A Scotch-yoke mechanism is used to convert rotary motion into reciprocating motion. As the disk rotates at the constant angular rate , a pin A slides in a vertical slot causing the slotted member to displace horizontally according to x = r sin(t) relative to the fi xed disk center O. Determine the expressions for the velocity and acceleration of a point P

Answer:

Explanation:

A- Specific gravity and Absorption Test: Specific gravity is a measure of a material’s density as compared to the density of water at 73.4°F (23°C). Therefore, by definition, water at a temperature of 73.4°F (23°C) has a specific gravity of 1. Absorption is also determined by the same test procedure and it is a measure of the amount of water that an aggregate can absorb into its pore structure.

Specific gravity is used in a number of applications including Superpave mix design, deleterious particle identification and separation and material property change identification while

B- Soundness Test : This determines an aggregate's resistance to disintegration by weathering and in particular, freeze-thaw cycles. Aggregates that are durable (resistant to weathering) are less likely to degrade in the field and cause premature HMA pavement distress and potentially failure.It is used to identify the excess amount of lime in cement.

C - Sieve analysis Test: is a practice or procedure used to assess the particle size distribution (also called gradation) of a granular material by allowing the material to pass through a series of sieves of progressively smaller mesh size and weighing the amount of material that is stopped by each sieve as a fraction of the whole mass. This test is used to describe the properties of the aggregate and to see if it is appropriate for various civil engineering purposes such as selecting the appropriate aggregate for concrete mixes and asphalt mixes as well as sizing of water production well screens.

Answer:

a) the two-way concrete joist framing system

Explanation:

A waffle slab is also known as ribbed slab, it is a slab which as waffle like appearance with holes beneath. It is adopted in construction projects that has long length, length more than 12m. The waffle slab is rigid, therefore it is used in building that needs minimal vibration.

Answer:

Power of the motor that kept the wheel rotating at 12 rev/hr despite friction is 342.79W.

Explanation:

Pls refer to the attached file. The explanation is long to pen down here.

Answer:

1121.7 × 10³⁰ photons per second

Explanation:

Data provided in the question:

Power transmitted by the AM radio,P = 550 kW = 550 × 10³ W

Frequency of AM radio, f = 740 kHz = 740 × 10³ Hz

Now,

P = [tex]\frac{NE}{t}[/tex]

here,

N is the number of photons

t is the time

E = energy = hf

h = plank's constant = 6.626 × 10⁻³⁴ m² kg / s

Thus,

P = [tex]\frac{NE}{t}[/tex] = [tex]\frac{N\times(6.626\times10^{-34}\times740\times10^{3})}{1}[/tex]          [t = 1 s for per second]

or

550 × 10³ = [tex]\frac{N\times(6.626\times10^{-34}\times740\times10^{3})}{1}[/tex]

or

550 = N × 4903.24 × 10⁻³⁴

or

N = 0.11217 × 10³⁴ = 1121.7 × 10³⁰ photons per second

The number of photons that are emitted by this AM radio transmitter is equal to [tex]1.12 \times 10^{33}\;photons.[/tex]

Given the following data:

Scientific data:

In order to determine the number of photons that are being emitted by this AM radio transmitter, we would solve for the quantity of energy it consumes by using Planck-Einstein's equation.

Mathematically, the Planck-Einstein relation is given by the formula:

[tex]E = hf[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]E = 6.626 \times 10^{-34}\times 740 \times 10^3\\\\E = 4.903 \times 10^{-28}\;Joules.[/tex]

For the number of photons:

[tex]n=\frac{Power}{Energy} \\\\n=\frac{550 \times 10^3}{4.903 \times 10^{-28}} \\\\n=1.12 \times 10^{33}\;photons.[/tex]

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Properties of Carpenter's hammer possess

Explanation:

1.The head of a carpenter's hammer should possess the impact resistance, so that the chips do not peel off the striking face while working.

2.The hammer head should also be very hard, so that it does not deform while driving or eradicate any nails in wood.

3.Carpenter's hammer is used to impact smaller areas of an object.It can drive nails in the wood,can crush  the rock and shape the metal.It is not suitable for heavy work.

How hammer head is manufactured :

1.Hammer head is produced by metal forging process.

2.In this process metal is heated and this molten metal is placed in the cavities said to be dies.

3.One die is fixed and another die is movable.Ram forces the two dies under the forces which gives the metal desired shape.

4.The third process is repeated for several times.

To solve this problem we will apply the concepts related to real power in 3 phases, which is defined as the product between the phase voltage, the phase current and the power factor (Specifically given by the cosine of the phase angle). First we will find the phase voltage from the given voltage and proceed to find the current by clearing it from the previously mentioned formula. Our values are

[tex]V = 690V[/tex]

[tex]P_{real} = 2.3MW[/tex]

Real power in 3 phase

[tex]P_{real} = 3V_{ph}I_{ph} Cos\theta[/tex]

Now the Phase Voltage is,

[tex]V_{ph} = \frac{V}{\sqrt{3}}[/tex]

[tex]V_{ph} = \frac{690}{\sqrt{3}}[/tex]

[tex]V_{ph} = 398.37V[/tex]

The current phase would be,

[tex]P_{real} = 3V_{ph}I_{ph} Cos\theta[/tex]

Rearranging,

[tex]I_{ph}=\frac{P_{real}}{3V_{ph}Cos\theta}[/tex]

Replacing,

[tex]I_{ph}=\frac{2.3MW}{3( 398.37V)(0.85)}[/tex]

[tex]I_{ph}= 2.26kA/phase[/tex]

Therefore the current per phase is 2.26kA

Answer:

a.The current is cut in half

b.the current stays the same

c.the current doubles

d.the current becomes zero

Explanation:

The current doubles

Answer:

Explanation:

val db = ("John", "x3456", 50.1) :: ("Jane", "x1234", 107.3) ::

        ("Joan", "unlisted", 12.7) :: Nil

type listOfTuples = List[(String, String, Double)]

def find_salary(name: String) = {

 def search(t: listOfTuples): Double = t match {

   case (name_, _, salary) :: t if name == name_ => salary

   case _ :: t => search(t)

   case Nil    =>

     throw new Exception("Invalid Argument in find_salary")

 }

 search(db)

}

def select(pred: (String, String, Double) => Boolean) = {

 def search(found: listOfTuples): listOfTuples = found match {

   case (p1, p2, p3) :: t if pred(p1, p2, p3)  => (p1, p2, p3) :: search(t)

   case (p1, p2, p3) :: t if !pred(p1, p2, p3) => search(t)

   case Nil => Nil

   case _ => throw new Exception("Invalid Argument in select function")

 }

 search(db)

}

println("Searching the salary of 'Joan' at db: " + find_salary("Joan"))

println("")

val predicate = (_:String, _:String, salary:Double) => (salary < 100.0)

println("All employees that match with predicate 'salary < 100.0': ")

println("\t" + select(predicate) + "\n")

Answer:

The answers to the question are

Explanation:

The number of employees in the firm = 62

Number of first-aid cases = 7

Number of medical treatment injuries = 3

Injury resulting restricted work activity = 1

Illness resulting in one week loss work day = 1

Illness resulting in loss of 6 weeks of work =1

Incident resulting in fatality = 1

Total hours worked = 40×62×50  = 124000 Hrs

Where 200,000 is the number of hours worked by Full time employees numbering 100 that  work for 40 Hours a week for 50 weeks in a year

Number of recordable incident =  Those incident that results in lost work days, death, restricted ability to work, or transfer to another task or more severe injury treatment beyond first aid

Therefore number recordabe incident = 7

Recordable Incident Rate is calculated by

IR = (Number of recordable incident Cases X 200,000)÷(Number of Employee labor hours worked)

= (7×200000)/124000= 11.29

The Lost Workday Rate is given by

Lost Workday Rate = (Total number of days lost to injury or illness)÷( Cumulative number of hours employees worked) × 200000

Total number of days lost to injury or illness = 42 days

Lost Workday Rate = (42/124000) × 200000 = 67.74

LWDI = (Number of incident resulting in lost workdays and restricted activity) ×200000 /(Total number of hours worked by all employees in one year)

LWDI = LWD×200000/ EH = 4×200000/124000 = 6.45

LWDI  = 6.45

Answer:

Detailed Answer is given below,

Explanation:

(a) Elastic strain

Elastic deformation is defined as the limit for the deformation values up to which the object will bounce and return to the original shape when the load is removed.

When the object is subjected to an external load, it deforms. If the load exceeds the load corresponding to the elastic limit of the object, then, after removing the load, the object cannot return to its original geometric specification.

(b) Plastic strain

Plastic Strain is a deformation that cannot be recovered after eliminating the deforming force. In other words, if the applied tension is greater than the elastic limit of the material, there will be a permanent deformation.

(c) Creep strain

The deformation of the material at a higher temperature is much more than at the normal temperature known as creep.

Subsequently, the deformation produced in heated material is called creep deformation. Creep deformation is a function of temperature.

(d) Tensile viscosity

Viscosity is a main parameter when measuring flux fluids, such as liquids, semi-solids, gases and even solids. Brookfield deals with liquids and semi-solids. Viscosity measurements are made together with the quality and efficiency of the product. Any person involved in the characterization of the flow, in research or development, quality control or transfer of fluids, at one time or another is involved with some kind of viscosity measurement.

(e) Recovery

Recovery is a process whereby deformed grains can reduce their stored energy by eliminating or reorganizing defects in their crystalline structure. These defects, mainly dislocations, are introduced by plastic deformation of the material and act to increase the elastic limit of a material.

(f) Relaxation

Stress relaxation occurs in polymers when they remain tense for long periods of time.

These alloys have very good resistance to stress relaxation and, therefore, are used as spring materials.

Stress relaxation is a gradual reduction of stress over time in constant tension.

Answer:

SaaS

Explanation:

Software as a service (SaaS) is also called software on demand, it involves a third party that centrally hosts the software and provides it to the end user.

All aspects of hosting is handled by the third party: application, data, runtime, middleware, operating system, server, virtualization, storage and networking are all handled by the provider.

This is an ideal software service for Fictional corp, as there will be no need to hire additional IT staff to maintain the new CRM software.

Answer:

[tex]\eta=0.303[/tex]

Explanation:

Given that

Temperature of the hot reservoir ,T₁ = 970 K

Temperature of the cold reservoir ,T₂ = 480 K

We know that only Carnot engine is the ideal engine which gives us the maximum power.The efficiency of Carnot engine is given as

[tex]\eta_{max}=1-\dfrac{T_2}{T_1}[/tex]

[tex]\eta_{max}=1-\dfrac{480}{970}[/tex]

[tex]\eta_{max}=0.505[/tex]

Therefore the efficiency of the given engine will be

[tex]\eta=\dfrac{3}{5}\eta_{max}[/tex]

[tex]\eta=\dfrac{3}{5}\times 0.505[/tex]

[tex]\eta=0.303[/tex]

Answer:

Due to differences in the nature of the adhesive force and cohesive forces in the molecules of the individual substances and the glass tube.

Explanation:

To understand why this is so, a deep understanding of adhesive and cohesive force is required.

First, what is adhesive force?

Note: Adhesive and cohesive forces are best discussed under macroscopic level.

Adhesive force is the Intermolecular forces that exist between atoms of different molecules e g the forces explain when unlike charges stick together.

Cohesive force on the other hand is the Intermolecular force that exist between atoms of the same molecules e.g the force between hydrogen bonding.

Hence to explain the case scenario above, the adhesive force between the water molecules and the glass molecules is higher than the cohesive force between the water molecules. Hence the high rise.

For the case of the Hexane, the cohesive forces between the molecules hexane is far greater then the adhesive force between the glass molecules and the hexane molecules.

The spacing between two adjacent bright fringes, when a helium-neon laser with a wavelength of 633 nm illuminates two slits 0.50 mm apart and a screen is placed 2.5 m behind the slits, is 3.16 mm.

To answer the question on the spacing between two adjacent bright fringes for a helium-neon laser with a wavelength (λ) of 633 nm illuminating two slits spaced 0.50 mm apart, with a viewing screen 2.5 m behind the slits, we use the formula for the fringe spacing in a double-slit interference pattern, Δy = (λL) / d, where Δy is the fringe spacing, λ is the wavelength of the light, L is the distance from the slits to the screen, and d is the distance between the slits.

Given λ = 633 nm = 633 × 10-9 m, L = 2.5 m, and d = 0.50 mm = 0.50 × 10-3 m, plugging these values into the formula gives:

Δy = (633 × 10-9 m × 2.5 m) / (0.50 × 10-3 m) = 3.16 × 10-3 m = 3.16 mm

Therefore, the spacing between two adjacent bright fringes is 3.16 mm.

Answer:

z=60.32°, i=0.32°, Beam Radiation = 1097.2 W/m²,  Id = 94.2 W/m², Ir=14.1W/m², total radiation = 1205.4 W/m², Local time=1:21PM

Explanation:

A. Zenith Angle:

As we know that,

Zenith angle=z=90⁰-α=L(latitude)=29.68⁰

Another way to do it is to find α first,

At solar time hour angle is 0⁰. So, solar altitude becomes equal to latitude which could be written as

sinα=cosL

α=sin⁻¹(cosL)=sin⁻¹(cos29.68⁰)=60.32°

B. Angle of incidence:

angle of incidence= cosi=sin(α+β)=sin(60.32°+32°)=sin92.32°

i=cos⁻¹(sin92.32°)=0.32°

C. Beam Radiation:

First we need to calculate extra terrestrial radiations

Iext.=1353[1+0.034cos(360n/365)]

where n=264

=1345 W/m²

Now,

Beam Radiation=CIext⁻ⁿ

where n=0.1/sin60.32°

Beam Radiation = 1097.2 W/m²

D. Diffude Radiation:

difuse radiation = Id = 0.0921ₙcos²(β/2)

where β=30°

Id = 94.2 W/m²

E. Reflected Radiations:

Ir=pIn(sinα+0.092)sin²(β/2)

= (0.2)(1097.1)(sin60.32+0.092)sin²(30/2)

= 14.1W/m²

F. Total Radiation:

total radiation = beam radiation + diffuse radiation + reflected raddiation

= 1205.4 W/m²

G. Local Time:

LST= ST-ET-(lₓ-l(local))4min/₀

     = 12:00-7.9min-(75°-82.27°)4min/₀

     =12:21PM

Local time

LDT=LST+=12:21+1:00=1:21PM

Answer:

The motor inertia is 7.958 X 10⁻² kg.m²

Explanation:

To determine the motor inertia, the following formula applies.

Neglecting the damping effect,

[tex]T = \frac{J}{9.55}.\frac{\delta n}{\delta T}[/tex]

Where;

T is the constant torque applied to the motor = 5Nm

J is the motor inertia = ?

δn is the change in angular speed of the motor = 1800 r/min

δT is change in time of the unloaded motor from rest = 3 sec

[tex]J = \frac{9.55* \delta T* T}{\delta n}[/tex]

[tex]J = \frac{9.55* 3* 5}{1800}[/tex] = 0.07958 kg.m² = 7.958 X 10⁻² kg.m²

Therefore, the motor inertia is 7.958 X 10⁻² kg.m²

In the process of analyzing a thermodynamic system it is important to identify what system is being worked on and the processes and properties if the system

The magnitude of the force acting on the shaft, is approximately 1,336.5 N

The reason the value for the force magnitude acting on the shaft is correct is as follows:

The known parameters are:

The cross-sectional area of the shaft, Aₐ = 0.8 cm²

The required gas pressure in the cylinder, P = 3 bar

The mass of the piston, m₁ = 24.5 kg

The mass of the shaft, m₂ = 0.5 kg

The diameter of the piston, D = 10 cm

The atmospheric pressure, Pₐ = 1 bar

Required:

The magnitude of the force F acting on the shaft

Solution:

The force due to the gas in the cylinder, [tex]\mathbf{F_{gas}}[/tex], is given as follows;

[tex]F_{gas}[/tex] = 3 bar × π × (10 cm)²/4 = 2,359.19449 N

The force due to the atmosphere, [tex]\mathbf{F_{atm}}[/tex], is given as follows;

[tex]F_{atm}[/tex] = 1 bar × ((π × (10 cm)²/4) -  0.8 cm²) ≈ 777.4 N

The force due to the piston and shaft, [tex]\mathbf{F_{ps}}[/tex], is given as follows;

[tex]F_{ps}[/tex] = (24.5 kg + 0.5 kg) × 9.81 m/s² = 245.25 N

The magnitude of the force acting on the shaft, F = [tex]F_{gas}[/tex] - ([tex]\mathbf{F_{atm}}[/tex] + [tex]\mathbf{F_{ps}}[/tex])

∴ F = 2,359.19449 N - (777.4 N + 245.25 N) ≈ 1,336.5449 N

The magnitude of the force acting on the shaft, F ≈ 1,336.5 N

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Answer: BULK RELATIVE DENSITY.

WHY?

BULK RELATIVE DENSITY GIVES A BETTER UNDERSTANDING OF THE QUALITY OF THE MATERIAL.

Explanation:Bulk relative density is a type of Specific gravity which is often used in determining the volume occupied by the aggregates in various mixtures containing aggregate including Portland cement concrete, bituminous concrete etc this mixtures are proportioned based on an absolute volume basis. Bulk relative density is considered because of its ability to give a better understanding of the materials which makes up the mixture.

Answer:

The question is incomplete, below is the complete question "The electric potential difference between the ground and a cloud in a particular thunderstorm is [tex]3.0*10^{9}V[/tex]. What is the magnitude of the change in the electric potential energy of an electron that moves between the ground and the cloud?"

Answer:

[tex]U=3.0*10^{9}eV[/tex]

Explanation:

data given,

Potential difference,V=3.0*10^9V

charge on an electron, q=1e.

Recall that the relationship between potential difference (v), charge(Q) and the potential energy(U) is expressed as

[tex]U=qV[/tex]

from the question, we asked to determine potential energy given the charge and the potential difference.

Hence if we substitute values into the equation, we arrive at

[tex]U=qV\\U=3.0*10^{9}*1e\\U=3.0*10^{9}eV[/tex]

Hence the magnitude of the change in the electric potential energy of an electron that moves between the ground and the cloud is [tex]3.0*10^{9}eV[/tex]

Answer:

A. 36 minutes

B. 120 minutes

C.

i. 144 minutes

ii. 984 minutes

D. Car 1 is 1.67km ahead of Cat 2 when Car 2 passed the toll B.

E. 98.33km

Explanation

A.

Given

dAb = 10km

dBc = 10km

Propagation Speed = 100km/hr

Delay time = 1 minute

Numbers of cars = 8

Number of tolls = 3

Total End to End delay = Propagation delay + Transition delay

Calculating Propagation Delay

Propagation delay = Total Distance/Propagation speed

Total distance = 10km + 10km = 20km

So, Propagation delay = 20km/100km/hr

Propagation delay = 0.2 hour

Translation delay = delay time* numbers of tolls * numbers of cars

Transitional delay = 1 * 3 * 8

Transitional delay = 24 minutes

Total End delay = 24 minutes + 0.2 hours

= 24 minutes + 0.2 * 60 minutes

= 24 minutes + 12 minutes

= 36 minutes

B.

Total End to End delay = Propagation delay + Transition delay

Calculating Propagation Delay

Propagation delay = Total Distance/Propagation speed

Total distance = 10km + 10km = 20km

So, Propagation delay = 20km/100km/hr

Propagation delay = 0.2 hour

Translation delay = delay time* numbers of tolls ------ Cars traveling separately

Transitional delay = 1 * 3

Transitional delay = 3 minutes

Total End delay for one car = 3 minutes + 0.2 hours

= 3 minutes + 0.2 * 60 minutes

= 3 minutes + 12 minutes

= 15 minutes

Total End delay for 8 cars = 8 * 15 = 120 minutes

C.

Given

dAb = 100km

dBc = 100km

Propagation Speed = 100km/hr

Delay time = 1 minute

Numbers of cars = 8

Number of tolls = 3

i. Cars travelling together

Total End to End delay = Propagation delay + Transition delay

Calculating Propagation Delay

Propagation delay = Total Distance/Propagation speed

Total distance = 100km + 100km = 200km

So, Propagation delay = 200km/100km/hr

Propagation delay = 2 hours

Translation delay = delay time* numbers of tolls * numbers of cars

Transitional delay = 1 * 3 * 8

Transitional delay = 24 minutes

Total End delay = 24 minutes + 2 hours

= 24 minutes + 2 * 60 minutes

= 24 minutes + 120 minutes

= 144 minutes

ii. Cars travelling separately

Total End to End delay = Propagation delay + Transition delay

Calculating Propagation Delay

Propagation delay = Total Distance/Propagation speed

Total distance = 100km + 100km = 200km

So, Propagation delay = 200km/100km/hr

Propagation delay = 2 hours

Translation delay = delay time* numbers of tolls ------ Cars traveling separately

Transitional delay = 1 * 3

Transitional delay = 3 minutes

Total End delay for one car = 3 minutes + 2 hours

= 3 minutes + 2 * 60 minutes

= 3 minutes + 120 minutes

= 123 minutes

Total End delay for 8 cars = 8 * 123 = 984 minutes

D.

Distance = 100km

Time = 1 min/car

Car 1 is 1 minute ahead of car 2 --- at toll A and B

If car 1 leaves toll B after 10 minutes then cat 2 leaves after 11 minutes

Time delay = 11 - 10 = 1 minute

Distance = time * speed

= 1 minute * 100km/hr

= 1 hr/60 * 100 km/hr

= 100/60

= 1.67km

E.

Given

Distance = 100km

Distance behind = 1.67

Maximum value of dBc = 100km - 1.67km = 98.33km

The maximum distance that can be reached is 98.33km

Complete question:

The heat capacity of solid lead oxide is given by Cp,m=44.35+1.47×10⁻³T/K in units of J K−1 mol−1.

Calculate the change in enthalpy of 1.94 mol of PbO(s) if it is cooled from 732 K to 234 K at constant pressure.

Answer:

The change in enthalpy of PbO(s) is -39.488 x10³J

Explanation:

Given:

Initial temperature of PbO(s) (T₁) = 732 K

Final temperature of PbO(s) (T₂) = 234 K

[tex]\delta H = n\int\limits^{T_2}_{T_1} {C_p m} \, dT[/tex]

where;

Cp,m is the specific heat capacity of PbO(s)

[tex]\delta H = 1.94 molX\int\limits^{234}_{732} {[44.35 +1.47 X10^{-3}\frac{T}{K} ]} \,d (\frac{T}{K})[/tex]

[tex]\delta H = 1.94 molX {[44.35 (234-732) +1.47 X10^{-3}(\frac{234^2 -732^2}{2}) ]}[/tex]

     = 1.94mol [(-19957.5)+(-396.9)]

     = -38717.55 J -769.986J

     = -39487.536 J

ΔH = -39.488 x10³J

Therefore, the change in enthalpy of PbO(s) is -39.488 x10³J

Answer:

A) while (num >= 0)

Explanation:

To understand why we need to focus on the module and division operation inside the loop. num % 10 divide the number by ten and take its remainder to then add this remainder to sum, the important here is that we are adding up the number in reverse order and wee need to repeat this process until we get the first number (1%10 = 1), therefore, num need to be one to compute the last operation.

A) this is the correct option because num = 1 > 0 and the last operation will be performed, and after the last operation, num = 1 will be divided by 10 resulting in 0 and 0 is not greater than 0, therefore, the cycle end and the result will be printed.

B) This can not be the option because this way the program will never ends -> 0%10 = 0 and num = 0/10 = 0

C) This can not be the option because num = 1 > 1 will produce an early end of the loop printing an incomplete result

D) The same problem than C

E) There is a point, before the operations finish, where sum > num, this will produce an early end of the loop, printing an incomplete result

Loops are program statements that are used to carry out repetitive and iterative operations

The missing loop header is (a) while (num > 0)

To calculate the sum of the digits of variable num, the following must be set to be true

The loop header must be set to keep repeating the loop operations as long as the value of variable num is more than 0

To achieve this, we make use of while loop,

And the loop condition (as described above) would be num > 0

Hence, the true option is (a) while (num > 0)

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Answer:

not provide the sprinklers, then the type of construction will be Type II B under IBC

Explanation:

given data

3 story office building = 20,000 square feet per floor

solution

we know when sprinkler is provide in high rise building to resist fire

and it provide in building as floor area exceed allowable permissible area of  building as IBC

so IBC for Type II B allowable area =  19000 square feet per floor

and type III B allowable area =  23000 square feet per floor

so when we design the building by type III B construction, the sprinklers require to provide

but not provide the sprinklers, then the type of construction will be Type II B under IBC

Answer:

attached below

Explanation:

Answer:

The PT station is at 485+20.02 and 21.92 ft are to be cleared from the lane's shoulder to provide adequate stopping sight distance.

Explanation:

From table 3.5 of Traffic Engineering by Mannering

R_v=835

R=835+(10ft/2)= 840 ft.

Now T is given as

T=R tan(Δ/2)

Here Δ is the central angle of curve given as 35°

So

T=R tan(Δ/2)

T=840 x tan(35/2)

T=840 x tan(17.5)

T=264.85

Now

STA PC=482+72-(2+64.85)=480+07.15

Also L is given as

L=(π/180)RΔ

Here R is the radius calculated as 840 ft, Δ is the angle given as 35°.

L=(π/180)RΔ

L=(π/180)x840 x35

L=512.87 ft

STA PT=480+07.15+5+12.87=485+20.02

Now Ms is the minimum distance which is given as

[tex]M_s=R_v(1-cos(\frac{90 \times SSD}{\pi Rv}))\\[/tex]

Here R_v is given as 835

SSD for 50 mi/hr is given as 425 ft from table 3.1 of Traffic Engineering by Mannering

So Ms is

[tex]M_s=R_v(1-cos(\frac{90 \times SSD}{\pi Rv}))\\M_s=835(1-cos(\frac{90 \times 425}{\pi 835}))\\M_s=26.92 ft[/tex]

Now for the clearance from the inside lane

Ms=Ms-lane length

Ms=26.92-5= 21.92 ft.

So the PT station is at 485+20.02 and 21.92 ft are to be cleared from the lane's shoulder to provide adequate stopping sight distance.

Answer:

The maximum temperature of the cycle is 1065⁰R

Explanation:

The maximum temperature in degree Rankin can be obtained using the formula below;

[tex]\frac{T_2}{T_1} =[\frac{V_1}{V_2}]^{1.4-1}[/tex]

Where;

T₂ is the  maximum temperature of the cycle

T₁ is the initial temperature of the cycle = 520 deg R = 520 ⁰R

V₁/V₂ is the compression ratio = 6

[tex]T_2 = T_1(\frac{V_1}{V_2})^{0.4}[/tex]

[tex]T_2=T_1(6)^{0.4}[/tex]

[tex]T_2=520^0R(6)^{0.4}[/tex]

T₂ = 1064.96 ⁰R

Therefore, the maximum temperature of the cycle is 1065⁰R

Answer:

net amount of energy change of the air in the room during a 30-min period = 660KJ

Explanation:

The detailed calculation is as shown in the attached file.

Answer:

660KJ

Explanation:

Given

Let Q = Heat Loss from room = 50kj/min

Let W = Work Supplied to room = 1.2KW

1 kilowatt = 1 kilojoules per second

So, W = 1.2KJ/s

In heat and work (Sign Convention)

We know that

1. Heat takes positive sign when it is added to the system

2. Heat takes negative sign when it is removed from the system.

3. Work done is considered positive when work is done by the system

4. Work done is considered negative when work is done on the system.

From the above illustration, heat loss (Q) = -50KJ/Min

In 30 minutes time, Q = -50Kj/Min * 30 Min

Work done in 30 minutes = -1500 KJ

Also, work supplied = -1.2Kj/s

Work supplied to the system in 30 minutes = -1.2Kj/s * 30 minutes

W = -1.2 KJ/s * 30 * 60 seconds

W = -2160KJ

In thermodynamics (First Law)

Q = W + ΔU

-1500 = -2160 + ΔU

∆U = 2160 - 1500

∆U = 660KJ

Answer:

T = 3600 lb

Explanation:

Given:

- coefficient of static friction @a u_a = 0.2

- coefficient of static friction @b u_b = 0.3

- Weight of the loaded bin W = 8500 lb

Find:

- Find the force in the cable needed to begin the lift.

Solution:

- Draw the forces on the diagram. see attachment.

- Take sum of moments about point B as zero:

                     (M)_b =   W*12 - N_a * 22 = 0

                      N_a = W*12 / 22 = 8500*12 / 22

                      N_a = 4636.364 lb

- Compute friction force F_a @ point A:

                      F_a = u_a*N_a = 4636.364*0.2

                      F_a = 927.2727 lb

- Take sum of moments about point A as zero:

                     -W*10 - F_b*sin(30)*22+ 22*N_b*cos(30) + 22*T*sin(30) = 0

Where,           F_b = u_b*N_b = N_b*0.3            

Hence,           -85000 - 3.3*N_b + 11sqrt(3)*N_b + 11 T = 0

                      15.753*N_b + 11*T = 85000    ...... 1    

- Take sum of forces in x-direction equal to zero:

                      T*cos(30) - N_b*sin(30) - u_b*N_b*cos(30) - F_a = 0

                      T*cos(30) - 0.75981*N_b = 927.2727   ..... 2

- Solve two equation simultaneously:

                      T = 3600 lb , N_b = 2882 lb

Answer:

box 2=highest

box3= 2

box 1=3

box 4=lowest

Explanation:

Decide how the sketches below would be listed, if they were listed in order of decreasing force between the charges. That is, select "1" beside the sketch with the strongest force between the charges, select "2" beside the sketch with the next strongest force between the charges, and so on.

take note that like charges repel while unlike charges attract

from the law of electric attraction, we know that

f=kQq/r^2

force is directly proportional to the charges,

-3-1= has the highest force of repulsion

the first bos, the balls are -2-1=-3 they are repulsive

second box=-3-1=-4

third box=-3-1=-4

fourth=-1-1=-2

box 2=highest

box3= 2

box 1=3

box 4=lowest

Answer:

The case with replacement has higher entropy

Explanation:

The complete question is given:

'Drawing with and without replacement. An urn contains r red,  w white  and b black balls. Which has higher entropy, drawing k ≥ 2 balls from the urn with  replacement or without replacement?'

Solution:

- n drawing is the same irrespective of whether there is replacement or not.

-  X to denotes drawing from an urn with r red balls,  w white balls and b black balls. So, n = b + r +  w.

We have:

                                      p_X(cr) = r / n

                                      p_X(cw) = w / n

                                      p_X(cb) = b / n

- Now, if  Xi is the ith drawing with replacement then Xi are independent and p_Xi (x) = pX(x) for x e ( cr , cb , cw ).

- Now, let  Yi be the ith drawing with replacement where Yi are not independent p_Yi (x) = pX(x) for x ∈ X.

- To see this, note  Y1 =  X and assume it is true for  Yi and consider  Yi+1:

    p_Y(i+1) (cr) = p(Y(i+1),Yi).(cr, cr) + p(Y(i+1),Yi).(cr, cw) + p(Y(i+1),Yi).(cr, cb)

= pY(i+1)|Yi  (cr|cr)*pYi  (cr) +pY(i+1)|Yi  (cr|cw)*pYi (cw) + pY(i+1)|Yi  (cr|cb)*pYi (cb)

= r*( r - 1 )/n*(n-1) + w*r/n*(n-1) + b*r/n*(n-1) = r / n =  p_X(cr)

- This means, using the chain rule and the conditioning theore m:

H(Y1, Y2, . . . , Yn) =  H(Y1) +  H(Y2|Y1) +  H(Y3|Y2, Y1) + ... H(Yn|Yn−1, . . . , Y1)

=< SUM H(Yi) = n*H(X) =  H(X1, X2, . . . , Xn)

- with equality if and only if the  Yi were independent:

                          H(Y1, Y2, . . . , Yn) < H(X1, X2, . . . , Xn)

Answer: The case with replacement has higher entropy