Static Equilibrium
KEY
1.
How many different positions of stable
equilibrium and unstable equilibrium are there for a
cube (consider each surface, edge and corner to be a
different position)?
• Stable: flat sides = 6
• Unstable: Corners + sides = 8 + 12 = 20
2. A window washer is standing on a scaffold supported by a
vertical rope at each end. The scaffold eights 200 N and is
3.00 m long. What is the tension in each rope when the 700
N worker stands 1.00 m from one end?
T1
T2
Sum torques around T1:
  0
T1 (0m) T2 (3m)  200N(1.5m)  700N(2m)
3T2  1700Nm
T2  567N
Sum torques around T2:
200N
700N
  0
T1 (3m) T2 (0m)  200N(1.5m)  700N(1m)
3T2  1000Nm
T2  333N
3. A student hangs a 25g mass from the 0.0 m mark on a
meterstick and another at the 20. cm point. How large of a
mass should the student hang at the 85 cm point if the
student wants to perfectly balance the meterstick on her
finger placed at the 50. cm mark?
0
20
50
85
0.025kg
m=?
0.025kg
  0
Sum torques around 50cm mark:
(0.025kg)(9.8m / s 2 )(0.5m) (0.025kg)(9.8m / s 2 )(0.3m)  m(9.8m / s 2 )(0.35m)
0.0125kgm 0.0075kgm  m(0.35m)
m  0.057kg  57g
4. A 245 N shop sign is hung from the end of a 1.70 m, 155
N beam. The beam is placed flat against the wall. 1.35 m
from the wall, a cable is attached, one end to the beam and
the other end to the wall. What is the tension in the wire if
the wire makes a 35o angle with the beam?
T
Tsin35o
Sum torques around the
wall because I don’t know
the frictional force provided
by the wall.
1.35m
35o
1.7m
  0
0.85m
155N(0.85m)  245N (1.7m) T sin 35(1.35m)  0
245N 131.75Nm  416.5Nm  0.775T
155N
T  708N

5. A 50.0 kg porch swing is
2.00 m long and is supported
by two cables vertically
connecting each side of the
swing to the ceiling of the
porch. If a 35 kg kid is
sitting 0.35 m from the right
end of the swing and a 45 kg
kid is sitting 0.45 m from the
left end, what is the tension
in each support cable?

T2
T1
0.45m
1.00m
0.35m
45kg(9.8m/s2)
35kg(9.8m/s2)
50.0kg(9.8m/s2)
T1
0
T1 (0m)  T2 (2.00m)  (441N )(1.55m)  (490 N )(1.00m)  (343N )(0.35m)  0
T2  646.8 N  650 N

T2
0
T2 (0m)  T1 (2.00m)  (441N )(0.45m)  (490 N )(1.00m)  (343N )(1.65m)  0
T2  627 N  630 N