Equilibrium and Elasticity

These flashcards cover key terms and concepts related to equilibrium and elasticity as discussed in the lecture notes.

Equilibrium

A state where the net external force and net external torque on an object are both zero (\Sigma F = 0, \Sigma \tau = 0), meaning it has no acceleration (translational or rotational) and is either at rest or moving at a constant velocity.

Center of Gravity (cg)

The point where an object's entire weight appears to act. It usually coincides with the center of mass, especially in a uniform gravitational field.

First Condition for Equilibrium

For translational equilibrium, the net external force on an object must be zero (\Sigma F = 0), meaning it has no linear acceleration. The SI unit for force is Newtons (N).

Second Condition for Equilibrium

For rotational equilibrium, the net external torque on an object must be zero (\Sigma \tau = 0) about any point, meaning no angular acceleration. The SI unit for torque is Newton-meters (Nm).

Static Equilibrium

A state of equilibrium where an object is completely at rest. Both the first (zero net force) and second (zero net torque) conditions for equilibrium are satisfied.

Hooke’s Law

A principle stating that, within a material's elastic limit, stress is directly proportional to strain. For a spring, this is F = -kx, where k is the spring constant (N/m).

Elastic Modulus

A measure of a material's stiffness, defined as the ratio of tensile stress to tensile strain within the elastic limit. The SI unit is Pascal (Pa or N/m^2).

Tensile Stress

The force per unit cross-sectional area applied to a material when it is stretched or pulled apart. The SI unit is Pascal (Pa or N/m^2).

Tensile Strain

The fractional change in length (\Delta L) of an object when stretched, calculated as \Delta L / L0, where L0 is the original length. It is a dimensionless quantity.

Bulk Stress

A uniform pressure or force per unit area applied perpendicular to all surfaces of an object, causing a change in its volume. The SI unit is Pascal (Pa or N/m^2).

Bulk Strain

The fractional change in volume (\Delta V) of an object under bulk stress, calculated as \Delta V / V0, where V0 is the original volume. It is a dimensionless quantity.

Shear Stress

The force per unit area applied parallel or tangential to a material's surface, causing deformation by layers sliding past each other. The SI unit is Pascal (Pa or N/m^2).

Shear Strain

The measure of deformation from shear stress, defined as the relative displacement of parallel planes divided by their perpendicular distance. It is represented as \tan \theta (shear angle) and is dimensionless.

Proportional Limit

The maximum stress on a stress-strain curve where stress remains directly proportional to strain (Hooke's Law holds). Beyond this point, the relationship becomes non-linear.

Elastic Limit

The maximum stress a material can withstand and still return to its original shape and size once the load is removed. Exceeding this causes permanent (plastic) deformation.

Ductile Material

A material capable of significant plastic (permanent) deformation, like stretching into a wire, before fracturing. Examples include copper and aluminum.

Brittle Material

A material that undergoes little to no plastic deformation and breaks suddenly when stressed. Examples include glass and ceramics.

Yield Point

The point on the stress-strain curve where a material begins to deform plastically, meaning it will not return to its original shape after the stress is removed.