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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

find the density of a fluid in which a hydrometer having a density of 0.750g/mL floats with 92.0% of its volume submerged.
Neshrin Reply
Uniform speed
Sunday
(a)calculate the buoyant force on a 2.00-L Helium balloon.(b) given the mass of the rubber in the balloon is 1.50g. what is the vertical force on the balloon if it is let go? you can neglect the volume of the rubber.
Neshrin Reply
To Long
Usman
pleaseee. can you get the answer? I can wait till 12
Neshrin
a thick glass cup cracks when hot liquid is poured into it suddenly
Aiyelabegan Reply
because of the sudden contraction that takes place.
Eklu
railway crack has gap between the end of each length because?
Aiyelabegan Reply
For expansion
Eklu
yes
Aiyelabegan
Please i really find it dificult solving equations on physic, can anyone help me out?
Big Reply
sure
Carlee
what is the equation?
Carlee
Sure
Precious
fersnels biprism spectrometer how to determined
Bala Reply
how to study the hall effect to calculate the hall effect coefficient of the given semiconductor have to calculate the carrier density by carrier mobility.
Bala
what is the difference between atomic physics and momentum
Nana Reply
find the dimensional equation of work,power,and moment of a force show work?
Emmanuel Reply
What's sup guys
Peter
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Okeh
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Nana
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Nana
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Joseph
Michelson Morley experiment
Riya Reply
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Naveed
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Celine
you
Celine
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Bala
Hi
Ahmed
Calculate the final velocity attained, when a ball is given a velocity of 2.5m/s, acceleration of 0.67m/s² and reaches its point in 10s. Good luck!!!
Eklu Reply
2.68m/s
Doc
vf=vi+at vf=2.5+ 0.67*10 vf= 2.5 + 6.7 vf = 9.2
babar
s = vi t +1/2at sq s=58.5 s=v av X t vf= 9.2
babar
how 2.68
babar
v=u+at where v=final velocity u=initial velocity a=acceleration t=time
Eklu
the answer is 9.2m/s
OBERT
express your height in Cm
Emmanuel Reply
my project is Sol gel process how to prepare this process pls tell me
Bala
the dimension of work and energy is ML2T2 find the unit of work and energy hence drive for work?
Emmanuel Reply
KgM2S2
Acquah
Two bodies P and Quarter each of mass 1000g. Moved in the same direction with speed of 10m/s and 20m/s respectively. Calculate the impulse of P and Q obeying newton's 3rd law of motion
Shimolla Reply
kk
Doc
the answer is 0.03n according to the 3rd law of motion if the are in same direction meaning they interact each other.
OBERT
definition for wave?
Doc Reply
A disturbance that travel from one medium to another and without causing permanent change to its displacement
Fagbenro
In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport (Mass transfer). ... There are two main types ofwaves: mechanical and electromagnetic. Mechanicalwaves propagate through a physical matter, whose substance is being deformed
Devansh
K
Manyo
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Doc
Thanks
AMADI
Note: LINEAR MOMENTUM Linear momentum is defined as the product of a system’s mass multiplied by its velocity: size 12{p=mv} {}
AMADI
what is physic
zalmia Reply
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zalmia
Study of matter and energy
Fagbenro
physics is the science of matter and energy and their interactions
Acquah
physics is the technology behind air and matter
Doc
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William
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Bala
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Easy to learn
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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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