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xz_007 [3.2K]
3 years ago
13

The small washer is sliding down the cord OA. When it is at the midpoint, its speed is 28 m/s and its acceleration is 7 m/s 2 .

Express the velocity and acceleration of the washer at this point in terms of its cylindrical components.

Engineering
1 answer:
Neporo4naja [7]3 years ago
3 0

Answer:

Velocity components

V_r = -16.28 m/s

V_z = -22.8 m/s

V_q = 0 m/s

For Acceleration components;

a_r = -4.07m/s^2

a_z = -5.70m/s^2

a_q = 0m/s^2

Explanation:

We are given:

Speed v_o = 28 m/s

Acceleration a_o= 7 m/s^2

We first need to find the radial position r of washer in x-y plane.

Therefore

r = \sqrt{300^2 + 400^2}

r = 500 mm

To find length along direction OA we have:

L = \sqrt{500^2 + 700^2}L = 860 mm

Therefore, the radial and vertical components of velocity will be given as:

V_r = V_o*cos(Q)

V_z = V_o*sin(Q)

Where Q is the angle between OA and vector r.

Therefore,

V_r = 28 * \frac{r}{L} = > 28 * \frac{500}{860}

V_r = -16.28 m/s

• V_z = 28 * \frac{700}{860} = -22.8

• V_q = 0 m/s

The radial and vertical components of acceleration will be:

a_r = a_o*cos(Q)

a_z = a_o*sin(Q)

Therefore we have:

• a_r = 7* \frac{500}{860} = -4.07m/s^2

• a_z = 7 * \frac{700}{860} = -5.70 m/s^2

• a_q = 0 m/s^2

Note : image is missing, so I attached it

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A thick steel slab (rho= 7800 kg/m3 , cp= 480 J/kg K, k= 50 W/m K) is initially at 300 °C and is cooled by water jets impinging
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Answer:

t = 2244.3 sec

Explanation:

calculate the thermal diffusivity

\alpha = \frac{k}{\rho c}

           = \frac{50}{7800\times 480} = 1.34 \times 10^{-5} m^2/s

                   

Temperature at 28 mm distance after t time  = =  50 degree C

we know that

\frac[ T_{28} - T_s}{T_i -T_s} = erf(\frac{x}{2\sqrt{at}})

\frac{ 50 -25}{300-25} = erf [\frac{28\times 10^{-3}}{2\sqrt{1.34\times 10^{-5}\times t}}]

0.909 = erf{\frac{3.8245}{\sqrt{t}}}

from gaussian error function table , similarity variable w calculated as

erf w = 0.909

it is lie between erf w = 0.9008  and erf w = 0.11246 so by interpolation we have

w = 0.08073

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0.08073 = \frac{3.8245}{\sqrt{t}}

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Rsidential Solar Solution:a. A type of photovoltaic solar panel manufactured in China receives a rating of 250W. The rating proc
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Answer:

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Explanation:

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A = (20\,ft^{2})\cdot (\frac{0.3048\,m}{1\,ft} )^{2}

A = 1.858\,m^{2}

The energy potential is determined herein:

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The efficiency of the solar panel is:

\eta = \frac{\dot E}{\dot E_{o}}\times 100\%

\eta = \frac{250\,W}{1858\,W}\times 100\%

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b) The energy generated by the solar panel is presented below:

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C_{month, total} = 18\cdot E_{month}\cdot c

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t = \frac{9500\,USD}{12\cdot (19.505\,USD)}

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