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10: Static Equilibrium, Elasticity, and Torque

Last updated

Jun 23, 2019
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- 9.18: Center of Mass
- 10.1: Prelude to Static Equilibrium and Elasticity

Boundless
Boundless

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Topic hierarchy

10.1: Prelude to Static Equilibrium and Elasticity
10.2: Conditions for Static Equilibrium
A body is in equilibrium when it remains either in uniform motion (both translational and rotational) or at rest. Conditions for equilibrium require that the sum of all external forces acting on the body is zero, and the sum of all external torques from external forces is zero. The free-body diagram for a body is a useful tool that allows us to count correctly all contributions from all external forces and torques acting on the body.
10.3: Examples of Static Equilibrium
In applications of equilibrium conditions for rigid bodies, identify all forces that act on a rigid body and note their lever arms in rotation about a chosen rotation axis. Net external forces and torques can be clearly identified from a correctly constructed free-body diagram. In setting up equilibrium conditions, we are free to adopt any inertial frame of reference and any position of the pivot point. We reach the same answer no matter what choices we make.
10.4: Stress, Strain, and Elastic Modulus (Part 1)
External forces on an object cause its deformation, which is a change in its size and shape. The strength of the forces that cause deformation is expressed by stress. The extent of deformation under stress is expressed by strain, which is dimensionless. Tensile (or compressive) stress, which causes elongation (or shortening) of the object or medium and is due to external forces acting along only one direction perpendicular to the cross-section.
10.5: Stress, Strain, and Elastic Modulus (Part 2)
Bulk stress causes a change in the volume of an object or medium and is caused by forces acting on the body from all directions, perpendicular to its surface. Compressibility of an object or medium is the reciprocal of its bulk modulus, the elastic modulus in this case. Shear strain is the deformation of an object or medium under shear stress. Shear stress is caused by forces acting along the object’s two parallel surfaces.
10.6: Elasticity and Plasticity
An object or material is elastic if it comes back to its original shape and size when the stress vanishes. In elastic deformations with stress values lower than the proportionality limit, stress is proportional to strain. An object or material has plastic behavior when stress is larger than the elastic limit. In the plastic region, the object does not come back to its original size or shape when stress vanishes but acquires a permanent deformation. Plastic behavior ends at the breaking point.
10.7: Static Equilibrium and Elasticity (Exercises)
10.8: Static Equilibrium and Elasticity (Summary)
10.9: Introduction
Torque is the force that causes objects to turn or rotate (i.e., the tendency of a force to rotate an object about an axis).
10.10: Conditions for Equilibrium
The first condition of equilibrium is that the net force in all directions must be zero.
10.11: Stability
An object in static equilibrium remains in the same state forever, but not all forms of equilibrium are the same.
10.12: Solving Statics Problems
When solving static problems, you need to identify all forces and torques, confirm directions, solve equations, and check the results.
10.13: Applications of Statics
A simple machine is a device that changes the direction of a force or augments a force; simple machines fall into six categories.
10.14: Elasticity, Stress, Strain, and Fracture
Elasticity is a measure of how much an object deforms (strain) when a given stress (force) is applied.
10.15: The Center of Gravity
The center of gravity is read mathematically as: ‘the position of the center of mass and weighted average of the position of the particles’.
10.16: Torque and Angular Acceleration

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