Which transition would result in the absorption of a photon with the shortest wavelength?.

Answers

Answer 1

The transition that would result in the absorption of a photon with the shortest wavelength is n=1 to n=∞.

An electron in an atom can move to a higher energy level, or shell, if it absorbs energy equal to the energy difference between its current and new levels. When the electron drops from a higher to a lower energy level, a photon is emitted, and when an electron moves from a lower to a higher energy level, it absorbs a photon of light.

The shorter the wavelength of light, the higher its energy. Thus, the transition from n=1 to n=∞ would absorb a photon with the shortest wavelength because it involves the electron moving to the highest possible energy level. At the n=∞ level, the electron has escaped the influence of the nucleus and is no longer bound to the atom. This is known as the ionization energy of the atom, and it requires the greatest amount of energy to be achieved.

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Related Questions

A toy car has a 1. 5 A current, and its resistance is 2 Ω. How much voltage does the car require? V.

Answers

Answer: Voltage = (current) x (resistance)

Voltage = (1.5 A) x (2 ohms)

In order to MAKE 1.5 A of current flow through the toy car, you have to PROVIDE 3 volts from the battery.

The first harmonic of a string tied down at both ends has a frequency of 26 Hz. The length of the string is 0. 83 mwhat is the speed of wave the string ?

Answers

The speed of the wave on the string is 21.58 m/s. This can be calculated using the formula v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength.

In this case, the first harmonic corresponds to the fundamental frequency of the string. The fundamental frequency of a string fixed at both ends is given by the equation f = v/2L, where f is the frequency, v is the wave speed, and L is the length of the string.The speed of the wave on the string is 21.58 m/s. This can be calculated using the formula v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength.

Rearranging the equation, we get v = 2Lf. Plugging in the given values, we have v = 2 * 0.83 m * 26 Hz = 21.58 m/s.

Therefore, the speed of the wave on the string is 21.58 m/s.

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Write a set of turtle instructions to draw an AND gate.

Answers

The turtle's position and direction appropriately after each instruction to ensure accurate drawing. You can also customize the colors, sizes, and shapes to enhance the visual appearance of the AND gate.

To draw an AND gate using turtle graphics, you can use the following set of instructions:

Set up the turtle:

a. Set the turtle's initial position.

b. Set the turtle's pen color and size.

Draw the first input line:

a. Move the turtle forward to the starting point of the line.

b. Draw a straight line segment to represent the first input.

Draw the second input line:

a. Move the turtle to the starting point of the second line.

b. Draw a straight line segment to represent the second input.

Draw the output line:

a. Move the turtle to the starting point of the output line.

b. Draw a straight line segment to represent the output.

Draw the logic gate shape:

a. Move the turtle to the starting point of the gate.

b. Draw a rectangle to represent the gate.

c. Add any necessary labels or symbols to indicate it as an AND gate.

Add connections between lines and gate:

a. Move the turtle to the intersection point of the first input line and the gate.

b. Draw a small line segment to connect the input line to the gate.

c. Repeat the above step for the second input line and the gate.

d. Draw a small line segment to connect the output line to the gate.

Repeat the above steps as necessary to draw multiple AND gates or any additional components.

Remember to adjust the turtle's position and direction appropriately after each instruction to ensure accurate drawing. You can also customize the colors, sizes, and shapes to enhance the visual appearance of the AND gate.

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Scientific notation is a method of expressing very small and very large numbers *

yes
No

Answers

The answer is yes:)
Scientific notation is the expression of a number in the form of x * 10^x

the area of a rectangle is 105 sq in and the length of one side is 7 in. what is the length of the perimeter?
A. 22 inches
B. 27 inches
C. 35 inches
D. 44 inches
E. 49 inches

Answers

Answer:

\( \huge{ \boxed{44 \: \: \text{inches}}}\)

Explanation:

To find the perimeter of the rectangle, we must first find the width of the rectangle given it's length and area then use it to find the perimeter of the rectangle.

Let the width be represented by w

Area of a rectangle = length × width

From the question.

Area = 105 sq. in

length = 7 in

\(105 = 7 \times w \\ 105 = 7w \: \: \: \: \: \: \\ \\ \frac{105}{7} = \frac{7w}{7} \\ w = 15\)

width = 15 in

Perimeter of a rectangle(p) = 2l + 2w

l is the length of the rectangle

w is the width of the rectangle

\(p = 2(7) + 2(15) \\ p = 14 + 30 \\ \\ p = 44\)

We have the final answer as

44 inches

The volume of empty space between gas particles is.

Answers

Answer:

either atoms or molecules

What is average wind speed in cities compared to rural areas?

Answers

The average wind speed in cities compared to rural areas is low.

The average wind speed in cities is generally lower compared to rural areas due to the presence of tall buildings and other structures that block and disrupt the natural flow of wind. This phenomenon is commonly known as the "urban heat island effect", where cities are warmer than their surrounding rural areas. Urbanization has led to the development of dense urban landscapes that create a wind shadow, reducing the wind speeds in the immediate vicinity of buildings.


In contrast, rural areas are generally more open and flat, with fewer obstructions to the natural flow of wind. This allows the wind to flow more freely and at higher speeds. However, it is important to note that wind speed can vary greatly depending on the specific location within a city or rural area. For example, a high-rise building in a city may experience much stronger winds on its upper floors compared to ground level, while a hilltop in a rural area may experience stronger winds than its surroundings.


Overall, the average wind speed in cities is generally lower compared to rural areas due to the presence of obstructions and the urban heat island effect, but specific locations within each area can experience significant variations in wind speed.

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Heat transfer between two substances is affected by specific heat and the
O chemical composition of the substances.
O state of matter of the substances at room temperature.
othermal equilibrium of the substances.
O amount of time and area of physical contact between the substances.

Answers

The correct answer is D. Amount of time and area of physical contact between the substances.

Explanation:

Heat transfer refers to the flow of thermal energy or heat between two or more objects. This process involves multiple factors and implies heat from the hottest object goes to the coldest one until there is an equilibrium. To begin, heat transfer depends on the amount of thermal energy in the objects because objects must have a different amount of thermal energy for heat to flow.

Besides this, the amount of energy that flows depends on the time and the contact between the substances of objects. Indeed, objects need to be in contact or close to each other for heat to transfer, and the time needs to be enough for the process to occur. For example, if you place a pot over the fire just for a few seconds it is likely the heat transferred is minimal, which does not occur if you leave the pot more time. At the same time if the pot is in close contact with fire more heat will be transferred.-

Answer:

the answer is D on edginuity.

Explanation:

if a diver were to descend to 10 m with air in her lungs without breathing in or out, what would be the approximate new value for the volume of the air in her lungs? treat the lung as 6 l of ideal gas.

Answers

Answer:

Its C

Explanation:

I took the test

As the volume of air in the lungs of the diver will reduce when she descends to 10m with air in her lungs without breathing in or out, the approximate new value will be 17.56 L, calculated using Boyle's law.

Boyle's law states that the pressure exerted by a given mass of gas is inversely proportional to its volume at a constant temperature. The mathematical expression for Boyle's law is: P1V1 = P2V2where, P1 and V1 are the initial pressure and volume of the gas, respectively, and P2 and V2 are the final pressure and volume of the gas, respectively.

Let V1 be the initial volume of air in the lungs of the diver, which is 6L. Let P1 be the atmospheric pressure at the surface of the water, which is 1 atm. Let P2 be the pressure at 10 m depth, which can be calculated using the hydrostatic equation: P2 = P1 + ρghwhere, ρ is the density of water, g is the acceleration due to gravity, and h is the depth of the water.

The density of water at standard temperature and pressure is 1000 kg/m3. Therefore, ρgh = 1000 kg/m3 × 9.81 m/s2 × 10 m = 98,100 Pa. Hence, P2 = 1 atm + 98,100 Pa = 2.05 atm. Substituting the values in Boyle's law equation, we get:1 atm × 6 L = 2.05 atm × V2. Therefore, V2 = (1 atm × 6 L) / 2.05 atm = 17.56 L. Approximately, the new value for the volume of air in the lungs of the diver would be 17.56 L.

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It costs $336.384 to run a given giant screen TV all the time for 365 days. By choosing to use your TV's power-saving feature, the average current drawn drops to 0.275 Amps on the same 120 Volt circuit. How much do you save per year by using this feature (cost per kWh is $0.20) versus leaving it on all the time?

Answers

Answer:

The amount saved in a year is $ 278.6.

Explanation:

current, I = 0.275 A

Voltage, V = 120 V

cost = $ 0.20 per kWh

The energy spent in 1 year is given by

E = V I t

E = 120 x 0.275 x 365 x 24 x 3600

E = 1.04 x 10^9 J

1 kWh = 3.6 x 10^6 J

So,

E = 288.9 kWh

So, the cost is

C = $ 0.2 x 288.9 = $ 57.78

So, the amount saved = $ 336.384 - $ 57.78 = $ 278.6  

a golf ball of mass 0.050 kg is at rest on the tee and has a velocity of 102 m/s immediately after being struck. if the club and ball were in contact for 0.94 ms what is the average force exerted on the ball?

Answers

A golf ball with a mass of 0.050 kg is at rest on the tee and accelerates to 102 m/s as soon as it is struck. The average force applied to the ball if the club and ball made contact for 0.94 ms is 6.3 kN.

Describe impulse.

Impulse is a term used to describe how a net force—a specific type of "moving force"—affects an object. An impulsive force is a strong force that acts quickly to cause a finite change in momentum. Impulsive forces were conceptualized separated from regular forces throughout science history.

How is impulse calculated in physics?

Force times time equals change in momentum for an impulse.

Briefing:

F = mv/t

F = (0.050 kg)(102 m/s) / 0.81 ms × 10⁻³ = 6.3 kN

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aluminium is metal or metalloid

Answers

Answer:

Aluminium is just on the metal side of the border between metals and metalloids, so it is not considered to be a metalloid

Explanation:

it is a metal

Answer:

Aluminum-(Al) is a metal

How can you does units help you to solve a problem?

Answers

Answer:

They help by knowing what you are using them for.

Explanation:

i.e: you know you're solving for length if the units are meters

you're solving for time if you are using seconds

etc..

Do any of y’all know the answer to this? Please help, I’ve been stuck on this question forever

Do any of yall know the answer to this? Please help, Ive been stuck on this question forever

Answers

Answer:

I think it's B , maybe wrong tho....

Calculate the pressure due to a water column of height 120m ( take density of water = 1000 kg/m raise to 3, g = 10 m/s raise to 2

Calculate the pressure due to a water column of height 120m ( take density of water = 1000 kg/m raise

Answers

Answer:

P = ρ g H       familiar expression for pressure due to column of liquid

P = 1000 kg/m^3 * 10 m/s^2 ^ 120 m = 1,200,000 kg / m/s^2

Can also be written P = 1.2E6 kg / (m/s^2)

Usually written as 1.2E6 N/m^2

Standard atmospheric pressure is written as

1.01E5 N/m^2

So the pressure due to the column of water would be about 12 X

that of a column of water as given

2.

A loaded Boeing 747 jumbo jet has a mass of 200,000 kg. What net force is required to give the plane an

acceleration of 3. 5 m/s down the runway for takeoffs?

Answers

Answer:

We can use Newton's second law of motion to calculate the net force required to accelerate an object. The equation is:

F = ma

Where:

F = net force (N)

m = mass of the object (kg)

a = acceleration (m/s^2)

Given that the mass of the loaded Boeing 747 is 200,000 kg and the desired acceleration is 3.5 m/s^2. We can substitute these values into the equation:

F = 200,000 kg * 3.5 m/s^2 = 700,000 N

Therefore, the net force required to give the plane an acceleration of 3.5 m/s^2 is 700,000 N. This is a significant force, which is required to overcome the inertia of the massive object, and to move it down the runway.

30 12
w
Find the total
equivalent
resistance for the
circuit.
40 12
w
9.0V
50 Ω
2012 10 12
Reg = [?] 12

Answers

Answer:

6

.40 recharge

1.0v

45.0v

5 ptsA rope is tied between two trees. The rope has a tension of 1.15 N. We discover that we can excite the second harmonic of the rope if we wiggle it at 4.71 Hz. What tension should we apply to the rope if we want to be able to excite the first harmonic by wiggling it at 4.71 Hz

Answers

To excite the first harmonic of the rope by wiggling it at 4.71 Hz, the tension applied should be 1.15 N.

To excite different harmonics of a rope, the tension applied to the rope plays a significant role. The fundamental frequency of a vibrating rope is inversely proportional to the tension. Therefore, to excite the first harmonic at the same frequency of 4.71 Hz, the tension should be adjusted accordingly.

Since the tension applied to the rope for the second harmonic is 1.15 N, we can use this information to determine the required tension for the first harmonic. The relationship between tension and the fundamental frequency (f) of a vibrating rope is given by:

f₁/f₂ = √(T₁/T₂)

where f₁ and f₂ are the frequencies of the first and second harmonics respectively, and T₁ and T₂ are the tensions for the first and second harmonics respectively.

Plugging in the given values:

f₁/4.71 Hz = √(T₁/1.15 N)

To find T₁, we rearrange the equation:

T₁ = (f₁/4.71 Hz)² × 1.15 N

Since we want to excite the first harmonic at the same frequency of 4.71 Hz, we can substitute f₁ with 4.71 Hz:

T₁ = (4.71 Hz/4.71 Hz)² × 1.15 N

Simplifying the expression:

T₁ = 1.15 N

Therefore, to excite the first harmonic of the rope by wiggling it at 4.71 Hz, the tension applied should be 1.15 N.

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The hog-nosed bat is the smallest mammal on Earth: it is about the same size as a bumblebee and has an average mass of 2.0 g. Suppose a hog-nosed bat with this mass flies at 2.0 m/s when it detects a bug with a mass of 0.20g flying directly toward it at 8.0 m/s. What fraction of the total kinetic energy
dissipated when it swallows the bug?

Answers

The fraction of the total kinetic energy dissipated is = \(0.67\)  

Given

\(m_1 = 2g\\\\m_2 = 0.2g\\\\v_1 = 2m/s\\\\v_2 = -8m/s\)

The expression for a perfectly inelastic collision,

\(m_1v_1 + m_2v_2 = (m_1+m_2)v_f\)

Therefore,

\(v_f = \frac{m_1v_1 + m_2v_2}{(m_1+m_2)} \\\\v_f = \frac{(2*2)+(0.2*-8)}{2+0.2}\\\\v_f = 1.09m/s\)

Since the bat and the bug fly towards each other, and after some time the bat swallows the bug, it is said to be a condition of perfectly inelastic collision.

The kinetic energy of the bat before it swallows the bug is,

\(KE_b = \frac{1}{2}m_1v_1^2\\\\KE_b = \frac{1}{2}2*2^2\\\\KE_b = 4gm^2/s^2\)

The kinetic energy of the bat after it swallows the bug is,

\(KE_f = \frac{1}{2}(m_1+m_2)v_f^2\\\\KE_f = \frac{1}{2}(2+0.2)1.09^2\\\\KE_f = 1.3gm^2/s^2\)

The total dissipation in the kinetic energy of the bat is calculated as,

\(\delta KE = KE_b - KE_f\\\\\delta KE = 4 - 1.3\\\\\delta KE = 2.7 gm^2/s^2\)

The fraction of the dissipated kinetic energy of the bat is calculated as,

\(d = \frac{\delta KE}{KE_b}\\\\d = \frac{2.7}{4}\\\\d = 0.67\)

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Which choice below explains what is happening in a liquid as it turns into a gas?
a. The particles speed up and spread apart
b. The particles speed up and come closer together
c. The particles slow down and spread apart
d. The particles slow down and come closer together

Answers

Answer:

a

Explanation:

As you add thermal energy the particles spread apart and are moving faster ..... a certain volume of water produces a much larger volume of steam as energy is added.....that is how steam engines work !

A motor boat is headed at a velocity of 25 kilometers/hour toward the north, while the velocity of the water current is 12 kilometers/hour to the west. What is the magnitude of the boat’s resultant velocity?

Answers

Explanation:

CON EL TEOREMA DE PITÁGORAS

v = \(\sqrt{(12 km/h)^{2} + (25 km/h)^{2}}\) = 27.7 km/h


Punnett squares are used by geneticists to determine the probability of
different offspring genotypes.

Answers

Answer:

are used by geneticists to determine the probability of different offspring genotypes.

Which frequency would be the third harmonic in a series for an open-pipe resonator if the fundamental is 440 Hz

Answers

Answer:

1320 Hz

Explanation:

The third harmonic is given as 3fo, where fo is the fundamental frequency.

The fundamental frequency is the lowest frequency that can occur in a pipe. In an open pipe, both even and odd harmonics occur which are multiples of the fundamental frequency fo. Hence the harmonics in an open pipe are; 2fo, 3fo,4fo..... etc.

For the third harmonic; 3fo = 3 (440 Hz) = 1320 Hz

what is a transformer? what are the primary and secondary coils and how does it make use of induction?

Answers

A transformer is a device that transfers electrical energy between two or more coils of wire through electromagnetic induction. The primary coil receives electrical energy, while the secondary coil delivers the transformed energy.

In a transformer, the primary coil is connected to the input voltage source, and the secondary coil is connected to the load. When an alternating current flows through the primary coil, it creates a changing magnetic field. This changing magnetic field induces an alternating current in the secondary coil, transferring energy to the load.

The principle behind a transformer is electromagnetic induction, which states that a changing magnetic field induces an electromotive force (EMF) in a nearby conductor. The ratio of the number of turns in the primary and secondary coils determines the voltage transformation. Transformers are widely used in electrical power distribution systems to increase or decrease voltage levels for efficient transmission and distribution of electricity.

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A piece of metal weighing 187.6 g is placed in a graduated cylinder containing 225.2 mL of water. The combined volume of solid and liquid is 250.3 mL. What is the density, in grams per milliliter, of the metal?

Answers

The density of the metal is 7.47 g/mL  which can be calculated by dividing the mass (187.6 g) of the metal by its volume (250.3 mL).

The volume of the metal by using the displacement method.

When the metal is placed in the graduated cylinder containing water, the water level rises by a certain amount equal to the volume of the metal. Therefore, we can calculate the volume of the metal as follows:

Volume of metal = Volume of solid and liquid - Volume of liquid

Volume of metal = 250.3 mL - 225.2 mL

Volume of metal = 25.1 mL

Now that we have the volume of the metal, we can find its density as follows:

Density of metal = Mass of metal / Volume of metal

Density of metal = 187.6 g / 25.1 mL

Density of metal = 7.47 g/mL

Therefore, the density of the metal is 7.47 g/mL.

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What types of cells are likely to have lots of smooth ER?

Answers

Answer:

eukaryotic cells

Explanation:

"Smooth endoplasmic reticulum (sER) is (a part of) endoplasmic reticulum that is tubular in form and lacks ribosomes. It is present in eukaryotic cells and is associated with lipid synthesis, carbohydrate metabolism, regulation of calcium concentration, and drug detoxification"

source: biologyonline

Specifications for a part for a 3-D printer state that the part should weigh between 24.7 and 25.7 ounces. The process that produces the parts has a mean of 25.2 ounces and a standard deviation of .20 ounce. The distribution of output is normal. Use Table-A.

a.What percentage of parts will not meet the weight specs? (Round your "z" value and final answer to 2 decimal places.)

b.Within what values will 99.74 percent of the sample means of this process fall if samples of n = 10 are taken and the process is in control (random)? (Round your answers to 2 decimal places.)

Answers

1.24% percentage of parts will not meet the weight specs amd the sample means will fall between 25.046 and 25.354 ounces.

a. To determine the percentage of parts that will not meet the weight specifications, we need to calculate the probability of a part weighing less than 24.7 ounces or more than 25.7 ounces. First, we need to calculate the z-scores for these values using the formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation. For 24.7 ounces:

z1 = (24.7 - 25.2) / 0.20 = -2.50

For 25.7 ounces:

z2 = (25.7 - 25.2) / 0.20 = 2.50

Using Table-A (Z-score table), we can find the area under the standard normal curve corresponding to these z-values. From the table, the area to the left of -2.50 is 0.0062, and the area to the right of 2.50 is also 0.0062. Therefore, the total probability of a part not meeting the weight specs is:

P(z < -2.50 or z > 2.50) = P(z < -2.50) + P(z > 2.50) = 0.0062 + 0.0062 = 0.0124

So, the percentage of parts that will not meet the weight specs is .

b. To determine the values within which 99.74% of the sample means will fall, we need to calculate the margin of error for a sample mean. The margin of error is given by the formula:

E = z * (σ / sqrt(n))

where E is the margin of error, z is the z-score corresponding to the desired level of confidence (in this case, 99.74% corresponds to a z-score of 2.75), σ is the standard deviation, and n is the sample size.

Plugging in the values:

E = 2.75 * (0.20 / sqrt(10)) ≈ 0.154

The range of sample means will be within ±E of the population mean. Therefore, the values within which 99.74% of the sample means will fall are:

25.2 ± 0.154 = (25.046, 25.354)

So, for samples of size 10, 99.74% of the sample means will fall between 25.046 and 25.354 ounces.

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Crates of masses 1 kg , 4 kg , and 6 kg are placed in a line on a frictionless table. They remain in contact as they are pushed by a 60 N force applied to the 1 kg block.

A) What is the magnitude of the force that the 4 kg block deals to the 6 kg block?
B) What is the magnitude of the force dealt by the 4 kg block on the 1 kg block?

Answers

Answer:

Approximately \(33\; {\rm m\cdot s^{-2}}\).

Approximately \(55\; {\rm m\cdot s^{-2}}\).

(Assume that the table is level, and that the \(60\; {\rm N}\) force is horizontal.)

Explanation:

Consider all three blocks as one object of mass \(m = (1 + 4 + 6)\; {\rm kg} = 11\; {\rm kg}\). Among all the forces that are in action, the only unbalanced external force on this \(m = 11\; {\rm kg}\) object will be the \(60\; {\rm N}\) force. Hence, the resultant force of this combined object of mass \(m = 11\; {\rm kg}\) will be \(F_{\text{net}} = 60\; {\rm N}\).

Acceleration \(a\) of this combined object will be:
\(\begin{aligned}a &= \frac{F_{\text{net}}}{m} \\ &= \frac{60\; {\rm N}}{11\; {\rm kg}} \\ &= \frac{60}{11}\; {\rm m\cdot s^{-2}}\end{aligned}\).

Since the three crate blocks are moving together, each will have the same acceleration, \(a = (60/11)\; {\rm m\cdot s^{-2}}\).

Resultant force on each of the crate blocks will be:

\(1\; {\rm kg}\) crate: \(F_{\text{net}} = m\, a = (1\; {\rm kg})\, (60/11\; {\rm m\cdot s^{-2}}) = (60/11)\; {\rm N}\).\(4\; {\rm kg}\) crate: \(F_{\text{net}} = m\, a = (4\; {\rm kg})\, (60/11\; {\rm m\cdot s^{-2}}) = (240/11)\; {\rm N}\).\(6\; {\rm kg}\) crate: \(F_{\text{net}} = m\, a = (6\; {\rm kg})\, (60/11\; {\rm m\cdot s^{-2}}) = (360/11)\; {\rm N}\).

Assume that the \(60\; {\rm N}\) external force on the \(1\; {\rm kg}\) block points to the right.

When the crates are considered individually, external forces on the \(1\; {\rm kg}\) crate will include:

the \(60\; {\rm N}\) external force to the right, anda normal force the \(4\; {\rm kg}\) block exerts on the \(1\; {\rm kg}\) block (to the left.) Assume that this force is of magnitude \(x\; {\rm N}\).(In the vertical direction, the weight of this block and the upward normal force from the table are balanced.)

Since these two forces are in opposite directions, the resultant force on this \(1\; {\rm kg}\) block will be \((60\; {\rm N} - x\; {\rm N})\). However, since the actual resultant force on this block (calculated from acceleration) is \((60 / 11)\; {\rm N}\):

\(\displaystyle 60\; {\rm N} - x\; {\rm N} = \frac{60}{11}\; {\rm N}\).

Therefore, the force that the \(4\; {\rm kg}\) block exerts on the \(1\; {\rm kg}\) block will be

\(\displaystyle 60\; {\rm N} - \frac{60}{11}\; {\rm N} = \frac{600}{11}\; {\rm N} \approx 55\; {\rm N}\).

When considered individually, the only unbalanced external force on the \(m = 6\; {\rm kg}\) block is the normal force from the \(4\; {\rm kg}\) block. Hence, this force will be equal to the resultant force on the \(m = 6\; {\rm kg}\) block, \((360 / 11)\; {\rm N} \approx 33\; {\rm N}\).

The function d(v) = 0.0067 v^2 + 0.15v can be used to determine the safe stopping distance, d(v), in metres for a car given its speed, v, in kilometres per house. determine the speed at which a car can be traveling in order to be able to stop at a distance of 24m. show your work and round your final answer(s) to the nearest meter.

Answers

Evaluate the function when d(v) = 24.

\(\begin{gathered} 24=0.0067v^2+0.15v \\ 0.0067v^2+0.15v-24=0 \end{gathered}\)

Use the quadratic formula to find v.

\(v=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)

Where a = 0.0067, b = 0.15, and c = -24.

\(\begin{gathered} v=\frac{-0.15\pm\sqrt[]{0.15^2-4\cdot0.0067\cdot(-24)}_{}}{2\cdot0.0067}=\frac{-0.15\pm\sqrt[]{0.6657}_{}}{0.0134} \\ v_1=49.7\cdot\frac{km}{hr}_{} \\ v_2=-72.1\cdot\frac{km}{hr} \end{gathered}\)

Therefore, the car should travel at 49.7 km/hr.

We take the positive speed as the answer.

A 600 ohm transmission line has load impedance Zl=424.3 explj pi/4) ohms. At the load the voltage is Vi=50 exp(jo) Volts. Find the value of the maximum voltage on the line

Answers

The maximum voltage on the line is \(V_m_a_x = 101.5 V\) which can be calculated using the voltage reflection coefficient.


To find the maximum voltage on the line, we need to use the voltage reflection coefficient. This is given by:

ρv = \((Z_L - Z_0) / (Z_L + Z_0)\), where \(Z_0\) is the characteristic impedance of the transmission line.

For a 600-ohm transmission line,

\(Z_0\) = 600 ohms.

Substituting the given values, we get:

ρv = \((424.3 exp(j\pi /4) - 600)\) / \((424.3 exp(j\pi /4) + 600)\)ρv

=  \((-175.7 - 348.5j)\)/ \((849.8 exp(j\pi /4))\)ρv = \(-0.2162 exp(-j1.1304)\)

The maximum voltage on the line is given by:

Vmax = Vi / (1 - ρv)

Substituting the given values, we get:

Vmax = \(50 exp(j0) / (1 - (-0.2162 exp(-j1.1304)))\)

Vmax = 101.5 V

Therefore, the maximum voltage on the line is Vmax = 101.5 V.

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