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Engineers and architects strive to achieve extremely stable equilibriums for buildings and other systems that must withstand wind, earthquakes, and other forces that displace them from equilibrium. Although the examples in this section emphasize gravitational forces, the basic conditions for equilibrium are the same for all types of forces. The net external force must be zero, and the net torque must also be zero.

Take-home experiment

Stand straight with your heels, back, and head against a wall. Bend forward from your waist, keeping your heels and bottom against the wall, to touch your toes. Can you do this without toppling over? Explain why and what you need to do to be able to touch your toes without losing your balance. Is it easier for a woman to do this?

Section summary

  • A system is said to be in stable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in a direction opposite the direction of the displacement.
  • A system is in unstable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in the same direction as the displacement from equilibrium.
  • A system is in neutral equilibrium if its equilibrium is independent of displacements from its original position.

Conceptual questions

A round pencil lying on its side as in [link] is in neutral equilibrium relative to displacements perpendicular to its length. What is its stability relative to displacements parallel to its length?

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Explain the need for tall towers on a suspension bridge to ensure stable equilibrium.

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Problems&Exercises

Suppose a horse leans against a wall as in [link] . Calculate the force exerted on the wall assuming that force is horizontal while using the data in the schematic representation of the situation. Note that the force exerted on the wall is equal in magnitude and opposite in direction to the force exerted on the horse, keeping it in equilibrium. The total mass of the horse and rider is 500 kg. Take the data to be accurate to three digits.

In part a, a horse is standing next to a wall with its legs crossed. A sleepy-looking rider is leaning against the wall. Part b is a drawing of the same horse from a rear view, but this time with no rider.  The horse is crossing its rear legs, and its rump is leaning against the wall. The reaction of the wall F is acting on the horse at a height one point two meters above the ground. The weight of the horse is acting at its center of gravity near the base of the tail. The center of gravity is one point four meters above the ground. The line of action of weight is zero point three five meters away from the feet of the horse.

F wall = 1.43 × 10 3 N size 12{F rSub { size 8{"wall"} } =1 cdot "43"` times `"10" rSup { size 8{3} } `N} {}

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Two children of mass 20.0 kg and 30.0 kg sit balanced on a seesaw with the pivot point located at the center of the seesaw. If the children are separated by a distance of 3.00 m, at what distance from the pivot point is the small child sitting in order to maintain the balance?

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(a) Calculate the magnitude and direction of the force on each foot of the horse in [link] (two are on the ground), assuming the center of mass of the horse is midway between the feet. The total mass of the horse and rider is 500kg. (b) What is the minimum coefficient of friction between the hooves and ground? Note that the force exerted by the wall is horizontal.

a) 2.55 ×10 3 N, 16.3º to the left of vertical (i.e., toward the wall) size 12{θ} {}

b) 0.292

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A person carries a plank of wood 2.00 m long with one hand pushing down on it at one end with a force F 1 size 12{F rSub { size 8{1} } } {} and the other hand holding it up at .500 m from the end of the plank with force F 2 size 12{F rSub { size 8{2} } } {} . If the plank has a mass of 20.0 kg and its center of gravity is at the middle of the plank, what are the magnitudes of the forces F 1 and F 2 size 12{F rSub { size 8{2} } } {} ?

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A 17.0-m-high and 11.0-m-long wall under construction and its bracing are shown in [link] . The wall is in stable equilibrium without the bracing but can pivot at its base. Calculate the force exerted by each of the 10 braces if a strong wind exerts a horizontal force of 650 N on each square meter of the wall. Assume that the net force from the wind acts at a height halfway up the wall and that all braces exert equal forces parallel to their lengths. Neglect the thickness of the wall.

A seventeen meter high wall is standing on the ground with ten braces to support it. At the base of the figure a brown colored ground is visible. Only one brace is visible from a side. A brace makes an angle of thirty five degree with the wall. The point of contact of the brace is eight point five meters high. You have to find the force exerted by this brace on the wall to support.

F B = 2.12 × 10 4 N size 12{F rSub { size 8{B} } =2 cdot "12" times "10" rSup { size 8{4} } `N} {}

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(a) What force must be exerted by the wind to support a 2.50-kg chicken in the position shown in [link] ? (b) What is the ratio of this force to the chicken’s weight? (c) Does this support the contention that the chicken has a relatively stable construction?

A chicken is trying to balance on its left foot, which is 9 point zero centimeters to the right of the chicken. The force of the wind is blowing from the left toward the chicken’s center of gravity c g, which is 20 cm above the ground. The weight of the chicken w is acting at the center of gravity.
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Suppose the weight of the drawbridge in [link] is supported entirely by its hinges and the opposite shore, so that its cables are slack. (a) What fraction of the weight is supported by the opposite shore if the point of support is directly beneath the cable attachments? (b) What is the direction and magnitude of the force the hinges exert on the bridge under these circumstances? The mass of the bridge is 2500 kg.

A small drawbridge is shown. There is one vertical and one horizontal wooden plank. The left end of the horizontal plank is attached to the vertical plank near its middle. At the point of contact, a hinge is shown. A wire is tied to the right end of the horizontal end, is passed over the top of the vertical plank and is connected to a pulley. The angle made by the wire with the horizontal plank is forty degrees. The reaction F at the hinge is inclined at an angle theta.
A small drawbridge, showing the forces on the hinges ( F size 12{F} {} ), its weight ( w size 12{w} {} ), and the tension in its wires ( T size 12{T} {} ).

a) 0.167, or about one-sixth of the weight is supported by the opposite shore.

b) F = 2 . 0 × 10 4 N size 12{F=2 "." 0 times "10" rSup { size 8{4} } N} {} , straight up.

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Suppose a 900-kg car is on the bridge in [link] with its center of mass halfway between the hinges and the cable attachments. (The bridge is supported by the cables and hinges only.) (a) Find the force in the cables. (b) Find the direction and magnitude of the force exerted by the hinges on the bridge.

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A sandwich board advertising sign is constructed as shown in [link] . The sign’s mass is 8.00 kg. (a) Calculate the tension in the chain assuming no friction between the legs and the sidewalk. (b) What force is exerted by each side on the hinge?

A sandwich board advertising sign is in form of a triangle. The base of the triangle is one point one zero meters. The other two sides are connected with a hinge at the top. A horizontal chain is connected to the two legs at zero point five zero meters below the hinge. The height of the hinge above the base is one point three zero meters. The centers of the gravity of the two legs are shown at their midpoints. The figure is labeled at uniform board with c g at the center.
A sandwich board advertising sign demonstrates tension.

a) 21.6 N

b) 21.6 N

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(a) What minimum coefficient of friction is needed between the legs and the ground to keep the sign in [link] in the position shown if the chain breaks? (b) What force is exerted by each side on the hinge?

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A gymnast is attempting to perform splits. From the information given in [link] , calculate the magnitude and direction of the force exerted on each foot by the floor.

A gymnast with two pompoms in her hands is shown. One of the hand is horizontal toward left and the other is vertical. The gymnast is attempting to perform a full split. The span of her legs is one point eight meters, and the distance of one foot from the center of gravity is zero point nine meters. The weight of the girl is labeled as seven hundred newtons. The vertical distance of one foot from the center of gravity is zero point three zero meter.
A gymnast performs full split. The center of gravity and the various distances from it are shown.

350 N directly upwards

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Questions & Answers

What interference
Moyinoluwa Reply
What is a polarized light called?
Moyinoluwa
what is a half life
Mama Reply
the time taken for a radioactive element to decay by half of its original mass
ken
what is radioactive element
mohammed
Half of the total time required by a radioactive nuclear atom to totally disintegrate
Justice
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
Justice
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
Justice
state the laws of refraction
Fabian
state laws of reflection
Fabian
Why does a bicycle rider bends towards the corner when is turning?
Mac
When do we say that the stone thrown vertically up wards accelerate negatively?
Mac
Give two importance of insulator placed between plates of a capacitor.
Mac
Macho had a shoe with a big sole moving in mudy Road, shanitah had a shoe with a small sole. Give reasons for those two cases.
Mac
when was the name taken from
Biola Reply
retardation of a car
Biola
when was the name retardation taken
Biola
did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
Sphere
Atomic transmutation
Basirat Reply
An atom is the smallest indivisible particular of an element
mosco Reply
what is an atomic
Awene Reply
reference on periodic table
Titus Reply
what Is resonance?
Mozam Reply
phenomena of increasing amplitude from normal position of a substance due to some external source.
akif
What is a black body
Amey Reply
Black body is the ideal body can absorb and emit all radiation
Ahmed
the emissivity of black body is 1. it is a perfect absorber and emitter of heat.
Busayo
Why is null measurement accurate than standard voltmeter
Neemat Reply
that is photoelectric effect ?
Sabir Reply
It is the emission of electrons when light hits a material
Anita
Yeah
yusuf
is not just a material
Neemat
it is the surface of a metal
Neemat
what is the formula for time of flight ,maxjmum height and range
agangan Reply
what is an atom
Awene
how does a lightning rod protect a building from damage due to lightning ?
Faith Reply
due to its surface lustre but due to some factors it can corrode but not easily as it lightning surface
babels
pls what is mirage
babels
light rays bend to produce a displaced image of distant objects; it's an natural & optical phenomenon......
Deepika
what is the dimensional formula for torque
Otto Reply
L2MT-2
Jolly
same units of energy
Baber
what is same units of energy?
Baber
Nm
Sphere
Ws
Sphere
CV
Sphere
M L2 T -2
Dokku
it is like checking the dimension of force. which is ML2T-2
Busayo
ML2T-2
Joshua
M L2 T-2
Samuel
what is the significance of moment of inertia?
study
an object of mass 200g moves along a circular path of radius 0.5cm with a speed of 2m/s. calculate the angular velocity ii period iii frequency of the object
Faith Reply
w = 2/(0.005) period = PIE(0.005) f = 1/(PIE(0.005)) assuming uniform motion idk..
Georgie
w=2/(0.005)×100
isaac
supposed the speed on the path is constant angular velocity w (rad/s) = v (m/s) : R (m) period T (s) = 2*Pi * R : v frequency f ( Hz) = 1: T
Sphere
a=w.w.r=mv.v/r,w=mv/r=0.2×2/0.005=80rads-s
Mac
Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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