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?
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.
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?
(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 person carries a plank of wood 2.00 m long with one hand pushing down on it at one end with a force
and the other hand holding it up at .500 m from the end of the plank with force
. 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
and
?
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) 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?
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) 0.167, or about one-sixth of the weight is supported by the opposite shore.
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.
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) 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?
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.
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
vjuvu
Elgoog
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
No
Richard
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
hello
Jackson
hi
Elyana
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
by big bang
universal
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
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