Statics
Statics is a fundamental branch of classical mechanics that focuses on the study of rigid objects or systems in a state of equilibrium, where all acting forces and torques are balanced. This field is essential for engineers who model forces in mechanical systems, such as the tension in cables and the stress on beams in structures like bridges and buildings. In static equilibrium, an object remains either stationary or moves at a constant velocity, as the net external forces and torques acting on it sum to zero.
A crucial aspect of analyzing static systems is the use of free-body diagrams, which visually represent all forces acting on an object. These diagrams help in understanding the vector nature of forces, as they include various types of forces like gravity, tension, and friction. For example, when a mass is suspended from multiple wires, free-body diagrams illustrate how the forces balance out, allowing for the determination of tension in each wire. Statics provides the necessary tools for tackling complex systems, making it a vital area of study in engineering and physics.
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Statics
Statics is the branch of classical mechanics concerned with rigid objects or physical systems for which the acting forces and torques are in equilibrium. Statics is a subfield of classical mechanics, along with dynamics (the study of objects in motion under the influence of unequilibrated forces), and kinematics (the study of objects in motion without consideration of the masses and forces involved). Engineers apply the principles of statics to model the forces involved in mechanical systems, including the tension in trusses and cables when designing bridges and the stress on load-bearing beams in building construction.
Static Equilibrium
When a rigid object is in static equilibrium, all forces and torques acting on the object are balanced, resulting in no acceleration or rotation of the object. Mathematically, this means two things:
- The vector sum of all external forces acting on the object must be zero (translational equilibrium).
- The vector sum of all external torques acting on the object must be zero (rotational equilibrium).
When a rigid object of mass m is acted on by a net force,
When an object's acceleration is zero, only motion at a constant velocity is possible. Thus, an object in static equilibrium is either stationary (at rest), or else the center of mass of the object is moving at a constant velocity.
The net torque, or rotational force, on an object in static equilibrium is zero (
Note that the study of statics makes the assumption that all objects are rigid; that is, they do not deform when acted upon by the forces in question. The analysis of forces acting on deformable objects requires detailed knowledge of the material and is beyond the scope of statics.
Free-Body Diagrams
Force is a vector quantity, which has both magnitude and direction. The net force acting on an object is the sum of the individual forces acting on the object. The net force is the vector sum of the forces involved, not the sum of the magnitudes of the forces.
An essential tool for analyzing the forces on an object in static equilibrium is a free-body diagram. An object in static equilibrium may be subject to a variety of forces, which might include push or pull, gravity, friction, tension, or torque. A free-body diagram of the system explicitly shows all the forces acting on the object. A visual representation of the system ensures that all forces are included and assists the component decomposition necessary to find the resultant vector sum of the applied forces.
The figure below shows a mass suspended from a wire and the corresponding free-body diagram.
The mass experiences a downward force,
When forces are applied to an object in multiple directions, it is important to remember their vector nature. The figure shows two forces acting on an object, one horizontally with a magnitude of 4 newtons (N), and the other vertically with a magnitude of 3 N.
The magnitude of the vector sum of the vertical and horizontal force vectors is the length of the hypotenuse of the right triangle they form. By the Pythagorean theorem,
When a mass is suspended from two wires, the situation becomes more complicated. The force of gravity pulls the mass down, but neither wire is individually responsible for supporting the full weight. The figure shows mass M suspended from two wires and the corresponding free-body diagram.
The system is in static equilibrium. The force due to gravity, or weight,
By symmetry, the two wires support the weight equally, and the tensions have equal magnitude, T. Each contributes an upward force of
To find the magnitude of the tension,
Free-body diagrams are essential tools for the analysis of physical systems in static equilibrium. These techniques can be extended to forces acting in three dimensions and to physical systems involving multiple objects.
Bibliography
Colwell, Catharine H. "Static Equilibrium." PhysicsLAB. Catherine H. Colwell. Web. 9 Mar. 2016. http://dev.physicslab.org/document.aspx?doctype=3&filename=dynamics‗staticequilibrium.xml
"Equilibrium and Statics." The Physics Classroom. The Physics Classroom. Web. 9 Mar. 2016. http://www.physicsclassroom.com/class/vectors/Lesson-3/Equilibrium-and-Statics
"Static Equilibrium, Elasticity, and Torque." Boundless. Boundless. Web. 9 Mar. 2016. https://www.boundless.com/physics/textbooks/boundless-physics-textbook/static-equilibrium-elasticity-and-torque-8
"Statics." LibreTexts, 28 Mar. 2024, phys.libretexts.org/Bookshelves/University‗Physics/Book%3A‗Introductory‗Physics‗-‗Building‗Models‗to‗Describe‗Our‗World‗(Martin‗Neary‗Rinaldo‗and‗Woodman)/06%3A‗Applying‗Newtons‗Laws/6.01%3A‗Statics. Accessed 19 Nov. 2024.