Engineering Mechanics - Statics Episode 1 Part 3 pptx

Express the position vector r in Cartesian vector form; then determine its magnitude and coordinate direction angles... Express force F as a Cartesian vector; thendetermine its coordinat

A position vector extends from the origin to point A(a, b, c) Determine the angles α , β , γ which

the tail of the vector makes with the x, y, z axes, respectively.

Express the position vector r in Cartesian vector form; then determine its magnitude and

coordinate direction angles.

Given:

a = 4 m

− 4

⎛⎜

⎝ ⎞⎟ ⎠

=

α β γ

⎝ ⎞⎟ ⎠

=

α β γ

Determine the length of the connecting rod AB by first formulating a Cartesian position vector

from A to B and then determining its magnitude.

Determine the length of member

AB of the truss by first

establishing a Cartesian position

vector from A to B and then

determining its magnitude.

The positions of point A on the building and point B on the antenna have been measured relative

to the electronic distance meter (EDM) at O Determine the distance between A and B Hint:

Formulate a position vector directed from A to B; then determine its magnitude.

− 239.2

Determine the length of the crankshaft AB by first formulating a Cartesian position vector from

A to B and then determining its magnitude.

r AD

c

− 2

Express force F as a Cartesian vector; then

determine its coordinate direction angles.

=

Determine the magnitude and coordinate direction angles of the resultant force acting at point A.

− 159.2

Problem 2-93

The plate is suspended using the three

cables which exert the forces shown.

Express each force as a Cartesian vector.

− 364.5

=

Problem 2-94

The engine of the lightweight plane

is supported by struts that are

connected to the space truss that

makes up the structure of the

plane The anticipated loading in

two of the struts is shown.

Express each of these forces as a

− 64.9

The window is held open by cable AB Determine the length of the cable and express the force

F acting at A along the cable as a Cartesian vector.

− 20.3

The force acting on the man, caused by his pulling on the anchor cord, is F If the length of

the cord is L, determine the coordinates A(x, y, z) of the anchor.

F

40 20 50

Express each of the forces in Cartesian vector form and determine the magnitude and coordinate

direction angles of the resultant force.

Given:

F 1 = 80 lb c = 4 ft

− 62.9

− 18.2

− 22.8

The cord exerts a force F on the hook If the cord is length L, determine the location x, y of the

point of attachment B, and the height z of the hook.

The cord exerts a force of magnitude F on the hook If the cord length L, the distance z, and the

x component of the force, Fx, are given, determine the location x, y of the point of attachment B

of the cord to the ground.

Each of the four forces acting at E has magnitude F Express each force as a Cartesian vector

and determine the resultant force.

Find the position vectors and

then the forces

r EA

b a

− 24

=

r EB

b a c

− 24

F R = F EA + F EB + F EC + F ED F R

0 0 96

The tower is held in place by three cables If the force of each cable acting on the tower is

shown, determine the magnitude and coordinate direction angles α , β , γ of the resultant force

Find the position vectors, then the force vectors

r DC

a b

− 423.5

− 1.467

The chandelier is supported by three chains which are concurrent at point O If the force in each

chain has magnitude F, express each force as a Cartesian vector and determine the magnitude and

coordinate direction angles of the resultant force.

− 49.9

− 49.9

=

Problem 2-106

The chandelier is supported by three chains which are concurrent at point O If the resultant

force at O has magnitude FR and is directed along the negative z axis, determine the force in

each chain assuming FA = FB = FC = F.

= ( A x B x + A y B y + A z B z ) + ( A x D x + A y D y + A z D z )

= ( A B ⋅ ) + ( A D ⋅ ) (QED)

Problem 2-108

Cable BC exerts force F on the top of the flagpole Determine the projection of this force along

the z axis of the pole.

Determine the two position vectors and use the dot

product to find the angle

r 1v r 1

sin ( ) ε cos ( ) φ sin ( ) ε

− sin ( ) φ cos ( ) ε

Write the vectors and unit vectors

r 1v r 1

sin ( ) ε cos ( ) φ sin ( ) ε

− sin ( ) φ cos ( ) ε

− 6.89

− 0.766

The magnitude of the projection of r1 along r2 r 1v ⋅ u 2 = 2.99 m

The magnitude of the projection of r2 along r1 r 2v ⋅ u 1 = 1.99 m

Determine the projected component of the force F acting in the direction of cable AC Express

the result as a Cartesian vector.

Given:

F = 12 lb

− 0.8

− 1.145

The perpendicular component is now found

F perpendicular = F v ⋅ F v − F parallel 2 F perpendicular = 591.8 N

Problem 2-116

Determine the components of F that act along rod AC and perpendicular to it Point B is located

a distance f along the rod from end C.

The perpendicular component is now found

F perpendicular = F v ⋅ F v − F parallel 2 F perpendicular = 594.3 N

Problem 2-117

Determine the magnitude of the projected component of the length of cord OA along the Oa axis.

Given:

Problem 2-118

Force F acts at the end of the pipe.

Determine the magnitudes of the

components F1 and F2 which are directed

along the pipe's axis and perpendicular to

− 10

− 58.8

− 2

− 0.3

The two cables exert the forces shown on

the pole Determine the magnitude of the

projected component of each force acting

along the axis OA of the pole.

Force F is applied to the handle of the wrench Determine the angle θ between the tail of the force

and the handle AB.

− 0

Two cables exert forces on the pipe Determine the magnitude of the projected component of

F1 along the line of action of F2.

We first need to find the third

angle ( > 90 deg) that locates

force F2.

Initial Guess: φ = 120 deg

cos ( ) ε 2

cos ( ) γ 2 + + cos ( ) φ 2 = 1

φ = Find ( ) φ φ = 135 deg

Find the force F1v and the unit vector u2.

F 1v F 1

cos ( ) α sin ( ) β cos ( ) α cos ( ) β sin ( ) α

We first need to find the third

angle ( > 90 deg) that locates

force F2.

Initial Guesses: φ = 120 deg

cos ( ) ε 2

cos ( ) γ 2 + + cos ( ) φ 2 = 1

Find the unit vectors u1 and u2.

u 1

cos ( ) α sin ( ) β cos ( ) α cos ( ) β sin ( ) α

r AC

d

− − b c

Determine the projection of the

force F1 along cable AB Determine

the projection of the force F2 along

Problem 2-127

Determine the angle θ between the edges of

the sheet-metal bracket.