# 12.3 Stress, strain, and elastic modulus  (Page 8/26)

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## Problems

The “lead” in pencils is a graphite composition with a Young’s modulus of approximately $1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{9}\text{N}\phantom{\rule{0.1em}{0ex}}\text{/}\phantom{\rule{0.1em}{0ex}}{\text{m}}^{2}.$ Calculate the change in length of the lead in an automatic pencil if you tap it straight into the pencil with a force of 4.0 N. The lead is 0.50 mm in diameter and 60 mm long.

0.3 mm

TV broadcast antennas are the tallest artificial structures on Earth. In 1987, a 72.0-kg physicist placed himself and 400 kg of equipment at the top of a 610-m-high antenna to perform gravity experiments. By how much was the antenna compressed, if we consider it to be equivalent to a steel cylinder 0.150 m in radius?

By how much does a 65.0-kg mountain climber stretch her 0.800-cm diameter nylon rope when she hangs 35.0 m below a rock outcropping? (For nylon, $Y=1.35\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{9}\text{Pa}\text{.)}$

9.0 cm

When water freezes, its volume increases by 9.05%. What force per unit area is water capable of exerting on a container when it freezes?

A farmer making grape juice fills a glass bottle to the brim and caps it tightly. The juice expands more than the glass when it warms up, in such a way that the volume increases by 0.2%. Calculate the force exerted by the juice per square centimeter if its bulk modulus is $1.8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}1{0}^{9}N\phantom{\rule{0.1em}{0ex}}\text{/}\phantom{\rule{0.1em}{0ex}}{m}^{2},$ assuming the bottle does not break.

$4.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{2}\phantom{\rule{0.2em}{0ex}}{\text{N/cm}}^{2}$

A disk between vertebrae in the spine is subjected to a shearing force of 600.0 N. Find its shear deformation, using the shear modulus of $1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}1{0}^{9}\phantom{\rule{0.2em}{0ex}}{\text{N/m}}^{2}.$ The disk is equivalent to a solid cylinder 0.700 cm high and 4.00 cm in diameter.

A vertebra is subjected to a shearing force of 500.0 N. Find the shear deformation, taking the vertebra to be a cylinder 3.00 cm high and 4.00 cm in diameter. How does your result compare with the result obtained in the preceding problem? Are spinal problems more common in disks than in vertebrae?

$0.149\phantom{\rule{0.2em}{0ex}}\text{μm}$

Calculate the force a piano tuner applies to stretch a steel piano wire by 8.00 mm, if the wire is originally 1.35 m long and its diameter is 0.850 mm.

A 20.0-m-tall hollow aluminum flagpole is equivalent in strength to a solid cylinder 4.00 cm in diameter. A strong wind bends the pole as much as a horizontal 900.0-N force on the top would do. How far to the side does the top of the pole flex?

0.57 mm

A copper wire of diameter 1.0 cm stretches 1.0% when it is used to lift a load upward with an acceleration of $2.0\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}.$ What is the weight of the load?

As an oil well is drilled, each new section of drill pipe supports its own weight and the weight of the pipe and the drill bit beneath it. Calculate the stretch in a new 6.00-m-long steel pipe that supports a 100-kg drill bit and a 3.00-km length of pipe with a linear mass density of 20.0 kg/m. Treat the pipe as a solid cylinder with a 5.00-cm diameter.

8.59 mm

A large uniform cylindrical steel rod of density $\rho =7.8\phantom{\rule{0.2em}{0ex}}{\text{g/cm}}^{3}$ is 2.0 m long and has a diameter of 5.0 cm. The rod is fastened to a concrete floor with its long axis vertical. What is the normal stress in the rod at the cross-section located at (a) 1.0 m from its lower end? (b) 1.5 m from the lower end?

A 90-kg mountain climber hangs from a nylon rope and stretches it by 25.0 cm. If the rope was originally 30.0 m long and its diameter is 1.0 cm, what is Young’s modulus for the nylon?

$1.35\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{9}\text{Pa}$

A suspender rod of a suspension bridge is 25.0 m long. If the rod is made of steel, what must its diameter be so that it does not stretch more than 1.0 cm when a $2.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\text{-kg}$ truck passes by it? Assume that the rod supports all of the weight of the truck.

A copper wire is 1.0 m long and its diameter is 1.0 mm. If the wire hangs vertically, how much weight must be added to its free end in order to stretch it 3.0 mm?

259.0 N

A 100-N weight is attached to a free end of a metallic wire that hangs from the ceiling. When a second 100-N weight is added to the wire, it stretches 3.0 mm. The diameter and the length of the wire are 1.0 mm and 2.0 m, respectively. What is Young’s modulus of the metal used to manufacture the wire?

The bulk modulus of a material is $1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{11}\phantom{\rule{0.2em}{0ex}}{\text{N/m}}^{2}.$ What fractional change in volume does a piece of this material undergo when it is subjected to a bulk stress increase of ${10}^{7}\phantom{\rule{0.2em}{0ex}}{\text{N/m}}^{2}\text{?}$ Assume that the force is applied uniformly over the surface.

0.01%

Normal forces of magnitude $1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}\text{N}$ are applied uniformly to a spherical surface enclosing a volume of a liquid. This causes the radius of the surface to decrease from 50.000 cm to 49.995 cm. What is the bulk modulus of the liquid?

During a walk on a rope, a tightrope walker creates a tension of $3.94\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}1{0}^{3}N$ in a wire that is stretched between two supporting poles that are 15.0 m apart. The wire has a diameter of 0.50 cm when it is not stretched. When the walker is on the wire in the middle between the poles the wire makes an angle of $5.0\text{°}$ below the horizontal. How much does this tension stretch the steel wire when the walker is this position?

1.44 cm

When using a pencil eraser, you exert a vertical force of 6.00 N at a distance of 2.00 cm from the hardwood-eraser joint. The pencil is 6.00 mm in diameter and is held at an angle of $20.0\text{°}$ to the horizontal. (a) By how much does the wood flex perpendicular to its length? (b) How much is it compressed lengthwise?

Normal forces are applied uniformly over the surface of a spherical volume of water whose radius is 20.0 cm. If the pressure on the surface is increased by 200 MPa, by how much does the radius of the sphere decrease?

0.63 cm

is the eye the same like the camera
I can't understand
Suraia
Josh
I think the question is that ,,, the working principal of eye and camera same or not?
Sardar
yes i think is same as the camera
what are the dimensions of surface tension
samsfavor
why is the "_" sign used for a wave to the right instead of to the left?
why classical mechanics is necessary for graduate students?
classical mechanics?
Victor
principle of superposition?
principle of superposition allows us to find the electric field on a charge by finding the x and y components
Kidus
Two Masses,m and 2m,approach each along a path at right angles to each other .After collision,they stick together and move off at 2m/s at angle 37° to the original direction of the mass m. What where the initial speeds of the two particles
MB
2m & m initial velocity 1.8m/s & 4.8m/s respectively,apply conservation of linear momentum in two perpendicular directions.
Shubhrant
A body on circular orbit makes an angular displacement given by teta(t)=2(t)+5(t)+5.if time t is in seconds calculate the angular velocity at t=2s
MB
2+5+0=7sec differentiate above equation w.r.t time, as angular velocity is rate of change of angular displacement.
Shubhrant
Ok i got a question I'm not asking how gravity works. I would like to know why gravity works. like why is gravity the way it is. What is the true nature of gravity?
gravity pulls towards a mass...like every object is pulled towards earth
Ashok
An automobile traveling with an initial velocity of 25m/s is accelerated to 35m/s in 6s,the wheel of the automobile is 80cm in diameter. find * The angular acceleration
(10/6) ÷0.4=4.167 per sec
Shubhrant
what is the formula for pressure?
force/area
Kidus
force is newtom
Kidus
and area is meter squared
Kidus
so in SI units pressure is N/m^2
Kidus
In customary United States units pressure is lb/in^2. pound per square inch
Kidus
who is Newton?
scientist
Jeevan
a scientist
Peter
that discovered law of motion
Peter
ok
John
but who is Isaac newton?
John
a postmodernist would say that he did not discover them, he made them up and they're not actually a reality in itself, but a mere construct by which we decided to observe the word around us
elo
how?
Qhoshe
Besides his work on universal gravitation (gravity), Newton developed the 3 laws of motion which form the basic principles of modern physics. His discovery of calculus led the way to more powerful methods of solving mathematical problems. His work in optics included the study of white light and
Daniel
and the color spectrum
Daniel
what is a scalar quantity
scalar: are quantity have numerical value
muslim
is that a better way in defining scalar quantity
Peter
thanks
muslim
quantity that has magnitude but no direction
Peter
upward force and downward force lift
upward force and downward force on lift
hi
Etini
hi
elo
hy
Xander
Hello
Jux_dob
hi
Peter
Helo
Tobi
Daniel
what's the answer? I can't get it
what is the question again?
Sallieu
What's this conversation?
Zareen
what is catenation? and give examples
sununu
How many kilometres in 1 mile
Nessy
1.609km in 1mile
Faqir
what's the si unit of impulse
The Newton second (N•s)
Ethan
what is the s. I unit of current
Amphere(A)
imam
thanks man
Roland
u r welcome
imam
the velocity of a boat related to water is 3i+4j and that of water related to earth is i-3j. what is the velocity of the boat relative to earth.If unit vector i and j represent 1km/hour east and north respectively
what is head to tail rule?
kinza
The resultant vector is the sum of two vectors (one vector's head lies on the tail of the other). The resultant vector has it's starting point (tail) as the "free" tail of one vector and the end (head) as the "free" head of the other vector. Thinking of it as "overall effect" can be easier.
Kamalesh
For example: moving from A to B (vector AB) and then B to C (vector BC) is the same as moving from A to C (at least when it comes to vectors). Vector AC is called the resultant vector.
Kamalesh