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My name is Ann [436]
3 years ago
7

A cylindrical bar of steel 10.1 mm (0.3976 in.) in diameter is to be deformed elastically by application of a force along the ba

r axis. Determine the force that will produce an elastic reduction of 2.7 ×10-3 mm (1.063 ×10-4 in.) in the diameter. For steel, values for the elastic modulus (E) and Poisson's ratio (ν) are, respectively, 207 GPa and 0.30.
Physics
1 answer:
amm18123 years ago
3 0

Answer:

14778.29 N

Explanation:

Diameter, d=10.1mm= 10.1*10^{-3}m

Since stress, \sigma= \frac {F}{A} where F is force, A is area and since specimen is cylindrical,  

A= \pi *(d/2)^{2}  Therefore, \sigma= \frac {F}{\pi*(0.5d)^{2}}

Also strain \epsilon= \frac { \triangle L}{L} where L is length

Poison’s ratio,v is the ratio of lateral strain to longitudinal strain hence

V= -\frac {\epsilon_{x}}{\epsilon_{z}}= \frac {\triangle dl_{o}}{d \triangle l}

From Hooke’s law, \sigma=E \epsilon_{z}

Conclusively, E* \epsilon_{z}=E* \frac {- \epsilon_{x}}{v}=\frac {F}{\pi*(0.5d)^{2}}

\frac {4F}{ \pi *d^{2}}=- \frac {E \triangle d}{vd}

F=- \frac {\pi *Ed \triangle d}{4v}

F= - \frac {\pi *207*10^{9} *10.1*10^{-3}* (-2.7*10^{-6})}{4*0.3}= 14778.29N

Therefore, required force F is 14778.29 N

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2 years ago
There are many interesting applications of our energy density model to the flow of blood in the human circulatory system. One in
qaws [65]

Answer:

Pressure increases due to enlargement

Explanation:

Energy density is just a fancy name for pressure

Pressure is same at the bottom of the cups (same level-Pascal's law)

thus, Air pressure 1 + h1d1g = Air pressure 2 + h2d1g

= Air pressure 3 + (h2-h1)d2g +h1d1g

from the first 2, we get that since h2>h1, AP2<AP1

from the next 2, we get that since d2<d1, AP3>AP2

from first and third, we get that AP1>AP3

thus, finally AP1>AP3>AP2

for fluids flowing in tubes (blood vessel in this case)

P+0.5dv^2 + gh is constant (also called the bernoulli equation

for the same blood vessel, the heights remain same i.e h1=h2

for same flow rate, inc in area decreases the speed at which the blood flows as vA must remain same

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5 0
3 years ago
Read 2 more answers
The wavelength of a light wave is 700 nm in air; this light appears red. If this wave enters a pool of water, its wavelength bec
hodyreva [135]

Answer

given,

wavelength of light in air = 700 nm

Wavelength of light in water = 530 nm

We know that speed of light changes when it moves from one medium to another.

And the frequency of the wavelength does not changes if the medium changes.

we also know that,

                                    v = ν λ

From the above equation we can say that if frequency is constant so, with the change in  velocity changes wavelength will also change.

Hence, wavelength is the property of the wave which determines color.

6 0
3 years ago
A battery-operated car utilizes a 12.0 V system. Initially, the car is at rest at the base of a 195 m high hill. Some time later
ale4655 [162]

Answer:

140265.8 C = 1.403 × 10⁵ C

Explanation:

The battery's electric potential energy is used to account for the kinetic and potential work done in moving the car up this hill.

Potential work required to move the 757 kg car up a vertical height of 195 m = mgh

P.E = 757 × 9.8 × 195 = 1446627 J

Kinetic work done = (1/2)(m)(v²)

K.E = (1/2)(757)(25²) = 236562.5 J

Total work done in moving the car up that height = 1446627 + 236562.5 = 1683189.5 J

And this would be equal to the potential of the battery.

For the battery, potential difference = (electric potential energy)/(charges moved)

ΔV = ΔU/q

q = ΔU/ΔV

ΔU = 1683189.5 J

ΔV = 12.0 V

q = 1683189.5/12 = 140265.8 C

7 0
3 years ago
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A boxer punches a sheet of paper in mid air, and brings it from rest up to a speed of 25 m/s in 0.05 s. if the mass of the paper
zepelin [54]
Ok, so you've got to figure out a force F and you have the speed in which the boxer punches on determinate time and the mass of the sheet of paper.

So based on the formula that says that the Force is equal to the mass multiplied by the acceleration => F=ma.
You look at it and see that you only have mass which is measured on KG so there is no problem.
then you have the acceleration which is measured on meters and is defined by: a = Δv/Δt 
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⇒ a 25m/s / 0.05s 
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F=(0.005kg)(50)
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so the boxer will have a force of 0.25 Newton's.

6 0
3 years ago
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