What is the crankshaft's angular acceleration at t = 1 s?

Resolving power refers to the ability of a lens to distinguish between two closely spaced objects. It is determined by the wavelength of light and the numerical aperture of the lens.

Magnifying power, on the other hand, refers to the ability of a lens to enlarge the size of an object. It is determined by the focal length of the lens.
The term "parfocal" refers to a type of lens system where multiple lenses have the same focal point when the focus is adjusted. This means that when switching between different lenses, the focus remains the same, making it easier for the user to switch between lenses without losing focus.
Differentiating between the resolving power and magnifying power of a lens involves understanding their respective functions. Resolving power refers to the ability of a lens to distinguish between two closely spaced objects, or in other words, the clarity with which the lens can produce an image. Magnifying power, on the other hand, refers to the degree to which a lens can enlarge the image of an object.

The term "parfocal" is used to describe a set of lenses that, when interchanged on a microscope or other optical instrument, maintain their focus on the same object. This means that when you switch from one parfocal lens to another, only minimal adjustments to the focus are needed, allowing for a seamless transition between lenses with different magnifying powers.

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Resolving Power: It is the ability of a lens to separate or distinguish between closely spaced objects, reflecting the detail that can be seen with the lens.

Magnifying Power: It denotes how much larger an object appears through a lens compared to its actual size. High magnification doesn't necessarily mean better image quality.

Parfocal: This term refers to lenses that remain in focus even when the magnification or focal length changes. It enables swift adjustments in magnification without needing constant refocusing.

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The type II error in this scenario would be failing to reject the null hypothesis (H0) when the alternative hypothesis (Ha) is actually true.

This would mean concluding that no more than 90% of homes in the city are up to the current electric codes when in reality, more than 90% of homes are up to code. In this scenario, the Type II error occurs when we fail to reject the null hypothesis (H0) when the alternative hypothesis (Ha) is actually true. So, the Type II error would be:

Failing to reject the null hypothesis (H0) that no more than 90% of homes in the city are up to the current electric codes when, in fact, the electrician's claim (Ha) that more than 90% of homes are up to the current electric codes is true.

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Approximately 1.92 x [tex]10^2^2[/tex] photons strike a single 4.5-cm-diameter mirror from one 100ps laser pulse with a wavelength of 532 nm and intensity of 400W/m².

To calculate the number of photons that strike a single mirror, we need to use the formula for photon energy:

E = hc/λ

where E is the energy of a photon, h is Planck's constant, c is the speed of light, and λ is the wavelength of the laser.

First, we can calculate the energy of one photon:

E = hc/λ = (6.626 x [tex]10^-^3^4[/tex] J s) x (3 x [tex]10^8[/tex] m/s) / (532 x [tex]10^-^9[/tex] m)

E = 3.94 x [tex]10^-^1^9[/tex] J

Next, we can calculate the total energy of the laser pulse:

[tex]E_p_u_l_s_e[/tex] = P x t = (400 W/m²) x (4π(2.25 x [tex]10^7[/tex] m)²) x (100 x [tex]10^-^1^2[/tex] s)

[tex]E_p_u_l_s_e[/tex] = 7.55 x [tex]10^4[/tex] J

where P is the power per unit area of the laser pulse, t is the pulse duration, and the factor of 4π(2.25 x [tex]10^7[/tex] m)² is the total area of the reflecting mirrors on the moon.

Finally, we can calculate the number of photons that strike a single mirror:

N = [tex]E_p_u_l_s_e[/tex] / E = 7.55 x [tex]10^4[/tex] J / 3.94 x [tex]10^-^1^9[/tex] J

N ≈ 1.92 x [tex]10^2^2[/tex] photons

So approximately 1.92 x [tex]10^2^2[/tex] photons strike a single 4.5-cm-diameter mirror from one laser pulse.

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An air mass moving inland from the coast in winter can result in a few different weather phenomena, but the most likely of the options provided would be fog.

As the air mass moves over colder land surfaces, it can cool rapidly and become saturated with moisture. This can lead to the formation of fog, which can reduce visibility and make driving or other activities hazardous. While hail can occur in winter storms, it typically requires more unstable atmospheric conditions than a simple air mass moving in from the coast. Frost is also a possibility, particularly on clear, calm nights when the ground can radiate heat away into the atmosphere, but again this may not be as likely as fog. Ultimately, the specific outcome of an air mass moving inland will depend on a number of factors, including the temperature and humidity of the air, the characteristics of the land surface, and the prevailing wind patterns. However, in general, winter weather conditions can be challenging and unpredictable, and it is important to stay aware of any weather alerts or warnings that may be issued in your area.

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The frequency of recombination is generally higher for genes that are further apart compared to those that are closer together on the same chromosome.

This is because crossing-over events are more likely to occur between distant genes, allowing for more exchange of genetic material between homologous chromosomes. Conversely, genes that are located closer together experience fewer crossover events and therefore have a lower frequency of recombination. However, it is important to note that the frequency of recombination can also be influenced by other factors such as the size and structure of the chromosome, as well as the presence of DNA sequence variations that can affect the recombination process.

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Position between center of curvature and focal point for blurred image.

If you place your face in front of a concave mirror, several statements can be made about the image formed.

One correct statement is that if you position yourself between the center of curvature and the focal point of the mirror, you will not be able to see a sharp image of your face.

This is because in this region, the mirror produces a virtual and magnified image, which is not focused on a screen or surface.

The image formed by a concave mirror can be either real or virtual, depending on the position of the object.

However, the other statements provided are not universally correct. The size and orientation of the image depend on the position of the object relative to the focal point and the center of curvature.

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The accurate explanation for the observation that the length of daylight increased with each observation from December to June is option d.

Jonathan compared the length of daylight in the United States during the months of December, February, and June. The amount of daylight increased with each observation, with December having the fewest hours of daylight and June having the most:

The Northern Hemisphere is tilted toward the sun in the summer months. This tilt causes the sunlight to spread over a larger area, resulting in longer daylight hours during the summer months. Conversely, in the winter months, the Northern Hemisphere is tilted away from the sun, resulting in shorter daylight hours.

Option a is incorrect because the Earth's rotation does not change throughout the year. Option b is also incorrect because atmospheric gases do not significantly affect the amount of daylight.

Option c is incorrect because the Earth's distance from the sun does not significantly affect the amount of daylight.

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Answer:

θ = sin^-1 (1.22 × 550 × 10^-9 m / 0.63 m)

θ ≈ 1.59 × 10^-6 rad

d = sin (1.59 × 10^-6 rad) × (19 × 9.461 × 10^15 m)

d ≈ 5.6 × 10^12 m

Therefore, the stars are approximately 5.6 × 10^12 m or 5.6 trillion kilometers apart.

At resonance in an LRC (inductor-resistor-capacitor) circuit, the frequency of the driving AC voltage matches the natural frequency of the circuit. At this point, the reactive effects of the inductor and capacitor cancel out, leaving only the resistive effects of the circuit.

Therefore, at resonance in an LRC circuit:

A) The current is in phase with the driving voltage because the circuit behaves like a purely resistive circuit.

B) The peak voltage across the resistor is equal to the peak voltage across the inductor because the reactances of the inductor and capacitor cancel out, and the only voltage drop is across the resistor.

C) The peak voltage across the capacitor is equal to the peak voltage across the inductor because they have equal and opposite reactances at resonance, which cancel each other out, leaving only the voltage drop across the resistor.

D) and E) are incorrect because the peak voltage across the inductor and capacitor are equal at resonance, and the voltage drop across the resistor is the same as the peak voltage across the inductor and capacitor.

Therefore, the correct options are A), B) and C).

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The presence of the wire reduces the flow rate, but the amount of reduction depends on the ratio d/D and the specific conditions within the pipe.

We would like to know how the presence of a wire with diameter d affects the flow rate in a pipe with diameter D, given a pressure drop per unit length.

Let's consider two cases: (a) d/D is small and (b) d/D is significant.

(a) If d/D is small, the presence of the wire minimally affects the flow rate, as the wire occupies only a small portion of the pipe's cross-sectional area.

The flow rate reduction can be calculated using the ratio of the wire's area to the pipe's area. The reduction factor is (d^2)/(D^2), and the flow rate will be reduced by a small amount based on this ratio.

(b) If d/D is significant, the presence of the wire will have a more pronounced effect on the flow rate.

In this case, the reduction in flow rate depends on multiple factors, such as the shape of the wire and the interaction between the wire, fluid, and pipe wall. Calculating the exact flow rate reduction may require experimental data or more complex mathematical models.

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The jovian planets (Jupiter, Saturn, Uranus, and Neptune) and terrestrial planets (Mercury, Venus, Earth, and Mars) both formed from the same solar nebula according to the nebular theory of solar system formation.

The key difference in their early formation that explains why they ended up different is not based on the composition of planetesimals (i.e., ice or rock/metal), but rather the distance from the sun at which they formed.

Jovian planets formed farther from the sun where temperatures were lower, allowing for the accumulation of large amounts of gas and ice, resulting in their large size and gaseous composition. Terrestrial planets formed closer to the sun where temperatures were higher, leading to the formation of smaller rocky planets with solid surfaces.

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The correct option is C, Each point of a light-emitting object sends an infinite number of rays.

Light-emitting refers to the process by which a material emits light. This can happen through a variety of mechanisms, such as thermal radiation, fluorescence, or phosphorescence. When a material absorbs energy, such as through exposure to light or heat, it can become excited and release this energy in the form of light.

For example, in fluorescence, a material absorbs high-energy light and then emits lower-energy light as it returns to its ground state. This is the process that makes fluorescent materials glow under UV light. In phosphorescence, the material continues to emit light even after the excitation source has been removed, due to a delayed release of energy. Light-emitting is an important phenomenon in many areas of science and technology, such as lighting, displays, and lasers.

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The type of stress necessary are:  Basin and Range province: Tension, San Andreas Fault: Shear, Grand Teton Mountains, Appalachian Mountains and Dakota Hogback: Compression.

1. Basin and Range province: Tension
Tension stress causes the crust to be pulled apart, resulting in the formation of alternating mountain ranges and valleys, such as those found in the Basin and Range province.
2. San Andreas Fault: Shear
Shear stress causes adjacent crustal blocks to slide past one another, which is what happens along the San Andreas Fault. This type of stress is responsible for the formation of transform faults.
3. Grand Teton Mountains: Compression
Compression stress pushes crustal blocks together, resulting in the formation of mountains. The Grand Teton Mountains were formed by the compression of crustal blocks due to tectonic forces.
4. Appalachian Mountains: Compression
Similar to the Grand Teton Mountains, the Appalachian Mountains were also formed by compression stress. The crustal blocks were pushed together, leading to the formation of these mountains.
5. Dakota Hogback: Compression
The Dakota Hogback is a geological feature that was formed by compression stress. This stress caused the uplift and folding of the rock layers, resulting in the distinctive ridge-like feature of the Dakota Hogback.

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The nurse determined that the heart beats periodically 60 times in 60 seconds, which means that the heart beats once every second. which in this case is one heartbeat. the period of the heartbeat is 1 second.

Therefore, the period of the heartbeat is 1 second. Option A (1 Hz) is incorrect because 1 Hz refers to the frequency, which is the number of cycles per second, not the period. Option B (60 Hz) is incorrect because it is an extremely high frequency that is not consistent with the human heartbeat. Option D (60 s) is incorrect because it is too long of a period for one heartbeat.
"A nurse takes the pulse of a heart and determines the heart beats periodically 60 times in 60 seconds. The period of her heartbeat is The period of her heartbeat is C: 1 s.

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The incompatibility between calcium and phosphate salts found in whole grain cereals and nuts is a type of chemical incompatibility.

Chemical incompatibility occurs when two or more substances react with each other to form an undesirable product or cause a loss of therapeutic effect. In the case of calcium and phosphate salts, when combined, they can form calcium phosphate precipitates.

This precipitation can reduce the bioavailability of both calcium and phosphate, making them less effective as nutrients or therapeutic agents in the body.

The interaction between calcium and phosphate salts in whole grain cereals and nuts is an example of chemical incompatibility. This can result in reduced bioavailability of these essential nutrients, which is undesirable for optimal health and well-being.

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The frequency of the spring oscillator is 2 Hz.the period of the spring oscillator is 0.5 seconds.the amplitude of the spring oscillator is 0.26 m

1. The frequency of a spring oscillator is the number of complete oscillations (or cycles) it makes per unit of time. In this case, the weight bobs up and down twice each second, so the frequency is:

f = 2 cycles/second = 2 Hz (to two significant figures)

Therefore, the frequency of the spring oscillator is 2 Hz.

2. The period of a spring oscillator is the time it takes to complete one full oscillation (or cycle). The period is the inverse of the frequency, so:

T = 1/f = 1/2 Hz = 0.5 seconds (to two significant figures)

Therefore, the period of the spring oscillator is 0.5 seconds.

3. The amplitude of a spring oscillator is the maximum displacement from the equilibrium position. In this case, the weight bobs up and down over a distance of 26 cm, which is the amplitude of the oscillation. Converting to meters:

A = 26 cm = 0.26 m (to two significant figures)

Therefore, the amplitude of the spring oscillator is 0.26 m.

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The actual mechanical advantage of the nutcracker, which is defined as the ratio of output force to input force, is 4, where the output force is 50.0 N and the input force is 12.5 N.

The mechanical advantage of a simple machine is defined as the ratio of the output force to the input force. In the case of the nutcracker, the input force is 12.5 N and the output force is 50.0 N, so the actual mechanical advantage of the nutcracker can be calculated as:

Actual mechanical advantage = output force / input force

Actual mechanical advantage = 50.0 N / 12.5 N

Actual mechanical advantage = 4

Therefore, the actual mechanical advantage of the nutcracker is 4. This means that for every 1 unit of input force applied to the nutcracker, the nutcracker provides 4 units of output force.

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the velocity of the wave is 400m/s

The formula for the velocity of the wave is, V = w/k

where ,  w is the coefficient of t and k is the coefficient of x

now putting values we get, v = 200/0.5 = 400

Hence the velocity of the wave is 400 m/s

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In a photoelectric experiment, if both the intensity and frequency of the incident light are doubled, the saturation photoelectric current is doubled. The correct option is C.

The intensity and frequency of light are related to the number of photons and the energy of the photons, respectively. Doubling the intensity increases the number of incident photons, thus increasing the number of emitted photoelectrons and the current.

However, doubling the frequency increases the energy of each photon but does not affect the number of photons striking the surface. Since the work function (the energy required to emit an electron) remains the same, the excess energy goes into the kinetic energy of the emitted photoelectrons, not into increasing the current.

Therefore, the combined effect of doubling both intensity and frequency results in a doubled saturation photoelectric current.

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The answer is A) 1000 millivolts. 1.000 Volt is equal to 1000 millivolts since there are 1000 millivolts in 1 Volt.

1 volt is equal to 1000 millivolts. Voltage is a measure of electric potential difference between two points in an electrical circuit, and it is commonly measured in volts (V). Millivolts (mV) is another unit used to express voltage, which is equal to one-thousandth of a volt. This unit is commonly used in electronics and electrical engineering to measure small voltage values. Additionally, microvolts (μV) is another unit used to measure voltage, which is equal to one millionth of a volt. It is commonly used in scientific research and measurement applications, such as in studies of brain activity or radio communications.

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Current is the flow of charges along a conducting path and is measured in amperes. So the correct option is B.

Current is the flow of electric charge along a conducting path, typically in the form of electrons moving through a wire or other conductive material. The unit of current is the ampere, which is defined as the flow of one coulomb of charge per second. It's abbreviated as "A".

Voltage, on the other hand, is the electrical potential difference between two points in a circuit or electrical system. It's measured in volts and represents the force that drives the flow of current. Voltage is often compared to the pressure in a water pipe - just as water will flow from a high-pressure area to a low-pressure area, electrical charge will flow from a high-voltage area to a low-voltage area.

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When the light of a specific wavelength (in this case, 400 nm) is transmitted through an interference filter and strikes a metal surface, a phenomenon called the photoelectric effect occurs, where electrons are emitted from the metal.

If the intensity of the light is doubled, more electrons are emitted in a given time interval (option b), but the other options are not necessarily true. The stopping potential, which is the voltage needed to stop the flow of electrons, may or may not increase depending on the conditions. The work function of the metal surface, which is the energy required to remove an electron from the metal, is not affected by the intensity of the light. Finally, the average kinetic energy of the emitted electrons is not necessarily doubled, and may even decrease if the electrons experience collisions or interactions with other particles before being emitted from the metal surface.

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The number of hydrogen atoms in the sun is 1.19 x 10⁵⁷.

Mass of the sun, M = 2 x 10³⁰kg

Mass of hydrogen, m = 1.67 x 10⁻²⁷kg

There are roughly 1057 hydrogen atoms in the Sun. There are 1080 atoms in the known universe, which is equal to the product of the number of atoms per star (1057) and the estimated number of stars in the universe (1023).

The equation for the number of hydrogen atoms in the sun is given by,

n = M/m

n = 2 x 10³⁰/1.67 x 10⁻²⁷

n = 1.19 x 10⁵⁷

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A neutron decays into a proton, electron, and a nearly massless neutrino. We need to find the energy released, momentum of the proton and the neutrino after the decay, and the kinetic energy of the proton.

i) The energy released in the decay is equal to the difference in rest mass between the neutron and the proton, electron, and neutrino. It is approximately 1.29 MeV.

ii) By conservation of momentum, the momentum of the proton and neutrino after the decay must be equal in magnitude and opposite in direction. Since the neutrino is massless, it moves at the speed of light and its momentum is given by ΔE/c, where ΔE is the energy released. The momentum of the proton can be calculated using the conservation of energy equation, and it is approximately 1.40 × 10^-22 kg m/s (opposite in direction to the neutrino).

iii) The kinetic energy of the proton can be calculated using the conservation of energy equation and the rest energy of the proton. It is approximately 931 keV.

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The total resistance in a series circuit is equal to the sum of the individual resistances. Therefore, the total resistance in this circuit would be 1 + 2 + 10 = 13 Ohms. So the answer is A) 13 Ohms.

the total resistance in a series circuit consisting of three resistances: 1 Ohm, 2 Ohms, and 10 Ohms.

To find the total resistance in a series circuit, you simply add the individual resistances together.
Add the resistances
1 Ohm + 2 Ohms + 10 Ohms = 13 Ohms

So, the total resistance in this series circuit is 13 Ohms.

The total resistance in a series circuit is equal to the sum of the individual resistances. Therefore, the total resistance in this circuit would be  13 Ohms.

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In fully developed laminar flow in a circular pipe, the velocity profile is parabolic in shape with the highest velocity at the centerline and decreasing towards the wall. Using the continuity equation, which states that the mass flow rate is constant throughout the pipe, we can determine the velocity at the center of the pipe.

Assuming that the pipe is fully developed laminar flow, the velocity profile is symmetrical about the centerline. Therefore, the velocity at the centerline is twice the velocity at r=0.5R (where R is the radius of the pipe).

Using this relationship and the measured velocity of 11 m/s at r=0.5R, we can calculate that the velocity at the center of the pipe is 22 m/s. It is important to note that this calculation is only valid for laminar flow conditions and assumes that there is no turbulence present in the flow.

If the flow becomes turbulent, the velocity profile will no longer be parabolic and the calculation of the centerline velocity will become more complex.

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Increasing the width of the slit and decreasing the wavelength of the red light would decrease the angles at which the diffraction minima appear.

There are several alterations that can decrease the angles at which the diffraction minima appear when red light is diffracted through a single slit. These alterations include:

Decreasing the width of the single slit: Reducing the width of the slit narrows the diffracted light pattern, resulting in smaller angles between the minima.

Decreasing the wavelength of the red light: A shorter wavelength leads to a smaller diffraction angle. By using red light with a shorter wavelength, the angles at which the minima appear will decrease.

Increasing the distance between the single slit and the screen: Increasing the distance between the slit and the screen leads to a larger diffraction pattern. As a result, the angles at which the minima appear will decrease.

These alterations directly affect the characteristics of the diffraction pattern, causing a decrease in the angles at which the diffraction minima occur.

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The temperature of the water before the insertion of the thermometer was 22.6 °C.

We can use the equation Q = mcΔT to solve this problem, where Q is the heat gained or lost, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

First, we need to find the heat gained by the thermometer from the water:

Q₁ = mcΔT = (0.026 kg)(896 J/(kg⋅°C))(65.6 °C - 16.4 °C) = 120.64 J

Next, we can use the heat gained by the thermometer to find the initial temperature of the water:

Q₂ = mcΔT = (0.166 kg)(4184 J/(kg⋅°C))(T₂ - 65.6 °C) = -120.64 J

Solving for T₂, we get:

T₂ = (120.64 J)/((0.166 kg)(4184 J/(kg⋅°C))) + 65.6 °C = 22.6 °C

Therefore, the temperature is 22.6 °C.

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The charge of particle A is two times that of particle B nearby. The force acting on particle B is D) the same that acting on particle A.

In this scenario, we are considering two particles, A and B, with particle A having twice the charge of particle B. Coulomb's Law, which states that the electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of their distance, can be used to calculate the force acting on each particle.

Mathematically, Coulomb's Law is expressed as F = k * (|q1 * q2| / r^2), where F is the force, k is Coulomb's constant, q1 and q2 are the charges of the particles, and r is the distance between them. Since particle A has twice the charge of particle B, we can denote the charges as qA = 2 * qB. When we substitute these values into Coulomb's Law, we can analyze the relationship between the forces on each particle.

For particle A: FA = k * (|2 * qB * qB| / [tex]r^2[/tex]) For particle B: FB = k * (|qB * 2 * qB| / [tex]r^2[/tex]) As we can see, both equations are identical, meaning that force on particle A is the same as the force on particle B. Therefore, the correct answer is: D) the same.

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(a) The speed of the pulse is approximately 38.82 m/s.

(b) The tension in the cable is approximately 1,086,224.39 N.

(a) To calculate the speed of the pulse, we need to use the formula for wave speed, which is given by v = λ/T, where v is the wave speed, λ is the wavelength, and T is the period.

In this case, since the pulse travels along the cable and returns to the starting point, the wavelength is equal to the length of the cable, λ = 660 m. The period, T, is the time it took for the pulse to return, T = 17 s. Plugging in these values into the formula, we have v = 660 m / 17 s ≈ 38.82 m/s.

Therefore, the speed of the pulse is approximately 38.82 m/s.

(b) The tension in the cable can be determined using the formula for wave speed, v = √(T/μ), where T is the tension and μ is the linear mass density of the cable.

The linear mass density is given by μ = (mass/length), and we need to find the mass of the cable. To calculate the mass, we can use the formula for the volume of a cylinder, V = πr²h, where r is the radius and h is the height.

The radius is half of the diameter, r = 1.5 cm / 2 = 0.75 cm = 0.0075 m, and the height is the length of the cable, h = 660 m. Thus, V = π(0.0075 m)²(660 m) ≈ 0.091 m³.

The density of steel is approximately 7850 kg/m³. Therefore, the mass of the cable is m = V * density = 0.091 m³ * 7850 kg/m³ ≈ 714.35 kg. Substituting the values into the wave speed formula, we have 38.82 m/s = √(T / 714.35 kg).

Solving for T, we find T ≈ (38.82 m/s)² * 714.35 kg ≈ 1086224.39 N. Hence, the tension in the cable is approximately 1,086,224.39 Newtons.

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