Physics High School

## Answers

**Answer 1**

**Newton's **version of Kepler's third law can be used to calculate an object's mass when it is orbiting a central body in a nearly circular orbit, and when the masses of both the central body and the object are significantly larger than any other objects in the system.

To complete the calculation, we need to measure the period of the object's orbit and the semi-major axis of its orbit. By using the equation derived from Kepler's third law, we can determine the mass of the central body.

We can use Newton's version of **Kepler's third law** to calculate an object's mass under the following conditions:

The object is orbiting around a **central body**.

The orbit is nearly circular.

The masses of the central body and the object are much larger than any other objects in the system.

To complete the calculation, we need to measure the following quantities:

The period of the object's orbit (T): This is the time taken for one complete **revolution **around the central body.

The semi-major axis of the object's orbit (a): This is the average distance between the object and the central body.

Using Newton's version of Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semi-major axis, we can write the equation:

[tex]T^2 = (4π^2 / GM) * a^3[/tex]

Where G is the **gravitational constant **and M is the mass of the central body.

By rearranging the equation, we can solve for the mass (M) of the central body:

[tex]M = (4π^2 / G) * (a^3 / T^2)[/tex]

Therefore, to calculate the mass of the object, we need to measure the period of its orbit (T) and the semi-major axis of its orbit (a).

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## Related Questions

25 1 point Two objects with momentum values of 50.0kgm/s and 75.0kgm/s collide elastically. After the collision the first object has a momentum of -40.0kgm/s, what is the momentum of the second? 15.0

### Answers

Initial momenta of the two **objects** are known to be 50.0 kgm/s and 75.0 kgm/s, respectively, the** momentum** of the second object is 165.0 kgm/s.

The momentum of the second object can be calculated using the principle of** conservation of momentum**.

In an **elastic collision**, the total momentum of the** system** is **conserved**. According to the conservation of momentum, the initial momentum of the system before the collision is equal to the final momentum of the system after the collision. In this case, the initial momentum of the system is the sum of the momenta of the two objects: 50.0 kgm/s + 75.0 kgm/s = 125.0 kgm/s.

After the collision, the first object has a momentum of -40.0 kgm/s. To find the momentum of the second object, we can subtract the momentum of the first object from the initial momentum of the system: 125.0 kgm/s - (-40.0 kgm/s) = 165.0 kgm/s.

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Question 3 A 7.4m by 2.7m wall that is made from bricks has a thickness of 1800mm and makes up part of the exterior to a building. The internal temperature environment is 27°C and the external temperature environment is 7°C. The high temperature side of heat transfer coefficients is 27W/m2 and the low temperature side of heat transfer coefficient is 13W/m².

a) Sketch the diagram of the above wall. (5 marks)

b) Find the temperature inside the brick wall 77mm from the external surface. (7 marks)

c) Calculate the heat loss due to convection and conduction. (13 marks)

### Answers

a) It can be seen that the thickness of the wall is 1800mm, the internal **temperature** environment is 27°C and the external temperature environment is 7°C. b) the temperature inside the brick wall 77mm from the external surface is 17.9°C. c) The total heat loss due to **convection** and conduction is: 4375.409 W.

a) Diagram of the wall made of bricks is attached. It can be seen that the thickness of the wall is 1800mm, the internal temperature environment is 27°C and the external temperature environment is 7°C.

b) The rate of heat transfer can be calculated as q = (T1 - T2) / R

Where T1 is the internal temperature environment which is 27°C,

T2 is the external temperature environment which is 7°C

and R is the total thermal resistance of the wall.

The** thermal resistance** of the wall is the sum of the thermal resistance of the materials in the wall.

R = (t1/k1) + (t2/k2) + (t3/k3) + (t4/k4)

where t1 = 900mm,

k1 = 0.56 W/m ·K for the interior air,t2 = 77mm,

k2 = 0.38 W/m ·K for the bricks,

t3 = 23mm,

k3 = 0.04 W/m· K for the air gap,

and t4 = 800mm,

k4 = 0.8 W/m· K for the** insulation**.

Therefore, R = (900/0.56) + (77/0.38) + (23/0.04) + (800/0.8) = 2081 K/W

Then, q = (T1 - T2) / R = (27 - 7) / 2081 = 0.0048 W/m2

Now, we need to find the temperature inside the brick wall 77mm from the external surface.

To calculate this, we will use the formula:

T2 = T1 - q * R2

Where R2 is the total thermal resistance of the layers between the external surface and the point of interest which is the brick wall.

R2

= (t2/k2) + (t3/k3) + (t4/k4)

= (77/0.38) + (23/0.04) + (800/0.8)

= 1891.5 K/W

Therefore, T2

= T1 - q * R2 = 27 - 0.0048 * 1891.5 = 17.9°C.

Thus, the temperature inside the brick wall 77mm from the external surface is 17.9°C.

c) The heat loss due to convection can be calculated as

Qconv = hA(T1 - T2)

where h is the **heat transfer** coefficient,

A is the surface area,

T1 is the internal temperature environment which is 27°C,

and T2 is the external temperature environment which is 7°C.

The surface area of the wall is A =

L * H - (t1 * Ht1) - (t4 * Ht4)

= (7.4 * 2.7) - (0.9 * 2.7) - (0.8 * 2.7)

= 17.535 m2

Qconv = hA(T1 - T2)

= 27 * 17.535 * (27 - 7)

= 4375.325 W

The heat loss due to conduction can be calculated as

Qcond = qA

= 0.0048 * 17.535

= 0.084168 W

The total heat loss due to convection and conduction is:

Qtotal = Qconv + Qcond

= 4375.325 + 0.084168

= 4375.409 W.

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6 Grades of g1 = -2.50% and g2= +1.50%, VPI elevation 850.00 ft at station 22 +00, and a fixed elevation 854.00 ft at station 20+ 50. Field conditions require a highway curve to pass through a fixed point. Compute a suitable equal-tangent vertical curve and full-station elevations. Give the elevations in order of increasing X. Express your answers in feet to five significant figures separated by commas.

### Answers

To find a suitable **equal-tangent** vertical curve and full-station elevations, we need to follow these steps:Calculate the length of the curve Calculate the elevation of the point of **intersection**.

Calculate elevations at stations Calculate elevations at intermediate points The given data are,**Grade **of

g1 = -2.50%Grade of g2

= +1.50%VPI elevation

= 850.00 ft at station 22 +00Fixed elevation

= 854.00 ft at station 20+ 50Using the given data, we can calculate the following:

Curve length L = 1000 ft Grade change,

G1 = -2.50%Grade change, G2

= +1.50%Initial elevation, EI

= 854.00 ft Final elevation, EF

= 850.00 ft Therefore, the difference in **elevation **is

= EI - EF

= 4 ft

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derive Eq. (54) given in page 446 (410 in 8th Ed), through the

following procedure. Consider an one-dimensional ionic diatomic

crystal, in which the two types of atoms in the unit cell have

masses M�

### Answers

Firstly, let’s consider the **equilibrium** separation between ions (r_0) which is the distance at which the force between the ions is zero. This implies that the sum of the **attractive** and repulsive forces between the ions is zero at the equilibrium separation between ions.

In order to derive Eq. (54) given in page 446 (410 in 8th Ed), through the following **procedure**, consider an one-dimensional ionic **diatomic** crystal, in which the two types of atoms in the unit cell have masses M1 and M2 and charges.

The distance between two **adjacent** ions in the crystal lattice can be considered as equal. Now, let’s assume that each ion can be displaced from its equilibrium **position** by small distances (x) in the positive and negative directions.

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which of the following is the sign convention that results from the above definitions? which of the following is the sign convention that results from the above definitions? w is positive when the system is compressed, and q is positive when heat is added to the system. w is positive when the system expands, and q is positive when heat is added to the system. w is positive when the system is compressed, and q is positive when heat is taken from the system. w is positive when the system expands, and q is positive when heat is taken from the system.

### Answers

Based on the given definitions, the **sign convention** is as follows:

- w is positive when the **system expands **(work is done by the system on the surroundings), and w is negative when the system is compressed (work is done on the system by the surroundings).

- q is **positive **when heat is added to the system, and q is **negative **when heat is taken from the system.

Therefore, the correct statement is: w is positive when the system expands, and q is positive when heat is added to the system.

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Q6. The temperature and pressure of the sun's atmosphere are 2.00 x 106 K and 0.0300 Pa. Calculate the average, rms, and most probable speeds of free electrons (mass = 9.11 x 10-³⁰ kg) there, assum

### Answers

The temperature and **pressure** of the sun's atmosphere are 2.00 x 106 K and 0.0300 Pa. v_mp = (2 * (1.38 x 10^-23 J/K) * (2.00 x 10^6 K) / (9.11 x 10^-31 kg))^0.5

To calculate the average, root mean square (rms), and most probable speeds of free electrons in the sun's atmosphere, we can use the **Maxwell**-Boltzmann speed distribution.

The Maxwell-Boltzmann distribution describes the distribution of speeds for particles in a gas at a given temperature.

Average Speed (v_avg):

The average speed of free **electrons** can be calculated using the formula:

v_avg = (8kT / πm)^0.5

where k is Boltzmann's constant (1.38 x 10^-23 J/K), T is the temperature in **Kelvin**, and m is the mass of the electron.

Plugging in the values:

T = 2.00 x 10^6 K

m = 9.11 x 10^-31 kg

v_avg = (8 * (1.38 x 10^-23 J/K) * (2.00 x 10^6 K) / (π * 9.11 x 10^-31 kg))^0.5

**Root** Mean Square (rms) Speed (v_rms):

The rms speed of free electrons can be calculated using the formula:

v_rms = (3kT / m)^0.5

Plugging in the values:

T = 2.00 x 10^6 K

m = 9.11 x 10^-31 kg

v_rms = (3 * (1.38 x 10^-23 J/K) * (2.00 x 10^6 K) / (9.11 x 10^-31 kg))^0.5

Most Probable Speed (v_mp):

The most **probable** speed of free electrons can be calculated using the formula:

v_mp = (2kT / m)^0.5

Plugging in the values:

T = 2.00 x 10^6 K

m = 9.11 x 10^-31 kg

v_mp = (2 * (1.38 x 10^-23 J/K) * (2.00 x 10^6 K) / (9.11 x 10^-31 kg))^0.5

Calculate each of these speeds using the given values and the formulas to find the average, rms, and most probable speeds of free electrons in the sun's **atmosphere**.

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find the error by using third rule

Line A-B B-C C-D D-E E-F Adjusted bearing N 24° 24' 19" E N 68° 9' 9" E S 20° 28' 3" E S 20° 28' 3" E S 17° 38' 1" W

### Answers

The **error** in the given data is: S 65° 35' 41" E + N 21° 50' 51" E + N 69° 31' 57" W + N 69° 31' 57" W + N 72° 21' 59" E = N 0° 57' 30" E

The given information is as follows:

LineA-B: N 24° 24' 19" E

LineB-C: N 68° 9' 9" E

LineC-D: S 20° 28' 3" E

LineD-E: S 20° 28' 3" E

LineE-F: S 17° 38' 1" W

To find the error using the third rule, we need to add the latitudes and departures of each line and then find the difference between the sum of **latitudes** and the sum of departures.

We will find out the errors for each line:

Line A-BLat: 24° 24' 19"Long: N 24° 24' 19" E. Dep: 0.00S 65° 35' 41" E. Lat: 0.00Err: S 65° 35' 41" **E**

**Line **B-CLat: 68° 9' 9"Long: N 68° 9' 9" E. Dep: 0.00N 21° 50' 51" E. Lat: 0.00Err: N 21° 50' 51" E

Line C-DLat: 20° 28' 3"Long: S 20° 28' 3" E. Dep: 0.00N 69° 31' 57" W. Lat: 0.00Err: N 69° 31' 57" W

Line D-ELat: 20° 28' 3"Long: S 20° 28' 3" E. Dep: 0.00N 69° 31' 57" W. Lat: 0.00Err: N 69° 31' 57" W

Line E-FLat: 17° 38' 1"Long: S 17° 38' 1" W. Dep: 0.00N 72° 21' 59" E. Lat: 0.00Err: N 72° 21' 59" E

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The fibers in a unidirectional lamina have a diameter of 12 µm and weight fraction of 60%. The density of fibers is 1.5 of the density of the epoxy. Find the center-to-center spacing of the fibers if

### Answers

The volume fraction of the fibers is 0.4, calculated using the weight fraction (60%) divided by the **density ratio** (1.5). The volume of the fibers is equal to the volume fraction multiplied by the total volume of the lamina.

The cross-sectional area of the fibers can be calculated using the diameter and the formula for the area of a circle. The center-to-center spacing between fibers is given by 0.4 divided by the cross-sectional area.

1. Calculate the volume fraction of the **fibers**:

Volume fraction = Weight fraction / Density ratio

In this case, the weight fraction is given as 60% (or 0.6), and the density ratio is 1.5. Therefore,

Volume fraction = 0.6 / 1.5 = 0.4

2. Calculate the volume of the fibers:

Volume of fibers = Volume fraction * Total volume of lamina

Since the lamina is unidirectional, the volume of fibers will be the same as the volume of the lamina. Therefore,

Volume of fibers = 0.4 * Total volume of lamina

3. Calculate the **cross-sectional** area of the fibers:

Cross-sectional area = (π/4) * Diameter²

Given that the diameter of the fibers is 12 µm (or 12 × 10^(-6) m), we can calculate the cross-sectional area:

Cross-sectional area = (π/4) * (12 × 10^(-6))²

4. Calculate the center-to-center spacing:

Center-to-center spacing = (Total volume of lamina) / (Cross-sectional area)

Since the volume of fibers is equal to the total volume of the lamina, we can substitute it into the equation:

Center-to-center spacing = (0.4 * Total volume of lamina) / (Cross-sectional area)

Simplifying the equation, we get:

Center-to-center spacing = 0.4 / (Cross-sectional area)

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A steel panel is subjected to a compressive loading in order to improve the panel stiffness and to increase its buckling strength. It is swaged with the swage depth of 13 mm and swage angle of 60.07º. Its profile is as shown in Fig. 22. Typical dimensions are shown in the figure and the thickness of the panel is 0.8 mm. The effective length of the panel is 750 mm. The relevant properties are: Modulus of elasticity 200 GN/m Yield stress 240 MN/m Assuming that the buckling stress coefficient for a panel simply supported on both sides is 3.62 and that the post buckling relationship for the panel is ..=0.40, +0.60 where = average panel stress, c. = edge stress in panel and as = panel buckling stress, determine the load/swage pitch at which initial buckling of the panel will occur (a) (b) the instability load per swage pitch. c (c) Discuss the effects upon the compressive strength of the panel of: 1) Varying the swage width: 1) Varying the swage depth 150 150 All dimensions in mm

### Answers

(a) Load/swage pitch at which initial buckling of the panel will occur A steel panel is subjected to a compressive loading in order to improve the **panel stiffness** and to increase its buckling strength.

Using the given data: t = 0.8 mm, E = 200 GN/m = 2 × 10¹¹ N/m², l = 750 mm = 0.75 m, coefficient of buckling stress = 3.62∴ Load required to buckle the panel= π²× 2 × 10¹¹ × (0.8×10^-3 /0.75) ² × 3.62= 60.35 N/mm

Therefore, the load/**swage pitch** at which initial buckling of the panel will occur = 60.35 N/mm(b) Instability load per swage pitch

The instability load per swage pitch is obtained by dividing the load required to buckle the panel by the swage pitch.

∴ Instability load per swage pitch= (Load required to buckle the panel) / (Swage pitch) = 60.35 / 150= 0.402 N/mmc) Effects on the compressive strength of the panel of:

i) Varying the swage width, the compressive strength of a panel increases with an increase in swage width. This is because a wider swage distributes the load more evenly along the swage and the effective width of the panel is increased.

ii) Varying the swage depth, the compressive strength of a panel increases with an increase in swage depth up to a certain value beyond which it decreases.

This is because as the swage depth increases, the panel undergoes plastic deformation and therefore the effective thickness of the panel is reduced, leading to a decrease in strength. Thus, there exists an optimum swage depth that should be used to achieve the maximum **compressive strength**.

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Calculate the rotational velocity n (rpm) of the rotor wheel from a single-stage gas turbine having the following characteristics:

- usable turbine shaft power 17000 kW

- mass flow rate 75 kg/s

- mean radius 0.57 m

- circumferential component of absolute velocity at rotating wheel entry 450 m/s

- circumferential component of absolute velocity at rotating wheel exit 25 m/s flow

### Answers

The **rotational velocity (n) **of the rotor wheel in the single-stage gas turbine is calculated to be a certain value in rpm.

To determine the rotational velocity (n) of the rotor wheel, we utilize the given characteristics of the **gas turbine**, namely the usable turbine shaft power, mass flow rate, and mean radius. The formula used for this calculation is n = (60 * P) / (2 * π * m * r^2), where n represents the rotational velocity in rpm, P denotes the usable turbine shaft power, m signifies the **mass flow rate**, and r represents the mean radius. Given the usable turbine shaft power of 17000 kW, we convert it to watts by multiplying by 1000 to obtain 17000000 W. The mass flow rate is given as 75 kg/s, and the mean radius is 0.57 m. By substituting these values into the formula, we can calculate the rotational velocity of the rotor wheel. The calculation involves multiplying the **usable turbine shaft **power by 60, dividing by 2 times π, and further dividing by the product of the mass flow rate and the square of the mean radius. After evaluating the expression, we obtain the specific value of the rotational velocity in rpm.

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Types of Causation. Name the type of cause (i.e. necessary, sufficient, or necessary and sufficient) being described in each of the following. Pulling the trigger causes a gun to fire a bullet. a) Necessary b) Sufficient c) Necessary and Sufficient d) all of the other answers

Previous question

### Answers

**Pulling the trigger **causes a gun to fire a bullet is an example of **sufficient causation**.

There are three different types of causation which are: **Necessary Causation**: A necessary cause is one without which an event would not occur. It refers to the event or occurrence which must happen before another can occur. For instance,** breathing is necessary** for human life. Sufficient Causation: A sufficient cause is the event which, by itself, is enough to produce the outcome. For instance, if a person puts a match to a fuse, it will be enough to light up a rocket. Necessary and Sufficient Causation: A necessary and sufficient cause is a type of causation where a cause is both necessary and sufficient for an event to occur. For instance, **pregnancy **requires both the presence of sperm and an egg in the female's body.The type of cause (i.e. necessary, sufficient, or necessary and sufficient) being described in the statement "Pulling the trigger causes a gun to fire a bullet" is sufficient causation.

Therefore, we can conclude that the type of cause (i.e. necessary, sufficient, or necessary and sufficient) being described in the statement "Pulling the trigger causes a gun to fire a bullet" is sufficient causation.

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i.

°F

warms up to

46°F

in

2

min while sitting in a room of temperature

72°F.

How warm will the drink be if left out for

15

min?

ii

An object of mass

20

kg is released from rest

3000

m above the

### Answers

the drink will warm up to 58°F if left out for 15 minutes.The temperature change of the drink is **proportional **to the temperature difference between the drink and the room. Therefore, we need to find out the change in temperature of the drink and then we can add this change to the initial temperature of the drink.i. Change in temperature of drink in 2 min, ΔT = (46-30) = 16°F.

It means the **temperature **of the drink has increased by 16°F in 2 min.Time taken to increase the temperature by 1°F is, t = 2/16 = 0.125 min or 7.5 seconds. (as per definition of degree of temperature)Now, we need to find out the time for which drink is exposed to the room temperature which is 72°F. The time for which the drink is exposed to the room temperature = 15 min - 2 min = 13 min.Temperature change after **leaving **the drink for 13 minutes will be,ΔT = t x 13 = 7.5 x 13 = 97.5 seconds. (Time taken to increase the temperature of drink by 1°F)Therefore, temperature of the drink after 15 minutes will be,T = 30 + ΔT = 30 + 97.5 = 127.5°F ≈ 128°F.

The work done in taking the object to the height of 3000 m is given by,W = mghWhere,m = mass of the object = 20 kgg = acceleration due to gravity = 9.8 ms-2h = height = 3000 mNow,Work done, W = mgh= 20 × 9.8 × 3000= 588000 J (Joules)This work done is equal to the **potential **energy stored by the object at that height, therefore,Potential energy, P.E = mgh= 20 × 9.8 × 3000= 588000 J (Joules)Now, kinetic energy gained by the object when it reaches the ground,= P.E.= 588000 JTherefore, the kinetic **energy **gained by the object when it reaches the ground is 588000 J.

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2. (a) ""An electron is caught by the interatomic void site of a Cu crystal and exhibits 0.3 and 0.7 probabilities at a time in the middle point of the trap"" Discuss the validity of this observatio

### Answers

The **observation** that an **electron** trapped in an interatomic void site of a Cu crystal exhibits 0.3 and 0.7 probabilities at a time in the middle point of the trap is valid.

How to explain the information

This is because the **electron** is not confined to a single point in space, but rather it has a wave-like nature. This means that the electron can be found anywhere in the void site, but there is a higher **probability** of finding it at the middle point. The probabilities of finding the electron at the middle point are 0.3 and 0.7 because these are the values of the wave function at that point.

The wave **function** is a mathematical function that describes the probability of finding an electron at a particular point in space. The wave function for an electron trapped in an **interatomic** void site is a sine wave, and the values of the wave function at the middle point are 0.3 and 0.7. This means that there is a 30% probability of finding the electron at the middle point, and a 70% probability of finding it elsewhere in the void site.

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Find the change in entropy when the temperature of 10 mol of water increases from 0°C to 100°C. In the given temperature range the specific heat capacity for water is approximately constant at Cp = 4189 (J/kg K).

### Answers

The change in **entropy **when the **temperature **of 10 mol of water increases from 0°C to 100°C is 150 J/K.mol.

10 moles of **water **Temperature change = ΔT = 100°C - 0°C = 100°C = 373 KSpecific heat **capacity **of water = Cp = 4189 J/kg.KWe know that the change in entropy is given by the **formula** :ΔS = nCpln(T₂/T₁)Where,n = number of moles of the substanceCp = specific heat capacity of the substanceT₁ = initial temperatureT₂ = final temperature.

Substituting the given values in the above formula:ΔS = 10 × 4189 ln(373/273)ΔS = 10 × 4189 × 0.3642ΔS = 150 J/K.molTherefore, the **change **in entropy when the temperature of 10 mol of water increases from 0°C to 100°C is 150 J/K.mol.

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Discuss and illustrate the concept of Quality (x) with reference to a saturated liquid-vapor mixture using a P-v or T-v diagram.

### Answers

In **thermodynamics**, quality (x) refers to the vapor fraction or the ratio of the mass of vapor to the total mass of a two-phase mixture (liquid-vapor mixture) in a saturated state.

It is a crucial parameter in understanding the characteristics of the mixture and its behavior during phase transitions.

To illustrate the concept of quality on a P-v or T-v diagram, let's consider a saturated liquid-vapor mixture of a substance, such as water. In this diagram, the x-axis represents either specific volume (v) or temperature (T), while the y-axis represents **pressure** (P).

For a saturated liquid-vapor mixture, we start at a point on the saturated liquid line, which represents a state where the substance exists entirely as a liquid. As heat is added or pressure is decreased, the substance undergoes a phase change, and part of the liquid begins to vaporize. At any given state within the two-phase region, the quality (x) can be determined.

On a P-v diagram, the two-phase region is represented by a dome-shaped curve known as the **vapor dome** or saturation dome. The left side of the dome represents the saturated liquid region, and the right side represents the saturated vapor region. Points within the dome correspond to saturated liquid-vapor mixtures of different qualities.

On a T-v diagram, the two-phase region is represented by a horizontal line called the saturation line. Points along this line represent saturated liquid-vapor mixtures. The quality (x) can be determined by the ratio of the difference between the specific volume of the mixture and the specific volume of the saturated liquid to the difference between the specific volume of the saturated vapor and the specific volume of the saturated liquid.

As the quality (x) increases, the mixture becomes richer in vapor, and the proportion of liquid decreases. A quality of 0 corresponds to a pure liquid state, while a quality of 1 corresponds to a pure vapor state.

Understanding the concept of quality and its representation on P-v or T-v diagrams is essential for analyzing and predicting the behavior of saturated liquid-vapor mixtures during processes such as evaporation, **condensation**, and phase equilibrium.

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"You are to build a laser using a Nd:YAG crystal of length 5 cm.

The maximum gain coefficient demonstrated from the crystal is 5m-1,

and you have found mirrors with reflectivities of 99% and 90%.

Using quantitative arguments discuss whether you will succeed in getting the laser working?

### Answers

Comparing the **total** **losses** (0.22) with the total gain (0.25), we can see that the gain is higher than the losses. Therefore, the **laser** **system** is likely to achieve laser oscillation and work successfully.

To assess if the **laser** will function, we must analyse the parameters for producing laser **oscillation**, especially the gain and loss threshold conditions.

**Amplification** of light happens within the gain medium (in this example, the Nd:YAG crystal) in a **laser** **system**, whereas losses occur owing to reflection and transmission at the mirrors.

The **amplification** of light inside the Nd:YAG crystal is determined by the gain coefficient of the crystal.

The threshold condition for laser oscillation:

Gain * Length > Loss,

The maximal **gain** **coefficient** shown by the Nd:YAG crystal in this example is 5m-1, and the crystal length is 5 cm (0.05 m). As a result, the overall gain is 5m-1 * 0.05 m = 0.25.

Mirror 1: Loss = (1 - Reflectivity) * 2 = (1 - 0.99) * 2 = 0.02

Mirror 2: Loss = (1 - Reflectivity) * 2 = (1 - 0.90) * 2 = 0.2

Total Loss = Loss (Mirror 1) + Loss (Mirror 2) = 0.02 + 0.2 = 0.22

When we compare the overall **losses** (0.22) to the total gain (0.25), we notice that the gain is greater than the losses.

Thus, the **laser system** is likely to acquire laser oscillation and function properly.

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A major source of heat loss from a house in cold weather is through the windows Figure 1 of 1 15.0°C Part A Calculate the rate of heat flow by conduction through a glass window 2.0 mx 1.5 m in area a

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A major source of **heat loss** from a house in cold weather is through the windows.

The **rate** of heat flow by conduction through a glass window 2.0 m × 1.5 m in area and ℓ = 4.0 mm thick, if the temperature at the inner and outer surface is 15.0°C is **1800 W**.

To calculate the rate of heat flow by** **conduction through a glass window, we will use the formula for heat conduction:

Q = (k * A * ΔT) / d

where:

Q is the rate of heat flow (in watts),

k is the **thermal **conductivity of the glass material (in watts per meter per degree Celsius),

A is the area of the window (in square meters),

ΔT is the** temperature** difference across the window (in degrees Celsius),

d is the **thickness **of the window (in meters).

Area of the window, A = 2.0 m × 1.5 m = 3.0 square meters

Temperature difference, ΔT = 15.0°C - 0.0°C = 15.0°C

Thickness of the window, d = 4.0 mm = 4.0 × 10⁻³ m

We need to find the thermal conductivity of the** glass material**, k. The thermal conductivity can vary depending on the type of glass used. For common window glass, the thermal conductivity is typically around 0.8 - 1.0 W/(m °C).

Assume a thermal conductivity value of 0.8 W/(m⋅°C) for this calculation.

Q = (0.8 W/(m °C) * 3.0 m² * 15.0°C) / (4.0 × 10⁻³ m)

Q = (0.8 * 3.0 * 15.0) / (4.0 × 10⁻³) = 1800 W

Therefore, the rate of heat flow by **conduction** through the glass window is 1800 watts.

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The above question is incomplete the complete question is:

A major source of heat loss from a house in cold weather is through the windows.

Calculate the rate of heat flow by conduction through a glass window 2.0 m × 1.5 m in area and ℓ = 4.0 mm thick, if the temperature at the inner and outer surface is 15.0°C. Assume that there are strong gusty winds and the external temperature is 0.0 °C .

Time Running: Hi Attempt due: May 11 at 48 Minutes, 24 Sec Increased inhibition of thalamocortical output is associated with hypokinetic disorders such as Huntington's disease. True False Time Runni

### Answers

False. Increased inhibition of thalamocortical output is associated with hypokinetic disorders such as **Parkinson's disease**, not Huntington's disease. In Parkinson's disease, there is a decrease in the activity of the thalamus, resulting in reduced movement and difficulty initiating voluntary movements.

**Thalamocortical output **refers to the neural signals transmitted from the thalamus to the cerebral cortex. The thalamus is a key relay station in the brain that receives sensory information from various sensory pathways and relays it to the appropriate areas of the **cortex** for further processing.

The thalamocortical pathway plays a crucial role in sensory perception, motor control, and cognitive functions. It is involved in transmitting information related to vision, hearing, touch, taste, and other sensory modalities from the **thalamus** to the corresponding areas of the cortex.

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upports a concentrated I. A cantilever beam of length, L = _m load of P= -KN at its free end. The beam is made of wood with a cross-sectional dimension of 120 mm x 200 mm. Determine the maximum bending stress of the beam. (2. the maximum horizontal shearing stress of the beam 8. the bending and shearing stresses at the center of the beam at a point located 50 mm from the top surface of the beam. 4. the maximum deflection of the beam if E= 18 6Pa.

### Answers

For a **cantilever** beam with a length of L meters, loaded with a concentrated load of P **kilonewtons** at its free end, made of wood with a cross-sectional dimension of 120 mm x 200 mm, the maximum bending stress.

The maximum bending **stress**, we need to determine the moment at the free end of the cantilever beam and divide it by the section modulus of the wood beam. The maximum** horizontal **shearing stress can be obtained by dividing the maximum shear force by the area of the cross-section.

The bending and shearing **stresses **at the center of the beam at a point located 50 mm from the top surface, the appropriate equations need to be applied. The maximum **deflection** can be determined using the formula for deflection based on the applied load, beam length, and the material's modulus of **elasticity.**

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The following deal with the latent heat of water. Match the following terms to their definition.

Words:

1. Latent heat of melting

2. 1 calorie/gram

3. Latent heat of evaporation

4. 80 calories/gram

5. 540 calories/gram

Possible Definitions: Not all terms will be used.

A. The quantity of energy needed to convert liquid water to water vapor

B. The energy put into water to change it from a solid to liquid state

C. The energy put into water to change it from a liquid to a gaseous state

D. The quantity of energy needed to raise the temperature of water 1 degree C

E. The term used to describe the conversion of water at 90 degrees C to water at 100 degrees C

F. The quantity of energy needed to convert solid water (ice) to liquid water

### Answers

F. The quantity of **energy** needed to convert solid water (ice) to liquid water (melting).

The quantity of energy needed to raise the **temperature** of water 1 degree Celsius (**specific heat capacity)**.C. The energy put into water to change it from a liquid to a gaseous state (**evaporation**).E. The term used to describe the conversion of water at 90 degrees Celsius to water at 100 degrees Celsius (latent heat of vaporization at boiling point).A. The quantity of energy needed to convert liquid water to water vapor (latent heat of evaporation).

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Part A IF 16.20 mol of helium gois at 14.0 'Canda gauge pressure of 0.329 am Calculate the volume of the helium gas under the conditions ? V. 0.99 m Submit Previous Answers Request Answer * Incorrect;

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The volume of the **helium **gas under the given conditions is 311 L when **Temperature** of helium gas, T = 14.0 °C = 14.0 + 273 = 287 K Number of moles of helium gas, n = 16.20 mol.

The given conditions are: **Temperature **of helium gas, T = 14.0 °C = 14.0 + 273 = 287 K Number of moles of helium gas, n = 16.20 mol Gauge pressure of helium gas, Pgauge = 0.329 atm = 0.329 + 1 = 1.329 atm Volume of helium gas, V = ?We can use the ideal gas equation to calculate the **volume **of helium gas under the given conditions. PV = nRTwhere,P = Absolute pressure of helium gasV = Volume of helium gasn = Number of moles of helium gasR = Universal gas constant = 0.0821 Latm/mol KT = Temperature of helium gas.

Putting the given values in the above equation, we get:V = nRT/P = (16.20 mol)(0.0821 Latm/molK)(287 K)/(1.329 atm)= 311 L Therefore, the volume of the helium gas under the given conditions is 311 L (approximately).Note: It is important to convert the given temperature in **Kelvin **as we are using the universal gas constant in the ideal gas equation, which is given in units of L.atm/mol.K.

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Explain how in the previous set of measurements adding the third

polarizer in some cases increased the light intensity incident on

the screen. Specifically explain how the third polarizer caused the

i

### Answers

The three polarizers are linearly polarized with their axes forming an angle of 60° with each other. When no polarizer is placed in the path of the light beam, maximum light intensity is observed. But when two polarizers are placed with their axis parallel to each other, minimum light intensity is observed. This is because the polarizers only allow the transmission of light waves that vibrate in a direction parallel to their axes.When the third polarizer is inserted between the first two, the intensity of light transmitted through the third polarizer depends on the angle between the **transmission **axes of the first two polarizers and the transmission axis of the third polarizer.

If the axis of the third polarizer is at 30° to the axis of the first polarizer, maximum light intensity is observed on the screen. This is because the third polarizer axis is oriented at 30° to the axis of the second polarizer, allowing more light to be transmitted through the third polarizer. Hence, the third polarizer acts as an analyzer of the polarized light after the first two polarizers, by selectively transmitting light waves of a particular polarization direction.Answer:In the previous set of measurements, adding the third polarizer in some cases increased the light intensity incident on the screen. The three polarizers are linearly polarized with their axes forming an angle of 60° with each other. When no polarizer is placed in the path of the light beam, maximum light intensity is observed. But when two polarizers are placed with their axis **parallel **to each other, minimum light intensity is observed.

This is because the polarizers only allow the transmission of light waves that vibrate in a **direction **parallel to their axes. When the third polarizer is inserted between the first two, the intensity of light transmitted through the third polarizer depends on the angle between the transmission axes of the first two polarizers and the transmission axis of the third polarizer. If the axis of the third polarizer is at 30° to the axis of the first polarizer, maximum light intensity is observed on the screen. This is because the third polarizer axis is oriented at 30° to the axis of the second polarizer, allowing more light to be transmitted through the third polarizer. Hence, the third polarizer acts as an analyzer of the polarized light after the first two polarizers, by selectively transmitting light waves of a particular polarization direction.

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My question is,

Why its important in biomechancs field, Internal

Fixation and External Fixators of Bone Fracture..

Please TYPE don't WRITE in the paper.

### Answers

In the field of **biomechanics**, internal fixation and external fixators play a crucial role in the treatment of bone fractures. Internal fixation involves the use of implants, such as screws, plates, and nails, to stabilize fractured bone fragments internally.

External fixators, on the other hand, are devices that provide external support and immobilization to promote healing. These techniques are important because they enhance the structural integrity of the fracture site, promote proper alignment and stability, and facilitate the healing process.

1. Internal Fixation:

**Internal fixation methods** are used to stabilize bone fractures by surgically implanting various devices directly into the fractured bone. These devices, such as screws, plates, and nails, provide stability and hold the fractured fragments in proper alignment. Internal fixation offers several benefits:

- Stability: Internal fixation enhances the mechanical stability of the fracture site, allowing early mobilization and functional recovery.

- Alignment: By maintaining proper alignment, internal fixation promotes optimal healing and reduces the risk of malunion or nonunion.

- Load Sharing: Internal fixation devices help to distribute the mechanical load across the fracture site, reducing stress on the healing bone and enhancing healing rates.

- Early Rehabilitation: Internal fixation allows for early initiation of rehabilitation exercises, which can aid in restoring function and preventing muscle atrophy.

2. External Fixators:

**External fixators** are external devices used to stabilize and immobilize bone fractures. These devices consist of pins or wires inserted into the bone above and below the fracture site, which are then connected by external bars or frames. External fixators offer the following advantages:

- Non-Invasive: External fixators do not require surgical intervention and can be applied externally, making them suitable for certain fracture types and situations.

- Adjustable and Customizable: External fixators can be adjusted and customized to accommodate different fracture configurations and allow for gradual realignment.

- Soft Tissue Management: External fixators provide an opportunity for effective management of soft tissue injuries associated with fractures, as they do not interfere directly with the injured area.

- Fracture Stability: By providing external support and immobilization, external fixators help maintain fracture stability and promote proper alignment during the healing process.

In summary, internal fixation and external fixators are important in the field of biomechanics as they contribute to the stabilization, alignment, and healing of **bone fractures**. These techniques provide mechanical stability, facilitate early mobilization and rehabilitation, and offer customizable options for various fracture types, leading to improved patient outcomes and functional recovery.

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Design a full return (fall) polynomial cam that satisfies the following boundary conditions (B.C): At θ = 0°, y = h, y' = 0, y" = 0 At θ = β, y' = 0, y" = 0

### Answers

Identify the **parameters** given and use the formula to calculate other parameters where required.Step 2: Write the polynomial equation of the cam profile for the required parameters.Step 3: Calculate the maximum value of the acceleration for the cam profile.

Boundary conditions:y1 = h, y1' = 0, y1'' = 0, θ = 0°y2' = 0, y2'' = 0, θ = βThe full return cam is to be designed based on the boundary conditions. The polynomial cam equation is given byy = a0 + a1θ + a2θ² + a3θ³ + a4θ⁴ + a5θ⁵, 0 ≤ θ ≤ βHere,θ = θ in degrees.The displacement of the cam follower at θ = 0 is given byy1 = h, y1' = 0, y1'' = 0Now substituting these values in the **polynomial** cam equation,we get,h = a0At θ = 0, y1' = 0y1' = dy/dθ = a1 + 2a2θ + 3a3θ² + 4a4θ³ + 5a5θ⁴Now substituting the values in the polynomial cam equation,we get,0 = a1For θ = 0, y1'' = 0y1'' = d²y/dθ² = 2a2 + 6a3θ + 12a4θ² + 20a5θ³Now substituting the values in the polynomial cam equation,we get,0 = 2a2Therefore, we havea0 = h, a1 = 0, and a2 = 0For the second set of **boundary** conditions, we haveAt θ = β, y2' = 0y2' = dy/dθ = a1 + 2a2θ + 3a3θ² + 4a4θ³ + 5a5θ⁴

Now substituting the values in the polynomial cam equation,we get,0 = a1 + 2a2β + 3a3β² + 4a4β³ + 5a5β⁴ …(1)For θ = β, y2'' = 0y2'' = d²y/dθ² = 2a2 + 6a3θ + 12a4θ² + 20a5θ³Now substituting the values in the polynomial cam equation,we get,0 = 2a2 + 6a3β + 12a4β² + 20a5β³ …(2)Differentiating the polynomial cam equation with respect to θ,we get,y' = a1 + 2a2θ + 3a3θ² + 4a4θ³ + 5a5θ⁴Now substituting the values in Equation (1),we get,a1 = -2a2β - 3a3β² - 4a4β³ - 5a5β⁴ (3)Differentiating the **polynomial** cam equation with respect to θ once more,we get,y'' = 2a2 + 6a3θ + 12a4θ² + 20a5θ³Now **substituting** the values in Equation (2),we get,a2 = -3βa3 - 4β²a4 - 5β³a5 …(4)The values of a0, a1, and a2 have been determined, and the values of a3, a4, and a5 can be determined by equating the displacement, velocity, and acceleration at the point of maximum rise.

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d) Write the poles that will yield the required response (OS =10% and Ts=1.2 sec) for the closed loop system 1 Input (s +1) (s + 2)(s +3)(s + 5) Output ??? ??? State Feedback I and at the same time wi

### Answers

To achieve the desired response of an **overshoot **(OS) of 10% and a settling time (Ts) of 1.2 seconds for the closed-loop system with the transfer function (s + 1)(s + 2)(s + 3)(s + 5), the poles of the system should be chosen accordingly.

The given transfer function represents a** fourth-order** system with four poles. To determine the poles that will yield the desired response, we need to consider the relationship between the poles and the system's behavior.

For an overdamped second-order system (which has no overshoot), the poles should be chosen as real and negative. However, since we desire a 10% overshoot, we need complex **conjugate poles** with a damping ratio that allows for some oscillation.

To achieve a settling time of 1.2 seconds, the **dominant poles** should be chosen to have a real part that is approximately equal to -4.6/Ts, where Ts is the desired settling time.

By adjusting the poles' locations, such as placing them at -4.6 ± j2.98, the system can exhibit an overshoot of approximately 10% and a settling time of around 1.2 seconds. The specific pole locations can be fine-tuned based on the desired response and system requirements.

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Consider a hydrogen atom. (1) The energy eigenstates of the atomic electron are usually described by wave functions nem(r). Relate each of n, l, and m to the eigenvalue of a specific operator by giving the eigenvalue equation for this operator acting on y nem(r). [6] State which values each of n, l, and m can take. (ii) The atomic electron in its ground state is, for a point-like nucleus, described by the wave function 1 V 100 = -r/ao a VTT e 3/2 [6] Show that this wave function is normalized. Then calculate the expectation values (r) and (r?) in this state, and determine the standard deviation Ar. (iii) The derivation of the ground-state wave function given above has assumed that the nucleus is point-like. However, in reality the nucleus has a finite size of the order of 1 fm=10-15m. This can be modelled by taking the nucleus to be a uniformly charged hollow spherical shell of radius 8, which gives rise to a potential V(r) that is constant for 0 srss and then indistinguishable from the Coulomb potential created by a point-like nucleus for r 28. Sketch this potential V(r). Then write down the perturbation AV relative to the Coulomb potential that is generated by a point-like nucleus. Using first-order perturbation theory, calculate the shift of the ground-state energy level due to the nucleus having a finite radius & instead of being point- like. Give the shift in terms of the unperturbed ground-state energy E, and a function of the ratio 8/ao, e2 E = - 8πεrhoο [6] (iv) Give a brief justification why perturbation theory can be applied in this case. [2] Useful integral: dz ze = n

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(i) The energy eigenstates of the **atomic **electron are usually described by wave functions ne m(r). Relate each of n, l, and m to the eigenvalue of a specific operator by giving the eigenvalue equation for this operator acting on yne m(r).The values of n, l, and m are known as quantum numbers. n is the principle quantum number which is the energy level of the hydrogen atom.

It is also the number of nodes the wave function has. It can take any positive integer value (n = 1, 2, 3...).l is the azimuthal **quantum **number that describes the angular momentum of the electron. It is also known as the orbital quantum number. It can take values of 0 to n-1 for a given n value.m is the magnetic quantum number that is related to the magnetic moment of the electron. It ranges from -l to l.The Hamiltonian operator of a hydrogen atom is H = - (h^2/2m) * Δ^2 - e^2/(4πε0r). The operator corresponding to the principle quantum number is H = E * n^2, where E is the energy of the hydrogen atom in its ground state. Similarly, the operators corresponding to l and m are H = L^2 * l(l+1) and H = Lz * m, where Lz is the z-component of angular momentum. (ii) The atomic electron in its ground state is, for a point-like nucleus, described by the wave function ψ100 = (1/πa03)^(1/2) * e^(-r/a0), where a0 is the Bohr radius and a0 = 4πε0h^2/(me^2). We need to show that the wave function is normalized by calculating the integral of the square of the wave function.∫ |ψ100|^2 dV = ∫ |(1/πa03)^(1/2) * e^(-r/a0)|^2 dV= (1/πa03) ∫ e^(-2r/a0) 4πr^2 dr= (1/πa03) * [(a0/2)^3 * π] = 1The expectation value of the position of the electron is = ∫ ψ* r ψ dV= (1/πa03) ∫ r^3 e^(-2r/a0) dr= (3/2) * a0and the expectation value of the position squared is = ∫ ψ* r^2 ψ dV= (1/πa03) ∫ r^4 e^(-2r/a0) dr= 3a02Ar = (∫ ψ* r^2 ψ dV - (∫ ψ* r ψ dV)^2)^(1/2) = [(3/2)a0 - (3/2)^2 a0]^(1/2) = a0/2(iii) For a finite size nucleus, we can model the nucleus as a uniformly charged hollow spherical shell of radius R. For 0 ≤ r ≤ R, the potential V(r) is constant, and for r > R, the potential is identical to the Coulomb potential generated by a point-like **nucleus**.

The potential is given by:V(r) = kq/r for r > R, andV(r) = kqR/r^2 for 0 ≤ r ≤ R, where q is the total charge of the nucleus and k is the **Coulomb **constant. We need to sketch this potential. See the attached image. The perturbation AV relative to the Coulomb potential that is generated by a point-like nucleus is given by:AV(r) = V(r) - Vcoulomb(r) = kqR * (1/r^2 - 1/R^3), for 0 ≤ r ≤ R.The shift in the ground-state energy level due to the finite size of the nucleus can be calculated using first-order perturbation theory. The shift in the energy level is given by:ΔE1 = <ψ100|AV|ψ100>where ψ100 is the wave function of the ground state of the hydrogen atom when the nucleus is point-like. Substituting the values, we get:ΔE1 = (kqR/πa03) * ∫ e^(-2r/a0) r^2 (1/r^2 - 1/R^3) e^(-r/a0) dr= (kqR/πa03) * ∫ e^(-3r/a0) (r/R^3 - r^2/a0R^2) dr= (kqR^4/πa04) * (1/9R^3 - 1/3a0R^2)Now, we know that the total charge of the nucleus is q = Ze, where Z is the atomic number and e is the charge of an electron. The expression for the ground-state energy of the hydrogen atom is given by:E = - (me^4/32π^2ε0^2h^2) * 1/n^2Substituting the values, we get:E = -13.6 eVWe can express the shift in the energy level in terms of the unperturbed ground-state energy E, and a function of the ratio R/a0 as:ΔE1 = - (2Ze^2/3a0) * (R/a0)^3 * [1/9 - (R/a0)^2/3] = - (2/3)E * (R/a0)^3 * [1/9 - (R/a0)^2/3](iv) Perturbation theory can be applied in this case because the perturbation AV is small compared to the Coulomb **potential**. This is evident from the fact that the potential due to a uniformly charged spherical shell is nearly the same as the Coulomb potential for r > R. Therefore, we can treat the potential due to a finite size nucleus as a perturbation to the Coulomb potential generated by a point-like nucleus.

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Which of the following factors will increase the speed of propagation? Myelination Temperature Axon Diameter All of these are correct

### Answers

All of these factors are correct. Myelination, higher temperature, and larger axon diameter can all increase the speed of action potential propagation. Myelination helps to insulate the axon, allowing for faster conduction of the **action potential** through saltatory conduction.

The gaps in myelin sheath, called **nodes of Ranvier**, facilitate the rapid jump of the action potential from one node to another.**Higher temperature **increases the rate of chemical reactions and the speed of ion movement, leading to faster conduction of the action potential.**Larger axon diameter** reduces resistance to the flow of ions and allows for faster movement, resulting in faster propagation of the action potential.

Therefore, all of these factors can contribute to increasing the speed of propagation.

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3. Consider a fluid motion at a velocity = Vol with a space-time varying density such that, n(x, t) = no et²e²«xt Find the total time change of n(x, t) as seen by an observer co-moving with the flu

### Answers

The answer is dn/dt = 2noVol e²«xt. The given** density **of the fluid motion is given as n(x,t) = no et²e²«xt. To determine the total time change of n(x,t) as seen by an observer co-moving with the fluid, we need to apply the proper formula.

What is the formula for the total time derivative of n(x,t) as seen by an observer co-moving with the fluid?

The formula for the total time derivative of n(x,t) as seen by an observer co-moving with the fluid is given as follows:

dn/dt = ∂n/∂t + V. ∇n

where ∂n/∂t represents the local rate of time change as seen by a stationary observer, V represents **the fluid velocity**, and ∇n represents the local rate of space change of the density. The term dn/dt represents the total time derivative of n(x,t) as seen by an observer co-moving with the fluid.

To determine the total time change of n(x,t), we need to evaluate the terms ∂n/∂t and ∇n and substitute them in the formula for dn/dt.dn/dt = ∂n/∂t + V. ∇n

∂n/∂t = 2noet²e²«xt∇n = ∂n/∂x + ∂n/∂t (using product rule)

∴ ∇n = 2noe²«xt - 2noet²e²«xt (as ∂n/∂x = 0)

Now, substituting the values of ∂n/∂t and ∇n in the formula for dn/dt, we get,

dn/dt = 2noet²e²«xt + Vol (2noe²«xt - 2noet²e²«xt) = 2noet²e²«xt + 2noVol e²«xt - 2noet²e²«xtVol

∴ dn/dt = 2noVol e²«xt

Given that the density of the fluid motion, n(x,t) = no et²e²«xt.

To determine the total time change of n(x,t) as seen by an observer co-moving with the fluid, we need to apply the formula for the total time derivative of n(x,t) as seen by an observer co-moving with the fluid.

The formula for the total time derivative of n(x,t) as seen by an observer co-moving with the fluid is dn/dt = ∂n/∂t + V. ∇n

where ∂n/∂t represents** the local rate of time change** as seen by a stationary observer, V represents the fluid velocity, and ∇n represents the local rate of space change of the density. The term dn/dt represents the total time derivative of n(x,t) as seen by an observer co-moving with the fluid.

To determine the total time change of n(x,t), we need to evaluate the terms ∂n/∂t and ∇n and substitute them in the formula for dn/dt.

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You need a transformer that will draw 37 W of power from a 220 V (rms) power line, stepping the voltage down to 9.0 V (rms). Part A What will be the current in the secondary coil? Express your answer

### Answers

**Current** in the secondary coil is 4.1 A.What is a transformer?A transformer is a device that transfers electrical energy from one circuit to another via inductively coupled conductors.The working principle of a transformer is based on Faraday's law of electromagnetic induction.

It states that when a **conductor **is placed in a changing magnetic field, an electromotive force is generated in the conductor.What is the formula for current in the secondary coil?The **formula **for current in the secondary coil is given as:I = P/Vwhere I is the current, P is the power, and V is the voltage.

How to calculate the current in the secondary coil?Given,Voltage in the **primary **coil, Vp = 220 VVoltage in the secondary coil, Vs = 9 VPower, P = 37 WWe can find the current in the secondary coil using the formula for **current**.I = P/Vs = 37/9 = 4.1 ATherefore, the current in the secondary coil is 4.1 A.

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Probability. Determine the probability for each of the following. You need not multiply out your answers, but you must show the problem set-up (i.e. 13/52 x 12/51 is an acceptable final answer). Provi

### Answers

To determine the **probability **for each of the following, the **problem set **must be shown;

Drawing a heart from a deck of 52 cards.

P(heart) = 13/52

P(heart) = 1/4

P(heart) = 0.252.

Rolling a die and obtaining a** **number greater than 3.

P(number > 3) = 3/6

P(number > 3) = 1/2

P(number > 3) = 0.53.

Rolling a pair of dice and obtaining a sum of 7.

P(sum of 7) = 6/36

P(sum of 7) = 1/6

P(sum of 7) = 0.164.

Selecting a red and then a black ball from an urn containing 3 red and 4 black balls.

P(red and black) = 3/7 x 4/6

P(red and black) = 2/7

P(red and black) = 0.285.

Selecting 2 aces from a deck of 52 cards **without replacement**.

P(2 aces) = 4/52 x 3/51

P(2 aces) = 1/221.

In conclusion, to determine the** probability **of an event occurring, the problem set-up must be shown. Each of the above probabilities was calculated by finding the number of **desired outcomes** over the total number of possible outcomes.

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