Answer:
9 cm
Explanation:
The liquid on the bend will be affected by two accelerations: gravity and centripetal force.
Gravity will be of 9.81 m/s^2 pointing down at all points.
The centripetal acceleration will be of
ac = v^2/r
Pointing to the center of the bend (perpendicular to gravity).
The velocity will depend on the radius
v = (1 m^2/s) / r
Replacing:
ac = (1/r)^2 / r
ac = (1 m^4/s^2) / r^3
If we set up a cylindrical reference system with origin at the center of the bend, the total acceleration will be
a = (-1/r^3 * i - 9.81 * j)
The surface of the liquid will be an equipotential surface, this means all points on the surface have the same potential energy.
The potential energy of the gravity field is:
pg = g * h
The potential energy of the centripetal force is:
pc = ac * r
Then the potential field is:
p = -1/r^2 * - 9.81*h
Points on the surface at r = 1 m and r = 3 m have the same potential.
-1/1^2 * - 9.81*h1 = -1/3^2 * - 9.81*h2
-1 - 9.81*h1 = -1/9 - 9.81*h2
-1 + 1/9 = 9.81 * (h1 - h2)
h1 - h2 = (-8/9) / 9.81
h2 - h1 = 0.09 m
The outer part will be 9 cm higher than the inner part.
How many joules are required to raise the temperature of a cubic meter of water by 10K?
Answer:
4.186 × 10⁷ J
Explanation:
Heat gain by water = Q
Thus,
[tex]m_{water}\times C_{water}\times \Delta T=Q[/tex]
For water:
Volume = 1 m³ = 1000 L ( as 1 m³ = 1000 L)
Density of water= 1 kg/L
So, mass of the water:
[tex]Mass\ of\ water=Density \times {Volume\ of\ water}[/tex]
[tex]Mass\ of\ water=1 kg/L \times {1000\ L}[/tex]
Mass of water = 1000 kg
Specific heat of water = 4.186 kJ/kg K
ΔT = 10 K
So,
[tex]1000\times 4.186\times 10=Q[/tex]
Q = 41860 kJ
Also, 1 kJ = 1000 J
So, Q = 4.186 × 10⁷ J
What % of Nickel is needed to increase toughness?
Answer:
2% to 20% Ni
Explanation:
If we will talk about steel then ,for increasing the toughness property of steel generally 2% to 20% Ni added .Ni also increase resistance to corrosion and oxidation, impact strength and strength.
We know that steel is an alloy of iron and carbon.But to improve the property of steel different alloying elements added by this steel become desirable to use at different situations.
What is the atmospheric temperature on Venus if the density is 67 kg/m^3 and the pressure is 9.3 mPa, absolute? Express in °C and °F. The atmosphere is composed of CO2.
Answer:
461 C
862 F
Explanation:
The specific gas constant for CO2 is
R = 189 J/(kg*K)
Using the gas state equation:
p * v = R * T
T = p * v / R
v = 1/δ
T = p / (R * δ)
T = 9.3*10^6 / (189 * 67) = 734 K
734 - 273 = 461 C
461 C = 862 F
What is the difference between point-to-point and continuous path control in a motion control system?
Answer:
Point to point control motion system:
In point to point control motion system tool perform specific task at a particular location.Point to point control motion system is also called positioning system.It perform intermittent operation.
Ex: Drilling operation is a point to point motion control system.
Continuous path control system:
Continuous path control system is continuous operation that perform by tool.The program used in continuous path control system is more complex than point to point motion control system.
Ex :Milling operation is a continuous path control system.
What is a quasi-equilibrium process? What is its importance in engineering?
Answer:
Infinite slow thermodynamic process is Quasi-equilibrium process. All the thermodynamic model or equation is based on Quasi-equilibrium process. So, Quasi-equilibrium process is very important process in engineering.
Explanation:
Step1
Quasi-equilibrium process is the thermodynamic process which is infinitely slow. All the thermodynamic variables or properties are taken as uniform. Pressure or temperature is uniform throughout the process. Quasi-equilibrium process is represented by complete joint line in thermodynamics not with the dash line. So, this process has infinite equilibrium points near to each other.
Step2
All the thermodynamic analysis or equations are based on Quasi-equilibrium process. This gives estimation of heat, work, enthalpy, entropy etc. Quasi-equilibrium process gives maximum power output in power producing devices like turbine or engine. The entire thermodynamic engineering model is designed on the basis of Quasi-equilibrium process. Thus, this process is very important in terms of engineering.
An object is supported by a crane through a steel cable of 0.02m diameter. If the natural swinging of the equivalent pendulum is 0.95 rad/s and the natural time period of the axial vibration is found to be 0.35 sec. What is the mass of the object.
Answer:
22.90 × 10⁸ kg
Explanation:
Given:
Diameter, d = 0.02 m
ωₙ = 0.95 rad/sec
Time period, T = 0.35 sec
Now, we know
T= [tex]2\pi\sqrt{\frac{L}{g}}[/tex]
where, L is the length of the steel cable
g is the acceleration due to gravity
0.35= [tex]2\pi\sqrt{\frac{L}{9.81}}[/tex]
or
L = 0.0304 m
Now,
The stiffness, K is given as:
K = [tex]\frac{\textup{AE}}{\textup{L}}[/tex]
Where, A is the area
E is the elastic modulus of the steel = 2 × 10¹¹ N/m²
or
K = [tex]\frac{\frac{\pi}{4}d^2\times2\times10^11}{0.0304}[/tex]
or
K = 20.66 × 10⁸ N
Also,
Natural frequency, ωₙ = [tex]\sqrt{\frac{K}{m}}[/tex]
or
mass, m = [tex]\sqrt{\frac{K}{\omega_n^2}}[/tex]
or
mass, m = [tex]\sqrt{\frac{20.66\times10^8}{0.95^2}}[/tex]
mass, m = 22.90 × 10⁸ kg
What is the density of an alloy formed by 10 cm^3 of copper (density = 8.9g / cm^3) and 10 cm^3 of silver (density= 10.5 g / cm^3)?
Answer:
9.7g / cm^3
Explanation:
To calculate a conbined density we must find the ratio between the sum of the masses and the sum of the volumes remembering that the equation to find the density is α=m/v, taking into account the above the following equation is inferred.
αc=copper density
αs=silver density
Vs=volume of silver
Vc=volume of copper
α= density of alloy
[tex]\alpha =\frac{({\alpha c}{Vc} +{\alpha s }{Vs} )}{Vs+Vc} \\\alpha =\frac{(8.9)(10) +(10.5)(10) }{10+10} \\\\\alpha =9.7g / cm^3[/tex]
the density of the alloy is 9.7g / cm^3
A steel rectangular tube has outside dimensions of 150 mm x 50 mm and a wall thickness of 4 mm. State the inside dimensions, the area of its cross section, and the weight of a piece 1.22 m long.
Answer:
inside dimension [tex]= 142 mm \times 42 mm[/tex]
cross section area [tex]= 7.5\times 10^{-3} m^2[/tex]
mass of 1.2 meter log steel [tex] = 1.843\times 10^{-3} \rho[/tex]
Explanation:
given data:
Outside dimension of steel rectangular [tex]= 150 mm\times 50mm[/tex]
Thickness = 4 mm
Long = 1.22 m
inside dimension will be [tex]= (150- 8)mm \times ( 50-8)mm[/tex]
[tex]= 142 mm \times 42 mm[/tex]
cross section area [tex]= 150\times 50 mm^2[/tex]
[tex]= 7500\times 10^{-6} m^2[/tex]
[tex]= 7.5\times 10^{-3} m^2[/tex]
let the density be assumed as \rho
mass of 1.2 meter log steel will be [tex]= 1.2 \times (7.5\times 10^{-3} - 0.142\times 0.048)\times \rho[/tex]
[tex] = 1.843\times 10^{-3} \rho[/tex]
Two particles have a mass of 8 kg and 12 kg, respectively. If they are 800 mm apart, determine the force of gravity acting between them. Compare this result with the weight of each particle.
Answer:
The gravitational force between the masses is [tex]1.0\times 10^{-8}Newtons[/tex]
Explanation:
For 2 masses 'm' and 'M' separated by a distance 'd' the gravitational force between them is given by Newton as
[tex]F=G\cdot \frac{mM}{d^{2}}[/tex]
where
'G' is universal gravitational constant whose value is [tex]6.67\times 10^{-11}m^3kg^{-1}s^{-2}[/tex]
Applying the values in the above relation we get
[tex]F=6.67\times 10^{-11}\times \frac{8\times 12}{(800\times 10^{-3})^{2}}=1.0\times 10^{-8}Newtons[/tex]
Weight of 8 kg mass =[tex]8\times 9.81=78.45Newtons[/tex]
Weight of 12 kg mass =[tex]12\times 9.81=117.72Newtons[/tex]
thus we see that gravitational force between the masses is completely negligible as compared to the weight of the masses.
The two basic network administration models are ____ and ____
The two basic network administration models are centralized and decentralized, each with distinct advantages and challenges that affect network performance, security, and scalability.
Explanation:The two basic network administration models are centralized and decentralized. In a centralized model, network control and decision-making are located at a single point, typically within a dedicated device or group of servers. Conversely, a decentralized model distributes control across multiple nodes, allowing for individual nodes to operate independently while still being part of the overall network.
Understanding these models is crucial for designing efficient networks that cater to specific organizational needs and for implementing dynamics on network models, such as discrete state/time models or continuous state/time models. Each model presents different advantages and challenges that can influence network performance, security, and scalability.
A cable in a motor hoist must lift a 700-lb engine. The steel cable is 0.375in. in diameter. What is the stress in the cable?
Answer:43.70 MPa
Explanation:
Given
mass of engine [tex] 700 lb \approx 317.515 kg[/tex]
diameter of cable [tex]0.375 in.\approx 9.525 mm[/tex]
[tex]A=\frac{\pi d^2}{4}=71.26 mm^2[/tex]
we know stress([tex]\sigma [/tex])[tex]=\frac{load\ applied}{area\ of\ cross-section}[/tex]
[tex]\sigma =\frac{317.515\times 9.81}{71.26\times 10^{-6}}=43.70 MPa[/tex]
The engine is mounted on a foundation block which is spring - supported. Describe the steady - state vibration of the system if the block and engine have a total weight of 7500 N ( 750 kg) and the engine, when running, creates an impressed force F = (250 sin 2/) N, where t is in seconds. Assume that the system vibrates only in the vertical direction, with the positive displacement measured downward, and that the total stiffness of the springs can be represented as k = 30 kN/m. Determine the rotational speed omega of the engine which will cause resonance.
Answer:
wr = 6.32 rad/s
Explanation:
m = 750 kg
k = 30 kN/m
This system has no dampening, therefore the resonance frequency will simply be the natural frequency of the system.
[tex]wr = w0 = \sqrt{\frac{k}{m}}[/tex]
[tex]wr = \sqrt{\frac{30000}{750}} = 6.32 rad/s[/tex]
In this case the force applied doesn't matter. because we are calculating the resonance frequency.
Name the point of intersection, where the axis meet.
Answer:
origin
Explanation:
The point of intersection of axis is called origin.
In 2D origin is the intersection point of x-axis and y-axis if we go right to the origin then it is positive x axis, if we go left side of origin then it is negative x- axis
Similarly when we go above the origin then it positive y axis , and if we go bellow the origin then it is negative x axis
In 3D origin is the intersection of x-axis, y-axis and z-axis
NOTE- For defining i take here x axis as horizontal axis and y-axis as vertical axis
A cylindrical specimen of some metal alloy having an elastic modulus of 126 GPa and an original cross-sectional diameter of 4.0 mm will experience only elastic deformation when a tensile load of 2380 N is applied. Calculate the maximum length of the specimen before deformation if the maximum allowable elongation is 0.44 mm.
Answer:
The maximum length of the specimen is 0.2927 m or 292.7 mm
Solution:
Modulus of elasticity, E = 126 GPa = [tex]126\times 10^{9}[/tex]
Diameter of the cross-section, D = 4.0 mm = [tex]4.0\times 10^{- 3} m[/tex]
Force due to tension, F = 2380 N
Maximum elongation, [tex]\Delta L = 0.44 mm = 0.44\times 10^{- 3} m[/tex]
Now,
The maximum length of the specimen, [tex]L_{m}[/tex] can be calculated as follows:
The cross-sectional area, [tex]A_{c} = \frac{\pi D^{2}}{4} = \frac{\pi\times (4.0\times 10^{- 3})^{2}}{4} = 1.256\times 10^{- 5} m^{2}[/tex]
Now, the stress on the specimen, [tex]\sigma_{s} = \frac{F}{A_{c}} = \frac{2380}{1.256+\times 10^{- 5}}[/tex]
[tex]\sigma_{s} = 1.89\times 10^{8} N/m^{2}[/tex]
Now,
The strain on the specimen, [tex]\epsilon_{s}[/tex]:
[tex]\epsilon_{s} = \frac{\Delta L}{L_{m}}[/tex]
Also, from Hooke's law:
[tex]E = \frac{\sigma_{s}}{epsilon_{s}}[/tex]
⇒ [tex]E = \frac{1.89\times 10^{8}}{\frac{\Delta L}{L_{m}}}[/tex]
⇒ [tex]L_{m} = \frac{\Delta Ltimes E}{1.89\times 10^{8}}[/tex]
⇒ [tex]L_{m} = \frac{0.44\times 10^{- 3}\times 126\times 10^{9}}{1.89\times 10^{8}} = 0.2927 m[/tex]
The maximum length of the specimen before deformation is: 292.72 mm (0.2927 m).
Tensile PropertiesFor solving this question, it's necessary to know some concepts about the material's properties.
The tensile stress (σ) is determined from the ratio between load and original area before the load applied (σ=[tex]\frac{F}{Ao}[/tex]). Depending on the load applied, the material can have an elastic deformation (temporary deformation) and plastic deformation (permanent deformation). Both deformations can be calculated by the equation: ε=ΔL/Lo, where ΔL= deformation elongation and Lo= the original length before the load applied.
Elastic DeformationWhen the material is in the elastic portion, there is a linear relationship between stress and strain given by: σ=Eε. Due to this relationship, it is possible to find the elastic deformation (ε) when we know the stress (σ) and elastic modulus (E).
Now you have the necessary information to solve your question.
The question gives:
E (elastic modulus) =126 GPA
d (original cross-sectional diameter)=4 mm
F (tensile load)=2380 N
ΔL (maximum allowable elongation) =0.44 mm
1. Find the area of the cylindrical specimen.
[tex]Ao=\frac{\pi *d^2}{4} =\frac{\pi *4^2}{4}=\pi *4=12.57 mm^2[/tex]2. Find the tensile stress.
σ= [tex]\frac{F}{Ao} =\frac{2380 N }{12.57 mm^2} =189.39 MPa[/tex]
3. Calculate the maximum length of the specimen before deformation.
Knowing that ε=ΔL/Lo and σ=Eε, you can rewrite these equations as:
σ= E * (ΔL/Lo)
σ= (E * ΔL)/Lo
The question asks the maximum length of the specimen before deformation, therefore you should find Lo. Thus,
Lo= (E * ΔL)/σ
[tex]Lo=\frac{126*10^3 MPa*0.44 mm}{189.39 MPa} =292.72 mm= 0.2927 m[/tex]
Read more about the tensile stress here:
https://brainly.com/question/19756298
Water is flowing in a metal pipe. The pipe OD (outside diameter) is 61 cm. The pipe length is 120 m. The pipe wall thickness is 0.9 cm. The water density is 1.0 kg/L. The empty weight of the metal pipe is 2500 N/m. In kN, what is the total weight (pipe plus water)?
Answer:
1113kN
Explanation:
The ouside diameter OD of the pipe is 61cm and the thickness T is 0.9cm, so the inside diameter ID will be:
Inside Diameter = Outside Diameter - Thickness
Inside Diameter = 61cm - 0.9cm = 60.1cm
Converting this diameter to meters, we have:
[tex]60.1cm*\frac{1m}{100cm}=0.601m[/tex]
This inside diameter is useful to calculate the volume V of water inside the pipe, that is the volume of a cylinder:
[tex]V_{water}=\pi r^{2}h[/tex]
[tex]V_{water}=\pi (\frac{0.601m}{2})^{2}*120m[/tex]
[tex]V_{water}=113.28m^{3}[/tex]
The problem gives you the water density d as 1.0kg/L, but we need to convert it to proper units, so:
[tex]d_{water}=1.0\frac{Kg}{L}*\frac{1L}{1000cm^{3}}*(\frac{100cm}{1m})^{3}[/tex]
[tex]d_{water}=1000\frac{Kg}{m^{3}}[/tex]
Now, water density is given by the equation [tex]d=\frac{m}{V}[/tex], where m is the water mass and V is the water volume. Solving the equation for water mass and replacing the values we have:
[tex]m_{water}=d_{water}.V_{water}[/tex]
[tex]m_{water}=1000\frac{Kg}{mx^{3}}*113.28m^{3}[/tex]
[tex]m_{water}=113280Kg[/tex]
With the water mass we can find the weight of water:
[tex]w_{water}=m_{water} *g[/tex]
[tex]w_{water}=113280kg*9.8\frac{m}{s^{2}}[/tex]
[tex]w_{water}=1110144N[/tex]
Finally we find the total weight add up the weight of the water and the weight of the pipe,so:
[tex]w_{total}=w_{water}+w_{pipe}[/tex]
[tex]w_{total}=1110144N+2500N[/tex]
[tex]w_{total}=1112644N[/tex]
Converting this total weight to kN, we have:
[tex]1112644N*\frac{0.001kN}{1N}=1113kN[/tex]
A(n)______topology is a mixture of more than one type of topology.
Answer:
Hybrid topology is the connection of one or more than one topology.
Explanation:
Topology:
Topology is the arrangement of network.These network connects by line and nodes.
Type of topology:
1.Bus topology
2.Star topology
3.Ring topology
4.Mesh topology
Along with given above topology one topology is also used is known as hybrid topology.Hybrid topology is the connection of one or more than two one above given topology.
Find the diameter of the test cylinder in which 6660 N force is acting on it with a modulus of elasticity 110 x 103 Pa. The initial length of the rod is 380 mm and elongation is 0.50 mm.
Answer:
The diameter of the test cylinder should be 7.65 meters.
Explanation:
The Hooke's law relation between stress and strain is mathematically represented as
[tex]Stress=E\times strain\\\\\sigma =e\times \epsilon[/tex]
Where 'E' is modulus of elasticity of the material
Now by definition of strain we have
[tex]\epsilon =\frac{\Delta L}{L_{o}}[/tex]
Applying values to obtain strain we get
[tex]\epsilon =\frac{0.5}{380}=0.001316[/tex]
Thus the stress developed in the material equals
[tex]\sigma = 110\times 10^{3}\times 0.001316=144.76N/m^{2}[/tex]
Now by definition of stress we have
[tex]\sigma =\frac{Force}{Area}\\\\\therefore Area=\frac{Force}{\sigma }\\\\\frac{\pi D^{2}}{4}=\frac{6660N}{144.76}=46m^{2}[/tex]
Solving for 'D' we get
[tex]D=\sqrt{\frac{4\times 46}{\pi }}=7.653meters[/tex]
Define Plastic vs elastic deformation.
Answer:
Plastic deformation, irreversible or permanent. Deformation mode in which the material does not return to its original shape after removing the applied load. This happens because, in plastic deformation, the material undergoes irreversible thermodynamic changes by acquiring greater elastic potential energy.
Elastic deformation, reversible or non-permanent. the body regains its original shape by removing the force that causes the deformation. In this type of deformation, the solid, by varying its tension state and increasing its internal energy in the form of elastic potential energy, only goes through reversible thermodynamic changes.
When a fluid flows through a sharp bend, low pressures may
developin localized regions of the bend. Estimate the
minimumabsolute pressure (in psi) that can develop without
causingcavitation if the fluid is water at 160 oF.
To avoid cavitation for water at 160 °F flowing through a sharp bend, the minimum absolute pressure should be slightly above the vapor pressure of water at this temperature, which is approximately 0.363 psi.
Explanation:When water flows through a sharp bend, cavitation can occur if the local pressure falls to or below the fluid's vapor pressure. To estimate the minimum absolute pressure without causing cavitation for water at 160 °F, we must consider water's vapor pressure at this temperature. At 160 °F (about 71 °C), the vapor pressure of water is approximately 0.363 psi. Since fluids cannot have a negative absolute pressure, and to avoid cavitation, the absolute pressure must stay above this vapor pressure. Therefore, considering atmospheric pressure to be approximately 14.7 psi, to avoid cavitation, the minimum absolute pressure in the system should be slightly above 0.363 psi to ensure no cavitation occurs.
What is the pressure inside a tire in (N/mm^2) if a pressure gauge indicates 29.35 psi?
Answer:
The pressure inside the tire is [tex]0.304\frac{N}{mm^{2}}[/tex]
Explanation:
The pressure gauge indicates the difference between the atmospheric pressure and the pressure inside the tire, so we have the following equation:
Pressure inside the tire = Gauge pressure + Atmospheric pressure
Where the gauge pressure is given in the problem and is 29.35psi and the atmospheric pressure is 14.7psi.
Replacing the values, we have:
Pressure inside the tire = 29.35psi + 14.7psi
Pressure inside the tire = 44.05psi
Now we have to convert from psi to [tex]\frac{N}{mm^{2}}[/tex], so:
44.05psi = [tex]44.05\frac{lbf}{in^{2}}[/tex]
[tex]44.05\frac{lbf}{in^{2}}*(\frac{1in}{25.4mm})^{2}*\frac{4.4482N}{lbf}=0.304\frac{N}{mm^{2}}[/tex]
What is the mass in both slugs and kilograms of a 1000-lb beam?
Answer:
31.1 slug, 453.4 Kg
Explanation:
given,
mass of the beam is 1000 lb
to convert mass of beam into slugs and kilograms.
1 lb is equal to 0.0311 slug
1000 lb = 1000 × 0.0311
= 31.1 slug
now, conversion of lb into kg
1 lb is equal to 0.4534 kg
so,
1000 lb = 1000 × 0.4534
= 453.4 Kg
hence, 1000 lb of beam in slugs is equal to 31.1 slugs and in kilo gram is 453.4 Kg.
For which of 'water' flow velocities at 200C can we assume that the flow is incompressible ? a.1000 km per hour b. 500 km per hour c. 2000 km per hour d. 200 km per hour
Answer:d
Explanation:
Given
Temperature[tex]=200^{\circ}\approc 473 K[/tex]
Also [tex]\gamma for air=1.4[/tex]
R=287 J/kg
Flow will be In-compressible when Mach no.<0.32
Mach no.[tex]=\frac{V}{\sqrt{\gamma RT}}[/tex]
(a)[tex]1000 km/h\approx 277.78 m/s[/tex]
Mach no.[tex]=\frac{277.78}{\sqrt{1.4\times 287\times 473}}[/tex]
Mach no.=0.63
(b)[tex]500 km/h\approx 138.89 m/s[/tex]
Mach no.[tex]=\frac{138.89}{\sqrt{1.4\times 287\times 473}}[/tex]
Mach no.=0.31
(c)[tex]2000 km/h\approx 555.55 m/s[/tex]
Mach no.[tex]=\frac{555.55}{\sqrt{1.4\times 287\times 473}}[/tex]
Mach no.=1.27
(d)[tex]200 km/h\approx 55.55 m/s[/tex]
Mach no.[tex]=\frac{55.55}{\sqrt{1.4\times 287\times 473}}[/tex]
Mach no.=0.127
From above results it is clear that for Flow at velocity 200 km/h ,it will be incompressible.
Why do overhung rotors need to be balanced on or near resonance?
Explanation:
Balancing:
Generally balancing are of two types
1.Static balancing:In this only force balancing is done.
2.Dynamic balancing:in this force as well as moment balancing is done.
Balancing become compulsory for over hanging rotor because unbalance force produce lots of vibration and lots of sound due to this rotor or the whole system in which rotor is attached can be damage.
The "Crawler" developed to transport the Saturn V launch vehicle from the assembly building to the launch pad is the largest land 6 vehicle ever built, weighing 4.9 x 10 -Ibs at sea level. a- What is its mass in slugs ? b- What is its mass in kilograms ?
Answer:
a) 152000 slugs
b) 2220000 kg or 2220 metric tons
Explanation:
A body with a weight of 4.9*10^6 lbf has a mass of
4.9*10^6 lbm * 1 lbf/lbm = 4.9*10^6 lbm
This mass value can then be converted to other mass values.
1 slug is 32.17 lbm
Therefore:
4.9*10^6 lbm * 1 slug / (32.17 lbm) = 152000 slugs
1 lb is 0.453 kg
Therefore:
4.9*10^6 lbm / (1/0.453) * kg/lbm = 2220000 kg
A solid shaft and a hollow shaft of the same material have same length and outer radius R. The inner radius of the hollow shaft is 0.7R. a) If both the shafts are subjected to the same torque, compare their shear stresses, angle of twist and mass. b) Find the strength to weight ratio for both the shafts.
Answer with Explanation:
By the equation or Torque we have
[tex]\frac{T}{I_{p}}=\frac{\tau }{r}=\frac{G\theta }{L}[/tex]
where
T is the torque applied on the shaft
[tex]I_{p}[/tex] is the polar moment of inertia of the shaft
[tex]\tau [/tex] is the shear stress developed at a distance 'r' from the center of the shaft
[tex]\theta [/tex] is the angle of twist of the shaft
'G' is the modulus of rigidity of the shaft
We know that for solid shaft [tex]I_{p}=\frac{\pi R^4}{2}[/tex]
For a hollow shaft [tex]I_{p}=\frac{\pi (R_o^4-R_i^4)}{2}[/tex]
Since the two shafts are subjected to same torque from the relation of Torque we have
1) For solid shaft
[tex]\frac{2T}{\pi R^4}\times r=\tau _{solid} [/tex]
2) For hollow shaft we have
[tex]\tau _{hollow}=\frac{2T}{\pi (R^4-0.7R^4)}\times r=\frac{2T}{\pi 0.76R^4} [/tex]
Comparing the above 2 relations we see
[tex]\frac{\tau _{solid}}{\tau _{hollow}}=0.76[/tex]
Similarly for angle of twist we can see
[tex]\frac{\theta _{solid}}{\theta _{hollow}}=\frac{\frac{LT}{I_{solid}}}{\frac{LT}{I_{hollow}}}=\frac{I_{hollow}}{I_{solid}}=1.316[/tex]
Part b)
Strength of solid shaft = [tex]\tau _{max}=\frac{T\times R}{I_{solid}}[/tex]
Weight of solid shaft =[tex]\rho \times \pi R^2\times L[/tex]
Strength per unit weight of solid shaft = [tex]\frac{\tau _{max}}{W}=\frac{T\times R}{I_{solid}}\times \frac{1}{\rho \times \pi R^2\times L}=\frac{2T}{\rho \pi ^2R^5L}[/tex]
Strength of hollow shaft = [tex]\tau '_{max}=\frac{T\times R}{I_{hollow}}[/tex]
Weight of hollow shaft =[tex]\rho \times \pi (R^2-0.7R^2)\times L[/tex]
Strength per unit weight of hollow shaft = [tex]\frac{\tau _{max}}{W}=\frac{T\times R}{I_{hollow}}\times \frac{1}{\rho \times \pi (R^2-0.7^2)\times L}=\frac{5.16T}{\rho \pi ^2R^5L}[/tex]
Thus [tex]\frac{Strength/Weight _{hollow}}{Strength/Weight _{Solid}}=5.16[/tex]
Coulomb's Law Two point charges experience an attractive force of 10.8 N when they are separated by 2.4 m. VWhat force in newtons do they experience when their separation is 0.7 m?
Answer:
The force between the charges when the separation decreases to 0.7 meters equals 126.955 Newtons
Explanation:
We know that for two point charges of magnitude [tex]q_{1},q_{2}[/tex] the magnitude of force between them is given by
[tex]F=\frac{k_{e}q_{1}\cdot q_{2}}{r^{2}}[/tex]
where
[tex]k_{e}[/tex] is constant
[tex]r[/tex] is the separation between the charges
Initially when the charges are separated by 2.4 meters the force can be calculated as
[tex]F_{1}=\frac{k_{e}\cdot q_{1}q_{2}}{2.4^{2}}\\\\10.8=\frac{k_{e}\cdot q_{1}q_{2}}{2.4^{2}}\\\\\therefore k_{e}\cdot q_{1}q_{2}=10.8\times 2.4^{2}=62.208[/tex]
Now when the separation is reduced to 0.7 meters the force is similarly calculated as
[tex]F_{2}=\frac{k_{e}\cdot q_{1}q_{2}}{0.7^{2}}[/tex]
Applying value of the constant we get
[tex]F_{1}=\frac{62.208}{0.7^{2}}[/tex]
Thus [tex]F_{2}=126.955Newtons[/tex]
Which renewable sources are growing at the fastest rate? Which renewable source is used to produce most electricity?
Answer:
Wind
Hydro electric
Explanation:
Energy are of two types
1.Renewable energy
These have unlimited source of energy.
Ex: Solar energy,wind energy,geothermal energy,hydro power ,biomass etc
2.Non renewable energy
These have limited source of energy.
Ex: Petroleum,Coal
Wind is the fastest renewable source of energy.This energy is produce by using the natural velocity of air.
Hydro electric power plant is the mostly used renewable source of energy to produce electricity.
Answer with Explanation:
The growth of renewable sources of energy depend on various factor's and their grown is also a regional dependent process. Many different countries use different renewable sources of energy and the growth of the renewable sources of energy depend on the location of the place. As an example in India the solar energy is the most widely growing source of energy due to the location of the place. while as in European union Bio energy is the source of renewable energy that has shown the most growth.
Water is the renewable source which is used to produce the most electricity in the world accounting for 16.3% of the total global electricity production.
What is the lowest Temperature in degrees C?, In degrees K? in degrees F? in degrees R
Answer:
-273.16 °C
-459.677 °F
0 °K
0 °R
Explanation:
The lowest temperature is the absolute zero.
Absolute zero is at 0 degrees Kelvin, or 0 degrees Rankine, because these are absolute scales that have their zero precisely at the absolute zero.
Celsius and Fahrenheit degrees are relative scales, these have their zeroes above the absolute zero.
Celsius scale has the same degree separation as the Kelvin scale, but the zero is separated by 273.16 degrees. Therefore the lowest temperature in the Celsius scale is -273.16 °C.
The Fahrenheit degrees have the same degree separation as the Rankine degrees, and the zero is 459.67 degrees. Therefore the lowest temperature in the Fahrenheit scale is -459.67 °F.
You want a pot of water to boil at 105celcius. How heavy a
lid should you put on the 15 cm diameterpot when Patm =
101 kPa?
Answer:
36 kg
Explanation:
For water to boil at 105 C it needs a pressure of 121 kPa (this is the vapor pressure of water at 105 C).
In the lid there will be a difference of pressure from one side to the other, this will be compensated by the weight of the lid.
Δp = pwater - patm
Δp = 121 - 101 = 20 kPa
The pressure caused by the weigh of the lid is:
Δp = w / A
Δp = m * g / A
Rearranging
m = Δp * A / g
m = Δp * π/4 * d^2 / g
m = 20000 * π/4 * 0.15^2 / 9.81 = 36 kg
A window air conditioner unit is placed on a laboratory bench and tested in cooling mode using 750 W of electric power with a COP of 1.75. What is the cooling power capacity and what is the net effect on the laboratory?
Answer:
Q=1312.5 W
Explanation:
Given that
Cooling load or power input = 750 W
COP=1.75
We know that COP can be given as
COP is the ratio of cooling effect to the input power .
Lets take cooling effect is Q.So now by using COP formula
COP=Q/750
1.75=Q/750
Q=1312.5 W
So the cooling effect produce by air conditioning will be 1312.5 W.
The net effect on laboratory,the laboratory temperature will reduce.