Statics - Need to have No Motion or Constant Motion
Definition of Statics:
Application of math and Newton’s Laws to
study forces, both external and internal, in
machines and structures (which are in static
equilibrium) caused by loads.
1642-1727
Static Analysis always solves the SAME problem:
Given a set of known forces acting on a structure/machine…
Calculate a set of unknown external or internal forces
Key: Calculate unknown forces by solving a set of equilibrium equations for the system.
Applying Newton’s 2
nd
Law to a particle system
 F  m a but a  0
  F  0!
What is a Newton (N)?
How do we convert a mass given in kilograms (kg) to a weight in Newtons (N)?
If we are working on a problem with the following given “the car engine weighs
850 lb
lb”, what do we need to do to the 850 lbs before showing it as a force due
to gravity on our FBD?
What is a kip?
Review of Vector Operations Force Resultant Equilibrium
Today’s Learning Objectives:
Students will be able to…
Explain the difference between a concurrent force system and a nonconcurrent forces system
Resolve force vectors into Cartesian (rectangular or xx-y)
y) components
Determine the resultant force vector
from two, three or more vectors
using x-y components
Step 1 is to resolve each force
into its x and y components
Step 2 is to add all the x
components together and add all
the y components together. These
two totals become the resultant
vector’s x component and y
component.
Step 3 is to find the magnitude
and angle of the resultant vector
from its x and y components.
Statics:Hibbeler w/Thanks to Mehta, Danielson, & Berg
1
Quick Questions
Quick Questions
1. Resolve F along x and y axes and write it in
vector form. F = { ___________ } N
y
A) {80 cos (30°) i - 80 sin (30°) j }
1. Resolve F along x and y axes and write it in
vector form. F = { ___________ } N
y
A) {80 cos (30°) i - 80 sin (30°) j }
x
B) {80 sin (30°) i + 80 cos (30°) j }
{ sin ((30°)) i - 80 cos ((30°)) j }
C)) {80
30°
C) 50 N
30°
{ sin ((30°)) i - 80 cos ((30°)) j }
C)) {80
F = 80 N
2. Determine the magnitude of the resultant (F1 + F2) force in N
when F1 = { 10 i + 20 j } N and F2 = { 20 i + 20 j } N
B) 40 N
x
B) {80 sin (30°) i + 80 cos (30°) j }
D) {80 cos (30°) i + 80 sin (30°) j }
A) 30 N
Fx
D) 70 N
EXAMPLE # 1
D) {80 cos (30°) i + 80 sin (30°) j }
F = 80 N
Fy
2. Determine the magnitude of the resultant (F1 + F2) force when
F1 = { 10 i + 20 j } N and F2 = { 20 i + 20 j } N
A) 30 N
B) 40 N
C) 50 N
D) 70 N
EXAMPLE # 1 (cont.)
Given: Three concurrent
forces acting on a
bracket
Find: The magnitude and
angle direction of the
resultant force,, FR.
F1 = { (4/5) 850 i - (3/5) 850 j } N
F1 = { 680 i - 510 j } N
Plan:
F2 = { -625 sin(30°) i - 625 cos(30°) j } N
1) Resolve each force in its x-y components – Write in vector form.
F2 = { -312.5 i - 541.3 j } N
2) Add the respective components to get the resultant vector terms.
F3 = { -750 sin(45°) i + 750 cos(45°) j } N
3) Find magnitude and angle from the resultant components.
F3 = { -530.3 i + 530.3 j } N
EXAMPLE # 1 (cont.)
Summing up all the i and j components respectively, we get,
FR = { (680 – 312.5 – 530.3) i + (-510 – 541.3 + 530.3) j }N
EXAMPLE # 1 (cont.)
Summing up all the i and j components respectively, we get, the
Force Resultant, FR
FR = { (680 – 312.5 – 530.3) i + (-510 – 541.3 + 530.3) j }N
FR = { - 162.8 i - 521 j } N
FR = { - 162.8 i - 521 j } N
y
Calculate the angle of FR
||FR|| =
((162.8)2
+

(521)2) ½
= tan–1(521/162.8) = 72.64°
From the positive x-axis
Statics:Hibbeler w/Thanks to Mehta, Danielson, & Berg
= 546 N
x
FR
or
 = 180° + 72.64° = 253°
2
Given: Three concurrent forces acting on a bracket.
Find: Magnitude and direction, , of F1 so that the resultant
force is directed along the positive x’ axis and has a
magnitude of 1000 N.
Plan: Know FR but not F1
1) Write each force in vector form
(resolve into its x-y components)
2)Find ||F1|| and  using 2 equations
of the general form
FRx  F 1x  F 2 x  F 3 x
FRy  F 1 y  F 2 y  F 3 y
Statics:Hibbeler w/Thanks to Mehta, Danielson, & Berg
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