Chapter 8
Statics
Equilibrium


An object either at rest or moving
with a constant velocity is said to be
in equilibrium
The net force acting on the object is
zero (since the acceleration is zero)
F  0
1st Condition for Equilibrium

Net force vanishes
F  F  F
1

F
F
2
 F3  ...  0
x
F1x  F2 x  F3 x  ...  0
y
F1 y  F2 y  F3 y  ...  0
Method






Isolate object of interest
Draw picture, label all forces
Choose appropriate coordinate
system
Resolve into components
Write equations for equilibrium
Solve equations for unknowns
Example


Mass m on table top
200 lb man hanging from rope
Example (ex 2)
Find tensions in the ropes.
Example 8.4
Two objects are in equilibrium. Find
the weight of the one on the left and
tensions.
Force vs. Torque


Forces cause accelerations
Torques cause angular accelerations
• rotation

Force and torque are related
Torque


The door is free to rotate about an axis through
O
There are three factors that determine the
effectiveness of the force in opening the door:
• The magnitude of the force
• The position of the application of the force
• The angle at which the force is applied
Torque, cont

Torque, t, is the tendency of a force to
rotate an object about some axis
t  Fl


t is the torque
F is the force
• symbol is the Greek tau



l is the lever arm
SI unit is N.m
Lever Arm: Perpendicular distance from
the pivot point to the line of force
Direction of Torque

Torque is a vector quantity
• We will treat only 2-d torque so no
need for vector notion.
• If the turning tendency of the force is
counterclockwise, the torque will be
positive (+)
• If the turning tendency is clockwise,
the torque will be negative (-)
Multiple Torques

When two or more torques are acting
on an object, the torques are added
• with the signs

If the net torque is zero, the object’s
rate of rotation doesn’t change
General Definition of Torque


The applied force is not always
perpendicular to the position vector
The component of the force
perpendicular to the object will cause
it to rotate
t  FL sin 
l  L sin 

F is the force
L is distance
between pivot and
point of action


 is the angle
Example (8.20)
Torque problem
F1  F2  F3  F4  60 N
L  2m
Center of Gravity



The weight of an object can cause
object to pivot
C.G. used as pivot will have no
torque due to gravity
In finding the torque produced by
the force of gravity, all of the weight
of the object can be considered to be
concentrated at a single point, C.G.
Center of Gravity of a Uniform
Object


The center of gravity of a
homogenous, symmetric body must
lie on the axis of symmetry.
Often, the center of gravity of such
an object is the geometric center of
the object.
Experimentally Determining the
Center of Gravity



The wrench is hung
freely from two different
pivots
The intersection of the
lines indicates the center
of gravity
A rigid object can be
balanced by a single
force equal in magnitude
to its weight as long as
the force is acting
upward through the
object’s center of gravity
2nd Condition for Equilibrium


No rotation
Net torque vanishes
t t
1
 t 2  t 3  ...  0
Example
1000 N sign painter on an uniform
250N board suspended by two ropes.
The board is 5m long. If the rope can
hold only 900 N, is it safe for him to
stand 1m from a rope?
Example
600 N worker
standing 1.5 m
from the wall on
5m long and 300N
beam as show.
Find tension in the
cable and the
force on the beam
by the wall.