Answer:
f=1.59 Hz
Explanation:
Given that
Simple undamped system means ,system does not consists any damper.If system consists damper then it is damped spring mass system.
Velocity = 100 mm/s
Maximum amplitude = 10 mm
We know that for a simple undamped system spring mass system
[tex]V_{max}=\omega A[/tex]
now by putting the values
[tex]V_{max}=\omega A[/tex]
100 = ω x 10
ω = 10 rad/s
We also know that
ω=2π f
10 = 2 x π x f
f=1.59 Hz
So the natural frequency will be f=1.59 Hz.
The Phoenix with a mass of 390 kg was a spacecraft used for exploration of Mars. Determine the weight of the Phoenix, in N, (a) on the surface of Mars where the acceleration of gravity is 3.73 m/s2 and (b) on Earth where the acceleration of gravity is 9.81 m/s2.
Answer:
a) on mars W=1454.7N
b)on earth W=3825.9N
Explanation:
The weight of any body with mass is given by the following equation
W=mg
where
m=mass
g=gravity
W=weight
Remember that the weight is expresed in Newton and the units are kgm/s^2
A)weight on the surface of mars
W=(390kg)(3.73m/s^2)=1454.7N
b) on earth
W=(390kg)(9.81m/s^2)=3825.9N
Find the error in the following proof that 2 = 1. Consider the equation a = b. Multiply both sides by a to obtain a 2 = ab. Subtract b 2 from both sides to get a 2 − b 2 = ab − b 2 . Now factor each side, (a + b)(a − b) = b(a − b), and divide each side by (a − b) to get a + b = b. Finally, let a and b equal 1, which shows that 2 = 1.
Answer:
You can't divide by zero
Explanation:
The error appears when you divide each side by (a - b). If a = b, then (a - b) = 0 and you can't divide each side by 0. Moreover, the equation before division, that is, (a + b)(a − b) = b(a − b) is true after replacing (a - b) = 0 because it gives 0 = 0.
The error in the proof lies in the step where we divided both sides by (a - b) . Since [tex]\( a = b \), \( (a - b) \)[/tex] becomes 0, making the division by 0 undefined.
The error occurs when dividing both sides by (a - b) . Since ( a = b ), ( (a - b) becomes 0. Division by 0 is undefined, leading to the invalid conclusion.
To elaborate, dividing both sides by (a - b) in the equation (a + b)(a - b) = b(a - b) results in:
[tex]\[ \frac{(a + b)(a - b)}{(a - b)} = \frac{b(a - b)}{(a - b)} \]\[ \frac{(a + b)\cancel{(a - b)}}{\cancel{(a - b)}} = \frac{b\cancel{(a - b)}}{\cancel{(a - b)}} \]\[ a + b = b \][/tex]
This step assumes (a - b) is not equal to zero, leading to the false conclusion that ( a + b = b ), which is only true when a and ( b ) are equal.
Therefore, the proof incorrectly concludes that ( 2 = 1 ) due to the division by zero, highlighting the importance of avoiding such mathematical errors.
A worker's hammer is accidentally dropped from the 20th floor of a building under construction. With what velocity does it strike the pavement 304 ft below, and what time t is required?
Answer:
Final Velocity (Vf)= 139.864 ft/s
Time (t)= 4,34 s
Explanation:
This is a free fall problem, to solve it we will apply free fall concepts:
In a free fall the acceletarion is gravity (g) = 9,81 m/s2, if we convert it to ft/s^2 = g= 32.174 ft/s^2
Final velocity is Vf= Vo+ g*t[tex]Vf^{2} = Vo^{2} +2*g*hwhere h is height (304 ft in this case).
Vo =0 since the hammer wasn't moving when it stared to fall
Then Vf^2= 0 + 2* 32.174 ft/s^2 *304 ft
Vf^2= 19,561.8224 ft^2/s^2
Vf=[sqrt{19561.8224 ft^2/s^2}
Vf=139.864 ft/s
Time t= (Vf-Vo)/g => (139.864 ft/s-0)/32.174 ft/s^2 = 4.34 sec
Good luck!
Engineering controls are the physical changes that employers make to the work environment or to equipment that make it safer to use.
A) True B) False
Answer:
True
Explanation:
Engineering controls are those techniques used to reduce or eliminate hazards of any condition, thereby protecting the workers.
These are mostly products that act as barriers between the worker and the hazard. This may include machinery or equipment. The common engineering controls used are glovebox, biosafety cabinet, fume hood, vented balance safety enclosure, HVAC system, lockout-tagout, sticky mat and rupture disc.
An alloy has a yield strength of 818 MPa and an elastic modulus of 104 GPa. Calculate the modulus of resilience for this alloy [in J/m3 (which is equivalent to Pa)] given that it exhibits linear elastic stress-strain behavior.
Answer:
Modulus of resilience will be [tex]3216942.308j/m^3[/tex]
Explanation:
We have given yield strength [tex]\sigma _y=818MPa[/tex]
Elastic modulus E = 104 GPa
We have to find the modulus
Modulus of resilience is given by
Modulus of resilience [tex]=\frac{\sigma _y^2}{2E}[/tex], here [tex]\sigma _y[/tex] is yield strength and E is elastic modulus
Modulus of resilience [tex]=\frac{(818\times 10^6)^2}{2\times 104\times 10^9}=3216942.308j/m^3[/tex]
The absolute pressure in water at a depth of 9 m is read to be 185 kPa. Determine: a. The local atmospheric pressure b. The absolute pressure at a depth of 5 m in liquid whose specific gravity is 0.8 at the same location.
Answer:
a)Patm=135.95Kpa
b)Pabs=175.91Kpa
Explanation:
the absolute pressure is the sum of the water pressure plus the atmospheric pressure, which means that for point a we have the following equation
Pabs=Pw+Patm(1)
Where
Pabs=absolute pressure
Pw=Water pressure
Patm= atmospheric pressure
Water pressure is calculated with the following equation
Pw=γ.h(2)
where
γ=especific weight of water=9.81KN/M^3
H=depht
A)
Solving using ecuations 1 y 2
Patm=Pabs-Pw
Patm=185-9.81*5=135.95Kpa
B)
Solving using ecuations 1 y 2, and atmospheric pressure
Pabs=0.8x5x9.81+135.95=175.91Kpa
A particle moves with a constant speed of 6 m/s along a circular path of a radius of 4 m. What is the magnitude of its acceleration. Do not include units in your answer, assumed unit are m/s2.
Answer:
Acceleration in circular path will be 9
Explanation:
We have given speed of the particle in circular path = 6 m/sec
Radius of the circular path = 4 m
We have to find the centripetal acceleration [tex]a_c[/tex]
We know that centripetal acceleration is given by [tex]a_c=\frac{v^2}{r}=\frac{6^2}{4}=9[/tex]
As in question it is given that don't include the unit
So acceleration will be 9
A train which is traveling at 70 mi/hr applies its brakes as it reaches point A and slows down with a constant deceleration. Its decreased velocity is observed to be 52 mi/hr as it passes a point 1/2 mi beyond A. A car moving at 52 mi/hr passes point B at the same instant that the train reaches point A. In an unwise effort to beat the train to the crossing, the driver steps on the gas.
(a) Calculate the constant acceleration a that the car must have in order to beat the train to the crossing by 4.3 sec.
(b) find the velocity v of the car as it reaches the crossing.
Answer:
a) 0 mi/s^2
b) 52 mi/s
Explanation:
Assuming the crossing is 1/2 mile past point A and that point B is near point A (it isn't clear in the problem)
The train was running at 70 mi/h at point A and with constant deceleration reachesn the crossing 1/2 mile away with a speed of 52 mi/h
The equation for position under constant acceleration is:
X(t) = X0 + V0 * t + 1/2 * a * t^2
I set my reference system so that the train passes point A at t=0 and point A is X = 0, so X0 = 0.
Also the equation for speed under constant acceleration is:
V(t) = V0 + a * t
Replacing
52 = 70 + a * t
Rearranging
a * t = 52 - 70
a = -18/t
I can then calculate the time it will take it to reach the crossing
1/2 * a * t^2 + V0 * t - X(t) = 0
Replacing
1/2 (-18/t) * t^ + 70 * t - 1/2 = 0
-9 * t + 70 * t = 1/2
61 * t = 1/2
t = (1/2)/61 = 0.0082 h = 29.5 s
And the acceleration is:
a = -18/0.0082 = -2195 mi/(h^2)
To beath the train the car must reach the crossing in 29.5 - 4.3 = 25.2 s
X(t) = X0 + V0 * t + 1/2 * a * t^2
52 mi/h = 0.0144 mi/s
1/2 = 0 + 0.0144 * 25.2 + 1/2 * a * 25.2^2
1/2 = 0.363 + 317.5 * a
317.5 * a = 0.5 - 0.363
a = 0.137/317.5 = 0.00043 mi/s^2 (its almost zero)
The car should remain at about constant speed.
It will be running at the same speed.
What are factor of safety for brittle and ductile material
Explanation:
Step1
Factor of safety is the number that is taken for the safe design of any component. It is the ratio of failure stress to the maximum allowable stress for the material.
Step2
It is an important parameter for design of any component. This factor of safety is taken according to the environment condition, type of material, strength, type of component etc.
Step3
Different material has different failure stress. So, ductile material fails under shear force. Ductile material’s FOS is based on yield stress as failure stress as after yield point ductile material tends to yield. Brittle material’s FOS is based on ultimate stress as failure stress.
The expression for factor of safety for ductile material is given as follows:
[tex]FOS=\frac{\sigma_{yp}}{\sigma_{a}}[/tex]
Here,[tex]\sigma_{f}[/tex] is yield stress and [tex]\sigma_{a}[/tex] is allowable stress.
The expression for factor of safety for brittle material is given as follows:
[tex]FOS=\frac{\sigma_{ut}}{\sigma_{a}}[/tex]
Here,[tex]\sigma_{ut}[/tex] is ultimate stress and [tex]\sigma_{a}[/tex] is allowable stress.
A substance temperature was 62 deg R. What is the temperature in deg C? A.) 50.7 B.) 45.54 C) 80.0 D) 94.4
Answer:
The temperature in degree Celsius will be -238.7055°C
Explanation:
We have given the substance temperature = 62°R
We have to convert degree Rankine to degree Celsius
For conversion from Rankine to Celsius we use formula
[tex]T_C=(T_R-491.67)\times\frac{5}{9}[/tex]
So [tex]T_C=(62-491.67)\times\frac{5}{9}[/tex]
[tex]T_C=-238.7055^{\circ}C[/tex]
So temperature in degree Celsius will be -238.7055°C
After calculation i got -238.7055°C but in option this is not given
The temperature of the substance will be "94.4°C". To understand the calculation, check below.
TemperatureAccording to the question,
Substance temperature, T°R = 62
or,
T°C = (T°R - 491.67) × [tex]\frac{5}{9}[/tex]
By substituting the values,
= -238.706
If we take the value,
T°C = (662 - 491.67) × [tex]\frac{5}{9}[/tex]
= 94.62°C or,
= 94.4°C
Thus the above response "Option D" is correct.
Find out more information about temperature here:
https://brainly.com/question/16559442
Convert 250 lb·ft to N.m. Express your answer using three significant figures.
Answer:
It will be equivalent to 338.95 N-m
Explanation:
We have to convert 250 lb-ft to N-m
We know that 1 lb = 4.45 N
So foe converting from lb to N we have to multiply with 4.45
So 250 lb = 250×4.45 =125 N
And we know that 1 feet = 0.3048 meter
Now we have to convert 250 lb-ft to N-m
So [tex]250lb-ft=250\times 4.45N\times 0.348M=338.95N-m[/tex]
So 250 lb-ft = 338.95 N-m
Find the Hooke's law of orthotropic and transverse isotropic material in matrix form
Answer:
Hooke's law is a principle of physics that states that the force F needed to extend or compress a spring by some distance X is proportional to that distance. That is: F = kX, where k is a constant factor characteristic of the spring: its stiffness, and X is small compared to the total possible deformation of the spring.
Explanation:
A reversible cyclic device does work while exchanging heat with three constant temperature reservoirs. The three reservoirs (1,2, and 3) are at temperatures of 1000K, 300K, and 500K. Four hundred kilojoules of heat are transferred from reservoir 1 to the device, and the total work done is 100 kJ. Find the magnitude and direction of the heat transfer from the other two reservoirs.
Answer:
Lets take [tex]Q_2[/tex] heat transfer take place from 500 K reservoir to device and [tex]Q_3[/tex] from device to 300 K reservoir.
From the energy conservation we can say that
[tex]400+Q_2=100+Q_3[/tex]
[tex]300=Q_3-Q_2[/tex] -----1
For reversible process
[tex]\dfrac{400}{1000}+\dfrac{Q_2}{500}-\dfrac{Q_3}{300}=0[/tex]
[tex]5Q_3-3Q_2=600[/tex] ----2
By solving above two equation
[tex]Q_3=-150 KJ,Q_2=-450KJ[/tex]
But here sign come negative it means that
[tex]Q_2[/tex] heat transfer take place from device to 500 K reservoir and [tex]Q_3[/tex] from 300 K reservoir to device.
In this exercise we have to use the knowledge of heat transfer to calculate the heat transferred to the other two reservoirs will be:
The magnitude of the Q2 is -450 in the out direction while the Q3 is -150 in the inward direction.
From the information given in the statement, we have that:
Temperatures of 1000K, 300K, and 500K. Four hundred kilojoules of heat are transferred Total work done is 100 kJ.knowing that from conservation we can say:
[tex]400+Q_2=100+Q_3\\300=Q_3-Q_2\\\frac{400}{1000}+\frac{Q_2}{500}-\frac{Q_3}{300}=0\\[/tex]
So solving we have:
[tex]Q_3=-150KJ\\Q_2=-450KJ[/tex]
See more about heat transfer at brainly.com/question/12107378
Explain the following boundary layer concepts (i) Boundary layer thickness (ii) Boundary layer transition
Answer with Explanation:
i) Boundary layer thickness: It is the thickness of the boundary layer formed around an object that is placed in the path of a flowing viscous fluid.The boundary layer thickness is the thickness up to which the effect of the object on the flow can be felt. When a viscous flowing fluid encounters an object in it's path of flow, the flowing fluid forms a thin layer of fluid over the object and this layer of fluid is known as boundary layer. This is a phenomenon only observed in the viscous fluids. As shown in the below figure a uniform flow of a viscous fluid encounters a plate, as we can see the thickness of the boundary layer goes on increasing as we move away from the leading edge of the plate the thickness of the boundary layer at any position is termed as boundary layer thickness.
ii) Boundary layer transition: It is the transition of the flow from a laminar nature to fully developed turbulent flow as it moves over an object. It occurs due to change in the Reynolds number of the flow as the effect of boundary layer increases as we move away from the leading edge of the object.
The pulley has mass 12.0 kg, outer radius Ro=250 mm, inner radius Ri=200 mm, and radius of gyration kO=231 mm. Cylinder A weighs 71.0 N. Assume there is no friction between the pulley and its axle and that the rope is massless. At the instant when ω=69.0 rad/s clockwise, what is the kinetic energy of the system?
The total kinetic energy of the system is approximately 17128.26 J.T
What is the energy?
Calculate the moment of inertia (I) of the pulley:
= 0.5 * mass * (outer radius² + inner radius²)
= [tex]0.5 * 12.0 kg * ((0.250 m)² + (0.200 m)²)[/tex]
= 1.925 kg * m²
Use the parallel-axis theorem to find I:
I = [tex]1.925 kg * m² + 12.0 kg * (0.231 m)²[/tex]
I = 2.5683 kg * m²
Calculate the kinetic energy of the pulley:
= 0.5 * I * omega²
= [tex]0.5 * 2.5683 kg * m² * (69.0 rad/s)[/tex]
= 6555.63 J
Calculate the linear velocity of cylinder A:
v = outer radius * omega
v =[tex]0.250 m * 69.0 rad/s[/tex]
v = 17.25 m/s
Calculate the kinetic energy of cylinder A:
= 0.5 * mass * v²
= [tex]0.5 * 71.0 kg * (17.25 m/s)²[/tex]
= 10572.63 J
KEtotal = KEpulley + KEcylinder
= [tex]6555.63 J + 10572.63 J[/tex]
= 17128.26 J
The typical area of a commercial airplane's passenger window is 80.0 in^2 . At an altitude of 3.00 × 104 ft above the sea level, the atmospheric pressure is 0.350 atm. Determine the net force on the passenger window during flight at that altitude for both the English Engineering (EE) and SI unit systems. Use appropriate units and unit conversions in all steps of your calculations.
Answer:
The force over the plane windows are 764 lbf in the EE unit system and 3398 N in the international unit system.
Explanation:
The net force over the window is calculated by multiplying the difference in pressure by the area of the window:
F = Δp*A
The pressure inside the plane is around 1 atm, hence the difference in pressure is:
Δp = 1atm - 0.35 atm = 0.65 atm
Expressing in the EE unit system:
Δp = 0.65 atm * 14.69 lbf/in^2 = 9.55 lbf/in^2
Replacing in the force:
F = 9.55 lbf/in^2 * 80 in^2 = 764 lbf
For the international unit system, we re-calculate the window's area and the difference in pressure:
A = 80 in^2 * (0.0254 m/in)^2 = 0.0516 m^2
Δp = 0.65 atm * 101325 Pa = 65861 Pa = 65861 N/m^2
Replacing in the force:
F = 65861 N/m^2 *0.0516 m^2 = 3398 N
The Air Force One (Boeing 747-200) has a long-range mission takeoff gross load 833,000 pounds (Ibm). What is Air Force One's takeoff mass in: a. gram (9) b. kilogram (kg) c. tonne (ton) d. Mton
Answer:
The mass in:
1) Grams =[tex]377765.5\times 10^{3}grams[/tex]
2) Kilograms =[tex]377765.5kilograms[/tex]
3)Tonnes =[tex]377.7655tonnes[/tex]
4) Megatonnes =[tex]0.378megatonnes[/tex]
Explanation: The given mass of the aircraft in pounds is 833,000 pounds.
Part 1)
Since we know that 1 pound equals 453.5 grams thus by ratio we have
833,000 pounds =[tex]833000lb\times 453.5\frac{g}{lb}=377765.5\times 10^{3}grams[/tex]
Part 2)
Since we know that 1000 grams equals 1 kilogram
thus the above mass in kilograms equals[tex]\frac{377765.5\times 10^{3}}{1000}=377765.5kg[/tex]
Part 3)
Since there are 1000 kilograms in 1 tonne
thus the given mass is converted into tonnes as
[tex]mass_{tonnes}=\frac{377765.5kg}{1000}=377.765tonnes[/tex]
Part 4)
Since 1 Mega tonne(Mton) equals 1000 tonnes thus the given mass is converted into mega tonnes as
[tex]mass_{M\cdot tonn}=\frac{377.7655tonnes}{1000}=0.378Megatonnes[/tex]
Calculate the angle of banking on a bend of 100m radius so that vehicles can travel round the bend at 50km/hr without side thrust on the tyres.
Answer:
11.125°
Explanation:
Given:
Radius of bend, R = 100 m
Speed around the bend = 50 Km/hr = [tex]\frac{5}{18}\times50[/tex] = 13.89 m/s
Now,
We have the relation
[tex]\tan\theta=\frac{v^2}{gR}[/tex]
where,
θ = angle of banking
g is the acceleration due to gravity
on substituting the respective values, we get
[tex]\tan\theta=\frac{13.89^2}{9.81\times100}[/tex]
or
[tex]\tan\theta=0.1966[/tex]
or
θ = 11.125°
A 29-mm-diameter copper rod is 1.1 m long with a yield strength of 73 MPa. Determine the axial force necessary to cause the diameter of the rod to reduce by 0.01 percent, assuming elastic deformation. Check that the elastic deformation assumption is valid by comparing the axial stress to the yield strength. The axial force necessary to cause the diameter of the rod to reduce by 0.01 percent is ____kN.
Answer:
32.96 MPa
Explanation:
The Poisson ratio of copper is:
μ = 0.355
The Young's modulus of copper is:
E = 117 GPa
The equation for reduction of diameter of a rod is:
D = D0 * (1 - μ*σ/E)
Rearranging:
D = D0 - D0*μ*σ/E
D0*μ*σ/E = D0 - D
D0*μ*σ = E*(D0 - D)
σ = E*(D0 - D) / (D0*μ)
If the diameter is reduced by 0.01 percent
D = 0.9999*D0
σ = E*(D0 - 0.9999*D0) / (D0*μ)
σ = E*(0.0001*D0) / (D0*μ)
σ = 0.0001*E / μ
σ = 0.0001*117*10^9 / 0.355 = 32.96 MPa
This value is below the yield strength, therefore it is valid.
A 0.5 m^3 container is filled with a mixture of 10% by volume ethanol and 90% by volume water at 25 °C. Find the weight of the liquid.
Answer:
total weight of liquid = 4788.25 N or 488.09 kg
Explanation:
given data
total volume = 0.5 m³
volume of ethanol = 10 % of volume = 0.10 × 0.5 = 0.05 m³
volume of water = 90 % at 25 °C of volume = 0.90 × 0.5 = 0.45 m³
to find out
weight of the liquid
solution
we know that density of water at 25 is 997 kg/m³
and density of ethanol is 789 kg/m³
so weight of water is = density × volume × g
put here value and we take g = 9.81
weight of water is = 997 × 0.45 × 9.81
weight of water = 4401.25 N ......................1
weight of ethanol is = density × volume × g
put here value and we take g = 9.81
weight of ethanol is = 789 × 0.05 × 9.81
weight of ethanol = 387.00 N ...............2
so total weight of liquid = sum of equation 1 add 2
total weight of liquid = 4401.25 + 387
total weight of liquid = 4788.25 N or 488.09 kg
Explain the difference between planning and shaping by the help of sketch
Explanation:
In shaping work piece will be stationary and tool will reciprocates,but on the other hand in planning work piece will reciprocates and tool will be stationary.Shaping is used for small work piece and planning is used for large work piece.Both shaping and planning are not continuous cutting process,cutting action take place in forward stroke and return stroke is idle stroke.The velocity of return stroke is much more than the forward stroke.
A square isothermal chip is of width w = 5 mm on a side and is mounted in a substrate such that its side and back surfaces are well insulated; the front surface is exposed to the flow of a coolant at T[infinity] = 15°C. From reliability considerations, the chip temperature must not exceed T = 85°C.f the coolant is air and the corresponding convection 200 W/m2 K, what is the maximum coefficient is h allowable chip power? If the coolant is a dielectric liquid for which h 3000 W/m2 K, what is the maxi- mum allowable power?
Answer:
Q(h=200)=0.35W
Q(h=3000)=5.25W
Explanation:
first part h=200W/Km^2
we must use the convection heat transfer equation for the chip
Q=hA(Ts-T∞)
h= convective coefficient=200W/m2 K
A=Base*Leght=5mmx5mm=25mm^2
Ts=temperature of the chip=85C
T∞=temperature of coolant=15C
Q=200x2.5x10^-5(85-15)=0.35W
Second part h=3000W/Km^2
Q=3000x2.5x10^-5(85-15)=5.25W
The Torricelli's theorem states that the (velocity—pressure-density) of liquid flowing out of an orifice is proportional to the square root of the (height-pressure-velocity) of liquid above the center of the orifice.
Answer:
The correct answer is 'velocity'of liquid flowing out of an orifice is proportional to the square root of the 'height' of liquid above the center of the orifice.
Explanation:
Torricelli's theorem states that
[tex]v_{exit}=\sqrt{2gh}[/tex]
where
[tex]v_{exit}[/tex] is the velocity with which the fluid leaves orifice
[tex]h[/tex] is the head under which the flow occurs.
Thus we can compare the given options to arrive at the correct answer
Velocity is proportional to square root of head under which the flow occurs.
The position of a particle along a straight-line path is defined by s = (t3 - 6t2 - 15t + 7) ft, where t is in seconds. When t = 8 s, determine the particle’s (a) instantaneous velocity and instantaneous acceleration, (b) average velocity and average speed
To determine the instantaneous velocity and acceleration of a particle described by the position function s(t), one needs to calculate the first and second derivatives of the position function and evaluate them at the given time, t = 8 s. The average velocity and speed require the change in position over a specific time interval, which is not provided in the question.
Explanation:The position of a particle along a straight-line path is given by the equation s = (t3 - 6t2 - 15t + 7) feet, where t is time in seconds. To find the particle's instantaneous velocity and instantaneous acceleration at t = 8 s, we need to take the first and second derivatives of the position function with respect to time, respectively.
The first derivative of s with respect to t gives us the velocity v(t), and the second derivative gives us the acceleration a(t). At t = 8 s, the velocities and accelerations can be calculated by plugging in the value of t into those derivatives.
To determine the average velocity and average speed, we take the change in position over the change in time interval for the specific time range provided.
Note: The question lacks sufficient specific information to calculate these values as the time interval for the average velocity and average speed is not provided. However, the general process of calculation has been explained.
Acceleration, instantaneous velocity, and particle position at different times are essential concepts in physics and particle motion analysis.
Acceleration is the rate of change of velocity with respect to time. In the given scenarios, acceleration is provided in terms of a function of time or as a constant value.
Instantaneous velocity is the velocity of the particle at a specific moment. It can be calculated by taking the derivative of the position function with respect to time.
Position of the particle at different times can be found by substituting the respective time values into the position function.
What colour is best for radiative heat transfer? a. Black b. Brown c. Blue d. White
Answer:
The correct answer is option 'a': Black
Explanation:
As we know that for an object which is black in color it absorbs all the electromagnetic radiation's that are incident on it. Thus if we need to transfer energy to an object by radiation the most suitable color for the process is black.
In contrast to black color white color is an excellent reflector, reflecting all the incident radiation that may be incident on it hence is the least suitable material for radiative heat transfer.
You live on a street that runs East to West. You just had 2 inche of snow and you live on the North side of the street. You return from class at 2PM and notice all the snow on your sidewalk is gone but across the street it is still there. No one removed the snow. How did it go away?
Answer:
The heat from the sun melted it
Explanation:
If the street runs east to west, houses on the south (across the street) will project shadows on their sidewalk, while the northern sidewalk will be illuminated. This is for the northern hemisphere, on the southern hemisphere it would be the other way around.
A rectangular sheet of 120 mm x 160 mm can be used to develop the lateral surface of (a) A cylinder of radius 80/π (b) A square prism of side 40 mm (c) A hexagonal prism of side 20 mm (d) All of the above
Answer:
option D is correct
Explanation:
1) for a cylinder with radius is[tex]\frac{80}{\pi}[/tex]
lateral surface area of cylinder is [tex]2\pi rh[/tex]
[tex]= 2\pi \frac{80}{\pi}*120[/tex]
= 160* 120
2) fro square prism with side 40 mm
lateral surface area = 4ah
= 4*40 * 120
= 160*120
3)for hexagonal with side 20 mm
lateral surface area = 6ah
= 6*20*160
=120* 160
therefore option D is correcrt
A water tank is emptied through a pipe with an outlet 5m below the water surface level. What is the exit velocity? a) 2.1m/s b) 9.9 m/s c) -12.3m/s d)-4.8m/s e) 15.3m/s
Answer:
The correct answer is option 'b': 9.9 m/s
Explanation:
We know that for an ideal fluid the velocity of exit from a tank with the height of water 'h' is given by Torricelli's Law as
[tex]v=\sqrt{2gh}[/tex]
where,
'g' is acceleration due to gravity
'h' is the level of water
Applying the given values we obtain velocity as
[tex]v=\sqrt{2\times 9.81\times 5}=9.90m/s[/tex]
At the beginning of the compression process of an air-standard Diesel cycle, p1 = 95 kPa and T1 = 300 K. The maximum temperature is 2100 K and the mass of air is 12 g. For a compression ratio of 18, determine the net work developed in kJ (enter a number only)
Answer:
6.8 kJ
Explanation:
p1 = 95 kPa
T1 = 300 K
T3 = 2100 K
m = 12 g
Ideal gas equation:
p * v = R * T
v = R * T / p
R for air is 0.287 kJ/(kg K)
v1 = 0.287 * 300 / 95 = 0.9 m^3/kg
v2 = v1 / cr
v2 = 0.9 / 18 = 0.05 m^3/kg
Assuming an adiabatic compression
p*v^k = constant
k is 1.4 for air
p1 * v1 ^ k = p2 * v2 ^ k
p2 = p1 * (v1 / v2) ^k
p2 = p1 * cr^k
p2 = 95 * 18^1.4 = 5.43 MPa
p1*v1/T1 = p2*v2/T2
T2 = p2*v2*T1/(p1*v1)
T2 = 5430 * 0.05 * 300 / (95 * 0.9) = 952 K
The first principle of thermodynamics
Q = W + ΔU
Since this is an adiabatic process Q = 0
W = -ΔU
W1-2 = -m * Cv * (T2 - T1)
The Cv of air is 0.72 kJ/kg
W1-2 = -0.012 * 0.72 * (952 - 300) = -5.63 kJ
Next the combustion happens and temperature increases suddenly.
v3 = v2 = 0.05 m^3/kg
T2 * p2^((1-k)/k) = T3 * p3^((1-k)/k)
p3 = p2 * (T2/T3)^(k/(1-k)
p3 = 5430 * (952/2100)^(1.4/(1-1.4) = 86.5 MPa
The work is zero because the piston doesn't move.
Next it expands adiabatically:
v4 = v1 = 0.9 m^3/kg
T * v^(k-1) = constant (adiabatic process)
T3 * v3^(k-1) = T4 * v4^(k-1)
T4 = T3 * (v3 / v4)^(k-1)
T4 = 2100 * (0.05 / 0.9)^(1.4-1) = 661 K
p3*v3/T3 = p4*v4/T4
p4 = p3*v3*T4/(v4*T3)
p4 = 86500*0.05*661/(0.9*2100) = 1512 kPa
L3-4 = -m * Cv * (T4 - T3)
L3-4 = -0.012 * 0.72 * (661 - 2100) = 12.43 kJ
Net work:
L1-2 + L3-4 = -5.63 + 12.43 = 6.8 kJ
What are the units or dimensions of the shear rate dv/dy (English units)? Then, what are the dimensions of the shear stress τ= μ*dV/dy? Then, by dimensional analysis, show that the shear stress has the same units as momentum divided by (area*time).What are the unit or dimensions of viscosity?
Answer:
1) Dimensions of shear rate is [tex][T^{-1}][/tex] .
2)Dimensions of shear stress are [tex][ML^{-1}T^{-2}][/tex]
Explanation:
Since the dimensions of velocity 'v' are [tex][LT^{-1}][/tex] and the dimensions of distance 'y' are [tex][L][/tex] , thus the dimensions of [tex]\frac{dv}{dy}[/tex] become
[tex]\frac{[LT^{-1}]}{[L]}=[T^{-1}][/tex] and hence the units become [tex]s^{-1}[/tex].
Now we know that the dimensions of coefficient of dynamic viscosity [tex]\mu [/tex] are [tex][ML^{-1}T^{-1}][/tex] thus the dimensions of shear stress can be obtained from the given formula as
[tex][\tau ]=[ML^{-1}T^{-1}]\times [T^{-1}]\\\\[\tau ]=[ML^{-1}T^{-2}][/tex]
Now we know that dimensions of momentum are [tex][MLT^{-1}][/tex]
The dimensions of [tex]Area\times time[/tex] are [tex][L^{2}T][/tex]
Thus the dimensions of [tex]\frac{Moumentum}{Area\times time}=\frac{MLT^{-1}}{L^{2}T}=[MLT^{-2}][/tex]
Which is same as that of shear stress. Hence proved.