Answer:
acceleration=change in velocity/ time
Explanation:
The velocity of an object is its speed in a particular direction. Velocity is a vector quantity because it has both a magnitude and an associated direction. To calculate velocity, displacement is used in calculations, rather than distance.
A rectangular block of 1m by 0.6m by 0.4m floats in water with 1/5th of its volume being out of water. Find the weight of the block.
Answer:
Weight of block is 191.424 Kg
Explanation:
The volume of rectangular block = [tex]1*0.6*0.4 = 0.24[/tex] cubic meter
1/5th of its volume being out of water which means water of volume nearly 4/5 th of the volume of rectangular block is replaced
Volume of replaced water = [tex]\frac{4}{5} * 0.24 = 0.192[/tex] cubic meter
Weight of replaced water = weight of rectangular block = [tex]0.192 * 997[/tex] Kg/M3
= 191.424 Kg
A noisy transmission channel has a per-digit error probability p = 0.01.
(a) Calculate the probability of more than one error in 10 received digits?
Answer:
The appropriate answer is "0.0043".
Explanation:
The given values is:
Error probability,
p = 0.01
Received digits,
n = 10
and,
[tex]x\sim Binomial[/tex]
As we know,
⇒ [tex]P(x)=\binom{n}{x}p^xq^{n-x}[/tex]
Now,
⇒ [tex]P(x >1) =1- \left \{ P(x=0)+P(x=1) \right \}[/tex]
⇒ [tex]=1-\left \{\binom{10}{0}(0.01)^0(0.99)^{10-0}+\binom{10}{0}(0.01)^1(0.99)^{10-1} \right \}[/tex]
⇒ [tex]=1-0.9957[/tex]
⇒ [tex]=0.0043[/tex]
a tensile specimen with a 12mm initial diameter and 50mm gage length reaches maximum load at 90KN and fractures at 70KN
the minimum diameter at fracture is 10mm
determine the engineering stress at maximum load and the true fracture stress.
Answer:
i) 796.18 N/mm^2
ii) 1111.11 N/mm^2
Explanation:
Initial diameter ( D ) = 12 mm
Gage Length = 50 mm
maximum load ( P ) = 90 KN
Fractures at = 70 KN
minimum diameter at fracture = 10mm
Calculate the engineering stress at Maximum load and the True fracture stress
i) Engineering stress at maximum load = P/ A
= P / [tex]\pi \frac{D^2}{4}[/tex] = 90 * 10^3 / ( 3.14 * 12^2 ) / 4
= 90,000 / 113.04 = 796.18 N/mm^2
ii) True Fracture stress = P/A
= 90 * 10^3 / ( 3.24 * 10^2) / 4
= 90000 / 81 = 1111.11 N/mm^2
5. The pin support at A allows _______. Select the one that applies. (a) displacement in the x direction (b) rotation about its central axis (c) displacement in the y direction (d) none of the above 6. The support at B does not allow _______. Select the one that applies. (a) displacement in the x direction (b) rotation about its central axis (c) displacement in the y direction
Answer: Diagram associated with your question is attached below
5) B
6) C
Explanation:
5) The pin support at A allows ; Rotation about its central axis
This is because pin supports does not allow the translation of its structural member in any direction i.e. y or x but only rotation about its axis
6) The support at B does not allow displacement in y direction
This is because roller support allows displacement only in the direction that they are situated and in this case it is the x - direction
In a parking garage, each level is 18 feet apart, Each ramp to a level is 120 feet long. Find the measurement of elevation for each ramp?
Answer:
Sin(angle)=0.1538
Angle=arcsine(0.1538)
Angle is 8.85 degrees
Explanation:
Firstly draw a diagram showing a triangle with the required angle, a hypotenuse of 130 ft and an opposite side of 20 ft.
The sine of the angle required uses the formula Opposite/Hypotenuse
(i am not sure sure)
How will the proposed study contribute to your career?*
(quantity Surveying
Answer:
PROPOSED STUDY CONTRIBUTES TO YOUR CAREER. Proposed study is essential for career growth. It contributes to our career in a great way. It enhances leadership skills and polish our skills making us more competent. It expand our horizons and opportunities. It gives us better understanding of things. We become able of developing professional relationships with our students as well as development sector which helps in future projects.
Hope this help!:)
Some project managers prefer the PERT chart over the Gantt chart because it clearly illustrates task dependencies. A PERT chart, however, can be much more difficult to interpret, especially on complex projects. Alternatively, some project managers may choose to use both techniques. If you are the project manager of a residential construction project, will you prefer PERT chart to Gantt chart? Explain why?
Answer:
PERT Chart and GANTT Chart
As the project manager of a residential construction project, I will prefer the PERT chart to the GANTT chart because a PERT chart displays task dependencies unlike a Gantt chart. With the PERT chart, the sequence of tasks is clearly mapped out. Dependent tasks are carried out when other tasks that they depend on have been executed.
Explanation:
By definition, a Gantt chart is like a bar chart that lays out project tasks and timelines using bars. On the other hand, a PERT chart follows a structure in the form of flow charts or network diagrams. It displays all the project tasks in separate boxes. The boxes are then connected with arrows which clearly show the task dependencies.
In the production of soybean oil, dried and flaked soybeans are brought in contact with a solvent (often hexane) that extracts the oil and leaves behind the residual solids and a small amount of oil.
a. Draw flow diagram of the process, labeling the two feed streams (beans and solvent) and the leaving streams (solids and extract).
b. The soybeans contain 18.5 wt% oil and the remainder insoluble solids, and the hexane is fed at a rate corresponding to 2.0 kg hexane per kg beans. The residual solids leaving the extraction unit contain 35.0 wt% hexane, all of the non-oil solids that entered with beans, and 1.0% of the oil that entered the beans. For a feed rate of 1000 kg/h of dried flaked soybeans, calculate mass flow rates of extract and residual solids and the composition of extract.
Answer: its c
Explanation:
Which of these parts reduces the amount of pollutants in the engine exhaust?
A. Transmission
B. Catalytic converter
C. Tailpipe
D. Muffler
Answer:
Option B
Explanation:
Catalytic convertor with in the exhaust pipes of any vehicle converts harmful gases (such as hydrocarbons (HC), carbon monoxide (CO) and nitrogen oxides (NOx)) produced by combustion of fossil fuels (petrol, diesel etc.) into less harmful/toxic pollutants by acting as a catalyst for redox reaction. A catalytic convertor releases some mild gases from the exhaust like less harmful CO2, nitrogen and water vapour (steam)
Hence, option B is correct
You are performing a machining operation that approximates orthogonal cutting. Given that the chip thickness prior to chip formation is 0.5 inches and the chip thickness after separation is 1.125 inches, calculate the shear plane angle and shear strain. Use a rake angle of 10 degrees. 21. Suppose in the prior problem that the cutting force and thrust force were measured as 1559 N and 1271 N, respectively. The width of the cut is 3.0mm. Using this new information, calculate the shear strength of the material.
Answer:
A)
shear plane angle = 31.98°
shear strain = cot ( 31.98° ) + tan ( 31.98 - 10 )
B) shear strength = 7339.78
Explanation:
a) Determine the shear plane angle and shear strain
Given data :
Chip thickness before chip formation = 0.5 inches
Chip thickness after separation = 1.125 inches
rake angle ( ∝ ) = 10°
shear plane angle : Tan ∅ = [tex]\frac{rcos\alpha }{1-sin\alpha }[/tex] ----- ( 1 )
r = chip thickness ratio = 0.5 / 1.125 = 0.4444
back to equation 1 : Tan ∅ = ( 0.444 ) * cos 10 / 1 - sin 10
Tan ∅ = 0.4444 * 0.9848 / 1 - 0.1736 = 0.5296
hence ∅ = tan^-1 ( 0.5296 ) = 31.98°
shear strain : R = cot ∅ + tan ( ∅ - ∝ ) ---------- ( 1 )
R = cot ( 31.98° ) + tan ( 31.98 - 10 )
B) determine the shear strength of the material
cutting force = 1559 N
thrust force = 1271 N
width of cut ( diameter ) = 3.0 mm
shear strength = c + σ.tan ∅
c = cohesion force = 1271 * 3 = 3813
σ = normal stress = F / A = 1559 / π/4 * ( 0.5 )^2 = 1559 / 0.1963 = 7941.94
hence : shear strength of material = 3813 + 7941.94 * 0.6244 = 7339.78
Design a counter that counts the following sequence of 2-0-1-3 and repeat.
Answer:
Hello your question is incomplete below is the complete question
Design a counter that counts the following sequence of 2-0-1-3 and repeat. Use the JK flip-flops given to you at the start of the semester. These values will be displayed on a seven-segment display like the one used in Lab 3
answer : attached below
Explanation:
Designing a counter that counts in a given sequence can be done using Logic gates that will be used to control the counter. we will design the counter using the 7 segment display
Note : The first Image is the segment display and the second image is the design of the counter
In warm climates, a vapor barrier is placed on the exterior side of the insulation, and in cold climates it is installed on the interior side of the
insulation. Which of the following explains this placement of the barrier?
The barrier should always be placed on the side opposite from where the water condenses.
The barrier should always be placed on the side opposite where rain or snow hit.
The barrier should always be placed on the side where rain or snow hit.
The barrier should always be placed on the side where the water condenses
Answer: its c
Explanation:
How may the desire for a perfect lawn be related to environmental pollution? A. Lawns have little to do with environmental pollution. B. Perfect lawns require excess use of manual labor. C. Manicured lawns are subject to increased runoff. D. Lawns absorb pesticides and fertilizers and these chemicals leach out of the lawn and run into creeks, streams and eventually, rivers, with rain or watering, eventually reaching the ocean.
Answer: is b
Explanation:
Which of the following combinations of bends can be used in a conduit run?
A. One 90-degree, three 45-degree, and four 30-degree
B. TWO 90-degree, two 45-degree, and four 30-degree
C. Two 90-degree, four 45-degree, and one 30-degree
D. One 90-degree, six 45-degree, and one 30-degree
Answer:
Answer is A
Explanation:
Doesn't break 360 degrees of bend.
The bend that can be used in conduit run is one 90-degree, three 45-degree, and four 30-degree.
Bend that can be used in conduit run is equal or less than 360 degree.
One 90-degree, three 45-degree, and four 30-degree, the total sum is 345 degree.Two 90-degree, two 45-degree, and four 30-degree, the total sum is 390 degree.Two 90-degree, four 45-degree, and one 30-degree, the total sum is 390 degree.One 90-degree, six 45-degree, and one 30-degree, the total sum is 390 degree.So, One 90-degree, three 45-degree, and four 30-degree is the bend that can be used in conduit run.
Learn more: brainly.com/question/21199524
In the context of mechanical systems, what does the term efficiency mean? OA the factor by which a machine multiplies a force B. the ratio of a machine's power to the force of its input Ос. the rate at which a machine performs work D. the rate at which a machine consumes energy E. the ratio of the work output of a machine to the work input
Answer:
E
Explanation:
I have a big brain and I just took the test and got it correct.
The evaporator:
A. directs airflow to the condenser.
B. absorbs heat from the passenger compartment.
C. removes moisture from the refrigerant.
D. restricts refrigerant flow.
Answer:
Option B
Explanation:
An evaporator along with cold low pressure refrigerant absorbs heat from the air within the passenger compartment thereby supplying cool air for the occupants.
Hence, option B is correct
what is the answer to life the universe and everything
(worth 95 points!)
Answer:
In the absence of dark energy, a flat universe expands forever but at a continually decelerating rate, with expansion asymptotically approaching zero; with dark energy, the expansion rate of the universe initially slows down, due to the effects of gravity, but eventually increases, and the ultimate fate of the universe ...
Explanation:
I think it goes on forever.
Barries of effective
communication?
Answer: barries
Explanation:
Which option identifies the step of the implementation phase represented in the following scenario?
A company in the gaming industry decides to integrate movement controls in its newest hardware release. It sends an online survey to interactive gamers to identify their highest priorities.
establishing a process and budget
using communication tools
building and assembling a team
setting up a change order process
Answer:
Which option identifies the step of the implementation phase represented in the following scenario?
A company in the gaming industry decides to integrate movement controls in its newest hardware release. It sends an online survey to interactive gamers to identify their highest priorities.
establishing a process and budget
using communication tools
building and assembling a team
setting up a change order process
Explanation:
#carryonml
Answer:
using communication tools
Explanation:
The correct answer is using communication tools. Communication tools such as online surveys help project teams identify customers’ wants and needs.
If it is struck by a rigid block having a weight of 550 lblb and traveling at 2 ft/sft/s , determine the maximum stress in the cylinder. Neglect the mass of the cylinder. Express your answer to three significant figures and include appropriate units.
This question is incomplete, The missing image is uploaded along this answer below;
Answer:
the maximum stress in the cylinder is 3.23 ksi
Explanation:
Given the data in the question and the diagram below;
First we determine the initial Kinetic Energy;
T = [tex]\frac{1}{2}[/tex]mv²
we substitute
⇒ T = [tex]\frac{1}{2}[/tex] × (550/32.2) × (2)²
T = 34.16149 lb.ft
T = ( 34.16149 × 12 ) lb.in
T = 409.93788 lb.in
Now, the volume will be;
V = [tex]\frac{\pi }{4}[/tex]d²L
from the diagram; d = 0.5 ft and L = 1.5 ft
so we substitute
V = [tex]\frac{\pi }{4}[/tex] × ( 0.5 × 12 in )² × ( 1.5 × 12 in )
V = 508.938 in³
So by conservation of energy;
Initial energy per unit volume = Strain energy per volume
⇒ T/V = σ²/2E
from the image; E = 6.48(10⁶) kip
so we substitute
⇒ 409.93788 / 508.938 = σ²/2[6.48(10⁶)]
508.938σ² = 5,312,794,924.8
σ² = 10,438,982.5967
σ = √10,438,982.5967
σ = 3230.9414
σ = 3.2309 ksi ≈ 3.23 ksi { three significant figures }
Therefore, the maximum stress in the cylinder is 3.23 ksi
A tiger cub has a pattern of stripes on it for that is similar to that of his parents where are the instructions stored that provide information for a tigers for a pattern
probably in it's chromosomes
A cylindrical metal specimen having an original diameter of 10.33 mm and gauge length of 52.8 mm is pulled in tension until fracture occurs. The diameter at the point of fracture is 6.38 mm, and the fractured gauge length is 73.9 mm. Calculate the ductility in terms of (a) percent reduction in area (percent RA), and (b) percent elongation (percent EL).
Answer
a) 62 percent
b) 40 percent
Explanation:
Original diameter ( d[tex]_{i}[/tex] ) = 10.33 mm
Original Gauge length ( L[tex]_{i}[/tex] ) = 52.8 mm
diameter at point of fracture ( d[tex]_{f}[/tex] ) = 6.38 mm
New gauge length ( L[tex]_{f}[/tex] ) = 73.9 mm
Calculate ductility in terms of
a) percent reduction in area
percentage reduction = [ (A[tex]_{i}[/tex] - A[tex]_{f}[/tex] ) / A[tex]_{i}[/tex] ] * 100
A[tex]_{i}[/tex] ( initial area ) = π /4 di^2
= π /4 * ( 10.33 )^2 = 83.81 mm^2
A[tex]_{f}[/tex] ( final area ) = π /4 df^2
= π /4 ( 6.38)^2 = 31.97 mm^2
hence : %reduction = ( 83.81 - 31.97 ) / 83.81
= 0.62 = 62 percent
b ) percent elongation
percentage elongation = ( L[tex]_{f}[/tex] - L[tex]_{i}[/tex] ) / L[tex]_{i}[/tex]
= ( 73.9 - 52.8 ) / 52.8 = 0.40 = 40 percent
A 10 cm thick slab (density 8530 kg/m3 , specific heat 380J/kg K, conductivity 110 W/m K) initially at 650C is being cooled by air at 15C (convection coefficient 220 W/m2 K) at left surface. The right surface is insulated. We want to estimate temperature in the slab. a. What will be the temperature of the slab after a very long time
Answer:
The temperature after a long time will return to 15°C
Explanation:
Determine the temperature of the slab after a very long time
First we calculate the heat flow for m^2 area normal to the surface
= q / A = 650°c - 15°C / ( 1 / h + L / K )
= 635°c / ( 1 / 220 + 0.1 / 110 ) = 116.416 kw/m^2
Total heat content in the slab is calculated as
= m* c * ΔT
= 8530 * A * 0.1 * 380 * ( 650 - 15 )
= 205828.9 kJ/m^2
The temperature will return to 15°C after a long time
Refrigerant 134a enters the evaporator of a refrigeration system operating at steady state at -16oC and a quality of 20% at a velocity of 5 m/s. At the exit, the refrigerant is a saturated vapor at -16oC. The evaporator flow channel has constant diameter of 1.7 cm. Determine the mass flow rate of the refrigerant, in kg/s, and the velocity at the exit, in m/s.
Answer:
mass flow rate = 0.0534 kg/sec
velocity at exit = 29.34 m/sec
Explanation:
From the information given:
Inlet:
Temperature [tex]T_1 = -16^0\ C[/tex]
Quality [tex]x_1 = 0.2[/tex]
Outlet:
Temperature [tex]T_2 = -16^0 C[/tex]
Quality [tex]x_2 = 1[/tex]
The following data were obtained at saturation properties of R134a at the temperature of -16° C
[tex]v_f= 0.7428 \times 10^{-3} \ m^3/kg \\ \\ v_g = 0.1247 \ m^3 /kg[/tex]
[tex]v_1 = v_f + x_1 ( vg - ( v_f)) \\ \\ v_1 = 0.7428 \times 10^{-3} + 0.2 (0.1247 -(0.7428 \times 10^{-3})) \\ \\ v_1 = 0.0255 \ m^3/kg \\ \\ \\ v_2 = v_g = 0.1247 \ m^3/kg[/tex]
[tex]m = \rho_1A_1v_1 = \rho_2A_2v_2 \\ \\ m = \dfrac{1}{0.0255} \times \dfrac{\pi}{4}\times (1.7 \times 10^{-2})^2\times 6 \\ \\ \mathbf{m = 0.0534 \ kg/sec}[/tex]
[tex]\rho_1A_1v_1 = \rho_2A_2v_2 \\ \\ A_1 =A_2 \\ \\ \rho_1v_1 = \rho_2v_2 \\ \\ \implies \dfrac{1}{0.0255} \times6 = \dfrac{1}{0.1247}\times (v_2)\\ \\ \\\mathbf{\\ v_2 = 29.34 \ m/sec}[/tex]
An asphalt binder is mixed with aggregate and compacted into a sample. The mass of the dry sample is 1173.5 g, the mass of the sample submerged and then surface-dried with a damp towel is 1175.5 g, and the mass of the sample completely submerged in water is 652.5 g. Find the bulk specific gravity of the compacted sample.
Answer:
[tex]\mathbf{G_m = 2.25}[/tex]
Explanation:
From the given information:
Let the weight of the mix in the air be = [tex]W_{ma}[/tex]
Let the weight of the mix in water be = [tex]W_{mw}[/tex]; &
the bulk specific gravity be = [tex]G_m[/tex]
SO;
[tex]W_{mw} = W_{ma} - v \delta _{w} --- (1)[/tex]
Also;
[tex]G_m = \dfrac{W_{mw}}{v \delta_w} --- (2)[/tex]
From (2), make[tex]v \delta_w[/tex] the subject:
[tex]v \delta_w = \dfrac{W_{ma}}{G_m}[/tex]
Now, equation (1) can be rewritten as:
[tex]W_{mw} = W_{ma} - \dfrac{W_{ma}}{G_m}[/tex]
[tex]G_m = \dfrac{W_{ma}}{W_{ma} - W_{mw}}[/tex]
Replacing the values;
[tex]G_m = \dfrac{1173.5}{1173.5 -652.5}[/tex]
[tex]G_m = \dfrac{1173.5}{521}[/tex]
[tex]\mathbf{G_m = 2.25}[/tex]
MAPP gas, natural gas, propane, and acetylene can be used with oxygen to cut metal.
True
False
A 4-L pressure cooker has an operating pressure of 175 kPa. Initially, one-half of the volume is filled with liquid and the other half with vapor. If it is desired that the pressure cooker not run out of liquid water for 75 min, determine the highest rate of heat transfer allowed.
Answer:
the highest rate of heat transfer allowed is 0.9306 kW
Explanation:
Given the data in the question;
Volume = 4L = 0.004 m³
V[tex]_f[/tex] = V[tex]_g[/tex] = 0.002 m³
Using Table ( saturated water - pressure table);
at pressure p = 175 kPa;
v[tex]_f[/tex] = 0.001057 m³/kg
v[tex]_g[/tex] = 1.0037 m³/kg
u[tex]_f[/tex] = 486.82 kJ/kg
u[tex]_g[/tex] 2524.5 kJ/kg
h[tex]_g[/tex] = 2700.2 kJ/kg
So the initial mass of the water;
m₁ = V[tex]_f[/tex]/v[tex]_f[/tex] + V[tex]_g[/tex]/v[tex]_g[/tex]
we substitute
m₁ = 0.002/0.001057 + 0.002/1.0037
m₁ = 1.89414 kg
Now, the final mass will be;
m₂ = V/v[tex]_g[/tex]
m₂ = 0.004 / 1.0037
m₂ = 0.003985 kg
Now, mass leaving the pressure cooker is;
m[tex]_{out[/tex] = m₁ - m₂
m[tex]_{out[/tex] = 1.89414 - 0.003985
m[tex]_{out[/tex] = 1.890155 kg
so, Initial internal energy will be;
U₁ = m[tex]_f[/tex]u[tex]_f[/tex] + m[tex]_g[/tex]u[tex]_g[/tex]
U₁ = (V[tex]_f[/tex]/v[tex]_f[/tex])u[tex]_f[/tex] + (V[tex]_g[/tex]/v[tex]_g[/tex])u[tex]_g[/tex]
we substitute
U₁ = (0.002/0.001057)(486.82) + (0.002/1.0037)(2524.5)
U₁ = 921.135288 + 5.030387
U₁ = 926.165675 kJ
Now, using Energy balance;
E[tex]_{in[/tex] - E[tex]_{out[/tex] = ΔE[tex]_{sys[/tex]
QΔt - m[tex]_{out[/tex]h[tex]_{out[/tex] = m₂u₂ - U₁
QΔt - m[tex]_{out[/tex]h[tex]_g[/tex] = m₂u[tex]_g[/tex] - U₁
given that time = 75 min = 75 × 60s = 4500 sec
so we substitute
Q(4500) - ( 1.890155 × 2700.2 ) = ( 0.003985 × 2524.5 ) - 926.165675
Q(4500) - 5103.7965 = 10.06013 - 926.165675
Q(4500) = 10.06013 - 926.165675 + 5103.7965
Q(4500) = 4187.690955
Q = 4187.690955 / 4500
Q = 0.9306 kW
Therefore, the highest rate of heat transfer allowed is 0.9306 kW
The ____ neurons allow the body to move and are greatly influenced by electri
A. compression
B. motor
C. positive
D. mobile
Answer:
the answer would be B motor
A flat plate is subjected to a load of 5KN as shown in figure. The plate material is grey cast iron FFG 200 and the factor of safety is 2.5. Determine the thickness of the plate
Answer:
57.14 N/mm2
Explanation:
As part of a heat treatment process, cylindrical, 304 stainless steel rods of 100-mm diameter are cooled from an initial temperature of 500 C by suspending them in an oil bath at 30 C. If a convection coefficient of 500 W/m2 K is maintained by circulation of the oil, how long does it take for the centerline of a rod to reach a temperature of 50 C, at which point it is withdrawn from the bath
Answer:
Explanation:
Given that:
diameter = 100 mm
initial temperature = 500 ° C
Conventional coefficient = 500 W/m^2 K
length = 1 m
We obtain the following data from the tables A-1;
For the stainless steel of the rod [tex]\overline T = 548 \ K[/tex]
[tex]\rho = 7900 \ kg/m^3[/tex]
[tex]K = 19.0 \ W/mk \\ \\ C_p = 545 \ J/kg.K[/tex]
[tex]\alpha = 4.40 \times 10^{-6} \ m^2/s \\ \\ B_i = \dfrac{h(\rho/4)}{K} \\ \\ =0.657[/tex]
Here, we can't apply the lumped capacitance method, since Bi > 0.1
[tex]\theta_o = \dfrac{T_o-T_{\infty}}{T_i -T_\infty}} \\ \\ \theta_o = \dfrac{50-30}{500 -30}} \\ \\ \theta_o = 0.0426\\[/tex]
[tex]0.0426 = c_1 \ exp (- E^2_1 F_o_)\\ \\ \\ 0.0426 = 1.1382 \ exp (-10.9287)^2 \ f_o \\ \\ = f_o = \dfrac{In(0.0374)}{0.863} \\ \\ f_o = 3.81[/tex]
[tex]t_f = \dfrac{f_o r^2}{\alpha} \\ \\ t_f = \dfrac{3.81 \times (0.05)^2}{4.40 \times 10^{-6}} \\ \\ t_f= 2162.5 \\ \\ t_f = 36 mins[/tex]
However, on a single rod, the energy extracted is:
[tex]\theta = pcv (T_i - T_{\infty} )(1 - \dfrac{2 \theta}{c} J_1 (\zeta) ) \\ \\ = 7900 \\times 546 \times 0.007854 \times (500 -300) (1 - \dfrac{2 \times 0.0426}{1.3643}) \\ \\ \theta = 1.54 \times 10^7 \ J[/tex]
Hence, for centerline temperature at 50 °C;
The surface temperature is:
[tex]T(r_o,t) = T_{\infty} +(T_1 -T_{\infty}) \theta_o \ J_o(\zeta_1) \\ \\ = 30 + (500-30) \times 0.0426 \times 0.5386 \\ \\ \mathbf{T(r_o,t) = 41.69 ^0 \ C}[/tex]