ENGR2230U Statics
Tutorial 03 Exercises
Q1. Determine the projection of force F = 80 N along line BC. Express the result as a Cartesian vector.
1
Q2. Two cables exert forces on the pipe. (1) Determine the magnitude of the projected component of F 1 along
2-1. Determine the magnitude of the resultant force
FR -= F, + Fgand its dkecommeasured counterclockwise
from the positive x axis
3 ' cfw_500 + (3001 - 2(600)(800Jcos7s' = 866.91 . m
Ans
y 866.91 322
F1 = BMN 3 uODN ems" sins
a = 6105'
o = 63.05 + 45
8-62. Determine the minimum applied force I' required
to me wedge A to the right. meant-tn; hemmed
a distanced [75 anNegleet theweightoflt and 8.11:
coefcient of static friction for all contacting surfaces is
u, -= 0.35. Neglect friction at the rollers.
l
ENGR2230 - Statics lecture 02
FORCE VECTORS, VECTOR OPERATIONS &
ADDITION COPLANAR FORCES
Chapter 2 Sections 2.1 2.4
a) Resolve a 2-D vector into components.
b) Add 2-D vectors using Cartesian vector notations.
APPLICATION OF VECTOR ADDITION
FR
There are
ENGR2230 - Statics lecture 03
CARTESIAN VECTORS AND
THEIR ADDITION & SUBTRACTION
Chapter 2 Sections 2.5 2.6
a) Represent a 3-D vector in a Cartesian coordinate system.
b) Find the magnitude and coordinate angles of a 3-D vector
c) Add vectors (forces) in
611.
Determine the force in each member of the truss and state
if the members are in tension or compression.
4 kN
3m
3m
3m
C
B
D
3m
5m
A
F
SOLUTION
E
Support Reactions:
5 kN
a + MD = 0;
4162 + 5192 - Ey 132 = 0
+ c Fy = 0;
23.0 - 4 - 5 - Dy = 0
+ F = 0
:
ENGR2230 - Statics lecture 07
THREE-DIMENSIONAL FORCE SYSTEMS
Chapter 3 Sections 3.4
a) a) Drawing a 3-D free body diagram, and,
b) Applying the three scalar equations (based on one
vector equation) of equilibrium
APPLICATIONS
You know the weights
of elec
315.
The spring has a stiffness of k = 800 N>m and an unstretched
length of 200 mm. Determine the force in cables BC and BD
when the spring is held in the position shown.
C
400 mm
A
k
800 N/m
B
SOLUTION
300 mm
The Force in The Spring: The spring stretches
A 904!) load is suspended from the hook shown in Fig. 310.51. If the
load is supported by two cables and a spring having a stiffness
k = 500 lb/tt, determine the force in the cables and the stretch of the
spring for equilibrium. Cable AD lies in the xw-y
515.
Determine the horizontal and vertical components of
reaction at the pin at A and the reaction of the roller at B on
the lever.
14 in.
30
F 50 lb
A
SOLUTION
Equations of Equilibrium: From the free-body diagram, FB and A x can be obtained
by writing th
46.
The crane can be adjusted for any angle 0 u 90 and
any extension 0 x 5 m. For a suspended mass of
120 kg, determine the moment developed at A as a function
of x and u. What values of both x and u develop the
maximum possible moment at A? Compute this
938.
Determine the location r of the centroid C of the cardioid,
r = a11 - cos u2.
r
u
C
r
SOLUTION
dA =
1 2
r du
2
p
A = 2
1 2
3
(a )(1 - cos u)2 du = p a 2
2
2
L0
p
= 2
~
rx dA
LA
1
2
a r cos ub a b (a 2)(1 - cos u)2 du
2
L0 3
p
=
r =
~
2 3
a
(1 - cos u
THE METHOD OF SECTIONS
Todays Objectives:
Students will be able to determine:
1. Forces in truss members using the
method of sections.
APPLICATIONS
Long trusses are often used to construct large cranes and
large electrical transmission towers.
The method
Moment of Inertia of Inclined Axes and Mohrs Circle
Todays Objectives:
Students will be able to :
a) Determine the MI of inclined
axes and Mohrs circle
Moment of Inertia of Inclined Axes
Some designs require calculation of
the moment of inertia about incl
University of Ontario Institute of Technology
MECE 2230U: Statics
Assignment 2 (Due: October 01, 2013 at 4:00 pm)
Please, clearly write your name and student number on your solution sheet(s)
1. The spring in Fig. 1 has a stiffness of k = 800 N/m and an un
INTERNAL FORCES
Todays Objective:
Students will be able to:
1. Describe the internal shear and
moment throughout a member
using plots.
APPLICATIONS
This extended towing arm must resist both bending and shear
loading throughout its length due to the weight
1087.
Determine the radius of gyration kx of the paraboloid. The
density of the material is r = 5 Mg>m3.
y
y2
50 x
100 mm
x
SOLUTION
200 mm
Differential Disk Element: The mass of the differential disk element is
dm = rdV = rpy2 dx = rp(50x) dx. The mass m
*74.
The boom DF of the jib crane and the column DE have a
uniform weight of 50 lb>ft. If the hoist and load weigh 300 lb,
determine the normal force, shear force, and moment in the
crane at sections passing through points A, B, and C.
D
2 ft
F
A
B
8 ft
3
University of Ontario Institute of Technology
MECE 2230U: Statics
Assignment 6 (Due: November 13, 2013 at 4:00 pm)
Please, clearly write your name and student number on your solution sheet(s)
1. The boom DF of the jib crane and the column DE (Fig. 1) have
*24.
Determine the magnitude of the resultant force FR = F1 + F2
and its direction, measured clockwise from the positive u axis.
70
u
30
45
F2
SOLUTION
FR = 2(300)2 + (500)2 - 2(300)(500) cos 95 = 605.1 = 605 N
Ans.
500
605.1
=
sin 95
sin u
u = 55.40
f =
ENGR2230 - Statics lecture 05
DOT PRODUCT
Chapter 2 Sections 2.9
a) determine an angle between
two vectors.
b) Determine projection of a vector along a specified line
APPLICATIONS
If the design for the cable
placements required specific
angles between the
ENGR2230 - Statics Lecture 11
REDUCTION OF A SIMPLE DISTRIBUTED LOADING
Chapter 4 Sections 4.9
a) Determine an equivalent force for a distributed load
APPLICATIONS
There is a bundle (called a bunk) of 2 x 4 boards stored
on a storage rack. This lumber pla
EXAMPLE 2.16
Determine the magnitudes of the projection of the force F in Fig. 2-44
onto the u and v axes.
. -, '-'- 31-'z3~a'
- 3 5535-1 _,'l(< Fig. 2 44
SOLUTION
Projections of Force. The graphical representation of the projections
is shown in Fig. 24
EQUILIBRIUM OF A PARTICLE, THE FREE-BODY
DIAGRAM & COPLANAR FORCE SYSTEMS
Todays Objectives:
Students will be able to :
a) Draw a free body diagram (FBD), and,
b) Apply equations of equilibrium to solve
a 2-D problem.
APPLICATIONS
The crane is lifting a l
CARTESIAN VECTORS AND
THEIR ADDITION & SUBTRACTION
Todays Objectives:
Students will be able to:
a) Represent a 3-D vector in a
Cartesian coordinate system.
b) Find the magnitude and
coordinate angles of a 3-D vector
c) Add vectors (forces) in 3-D
space
AP
EXAMPLE
The man shown in Fig. 239a pulls on the cord with a force of 70 lb.
Represent this force acting on the support A as a Cartesian vector and
determine its direction.
SOLUTION
Force F is shown in Fig. 239b. The direction of this vector, u, is
determi