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Answer: Two solid cylindrical rods AB and BC are welded

Mechanics of Materials | 6th Edition | ISBN: 9780073380285 | Authors: Ferdinand Beer ISBN: 9780073380285 142

Solution for problem 1.20 Chapter 1

Mechanics of Materials | 6th Edition

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Mechanics of Materials | 6th Edition | ISBN: 9780073380285 | Authors: Ferdinand Beer

Mechanics of Materials | 6th Edition

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Problem 1.20

Two solid cylindrical rods AB and BC are welded together at B andloaded as shown. Knowing that d1 5 50 mm and d2 5 30 mm,find the average normal stress at the midsection of (a) rod AB,(b) rod BC.

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CNS Organization Wednesday, September 28, 208:25 PM Lecture06_CNSOrganization-2016 Nervous Systems Page 1 Nervous Systems Page 2 Nervous Systems Page 3 Nervous Systems Page 4 Nervous Systems Page 5 Nervous Systems Page 6 Nervous Systems Page 7 Nervous Systems Page 8 Nervous Systems Page 9 Nervous Systems Page 10 Nervous Systems Page 11 Nervous Systems Page 12 Nervous Systems Page 13 Nervous Systems Page 14 Nervous Systems Page 15 Nervous Systems Page 16 Nervous Systems Page 17 Nervous Systems Page 18 Nervous Systems Page 19 Nervous Systems Page 20 Nervous Systems Page 21 Nervous Systems Page 22 Auditory System Monday, September 26, 20163:06 PM Hair cell does not generate AP • Sound is a form of mechanical energy, and is produced by vibrations of a Lambda is ver long physical object, and in most cases occurring in the air. • Vibrations causes compression and rarefaction of the air, i.e. increased and decreased air pressure. (peak and trough of the graph) • This disturbance of the air radiates outward from the source as a pressure wave,a nd is transmitted through air by pressure wave. • The amplitude of the pressure wave is measure by SPL (sound pressure level) in dB. • The physical pressure is measured by Pascal (N/m^2), it is converted to acoustic pressure as SPL. • SPL is dB is a logarithmic scale. SPL relates acoustic pressure to a reference value just barely detectable by a young, healthy person for a sound of 1 kHz. That reference value is taken to be 20 μPa. SPL takes the measured acoustic pressure of sound (p!) and divides it by the reference acoustic pressure of 20 μPa (p0), the log10 of that value multiplied by 20 gives the SPL in dB. • SPL = 20 log (p!/p0) dB • 0-20 SPL is a ten-fold increase in acoustic pressure • Sound speed at the sea level is 340.29 m/s. Fourier transform: decompose complex wave into sine waves • Outer ear filters the sound pressure wave, and focus it on the eardrum. ○ Frequencies hit pinna in different angles and provide cues for location ○ Some frequencies are absorbed completely while others have no loss in energy • Inner ear contains the cochlear for audition and the vestibular apparatus for vestibular sense (balance and spatial orientation). Nervous Systems Page 1 • Ossicle bones: malleus, incus, stapes. • The impedance mismatch between air and water makes it difficult for pressure added to Vestibular apparatus: semicircular canals, saccule and utricle one to move to the other, only 0.1% of energy in a sound wave is transmitted from air to Same fluids and same type of receptorcell with cochlea water. Forces that produce fluid movement differ in cochlea vs. vestibular organs • The surface ratio of eardrum to oval window is about 20 to 1. Cochlea- detect vibrationsin the air • there is about 30 dB amplification of SPL through the middle ear conduction. Vestibular organs - detect movementsof head ○ 20log[Pi]/[Po] Scala media or cochlear duct is a fluid filled sack in the bony labyrinth Between the cochlear duct and the bone is the perilymph Ossicles conduct mechanical energy striking the tympanic membrane into fluid waves High concentration of sodium and low potassium inside the cochlea Scala media has endolymph Difference in density of air and water produces a difference in acoustic impedance Poor in sodium and rich in K Impedance mismatch betw air and water maeksit hard for pressure added to one to move the other Poor in calcium Acoustic impedance proportional to 1/surface area Difference in surface area of ear drum and stapes overcomethe mismatch Works for between 5 -500 hertz Nervous Systems Page 2 • Human cochlea is about 42 mm long. • Reissner’s membrane separates scala vestibuli and scala media; basilar membrane separates scala media and scala tympani. • Stria vescularis secrets high KCl to endolymph. • Organ of Corti, as strip of sensory epithelium, is about 33 mm long. • Scala media filled with kcl rich endolymph ○ Scala vesitbuli and scala tympani filled with perilymph ○ Basilar membrane separate the two lymphs • On top of basilar membrane are the hair cells ○ Above hair cells is the tecotiral membrane • Close to center of cochlea where neurons of spiral ganglion are is a single row of inner hair cells ○ Father out are three rows of outer hair cells ○ Supporting cells are between and around the populations to keep them happy ○ All of this called organ of Corti • Fluid that surrounds the entire basal surface has the same ion concentration as the extracellular fluid • At the apex, a hair cell has endolymph ○ Hair cells form tight junctions with supporting cells to set up a barrier to the two lymphs Organ of Corti. There are about 3500 inner hair cells in humans, and 12000 outer hair cells. • Outer hair cells --> converge Shortest to tallest stereocilia arrangement • Inner hair cells --> diverge Each sterecilia has two mechanically gated channels • Stereocilia- actin filled threads that grow out of the cuticular plate Open in response to mechanical energy ○ Extend from apical surface of hair cells ○ Stiff Allos all cations through them • Ribbon synapses along basal surface of hair cells Tiplinks hold channel of one sterecilium to channel of the other Made of cadherin 23 ○ Ball of structural proteins that gathers synaptic vesicles ready for release ○ Keep a suppy of vesicles when hair cell is slightly depolarized ○ Promoterelease of many vesicles Nervous Systems Page 3 Rarefaction phase of the sound cause upward deflection of the membrane and deflection of the cochlear travelling wave (traveling wave of basilar membrane) steroecilia toward the tallest one stereocilium. When a mammalian cochlea receives a pure-tone acoustic stimulus, pressure differences Traveling waves build to a peak and crash like an ocean wave between its liquid-filled compartments set the basilar membrane into oscillation at the High frequencies - they peak at the base frequency of stimulation. The membrane does not move as a unit; instead, successive waves Low frequencies - they peak at the apex propagate from the base of the cochlea towards its apex. Frequency detection and discrimination rely on difference in the location along the cochlea in The travelling waves progress along the membrane at a speed of some meters per second, far response to a sound wave below the velocity of sound in water. At any instant, the elastic membrane bears about three complete cycles of oscillation. the cochlear travelling wave (traveling wave of basilar membrane) Different regions of the cochlea respond selectively to different frequency of sound. Different regions of the cochlea respond selectively to different frequency of sound. • Low frequency - apex Tonotopic map • High frequency - base For every frequency there are two populations of hair cells that respond by changing their Apex- wide and floppy membrane poentials Base- narrow and stiff One depolarizing the other hyperpolarizing Change in membrane potential - passive beginning at the apical region Tiplinks are composed of cadherin-23 and protocadherin 15 proteins. Releases glutamate at basal region Movements toward tallest one open many channels Can form several synapses with several spiral ganglion dendrites Amplitude depends on # of mechanically gated ion channels open Spiral ganglion generatesAP and conduct the signal to the cochlear nuclei Base of cochlea- outer hair cells are tiny Movement towards smallest one hyperpolarizes When basilar membrane moves up, moved stereocilia towards tallest and vice versa Apex of basilar membrane - hair cells are larger For slower changes in current produced by low frequency Arrangement of stereocilia in a V The tallest is the point of the V Nervous Systems Page 4 Base of cochlea- outer hair cells are tiny When basilar membrane moves up, moved stereocilia towards tallest and vice versa Apex of basilar membrane - hair cells are larger For slower changes in current produced by low frequency Arrangement of stereocilia in a V The tallest is the point of the V Cells of the stria vascularis secrete KCl-rich endolymph into scala media. Rise of intracellular calcium producesrelease of neurotransmitter Inner hair cell - compute source of sound and recognize nature of sounds Gradient of perilymph vs endolymph moved cations into hair cell Out hair cells - mechanical filters Grow when the membrane poential is hyperpolarized and shrink when they are depolarized Push tectorial membrane away when they grow Bring tectorial membrane down when they depolarize Cause cochlear amplicification and adapt to background noise Basilar and tecoral membrane move upward at different angles when depolarizing Shearing force against stereocilia Shearing force bends all stereocilia towards the tallest one --> depolarization Voltage–sensitive protein Prestin Nervous Systems Page 5 Cochlear amplification is the addition of energy to inner hair cells cochlear amplifier, a positive regulation that increases response and sharpens tuning. Shrink when depolarized and allow tecorial membrane to come down Coupled with movement of basilar membrane, this amplifies the energy and therefore the signal Large time constant and short hair cell allow most of signal to pass onto spiral ganglion cells Large capacitance produces a temporal drag on change in membrane potential Discrimination of tone is hard for high frequency - due to long time constant .5 milliseconds Alternating current - matching of membrane potential to sound frequency Below 2 kHz Direct current - above 2 kHz the hair cell depolarizes at peak and remains there as long as sitmulus is on Nervous Systems Page 6 Nervous Systems Page 7

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Chapter 1, Problem 1.20 is Solved
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Textbook: Mechanics of Materials
Edition: 6
Author: Ferdinand Beer
ISBN: 9780073380285

The full step-by-step solution to problem: 1.20 from chapter: 1 was answered by , our top Engineering and Tech solution expert on 11/15/17, 02:40PM. This full solution covers the following key subjects: rod, average, Find, knowing, loaded. This expansive textbook survival guide covers 11 chapters, and 1493 solutions. Mechanics of Materials was written by and is associated to the ISBN: 9780073380285. This textbook survival guide was created for the textbook: Mechanics of Materials, edition: 6. The answer to “Two solid cylindrical rods AB and BC are welded together at B andloaded as shown. Knowing that d1 5 50 mm and d2 5 30 mm,find the average normal stress at the midsection of (a) rod AB,(b) rod BC.” is broken down into a number of easy to follow steps, and 39 words. Since the solution to 1.20 from 1 chapter was answered, more than 289 students have viewed the full step-by-step answer.

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Answer: Two solid cylindrical rods AB and BC are welded