Mec 260, Ams 261

Front 1

Mechanics

Back 1

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

Front 2

Mechanics is divided into three parts:

Back 2

-Rigid bodies
-Deformable bodies
-Fluids

Front 3

Mechanics of rigid bodies is subdivided into 2 categories:

Back 3

-Statics- bodies at rest.
-Dynamics- bodies in motion.

Front 4

Mechanics of fluids is subdivided into 2 categories:

Back 4

-Incompressible fluids- includes hydraulics.
-Compressible fluids

Front 5

Basic concepts used in mechanics:

Back 5

-Space
-Time
-Mass
-Force

Front 6

Force

Back 6

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.

Front 7

Particle

Back 7

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

Front 8

Rigid Body

Back 8

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

Front 9

Parallelogram Law for the Addition of Forces

Back 9

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.

Front 10

Principle of Transmissibility

Back 10

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.

Front 11

Newton's First Law

Back 11

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.

Front 12

Newton's Second Law

Back 12

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

Front 13

Newton's Third Law

Back 13

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

Front 14

Newton's Law of Gravitation

Back 14

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)

Front 15

Units of Force

Back 15

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

Front 16

Foot to Meter Conversion

Back 16

1 ft= .3048 m

Front 17

Vectors

Back 17

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.

Front 18

Directed Line Segment

Back 18

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

Front 19

Determine if two directed line segments are equivalent

Back 19

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

Front 20

Component form of a vector

Back 20

v = <v₁, v₂>

Front 21

Length (magnitude) of a vector

Back 21

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

Front 22

Unit Vector

Back 22

If ||v||=1, v is a unit vector.

Front 23

Zero Vector

Back 23

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

Front 24

Vector sum of u and v

Back 24

u+v=<u₁+v₁, u₂+v₂>

Front 25

Scalar multiple of c and u

Back 25

cu=<cu₁, cu₂>

c is a scalar (constant), u is a vector.

Front 26

Negative of vector v

Back 26

-v=(-1)v=<-v₁, -v₂>

Front 27

Difference of vectors u and v

Back 27

u-v=u+(-v)=<u₁-v₁, u₂-v₂>

Front 28

Scalar multiple of a vector v and a scalar c

Back 28

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.

Front 29

Resultant vector

Back 29

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.

Front 30

Vector Commutative Property

Back 30

u+v=v+u

Front 31

Vector Associative Property

Back 31

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

Front 32

Vector Additive Identity Property

Back 32

u+0=u

Front 33

Vector Additive Inverse Property

Back 33

u+(-u)=0

Front 34

Vector Distributive Property

Back 34

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

Front 35

Vector Space

Back 35

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

Front 36

Triangle Inequality

Back 36

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.

Front 37

Standard Unit Vectors

Back 37

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

Front 38

Linear combination of i and j

Back 38

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