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38 Cards in this Set
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Mechanics

Science which describes and predicts the conditions of rest or motion of bodies under the action of forces.


Mechanics is divided into three parts:

Rigid bodies
Deformable bodies Fluids 

Mechanics of rigid bodies is subdivided into 2 categories:

Statics bodies at rest.
Dynamics bodies in motion. 

Mechanics of fluids is subdivided into 2 categories:

Incompressible fluids includes hydraulics.
Compressible fluids 

Basic concepts used in mechanics:

Space
Time Mass Force 

Force

Represents the action of one body on another. It can be exerted by actual contact or at a distance, as in the case of gravitational forces and magnetic forces. A force is characterized by its point of application, its magnitude, and its direction; a force is represented by a vector.


Particle

A very small amount of matter which may be assumed to occupy a single point in space.


Rigid Body

A combination of a large number of particles occupying fixed positions with respect to each other.


Parallelogram Law for the Addition of Forces

Two forces acting on a particle may be replaced by a single force, called their resultant, obtained by drawing the diagonal of the parallelogram which has sides equal to the given forces.


Principle of Transmissibility

The conditions of equilibrium or of motion of a rigid body will remain unchanged if a force acting at a given point of the rigid body is replaced by a force of the same magnitude and same direction, but acting at a different point, provided that the two forces have the same line of action.


Newton's First Law

If the resultant force acting on a particle is zero, the particle will remain at rest or will move with constant speed in a straight line.


Newton's Second Law

If the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitude of the resultant and in the direction of this resultant force. F=ma


Newton's Third Law

The forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense.


Newton's Law of Gravitation

Two particles of masses M and m are mutually attracted with equal and opposite forces of magnitude F given by the formula: F=G(Mm/r^2)


Units of Force

1 N= 1 kg*m/s^2
1 slug= 1 lb*s^2/ft 

Foot to Meter Conversion

1 ft= .3048 m


Vectors

Quantities, such as force, velocity, and acceleration, that involve both magnitude and direction and cannot be characterized completely by a single real number. A directed line segment is used to represent such a quantity. Usually denoted by lowercase, boldface letters or an arrow over the letter.


Directed Line Segment

PQ has an initial point P and a terminal point Q. Its length (or magnitude) is denoted by PQ.


Determine if two directed line segments are equivalent

Calculate the length and slope of each directed line segment. If both are the same, they are equivalent.


Component form of a vector

v = <v₁, v₂>


Length (magnitude) of a vector

P(p₁,p₂) and Q(q₁,q₂) are the initial and terminal points of a directed line segment.
v=√((q₁p₁)^2 + (q₂p₂)^2)=√(v₁^2 + v₂^2) 

Unit Vector

If v=1, v is a unit vector.


Zero Vector

Both the initial and terminal points lie at the origin.
v=0=<0,0> v=0 

Vector sum of u and v

u+v=<u₁+v₁, u₂+v₂>


Scalar multiple of c and u

cu=<cu₁, cu₂>
c is a scalar (constant), u is a vector. 

Negative of vector v

v=(1)v=<v₁, v₂>


Difference of vectors u and v

uv=u+(v)=<u₁v₁, u₂v₂>


Scalar multiple of a vector v and a scalar c

The vector that is c times as long as v. If c is positive, cv has the same direction as v. If c is negative, cv has the opposite direction.


Resultant vector

Vector u+v
The sum of two vectors can be represented geometrically by positioning the vectors (without changing their magnitudes or directions) so that the initial point of one coincides with the terminal point of the other. The resultant vector is the diagonal of a parallelogram having u and v as its adjacent sides. 

Vector Commutative Property

u+v=v+u


Vector Associative Property

(u+v)+w=u+(v+w)


Vector Additive Identity Property

u+0=u


Vector Additive Inverse Property

u+(u)=0


Vector Distributive Property

(c+d)u=cu+du
c(u+v)=cu+cv c, d are scalars u, v are vectors 

Vector Space

Any set of vectors that satisfies the 8 properties known as vector space axioms.


Triangle Inequality

Generally, the length of the sum of two vectors is not equal to the sum of their lengths.
u+v≤u+v Equality occurs only if the vectors u and v have the same direction. 

Standard Unit Vectors

i=<1,0,0>
j=<0,1,0> k=<0,0,1> 

Linear combination of i and j

v= v₁i + v₂j
The scalars v₁ and v₂ are called the horizontal and vertical components of v. 