<< Chapter < Page Chapter >> Page >
  • State the first condition of equilibrium.
  • Explain static equilibrium.
  • Explain dynamic equilibrium.

The first condition necessary to achieve equilibrium is the one already mentioned: the net external force on the system must be zero. Expressed as an equation, this is simply

net F = 0 size 12{"net "F=0} {}

Note that if net F size 12{F} {} is zero, then the net external force in any direction is zero. For example, the net external forces along the typical x - and y -axes are zero. This is written as

net F x = 0 and F y = 0 size 12{"net "F rSub { size 8{y} } =0} {}

[link] and [link] illustrate situations where net F = 0 size 12{"net"`F=0} {} for both static equilibrium    (motionless), and dynamic equilibrium    (constant velocity).

In the figure, a stationary man is standing on the ground. His feet are at a distance apart. His hands are at his waist. The left side is labeled as net F is equal to zero. At the right side a free body diagram is shown with one point and two arrows, one vertically upward labeled as N and another vertically downward labeled as W, from the point.
This motionless person is in static equilibrium. The forces acting on him add up to zero. Both forces are vertical in this case.
A moving car is shown. Four normal vectors at each wheel are shown. At the rear wheel, a rightward arrow labeled as applied F is shown. Another arrow, which is labeled as f and points left, toward the front of the car, is also shown. A green vector at the top of the car shows the constant velocity vector. A free-body diagram is shown at the right with a point. From the point, the weight of the car is downward. Friction force vector f is toward left and applied force vector is toward right. Four normal vectors are shown upward above the point.
This car is in dynamic equilibrium because it is moving at constant velocity. There are horizontal and vertical forces, but the net external force in any direction is zero. The applied force F app size 12{F rSub { size 8{"app"} } } {} between the tires and the road is balanced by air friction, and the weight of the car is supported by the normal forces, here shown to be equal for all four tires.

However, it is not sufficient for the net external force of a system to be zero for a system to be in equilibrium. Consider the two situations illustrated in [link] and [link] where forces are applied to an ice hockey stick lying flat on ice. The net external force is zero in both situations shown in the figure; but in one case, equilibrium is achieved, whereas in the other, it is not. In [link] , the ice hockey stick remains motionless. But in [link] , with the same forces applied in different places, the stick experiences accelerated rotation. Therefore, we know that the point at which a force is applied is another factor in determining whether or not equilibrium is achieved. This will be explored further in the next section.

A hockey stick is shown. At the middle point of the stick, two red colored force vectors are shown one pointing to the right and the other to the left. The line of action of the two forces is the same. The top of the figure is labeled as net force F is equal to zero. At the lower right side the free body diagram, a point with two horizontal vectors, each labeled F and directed away from the point, is shown.
An ice hockey stick lying flat on ice with two equal and opposite horizontal forces applied to it. Friction is negligible, and the gravitational force is balanced by the support of the ice (a normal force). Thus, net F = 0 size 12{"net"`F=0} {} . Equilibrium is achieved, which is static equilibrium in this case.
A hockey stick is shown. The two force vectors acting on the hockey stick are shown, one pointing to the right and the other to the left. The lines of action of the two forces are different. Each vector is labeled as F. At the top and the bottom of the stick there are two circular arrows, showing the clockwise direction of the rotation. At the lower right side the free body diagram, a point with two horizontal vectors, each labeled F and directed away from the point, is shown.
The same forces are applied at other points and the stick rotates—in fact, it experiences an accelerated rotation. Here net F = 0 size 12{"net"`F=0} {} but the system is not at equilibrium. Hence, the net F = 0 size 12{"net"`F=0} {} is a necessary—but not sufficient—condition for achieving equilibrium.

Section summary

  • Statics is the study of forces in equilibrium.
  • Two conditions must be met to achieve equilibrium, which is defined to be motion without linear or rotational acceleration.
  • The first condition necessary to achieve equilibrium is that the net external force on the system must be zero, so that net F = 0 size 12{F rSub { size 8{ ital "net"} } =0} {} .

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 2

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Unit 7 - statics and torque. OpenStax CNX. Feb 03, 2016 Download for free at https://legacy.cnx.org/content/col11967/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Unit 7 - statics and torque' conversation and receive update notifications?

Ask