<< Chapter < Page Chapter >> Page >

Learning objectives

By the end of this section, you will be able to:

  • 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.

Phet explorations: torque

Investigate how torque causes an object to rotate. Discover the relationships between angular acceleration, moment of inertia, angular momentum and torque.

Torque

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} {} .

Conceptual questions

What can you say about the velocity of a moving body that is in dynamic equilibrium? Draw a sketch of such a body using clearly labeled arrows to represent all external forces on the body.

Got questions? Get instant answers now!

Under what conditions can a rotating body be in equilibrium? Give an example.

Got questions? Get instant answers now!

Questions & Answers

What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
Provakar Reply
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
Brhanu Reply
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
Saeed Reply
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
define variable velocity
Ali Reply
displacement in easy way.
Mubashir Reply
binding energy per nucleon
Poonam Reply
why God created humanity
Manuel Reply
Because HE needs someone to dominate the earth (Gen. 1:26)
Olorunfemi
why god made humenity
Ali
Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
Jun Reply
ok we can say body is electrically neutral ...conductor this quality is given to most metalls who have free electron in orbital d ...but human doesn't have ...so we re made from insulator or dielectric material ... furthermore, the menirals in our body like k, Fe , cu , zn
Abrar
when we face electric shock these elements work as a conductor that's why we got this shock
Abrar
how do i calculate the pressure on the base of a deposit if the deposit is moving with a linear aceleration
ximena Reply
why electromagnetic induction is not used in room heater ?
Gopi Reply
room?
Abrar
What is position?
Amoah Reply
What is law of gravition
sushil Reply
what is magnetism
Sandeep Reply
Practice Key Terms 2

Get the best College physics for ap... course in your pocket!





Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask