Check Your Understanding If the normal force acting on each face of a cubical
$1{\text{.0-m}}^{3}$ piece of steel is changed by
$1.0\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{7}\text{N},$ find the resulting change in the volume of the piece of steel.
The concepts of shear stress and strain concern only solid objects or materials. Buildings and tectonic plates are examples of objects that may be subjected to shear stresses. In general, these concepts do not apply to fluids.
Shear deformation occurs when two antiparallel forces of equal magnitude are applied tangentially to opposite surfaces of a solid object, causing no deformation in the transverse direction to the line of force, as in the typical example of shear stress illustrated in
[link] . Shear deformation is characterized by a gradual shift
$\text{\Delta}x$ of layers in the direction tangent to the acting forces. This gradation in
$\text{\Delta}x$ occurs in the transverse direction along some distance
${L}_{0}.$ Shear strain is defined by the ratio of the largest displacement
$\text{\Delta}x$ to the transverse distance
${L}_{0}$
Shear strain is caused by shear stress. Shear stress is due to forces that act
parallel to the surface. We use the symbol
${F}_{\parallel}$ for such forces. The magnitude
${F}_{\parallel}$ per surface area
A where shearing force is applied is the measure of shear stress
$\text{shear stress}=\frac{{F}_{\parallel}}{A}.$
The shear modulus is the proportionality constant in
[link] and is defined by the ratio of stress to strain. Shear modulus is commonly denoted by
S :
A cleaning person tries to move a heavy, old bookcase on a carpeted floor by pushing tangentially on the surface of the very top shelf. However, the only noticeable effect of this effort is similar to that seen in
[link] , and it disappears when the person stops pushing. The bookcase is 180.0 cm tall and 90.0 cm wide with four 30.0-cm-deep shelves, all partially loaded with books. The total weight of the bookcase and books is 600.0 N. If the person gives the top shelf a 50.0-N push that displaces the top shelf horizontally by 15.0 cm relative to the motionless bottom shelf, find the shear modulus of the bookcase.
Strategy
The only pieces of relevant information are the physical dimensions of the bookcase, the value of the tangential force, and the displacement this force causes. We identify
${F}_{\parallel}=50.0\phantom{\rule{0.2em}{0ex}}\text{N},\phantom{\rule{0.2em}{0ex}}\text{\Delta}x=15.0\phantom{\rule{0.2em}{0ex}}\text{cm},$${L}_{0}=180.0\phantom{\rule{0.2em}{0ex}}\text{cm},$ and
$A=\text{(30.0 cm)}\phantom{\rule{0.1em}{0ex}}\text{(90.0 cm)}=2700.0\phantom{\rule{0.2em}{0ex}}{\text{cm}}^{2},$ and we use
[link] to compute the shear modulus.
Solution
Substituting numbers into the equations, we obtain for the shear modulus
If the person in this example gave the shelf a healthy push, it might happen that the induced shear would collapse it to a pile of rubbish. Much the same shear mechanism is responsible for failures of earth-filled dams and levees; and, in general, for landslides.
The uniform seesaw shown below is balanced on a fulcrum located 3.0 m from the left end. The smaller boy on the right has a mass of 40 kg and the bigger boy on the left has a mass 80 kg. What is the mass of the board?
Consider a wave produced on a stretched spring by holding one end and shaking it up and down. Does the wavelength depend on the distance you move your hand up and down?
physics is the study of natural phenomena with concern with matter and energy and relationships between them
Ibrahim
a potential difference of 10.0v is connected across a 1.0AuF in an LC circuit. calculate the inductance of the inductor that should be connected to the capacitor for the circuit to oscillate at 1125Hza potential difference of 10.0v is connected across a 1.0AuF in an LC circuit. calculate the inducta
this greatly depend on the kind of energy. for gravitational energy, it is result of the shattering effect violent collision of two black holes on the space-time which caused space time to be disturbed. this is according to recent study on gravitons and gravitational ripple. and many other studies
tibebeab
and not every thing have to pop into existence. and it could have always been there . and some scientists think that energy might have been the only entity in the euclidean(imaginary time T=it) which is time undergone wick rotation.
some calculations is need. then you will get exact result.
Zahangir
i mean how? isn't it just a d over t?
Kyla
calculate the time it takes the stone to hit the ground then minus the stone's time to the total time... then divide the total distance by the difference of the time
Snuggly
awit lenard. Hahahah ari ga to!
Kyla
Why do we use mochromatic light? If white light is used, how would the pattern change