In a rectangular coordinate system the equilibrium equations can be represented by three scalar equations, where the sums of forces in all three directions are equal to zero.
The sample data used in this analysis are the result of measured data from an actual experimental setup. Equilibrium equations[ edit ] The static equilibrium of a particle is an important concept in statics. If the center of gravity coincides with the foundations, then the body is said to be metastable.
The moment of inertia plays much the same role in rotational dynamics as mass does in linear dynamics, describing the relationship between angular momentum and angular velocity, torque and angular acceleration, and several other quantities.
What is the weight of the sign? Solids[ edit ] Statics is used in the analysis of structures, for instance in architectural and structural engineering. Thus, a trigonometric function can be used to determine this vertical component. Fluids[ edit ] Hydrostaticsalso known as fluid staticsis the study of fluids at rest i.
If the sign is known to have a mass of 5 kg and if the angle between the two cables is degrees, then the Statics lab in the cable can be determined. Once the components are known, they can be compared to see if the vertical forces are balanced and if the horizontal forces are balanced.
The weight Statics lab the sign is equal to the sum of the upward components of the tension in the two cables. The concept was introduced by Leonhard Euler in his book Theoria motus corporum solidorum seu rigidorum; he discussed the moment of inertia and many related concepts, such as the principal axis of inertia.
A sketch of this situation see diagram below reveals that the tension in the cable can be found using the sine function. The idea is that the tension, the angle, and the weight are related.
As another example that illustrates this idea, consider the symmetrical hanging of a sign as shown at the right. The sign weighs 50 N.
Strength of materials is a related field of mechanics that relies heavily on the application of static equilibrium. If the net force is greater than zero the fluid will move in the direction of the resulting force.
The diagram below shows vectors A, B, and C and their respective components. It has many important applications in hydraulics.
The position of the point relative to the foundations on which a body lies determines its stability in response to external forces. Thinking Conceptually There is an important principle that emanates from some of the trigonometric calculations performed above.
While a simple scalar treatment of the moment Statics lab inertia suffices for many situations, Statics lab more advanced tensor treatment allows the analysis of such complicated systems as spinning tops and gyroscopic motion.
An engineering application of this concept is determining the tensions of up to three cables under load, for example the forces exerted on each cable of a hoist lifting an object or of guy wires restraining a hot air balloon to the ground.
To illustrate this, consider a Newton picture held by three different wire orientations as shown in the diagrams below. But what about the 0.
When finished, click the button to view the answers. The data in the table above show that the forces nearly balance. It is the inertia of a rotating body with respect to its rotation. Why do the components of force only nearly balance? If the center of gravity exists outside the foundations, then the body is unstable because there is a torque acting: The picture is in a state of equilibrium, and thus all the forces acting upon the picture must be balanced.
The angle that the wires make with the horizontal is varied from 60 degrees to 15 degrees. Therefore, the force of gravity also known as weight is 50 N, down. The magnitude and direction of each component for the sample data are shown in the table below the diagram.
Suppose the tension in both of the cables is measured to be 50 N and that the angle that each cable makes with the horizontal is known to be 30 degrees.Torques and Static Equilibrium Introduction The primary purpose of this lab is to introduce you to the quantity called the torque or, as engineers call it, the moment of a force and show how this quantity behaves in a system in static equilibrium.
A common physics lab is to hang an object by two or more strings and to measure the forces that are exerted at angles upon the object to support its weight. The state of the object is analyzed in terms of the forces acting upon the object.
Statics Statics lab the branch of mechanics that is concerned with the analysis of loads (force and torque, or "moment") acting on physical systems that do not experience an acceleration (a=0), but rather, are in static equilibrium with their environment.
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we notice that the third force required for equilibrium to be established is a vector that has the same magnitude as the resultant, but points in º the opposite direction. R = -E Each dog's force has been resolved into its x- and y-components.
Static Equilibrium Physics Lab IX Objective In this lab exercise the requirements for static equilibrium will be tested experimen-tally.
This will be done by analyzing problems of force balance, torque balance and a.Download