Equilibrium: the state of no acceleration– balanced
forces and balanced torques
First condition of equilibrium: Fnet = 0
Second condition of equilibrium: τnet = 0
Static Equilibrium: Forces and Torques balance
and the object is at rest
Center of Mass (cm)– the point around which
gravitational torques balance– it is where the Fw
can be considered to be “located” at
C
For a uniform object, the
cm is at the center:
Fw
Solving Statics Problems
1) Forces are balanced horizontally and vertically
2) Torques are balanced as counterclockwise (+)
and clockwise (-) around an arbitrarily placed
pivot point
F3
F1
PP
C
F2
C
CC
CC
F3
F2
PP
F3
F1
C
CC
C
F1
C
F2 CC
PP
A uniform meterstick with a weight of .150 N is
balanced at the 75.0 cm mark by a mass hung at
90.0 cm mark. How much is the mass that is
producing equilibrium? How much does the
stand push up?
Ø
Fs
PP
.750 m
C
.500 m
.400 m
CC
Fw
C
Fh
Tc = Tcc
Fw = .150 N
(Fh)(.150 m) = (.150 N)(.250 m)
mh = ?
Fh = (.150 N)(.250 m)
= .250 N
.150 m
m = Fh
= .250 N
= .0255 kg
g
Fup = Fdown
9.80 m/s2
Fdown = .150 N + .250 N
= .400 N
A large wooden beam weighs 820 N and is 3.2 m
long. The beam’s center of gravity is 1.4 m from
one end. Two workers begin carrying the beam
away. If they lift the beam at its ends, how much
weight must each worker support?
Fu Ø
CC
PP
1.4 m
1.8 m
Fw = 820 N
C
Fu 2
Tc = T cc
(820 N)(1.4 m) = (Fu2)(3.2 m)
Fu2 = (820 N)(1.4 m)
= 360 N
3.2 m
Fup = Fdown
Fu + Fu2 = 820 N
Fu = 820 N - 360 N = 460 N
1) A 10.0 N meterstick is suspended from two
spring scales, one at the 8.00 cm mark and the
other at the 90.0 cm mark. If a weight of 5.00 N is
hung at the 20.0 cm mark and a weight of 17.0 N is
hung at the 55.0 cm mark, what will each scale
read?
2) An 850 N painter stands 1.20 m from one end
of a 3.00 m scaffold plank supported at each end
by a stepladder. The scaffold plank weighs 250 N
and there is a 50.0 N paint bucket .50 m from the
other end of the plank. How much upward force
is exerted by each of the two ladders?
3) A 650.0 N boy and a 490.0 N girl sit on a 150.0
N porch swing that is 1.70m and supported at each
end by chains. What will be the tension in each
chain if the boy sits .750 m from one end and the
girl sits .500 m from the other end?
4) A uniform 2.50 N meterstick is hung from the
ceiling by a single rope. A 500.0 g mass is hung at
the 25.0 cm mark and a 650.0 g mass at the 70.0 cm
mark. What is the tension in the rope and at what
mark is the rope located on the meterstick?
5) A 125 N uniform wooden plank is 2.00 m long.
It is supported by two sawhorses each placed .500
m in from each end. A man weighing 855 N stands
0.750 m in from the left end. A bag of tools
weighing 55.0 N is .250 m in from the right end.
How much must each sawhorse push upward?
6) A 4.0 N meterstick is balanced at the 73.0 cm
mark when a weight is hung from the 92.0 cm
mark. How much weight is hanging from that
mark? How much does the stand push upward?