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Consequently, the object is in a state of static mechanical equilibrium. In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. [1]: 39 By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. [1]: 45–46 [2]
By the Pythagorean theorem, the magnitude of the resultant force is [(-10) 2 + (-8) 2] 1/2 ≈ 12.8 N, which is also the magnitude of the equilibrant force. The angle of the equilibrant force can be found by trigonometry to be approximately 51 degrees north of east. Because the angle of the equilibrant force is opposite of the resultant force ...
[23]: 58 When the net force on a body is equal to zero, then by Newton's second law, the body does not accelerate, and it is said to be in mechanical equilibrium. A state of mechanical equilibrium is stable if, when the position of the body is changed slightly, the body remains near that equilibrium. Otherwise, the equilibrium is unstable.
A body is said to be "free" when it is singled out from other bodies for the purposes of dynamic or static analysis. The object does not have to be "free" in the sense of being unforced, and it may or may not be in a state of equilibrium; rather, it is not fixed in place and is thus "free" to move in response to forces and torques it may experience.
Mechanical equilibrium, applies when an object is balanced so that the sum of the clockwise moments about a pivot is equal to the sum of the anticlockwise moments about the same pivot; Moment of inertia (=), analogous to mass in discussions of rotational motion. It is a measure of an object's resistance to changes in its rotation rate
This is the sum of all the force vectors and is equal to zero as there is mechanical equilibrium. Since the equilibrium holds for the external forces on the entire truss construction, it also holds for the internal forces acting on each joint. For a joint to be at rest the sum of the forces on a joint must also be equal to zero.
D'Alembert's principle generalizes the principle of virtual work from static to dynamical systems by introducing forces of inertia which, when added to the applied forces in a system, result in dynamic equilibrium. [1] [2] D'Alembert's principle can be applied in cases of kinematic constraints that depend on velocities.
Elastic energy is the mechanical potential energy stored in the configuration of a material or physical system as it is subjected to elastic deformation by work performed upon it. Elastic energy occurs when objects are impermanently compressed, stretched or generally deformed in any manner.