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vekshin1
3 years ago
8

Learning Goal: To use fundamental geometric and statics methods to determine the state of plane stress at the point on an elemen

t of material that is rotated clockwise through an angle from the in-plane stress representation of the point on an element of material is shown. Let |σx| = 320 MPa , ∣∣σy∣∣ = 110 MPa , and ∣∣τxy∣∣ = 85.0 MPa . Use this information to represent the state of stress of the same point that is rotated through an angle of θ = 35.0 Part A - Normal and shear stress on element sectioned at plane a–a Using the element sectioned at plane a–a and the rotated coordinate system shown, determine the normal and shear stresses, σx′ and τx′y′, respectively, acting on plane a–a.Part B - Normal and shear stress on element sectioned at plane b–b Using the element sectioned at plane b–b and the rotated coordinate system shown, determine the normal and shear stresses acting on plane b–b.
Engineering
1 answer:
tiny-mole [99]3 years ago
5 0

Answer:

Please see the attached file for the Complete answer.

Explanation:

Download pdf
You might be interested in
(a)Compute the electrical conductivity of a cylindrical silicon specimen 7.0 mm (0.28 in.) diameter and 57 mm (2.25 in.) in leng
igor_vitrenko [27]

Answer:

a) \sigma = 12.2 (Ω-m)^{-1}

b) Resistance = 121.4 Ω

Explanation:

given data:

diameter is 7.0 mm

length 57 mm

current I = 0.25 A

voltage v = 24 v

distance between the probes is 45 mm

electrical conductivity is given as

\sigma = \frac{I l}{V \pi r^2}

\sigma  = \frac{0.25 \times 45\times 10^{-3}}{24 \pi [\frac{7 \times 10^{-3}}{2}]^2}

\sigma = 12.2(Ω-m)^{-1}[/tex]

b)

Resistance = \frac{l}{\sigma A}

                  = \frac{l}{ \sigma \pi r^2}

= \frac{57  \times 10^{-3}}{12.2 \times \pi [\frac{7 \times 10^{-3}}{2}]^2}

Resistance = 121.4 Ω

8 0
3 years ago
What is the impedance of a 5μF capacitor at a frequency of 500Hz? What is the impedance of a60mH inductor at this frequency?
choli [55]

Answer:

1) 63.66 ohm

2) 188.49 ohm

Explanation:

Data provided in the question:

Part 1

Capacitance, C = 5μF = 5 × 10⁻⁶ F

Frequency = 500 Hz

Now,

Impedance = \frac{1}{2\times\pi\times f\times C}

or

Impedance = \frac{1}{2\times\pi\times500\times5\times10^{-6}}

or

Impedance = 63.66 ohm

Part 2

Inductance = 60 mH = 60 × 10⁻³ H

Frequency = 500 Hz

Now,

Impedance for an inductor = 2πfL

thus,

Impedance = 2 × π × 500 × 60 × 10⁻³

= 188.49 ohm

4 0
3 years ago
What is the De Broglie wavelength of an electron under 150 V acceleration?
yanalaym [24]

Answer:

0.1 nm

Explanation

Potential deference of the electron is given as V =150 V

Mass of electron m=9.1\times 10^{-31}

Let the velocity of electron = v

Charge on the electron =1.6\times 10^{-19}C

plank's constant h =6.67\times 10^{-34}

According to energy conservation eV =\frac{1}{2}mv^2

v=\sqrt{\frac{2eV}{M}}=\sqrt{\frac{2\times 1.6\times 10^{-19}\times 150}{9.1\times 10^{-31}}}=7.2627\times 10^{-6}m/sec

Now we know that De Broglie wavelength \lambda =\frac{h}{mv}=\frac{6.67\times 10^{-34}}{9.1\times 10^{-31}\times 7.2627\times10^6 }=0.100\times 10^{-9}m=0.1nm

4 0
3 years ago
Read 2 more answers
Find an expectation value in the n th state of the harmonic oscillator.Find an expectation value in the n th state of the harmon
s344n2d4d5 [400]

The classical motion for an oscillator that starts from rest at location x₀ is

                                           x(t) = x₀ cos(ωt)

The probability that the particle is at a particular x at a particular time t

is given by ρ(x, t) = δ(x − x(t)), and we can perform the temporal average

to get the spatial density. Our natural time scale for the averaging is a half

cycle, take t = 0 → π/ ω

Thus,

ρ =   \frac{1}{\pi / w} \int\limits^\pi_0 {d(x - x_o cos(wt))} \, dt

Limit is 0 to π/ω

We perform the change of variables to allow access to the δ, let y = x₀ cos(ωt)  so that

ρ(x) = -\frac{w}{\pi } \int\limits^x_x {\frac{d ( x - y)}{x_ow sin(wt)} } \, dy

Limit is x₀ to -x₀

\frac{1}{\pi } \int\limits^x_x {\frac{d (x-y)}{x_o\sqrt{1 - cos^2(wt)} } } \, dy

Limit is -x₀ to x₀

= \frac{1}{\pi } \int\limits^x_x {\frac{d(x-y)}{\sqrt{x_o^2 - y^2} } } \, dy\\ \\= \frac{1}{\pi\sqrt{x_o^2 - x^2}  }

This has \int\limits^x_x {p(x)} \, dx  = 1 as expected. Here the limit is -x₀ to x₀

The expectation value is 0 when the ρ(x) is symmetric, x ρ(x) is asymmetric and the limits of integration are asymmetric.

6 0
4 years ago
Refrigerant R-12 is used in a Carnot refrigerator
Sphinxa [80]

Answer:

Heat transferred from  the refrigerated space = 95.93 kJ/kg

Work required = 18.45 kJ/kg

Coefficient  of performance = 3.61

Quality at the beginning of the heat  addition cycle = 0.37

Explanation:

From figure  

Q_H is heat rejection process

Q_L is heat transferred from the refrigerated space

T_H is high temperature = 50 °C + 273 = 323 K

T_L is low temperature = -20 °C + 273 = 253 K  

W_{net} is net work of the cycle (the difference between compressor's work and turbine's work)

 

Coefficient of performance of a Carnot refrigerator (COP_{ref}) is calculated as

COP_{ref} = \frac{T_L}{T_H - T_L}

COP_{ref} = \frac{253 K}{323 K - 253 K}

COP_{ref} = 3.61

From figure it can be seen that heat rejection is latent heat of vaporisation of R-12 at 50 °C. From table

Q_H = 122.5 kJ/kg

From coefficient of performance definition

COP_{ref} = \frac{Q_L}{Q_H - Q_L}

Q_H \times COP_{ref} = (COP_{ref} + 1) \times Q_L

Q_L = \frac{Q_H \times COP_{ref}}{(COP_{ref} + 1)}

Q_L = \frac{122.5 kJ/kg \times 3.61}{(3.61 + 1)}

Q_L = 95.93 kJ/kg

Energy balance gives

W_{net} = Q_H - Q_L

W_{net} = 122.5 kJ/kg - 95.93 kJ/kg

W_{net} = 26.57 kJ/kg

Vapor quality at the beginning of the heat addition cycle is calculated as (f and g refer to saturated liquid and saturated gas respectively)

x = \frac{s_1 - s_f}{s_g - s_f}

From figure

s_1 = s_4 = 1.165 kJ/(K kg)

Replacing with table values

x = \frac{1.165 kJ/(K \, kg) - 0.9305 kJ/(K \, kg)}{1.571 kJ/(K \, kg) - 0.9305 kJ/(K \, kg)}

x = 0.37

Quality can be computed by other properties, for example, specific enthalpy. Rearrenging quality equation we get

h_1 = h_f + x \times (h_g - h_f)

h_1 = 181.6 kJ/kg + 0.37 \times 162.1 kJ/kg

h_1 = 241.58 kJ/kg

By energy balance, W_{t} turbine's work is

W_{t} = |h_1 - h_4|

W_{t} = |241.58 kJ/kg - 249.7 kJ/kg|

W_{t} = 8.12 kJ/kg

Finally, W_{c} compressor's work is

W_{c} = W_{net} + W_{t}

W_{c} = 26.57 kJ/kg + 8.12 kJ/kg

W_{c} = 34.69 kJ/kg

6 0
3 years ago
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