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

 Page 8 / 26

## 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

what is velocity
speed per unit time is called velocity. it is a vector quantity
Mukulika
velocity is distances overall time taking,it is a vector quantity, the units is metre per second.
Samuel
what is the difference between resultant force and net force
net force is when you add forces numerically I.e. the total sum of all positive and negative or balanced and unbalanced forces. resultant force is a single vector which is the combination or addition of all x and y axes vector component forces in a system.
emmanuel
thanks
Ogali
Damping is provided by tuning the turbulence levels in the moving water using baffles.How it happens? Give me a labelled diagram of it.
A 10kg ball travelling at 4meter per second collides elastically in a head-on collision with a 2kg ball.What are (a)the velocities and (b)the total momentum of the balls after collision?
a)v1 8/3s&v2 20/3s. b)in elastic collision total momentum is conserved.
Bala
The displacement of the air molecules in sound wave is modeled with the wave function s(x,t)=5.00nmcos(91.54m−1x−3.14×104s−1t)s(x,t)=5.00nmcos(91.54m−1x−3.14×104s−1t) . (a) What is the wave speed of the sound wave? (b) What is the maximum speed of the air molecules as they oscillate in simple harmon
practical 1st year physics
huh
Luminous
Whats the formular for newton law of motion
f=ma
F=m×a Where F=force M=mass of a body of an object a=acceleration due to gravity
Abubakar
what is speed
distance travelled per unit of time is speed.
distance travelled in a particular direction it is.
Andrew
Speed is define as the distance move per unit time. Mathematically is given as Speed = distance/time Speed = s/t
Abubakar
speed is a vector quantity. It is defined distance per unit time.It's unit in c.g.s cm/s and in S.I. m/s.It’s dimension is LT^-1
Mukulika
formula for velocity
v=ms^-1 velocity=distance time
Cleophas
(p-a/v)(v-b)=nrt what is the dimension of a
Amraketa
velocity= displacement time
Gold
Velocity = speed/time
Abubakar
what are evasive medical diagnosis?
If the block is displaced to a position y , the net force becomes Fnet=k(y−y0)−mg=0Fnet=k(y−y0)−mg=0 . But we found that at the equilibrium position, mg=kΔy=ky0−ky1mg=kΔy=ky0−ky1 . Substituting for the weight in the equation yields. Show me an equation of graph.
Shaina
where are you come from
Lida
samastipur Bihar
carrier
simple harmonic motion defination
how to easily memorize motion equation
Maharam
how speed destrog is uranium
where can we find practice problems?
I'm not well
YAZID
Sayed
can u tell me the expression for radial acceleeation
No
YAZID
Is equal to the square of the velocity divided by the radius of circular path of the object
Mukhtaar
how to find maximum acceleration and velocity of simple harmonic motion?
chander
how to find maximum acceleration and velocity of simple harmonic motion and where it occurres?
chander
you can use either motion equations or kinetic equation and potential equation .
lasitha
how destraction 1kg uranium
Sayed
A Radial Acceleration is defined as the upward movement of an object.
Andrew
A body of 2.0kg mass makes an elastic collision with another at rest and continues to more in the original direction but with 1/4 of its ori is the mass of the struck body?
pls help me solve this problem
bright