applied to a body are concurrent (their lines
of action must intersect at a common point), the body can be in
static equilibrium as illustrated above. To ensure the body is in
static equilibrium, the sum of the forces (and the torques) must
add up to zero. This condition of concurrent lines of action is notmentioned in your textbook (wink-wink).
Problem Solving Tips - Static Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 7
• Identify the object in equilibrium.
Problem Solving Tips - Static Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 7
• Identify the object in equilibrium.
• Identify all forces acting on the object, and
Problem Solving Tips - Static Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 7
• Identify the object in equilibrium.
• Identify all forces acting on the object, and draw a
free-body-diagram showing the force vectors.
Problem Solving Tips - Static Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 7
• Identify the object in equilibrium.
• Identify all forces acting on the object, and draw a
free-body-diagram showing the force vectors.
◦ It’s essential that the free-body-diagram shows the forces
drawn from their actual application points.
Problem Solving Tips - Static Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 7
• Identify the object in equilibrium.
• Identify all forces acting on the object, and draw a
free-body-diagram showing the force vectors.
◦ It’s essential that the free-body-diagram shows the forces
drawn from their actual application points.
• Choose (and label) an appropriate coordinate system.
Problem Solving Tips - Static Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 7
• Identify the object in equilibrium.
• Identify all forces acting on the object, and draw a
free-body-diagram showing the force vectors.
◦ It’s essential that the free-body-diagram shows the forces
drawn from their actual application points.
• Choose (and label) an appropriate coordinate system. Resolve
all vectors into components.
Problem Solving Tips - Static Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 7
• Identify the object in equilibrium.
• Identify all forces acting on the object, and draw a
free-body-diagram showing the force vectors.
◦ It’s essential that the free-body-diagram shows the forces
drawn from their actual application points.
• Choose (and label) an appropriate coordinate system. Resolve
all vectors into components.
• Apply Newton’s 2nd law as a set of equations (one for each
component).
Problem Solving Tips - Static Equilibrium
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 7
• Identify the object in equilibrium.
• Identify all forces acting on the object, and draw a
free-body-diagram showing the force vectors.
◦ It’s essential that the free-body-diagram shows the forces
drawn from their actual application points.
• Choose (and label) an appropriate coordinate system. Resolve
all vectors into components.
• Apply Newton’s 2nd law as a set of equations (one for each
component). Set each equation to zero.
Problem Solving Tips - Static Equilibrium - cont’d
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 8
• Choose a pivot point for calculating torques.
Problem Solving Tips - Static Equilibrium - cont’d
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 8
• Choose a pivot point for calculating torques. The choice is yours,
but a well-thought out choice will simplify the algebra.
Problem Solving Tips - Static Equilibrium - cont’d
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 8
• Choose a pivot point for calculating torques. The choice is yours,
but a well-thought out choice will simplify the algebra.
• Calculate the torque (~τ =∑
i(~ri ×
~Fi)) associated with each
force and sum the torques to zero.
Problem Solving Tips - Static Equilibrium - cont’d
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 8
• Choose a pivot point for calculating torques. The choice is yours,
but a well-thought out choice will simplify the algebra.
• Calculate the torque (~τ =∑
i(~ri ×
~Fi)) associated with each
force and sum the torques to zero.
• Solve the system of force and torque equations for the unknowns
of the problem.
Problem Solving Tips - Static Equilibrium - cont’d
Static Equilibrium of aRigid Body.
• Static Equilibrium of aRigid Body.
• TranslationalEquilibrium
• Rotational Equilibrium
• Lines of Action (TwoForces)?
• Lines of Action (ThreeForces)?
• Problem Solving Tips- Static Equilibrium
• Problem Solving Tips- Static Equilibrium -cont’d
PHYS101 Static Equilibrium – slide 8
• Choose a pivot point for calculating torques. The choice is yours,
but a well-thought out choice will simplify the algebra.
• Calculate the torque (~τ =∑
i(~ri ×
~Fi)) associated with each
force and sum the torques to zero.
• Solve the system of force and torque equations for the unknowns
of the problem.
• Sit back and relax - knowing that your efforts may have stabilized
a bridge or the building you helped design will remain static.