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yanalaym [24]
3 years ago
11

A rectangular region ABCD is to be built inside a semicircle of radius 10 m with points A and B on the line for the diameter and

points C and D on the semicircle with CD parallel to AB. The objective is to find the height h * that maximizes the area of ABCD.
Formulate the optimization problem.
Engineering
1 answer:
Talja [164]3 years ago
7 0

Answer:A rectangular region ABCD is to be built inside a semicircle of radius 10 m with points A and B on the line for the diameter and points C and D on the semicircle with CD parallel to AB. The objective is to find the height h * that maximizes the area of ABCD.

Formulate the optimization problem.

Explanation:A rectangular region ABCD is to be built inside a semicircle of radius 10 m with points A and B on the line for the diameter and points C and D on the semicircle with CD parallel to AB. The objective is to find the height h * that maximizes the area of ABCD.

Formulate the optimization problem.

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The 10 foot wide circle quarter gate AB is articulated at A. Determine the contact force between the gate and the smooth surface
slamgirl [31]

Answer:

F = 641,771.52 \dfrac{lb-ft}{s^2}

Explanation:

Given that

R=8 ft

Width= 10 ft

We know that hydro statics force given as

  F=ρ g A X

ρ is the density of fluid

A projected area on vertical plane

X is distance of center mass of projected plane from free surface of water.

Here

X=8/2  ⇒X=4 ft

A=8 x 10=80  ft^2

So now putting the values

F=ρ g A X

F=62.4(32.14)(80)(4)

F = 641,771.52 \dfrac{lb-ft}{s^2}

   

4 0
3 years ago
The basic barometer can be used to measure the height of a building. If the barometric readings at the top and at the bottom of
bixtya [17]

Answer:

h = 287.1 m

Explanation:

the density of mercury \rho =13570 kg/m3

the atmospheric pressure at the top of the building is

p_t = \rho gh  = 13570*908*0.73 = 97.08 kPa

the atmospheric pressure at bottom

p_b = \rho gh  = 13570*908*0.75 = 100.4 kPa

\frac{w_{air}}{A} =p_b -p_t

we have also

(\rho gh)_{air} = p_b - p_t

1.18*9.81*h = (100.4 -97.08)*10^3

h = 287.1 m

7 0
3 years ago
When replacing a timing belt, many experts and vehicle manufacturers recommend that all of the following should be replaced exce
lora16 [44]

Answer:

Correct Answer:

A. water pump

Explanation:

<em>Timing belt in a vehicle helps to ensure that crankshaft, pistons and valves operate together in proper sequence.</em> Timing belts are lighter, quieter and more efficient than chains that was previously used in vehicles.

<em>Most car manufacturers recommended that, when replacing timing belt, tension assembly, water pump, camshaft oil seal should also be replaced with it at same time. </em>

7 0
3 years ago
What is the metal removal rate when a 2 in-diameter hole 3.5 in deep is drilled in 1020 steel at cutting speed of 120 fpm with a
Studentka2010 [4]

Answer:

a) the metal removal rate is 14.4 in³/min

b) the cutting time is 0.98 min

Explanation:

Given the data from the question

first we find the rpm for the spindle of the drilling tool, using the equation

Ns = 12V/πD

V is the cutting speed(120 fpm) and D is the diameter of the hole( 2 in)

so we substitute

Ns = 12 × 120 / π2

Ns = 1440 / 6.2831

Ns = 229.18 rmp

Now we find the metal removal rate using the equation

MRR = (πD²/4) Fr × Ns

Fr is the feed rate( 0.02 ipr ),

so we substitute

MRR = ((π × 2²)/4) × 0.02 × 229.18

MRR = 14.3998 ≈ 14.4 in³/min

Therefore the metal removal rate is 14.4 in³/min

Next we find the allowance for approach of the tip of the drill

A = D/2

A = 2/2

= 1 in

now find the time required to drill the hole

Tm = (L + A) / (Fr × Ns)

Lis the the depth of the hole( 3.5 in)

so we substitute our values

Tm = (3.5 + 1) / (0.02 × 229.18  )

Tm = 4.5 / 4.5836

Tm = 0.98 min

Therefore the cutting time is 0.98 min

8 0
2 years ago
Determine the nature of the following cycle (reversible, irreversible, or impossible): a refrigeration cycle draws heat from a c
vlabodo [156]

Answer:

Impossible.

Explanation:

The ideal Coefficient of Performance is:

COP_{i} = \frac{250\,K}{300\,K-250\,K}

COP_{i} = 5

The real Coefficient of Performance is:

COP_{r} = \frac{950\,kJ-70\,kJ}{70\,kJ}

COP_{r} = 12.571

Which leads to an absurds, since the real Coefficient of Performance must be equal to or lesser than ideal Coefficient of Performance. Then, the cycle is impossible, since it violates the Second Law of Thermodynamics.

6 0
3 years ago
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