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!