11.5 - Elasticity
Elastic: An elastic object returns to its original
dimensions when a deforming force is removed.
In much of physics, the object being analyzed is assumed to be rigid and its dimensions
are unchanging. For instance, if a homework problems asks: “What is the effect of a net
force on a car?” and you answer, “The net force on the car caused a dent in its fender
and enraged the owner,” then you are thinking a little too much outside the box. The
question anticipates that you will apply Newton’s second law, not someone’s insurance
policy.
However, objects do stretch or compress when an external force is applied to them.
They may return to their original dimensions when that force is removed: Objects with
this property are called elastic. The external force causes the bonds between the
molecules that make up the material to stretch or compress, and when that force is
removed, the molecules can “spring back” to their initial configuration. The extent to
which the dimensions of an object change in response to a deforming force is a function
of the object’s original dimensions, the material that makes it up, and the nature of the
force that is applied.
It is also possible to stretch or compress an object to the point where it is unable to spring back. When this happens, the object is said to be
deformed.
It can require a great deal of force to cause significant stretching. For instance, if you hang a 2000 kg object, like a midsize car, at the end of a
two-meter long steel bar with a radius of 0.1 meters, the bar will stretch only about 6 × 10í^6 meters.
There are various ways to change the dimensions of an object. For instance, it can be stretched or compressed along a line, like a vertical steel
column supporting an overhead weight. Or, an object might experience compressive forces from all dimensions, like a ball submerged in water.
Calculating the change of dimensions is a slightly different exercise in each case.
Elastic
Shape changes under force
Elastic: when force is removed, original
shape is restored11.6 - Stress and strain
Stress: External force applied per unit area.
Strain: Fractional change in dimension due to
stress.
Above, you see a machine that tests the behavior of materials under stress. Stress is
the external force applied per unit area that causes deformation of an object. The
machine above stretches the rod, increasing its length. Although we introduce the topic
of stress and strain by discussing changes in length, stress can alter the dimensions of
objects in other fashions as well.
Strain measures the fractional change in an object’s dimensions: the object’s change
in dimension divided by its original dimension. This means that strain is dimensionless.
For instance, if a force stretches a two-meter rod by 0.001 meters, the resulting strain is
0.001 meters divided by two meters, which is 0.0005.
Stress measures the force applied per unit area. If a rod is being stretched, the area
equals the surface area of the end of the rod, called its cross-sectional area. If the force is being applied over the entirety of an object, such as
a ball submerged in water, then the area is the entire surface area of the ball.
For a range of stresses starting at zero, the strain of a material (fractional change in size) is linearly proportional to the stress on it. When the
stress ends, the material will resume its original shape: That is, it is elastic. The modulus of elasticity is a proportionality constant, the ratio of
Stress and strain
Stress: force per unit area
Strain: fractional change in dimension
due to stress
Modulus of elasticity: relates stress,
strain for given materialStress-strain graphs
Show behavior of material
·proportionality limit
·elastic limit
·rupture point