Equilibrium
00 and whenOccurs F
Static Equilibrium
0
,0,0
v
F and whenOccurs
Static Equilibrium Examples
1. A hinge attached to a wall connects a 3.0 m long pole while the other end is held up by a rope as shown. If the tension in the rope is 250 N, and the force makes a 37° angle with the pole, what is the mass of the pole?
Hinge
3.0 m
37
gF
TF
HF
37
gF
TF
HxF
HyF 37TyF
TxF
Static Equilibrium Examples
1. A hinge attached to a wall connects a 3.0 m long pole while the other end is held up by a rope as shown. If the tension in the rope is 250 N, and the force makes a 37° angle with the pole, what is the mass of the pole?
Hinge
3.0 m
37
gF
TF
HxF
HyF 37TyF
TxF
0xF
0 TxHx FF
37cosTHx FF
0yF
0 gTyHy FFF
37sinTHy FmgF
Static Equilibrium Examples
1. A hinge attached to a wall connects a 3.0 m long pole while the other end is held up by a rope as shown. If the tension in the rope is 250 N, and the force makes a 37° angle with the pole, what is the mass of the pole?
Hinge
3.0 m
37
gF
TF
HxF
HyF 37
0
0 gT
Tg
TyLFmgL
2
g
Fm T
37sin2
kgNN
m8.9
37sin2502
kgm 31
TyF
torque! exert and then
and hinge the around Analyze
0HyHx FF
TxF
Static Equilibrium Examples
2. A ladder whose length (l) is 15 m and whose mass m is 50. kg rests against a wall. The top of the ladder is a distance h = 11 m above the ground. The center of mass of the ladder is 1/3 of the way up. Assume that the wall, but not the ground is frictionless. What forces are exerted on the ladder by the wall and by the ground?
lh
a
gF
groundF
wallF
fsF
Static Equilibrium Examples
2. A ladder whose length (l) is 15 m and whose mass m is 50. kg rests against a wall. The top of the ladder is a distance h = 11 m above the ground. The center of mass of the ladder is 1/3 of the way up. Assume that the wall, but not the ground is frictionless. What forces are exerted on the ladder by the wall and by the ground?
gF
groundF
wallF
fsF
0xF
0 fswall FF
fswall FF
0yF
0 gground FF
gground FF
mgFground
)8.9(.50 kgNkgFground
NFground 490
Static Equilibrium Examples
2. A ladder whose length (l) is 15 m and whose mass m is 50. kg rests against a wall. The top of the ladder is a distance h = 11 m above the ground. The center of mass of the ladder is 1/3 of the way up. Assume that the wall, but not the ground is frictionless. What forces are exerted on the ladder by the wall and by the ground?
lh
a
gF
groundF
wallF
fsF
0
0 wallg
gwall
r r
But Fr
wallwall hF
r
torque! exert
and then and ground the
withpoint contact the around Analyze
0
groundfs FF
Static Equilibrium Examples
2. A ladder whose length (l) is 15 m and whose mass m is 50. kg rests against a wall. The top of the ladder is a distance h = 11 m above the ground. The center of mass of the ladder is 1/3 of the way up. Assume that the wall, but not the ground is frictionless. What forces are exerted on the ladder by the wall and by the ground?
lh
a
gF
groundF
wallF
fsF
rr
r
3a
gg Fa
3
gwall Fa
hF3
0
0 wallg
gwall
But Fr
wallwall hF
torque! exert
and then and ground the
withpoint contact the around Analyze
0
groundfs FF
Static Equilibrium Examples
2. A ladder whose length (l) is 15 m and whose mass m is 50. kg rests against a wall. The top of the ladder is a distance h = 11 m above the ground. The center of mass of the ladder is 1/3 of the way up. Assume that the wall, but not the ground is frictionless. What forces are exerted on the ladder by the wall and by the ground?
lh
a
3a
mga
hFwall 3
h
amgFwall 3
22 hla
22 1115 mma
ma 20.10
m
kgNkgm
Fwall
113
8.9.5020.10
NFwall .150
But 222 hal
Static Equilibrium Examples
3. Four identical bricks, each of length L, are put on top of one another in such a way that part of each extends beyond the one beneath. Find, in terms of L, the maximum values of a1, a2, a3, a4, and h, such that the stack is in equilibrium.
1a
2a
3a
4a
h
12
34
1
1gF
1NF
The normal force acts from the edge of the brick below since at maximum a1 the top brick balances
on the tip of the brick below.
Therefore, since the Fg acts from the center of gravity, the edge of the brick must be directly
below the center of gravity so that FN exerts an equal but opposite torque as Fg.
0 0yF
11 gN FF 11 gN
rotation of axis chosenany for
, Since
gN rr
Fr
block. top the on acting
forces the are and Ng FF
21L
a mgFN 1
Static Equilibrium Examples
3. Four identical bricks, each of length L, are put on top of one another in such a way that part of each extends beyond the one beneath. Find, in terms of L, the maximum values of a1, a2, a3, a4, and h, such that the stack is in equilibrium.
1a
2a
3a
4a
h
12
34 2
2gF
0yF
1NF
2a
2NF
0122 NgN FFF
122 NgN FFF
mgmgFN 2
mgFN 22
0
022 Ng
22 gN
222 2 gN FL
Fa
mgL
mga2
22
42L
a
Static Equilibrium Examples
3. Four identical bricks, each of length L, are put on top of one another in such a way that part of each extends beyond the one beneath. Find, in terms of L, the maximum values of a1, a2, a3, a4, and h, such that the stack is in equilibrium.
1a
2a
3a
4a
h
12
34 3
3gF
0yF
2NF
3a
3NF
0233 NgN FFF
233 NgN FFF
mgmgFN 23
mgFN 33
0
033 Ng
33 gN
333 2 gN FL
Fa
mgL
mga2
33
63L
a
Static Equilibrium Examples
3. Four identical bricks, each of length L, are put on top of one another in such a way that part of each extends beyond the one beneath. Find, in terms of L, the maximum values of a1, a2, a3, a4, and h, such that the stack is in equilibrium.
1a
2a
3a
4a
h
12
34 4
4gF
0yF
3NF4a
4NF
0344 NgN FFF
344 NgN FFF
mgmgFN 34
mgFN 44
0
044 Ng
44 gN
444 2 gN FL
Fa
mgL
mga2
44
84L
a
Static Equilibrium Examples
3. Four identical bricks, each of length L, are put on top of one another in such a way that part of each extends beyond the one beneath. Find, in terms of L, the maximum values of a1, a2, a3, a4, and h, such that the stack is in equilibrium.
1a
2a
3a
4a
h
12
34 4321 aaaah
8642
LLLLh
n
i n
LLLLLh
128642
Lh24
25
Brick 1 is actually out beyond the edge of the table!