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Natalka [10]
3 years ago
9

Prove that hoop stress is twice the longitudinal stress in a cylindrical pressure vessel.

Physics
1 answer:
Iteru [2.4K]3 years ago
6 0

Answer:

Proof in explanation.

Explanation:

Consider a thin cylinder, whose thickness to diameter ration is less than 1/20, the hoop stress can be derived as follows:

Let,

L = length of cylinder

d = internal diameter of cylinder

t = thickness of wall of cylinder

P = internal pressure

σH = Hoop Stress

σL = Longitudinal Stress

Total force on half-cylinder owing to internal pressure = P x  Projected Area = P x dL    (Refer fig 9.1)

Total resisting force owing to hoop stress setup in walls = 2 σH L t

Therefore,

P d L = 2 σH L t

σH = Pd/2t      _____________ eqn (1)

Now, for longitudinal stress:

Total force on end of cylinder owing to internal pressure = P x  Projected Area = P x πd²/4

Area resisting this force = π d t        (Refer fig 9.2)

Longitudinal Stress = Force/Area

σL = (Pπd²/4)/(πdt)

σL = Pd/4t        ____________ eqn (2)

Dividing eqn (1) by eqn (2)

σH/σL = 2

<u>σH = 2 σL</u>      (Hence, Proved)

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jeka94

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we can manipulate

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  • he traffic light change time
  • Change some condition of the pavement after the first vehicle passes

Autonomous systems are systems that take a series of signals from the outside, analyze them and carry out actions according to how to handle them.

In that case you have two cars one behind the other at a short distance a traffic light with a yellow light is approaching.

Some parameters can be modified to cause the crash:

  • The car in front accelerates to pass the traffic light, but the traffic light changed to red, in this case if the car behind also accelerated, there may not be enough distance to stop and crash.

  • You can change the traffic light to green whereby the first car continues its speed, but the traffic light time changes very quickly to red, whereby the first car stops, but the car behind cannot stop.

  • The car behind accelerates to also pass the yellow light, but turns red and the first one crashes to a stop.

  • We change some condition of the pavement after the first vehicle passes, for example wetting the pavement, which decreases the coefficient of friction, consequently the second vehicle does not have time to stop.

We can appreciate that if there is not a good and fast communication between the two vehicles, it is easy for them to crash.

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  • The second vehicle increases speed and the first must brake sharply

Learn more about stopping distance here:

brainly.com/question/24254597

6 0
2 years ago
A proton moves perpendicular to a uniform magnetic field B at a speed of 2.30 107 m/s and experiences an acceleration of 2.50 10
Katen [24]

Answer:

B = 6.18 10⁻⁶ T  

the magnetic field is in the negative direction of the y axis

Explanation:

The magnetic force is given by

         F = q v x B

as in the exercise indicate that the velocities perpendicular to the magnetic field,

         F = q v B

Newton's second law is

         F = m a

let's substitute

         q v B = m a

         B = m a / q v

let's calculate

         B = 9.1 10⁻³¹ 2.50 10¹³ / (1.6 10⁻¹⁹ 2.30 10⁷)

         B = 6.18 10⁻⁶ T

The direction of the field can be obtained with the right hand rule, where the thumb points in the direction of the velocity, the fingers extended in the direction of the magnetic field and the palm in the direction of the force for a positive charge.

In the exercise indicate that the velocity is the z axis

the acceleration and therefore the force in the x axis

therefore the magnetic field is in the negative direction of the y axis

7 0
3 years ago
A 37-cm-long wire of linear density 18 g/m vibrating at its second mode, excites the third vibrational mode of a tube of length
lora16 [44]

Answer:

T = 4.42 10⁴ N

Explanation:

this is a problem of standing waves, let's start with the open tube, to calculate the wavelength

        λ = 4L / n                 n = 1, 3, 5, ...    (2n-1)

How the third resonance is excited

       m = 3

       L = 192 cm = 1.92 m

       λ = 4 1.92 / 3

       λ = 2.56 m

As in the resonant processes, the frequency is maintained until you look for the frequency in this tube, with the speed ratio

      v = λ f

      f = v / λ

      f = 343 / 2.56

      f = 133.98 Hz

       

Now he works with the rope, which oscillates in its second mode m = 2 and has a length of L = 37 cm = 0.37 m

The expression for standing waves on a string is

           λ = 2L / n

           λ = 2 0.37 / 2

           λ = 0.37 m

The speed of the wave is

          v = λ f

As we have some resonance processes between the string and the tube the frequency is the same

          v = 0.37 133.98

          v = 49.57 m / s

Let's use the relationship of the speed of the wave with the properties of the string

              v = √ T /μ

              T = v² μ

              T = 49.57²   18

              T = 4.42 10⁴ N

4 0
3 years ago
Read 2 more answers
Energy conservation
balandron [24]

Answer:

7.328m/s

Explanation:

Given parameters:

height of table = 0.68m

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Unknown:

Initial velocity of ball = ?

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We must understand that this fall occurs in the presence of gravity;

            V = U + 2gH

Where;

 V is the final velocity

 U is the initial velocity

 g is the acceleration due to gravity

 H is the height of the pool table

    Since U is the unknown, let us make it the subject of the expression;

           U = V - 2gH

        U = 6 - (2 x 9.8 x 0.68)  = 7.328m/s(deceleration)

7 0
3 years ago
A sound wave, with speed of 340 m/s has a frequency of 17,000 Hz. What
Fiesta28 [93]
Wavelength = speed / frequency = 340 / 17000 = 0.02 m
6 0
3 years ago
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