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Definition
| Study of bodies at rest or in motion. |
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| Study of bodies at rest or in equilibrium. |
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Definition
Which six principles of Mechanics apply most often in statics.
1. Law of addition of forces
2. Principle of transmissibility of forces
3.Newton's first law
4.Newton's 2nd law
5.Newton's 3rd law
6.Newton's Law of Gravitation |
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Term
Particle (shape,size ignored)
Rigid Body (changes in shape,size ignored)
Deformable body (changes " " not ignored)
Fluids (Liquids incompressible, gases compressible) |
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Definition
| Real body simplified for analysis as: |
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Definition
| Action of one body onto another; characterized by its point of application, magnitude, LOA, and sense |
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External or Internal (to the body)
Planar or Spatial (one plane or 3-D)
Concurrent or
non-concurrent (parallel or non parallel) |
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Definition
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Definition
| Parameter possessing magnitude and direction which add according to the parallelogram law. Ex. displacements, velocities, accelerations. |
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Definition
| Parameter possessing magnitude but not direction. Ex. mass, volume, temperature |
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Definition
| ______ vectors have well defined points of app. that cannot be changed without affecting an analysis. |
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Definition
| _____ vectors may be freely moved in space without changing their effect on an analysis. |
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Definition
| _____ vectors may be applied anywhere along their line of action without affecting an analysis. |
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Definition
| ______ vector of a given vector has the same magnitude and the opposite direction. |
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Term
R2 = P2 + Q2 -2PQcosB
R = P + Q |
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Definition
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commutative
P + Q = Q + P
associative
P + Q + S = (P + Q) + S = P + (Q + S) |
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Definition
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Definition
| Set of forces which all pass through the same point |
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Definition
| two or more force vectors which, together, have the same effect as a single force vector. |
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Definition
| When the resultant of all forces acting on a particle is zero, the particle is in... |
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| If the resultant force on a particle is zero, the particle will remain at rest or will continue at constant speed in a straight line. |
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Definition
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Definition
| A sketch showing the physical conditions of the problem. |
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Definition
| A sketch showing only the forces on the selected particle. |
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Definition
| A collection of forces acting at specific points of a rigid body is called a _____. Forces acting on the SAME BODY |
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Definition
| Two systems of forces are said to be _______ if they have the SAME EFFECT on the rigid body. |
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Term
| Dot Product (scalar product) |
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Definition
| The result of this operation is scalar (numerically it could be postive or negative) It requires two vectors (binary operation). The product of the magnitudes of each of the two vectors and the angle between them. |
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| Multiplying it by a unit vector along a known axis. |
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Definition
| To convert a scalar into a vector what operation is necessary which we learned in Chap. 2? |
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Term
Commutative P•Q = Q•P
Distributive P•(Q1 + Q2) = P•Q1 + P•Q2
Not associative (P•Q)•S = undefined |
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Definition
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Determine the angle given the two vectors.
Determine the projection of one vector along a given axis. |
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Definition
| Two main applications of the dot product. |
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Term
| Cross product (vector product) |
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Definition
_______ of two vectors P and Q is defined as the new vector V which satisfies the following conditions.
- LOA of V is perpendicular to plane containing P and Q
- Magnitude of V is V = PQsinΘ
- Direction of V is obtained from the right-hand rule
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Term
Not commutative QxP = -(PxQ)
Distributive Px(Q1 + Q2) = PxQ1 + PxQ2
Not associative (PxQ)xS not= Px(QxS) |
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Definition
| Vector products ( cross products) are.... |
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Term
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Definition
| is thus a measure of the effect of a force on a rigid body the tendency for roation (sometimes called a torque) |
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Definition
| Two forces of equal magnitude, opposite in direction AND their LOA separated by a finite distance. |
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ZERO
Body is not in equilibrium b/c both forces tend to rotate the rigid body. |
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Definition
| Net (resultant) force of a couple... |
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Term
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Definition
| Obey the law of addition of vectors, are free vectors the POA is not significant, may be resolved into component vectors. |
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Definition
| The three forces may now be replaced by an equivalent force vector and couple vector. |
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Definition
| A system of forces may be replaced by a collection of _______ acting at a given point O. |
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Definition
| Two systems of forces are _______ if they can be reduced to the same force-couple system. |
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Definition
| The force-couple system at O may be moved to O' with the _______ of the moment of R about O' |
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mutually perpendicular
single force
new LOA |
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Definition
| If the resultant force and couple at O are __________, they can be replaced by a _______ acting along a ______ |
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Term
1. the forces are concurrent
2. the forces are coplanar
3. the forces are parallel |
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Definition
| The resultant force-couple system for a system of forces will be mutually perpendicular if... |
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Term
∑F acting on it is zero (no net translational effect)
∑M due to all forces about any arbitrary point is also zero (no net rotational effect) |
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Definition
| The necessary and sufficient conditions of equilibrium for a rigid body is that... |
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Definition
∑F = 0
∑Mo = 0
These two vector equations yield... |
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Term
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Definition
| ...are responses of one rigid body on to another due to the constraints placed on the system of rigid bodies to serve a certain purpose. They prevent the 2nd body from translation or rotation or both. Are either forces or couples or both and thus provide required constraints. |
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Term
- # of unknowns > # of independent equations
- Fewer # of unknowns than equations, partially constrained
- Equal # of unknowns and equations but improperly constrained
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Definition
| Statically Indeterminate Reactions |
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Term
| concurrent or parallel. If there is no single point of intersection then we could not show the sum of the moments about one point is zero. |
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Definition
| For equilibrium of a three-force body the lines of action of the three forces must be ________ or ________ |
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