stretching

Examples of stretching in the following topics:

• Benefits of Stretching

  • Stretching is a form of physical exercise, where specific skeletal muscles are stretched, improving elasticity and muscle tone.
  • Stretching can strengthen muscles, and in turn strong muscles are important to stretching safely and effectively.
  • Stretching can be dangerous when performed incorrectly.
  • It is also suggested that one stretching exercise may not be enough to prevent all types of injury, and therefore, multiple stretching exercises should be used to gain the full effects of stretching.
  • Over-stretching or stretching to a point where pain is felt may be inappropriate and detrimental.

• Group Frequencies

  • Following the color scheme of the chart, stretching absorptions are listed in the blue-shaded section and bending absorptions in the green shaded part.
  • Since most organic compounds have C-H bonds, a useful rule is that absorption in the 2850 to 3000 cm-1 is due to sp3 C-H stretching; whereas, absorption above 3000 cm-1 is from sp2 C-H stretching or sp2 C-H stretching if it is near 3300 cm-1.
  • Most of the absorptions cited are associated with stretching vibrations.

• Stretching and Shrinking

  • Stretching and shrinking refer to transformations that alter how compact a function looks in the $x$ or $y$ direction.
  • In algebra, equations can undergo scaling, meaning they can be stretched horizontally or vertically along an axis.  
  • This leads to a "stretched" appearance in the vertical direction.
  • If we want to vertically stretch the function by a factor of three, then the new function becomes:
  • The function $y=\sin(x)$ is stretched by a factor of three in the $y$ direction.

• When to Extend Product Lines

  • A company can extend its product line using a down-market stretch, an up-market stretch, or a move both ways.
  • The company can extend its product line with a down-market stretch, an up-market stretch, or a move both ways.
  • Companies serving the middle market might decide to stretch their line in both directions.
  • This two-way stretch won Texas Instruments (TI) an early market leadership in the hand-calculator market.

• Introduction to Ellipses

  • To change our circle into an ellipse, we will have to stretch or squeeze the circle so that the distances are no longer the same.
  • This has the effect of stretching the ellipse further out on the $x$-axis, because larger values of $x$ are now the solutions.
  • Now all the $y$ values are stretched vertically, further away from the origin.
  • If we stretch in both the $x$ and $y$ directions and distribute the powers of two through the parentheses, we get:
  • Connect the equation for an ellipse to the equation for a circle with stretching factors

• Muscle Tone

  • Muscle tone is a measure of a muscle's resistance to stretching while in a passive resting state.
  • Both are similar to muscle fibers in that they contain actin and myosin myofilaments that allow them to stretch with the muscle.
  • If tone decreases and the muscle stretches the spindle, an impulse results in a muscle contraction.
  • With this contraction, the spindle is no longer stretched.
  • Distinct stretch receptors called golgi tendon organs assess the level of stretch within the tendon.

• Elasticity, Stress, and Strain

  • Elasticity is a measure of how difficult it is to stretch an object.
  • Very elastic materials like rubber have small $k$ and thus will stretch a lot with only a small force.
  • For example, a long guitar string will stretch more than a short one, and a thick string will stretch less than a thin one .
  • Tension: The rod is stretched a length ΔL when a force is applied parallel to its length.
  • For larger deformations, the cross-sectional area changes as the rod is compressed or stretched.

• Hypotonia and Hypertonia

  • Hypertonia is the reduced ability of muscles to stretch due to increased muscle tension; hypotonia, due to chronic reduced muscle tension.
  • Hypertonia is a reduction in the ability of a muscle to stretch due to increased muscle tension; it is caused by lesions to upper motor neurons.
  • Dystonic hypertonia is the resistance to passive stretching in muscles, and the return of limbs to fixed positions after contraction.
  • The disruption of input from stretch receptors leads to decreased muscle innervation sensitivity, causing hypotonia.
  • Hypotonia is thought to be associated with the disruption of afferent input from stretch receptors and/or lack of the cerebellum's facilitatory efferent influence on the fusimotor system (the system that innervates intrafusal muscle fibers thereby controlling muscle spindle sensitivity ).

• Spinal Reflexes

  • Spinal reflexes include the stretch reflex, the Golgi tendon reflex, the crossed extensor reflex, and the withdrawal reflex.
  • The stretch reflex (myotatic reflex) is a muscle contraction in response to stretching within the muscle.
  • When a muscle lengthens, the muscle spindle is stretched and its nerve activity increases.
  • Although the tendon reflex is less sensitive than the stretch reflex, it can override the stretch reflex when tension is great, making you drop a very heavy weight, for example.
  • Like the stretch reflex, the tendon reflex is ipsilateral.

• Vibrational Spectroscopy

  • Vibrational modes are often given descriptive names, such as stretching, bending, scissoring, rocking and twisting.
  • Absorption bands associated with C=O bond stretching are usually very strong because a large change in the dipole takes place in that mode.
  • i) Stretching frequencies are higher than corresponding bending frequencies.
  • (It is easier to bend a bond than to stretch or compress it. )
  • ii) Bonds to hydrogen have higher stretching frequencies than those to heavier atoms.