# 0.3 7.4 stability  (Page 2/5)

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When we consider how far a system in stable equilibrium can be displaced before it becomes unstable, we find that some systems in stable equilibrium are more stable than others. The pencil in [link] and the person in [link] (a) are in stable equilibrium, but become unstable for relatively small displacements to the side. The critical point is reached when the cg is no longer above the base of support. Additionally, since the cg of a person’s body is above the pivots in the hips, displacements must be quickly controlled. This control is a central nervous system function that is developed when we learn to hold our bodies erect as infants. For increased stability while standing, the feet should be spread apart, giving a larger base of support. Stability is also increased by lowering one’s center of gravity by bending the knees, as when a football player prepares to receive a ball or braces themselves for a tackle. A cane, a crutch, or a walker increases the stability of the user, even more as the base of support widens. Usually, the cg of a female is lower (closer to the ground) than a male. Young children have their center of gravity between their shoulders, which increases the challenge of learning to walk.

Animals such as chickens have easier systems to control. [link] shows that the cg of a chicken lies below its hip joints and between its widely separated and broad feet. Even relatively large displacements of the chicken’s cg are stable and result in restoring forces and torques that return the cg to its equilibrium position with little effort on the chicken’s part. Not all birds are like chickens, of course. Some birds, such as the flamingo, have balance systems that are almost as sophisticated as that of humans.

[link] shows that the cg of a chicken is below the hip joints and lies above a broad base of support formed by widely-separated and large feet. Hence, the chicken is in very stable equilibrium, since a relatively large displacement is needed to render it unstable. The body of the chicken is supported from above by the hips and acts as a pendulum between the hips. Therefore, the chicken is stable for front-to-back displacements as well as for side-to-side displacements.

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.

## 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.

${F}_{\text{wall}}=1.43×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{N}$

A person carries a plank of wood 2 m long with one hand pushing down on it at one end with a force ${\text{F}}_{1}$ and the other hand holding it up at 50 cm from the end of the plank with force ${\text{F}}_{2}$ . If the plank has a mass of 20 kg and its center of gravity is at the middle of the plank, what are the magnitudes of the forces ${\text{F}}_{1}$ and ${\text{F}}_{2}$ ?

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.

${F}_{\text{B}}=2.12×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{N}$

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.

b) $F=2\text{.}0×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{N}$ , straight up.

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nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
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scanning tunneling microscope
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how did you get the value of 2000N.What calculations are needed to arrive at it
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