a 1118-kg car and a 2000-kg pickup truck approach a curve on the expressway that has a radius of 264 m .
As the car and truck round the curve at 61.1 mi/h , find the normal force on the truck to the highway surface.

We get: Magnifying Power = -(2.85 m / 0.029 m) ≈ -98.28. The magnifying power of an astronomical telescope can be calculated using the formula: Magnifying Power = -(fo/fe), where fo is the focal length of the objective (reflecting mirror) and fe is the focal length of the eyepiece.

Given that the radius of curvature of the reflecting mirror is 5.7 m, the focal length can be determined using the relation: Focal Length = Radius of Curvature / 2. So, the focal length of the objective is 5.7 m / 2 = 2.85 m.

Converting the focal length of the eyepiece to meters, we have 2.9 cm = 0.029 m.

Substituting the values into the magnifying power formula, we get: Magnifying Power = -(2.85 m / 0.029 m) ≈ -98.28

The negative sign indicates an inverted image, and the magnitude of the magnifying power suggests that the image appears 98.28 times larger than the object.

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The magnitude of the angular momentum of the Earth in a circular orbit around the Sun can be calculated as 3.53 x 10²⁹ kg·m²/s. It is reasonable to model the Earth's motion around the Sun as a particle due to its relatively small size compared to the orbital radius.

The magnitude of the angular momentum of the Earth due to its rotation around an axis through the north and south poles, modeling it as a uniform sphere, is approximately 7.07 x 10³³ kg·m²/s.

The Earth's rotation involves the collective angular momentum of its constituent particles. Modeling it as a uniform sphere provides a simplified representation, assuming a constant mass distribution throughout.

For a particle in circular motion, the angular momentum can be calculated as the product of the mass, velocity, and radius of the orbit.

Using the mass of the Earth (5.97 x 10²⁴ kg), the average orbital velocity (2.98 x 10⁴ m/s), and the distance from the Earth to the Sun (1.50 x 10¹¹ m),

we can calculate the angular momentum as L = (5.97 x 10²⁴ kg) * (2.98 x 10⁴ m/s) * (1.50 x 10¹¹ m) = 3.53 x 10²⁹ kg·m²/s.

For a rotating object, the angular momentum can be calculated as the product of the moment of inertia and the angular velocity.

Considering the Earth as a uniform sphere, the moment of inertia (I) can be approximated as (2/5) * M * R², where M is the mass of the Earth and R is its radius.

The angular velocity (ω) is determined by the Earth's rotational period (T), with ω = 2π/T.

Substituting the values of M (5.97 x 10²⁴ kg) and R (6.37 x 10⁶ m) and using the rotational period of the Earth (T = 24 hours or 8.64 x 10⁴ s),

we can calculate the angular momentum as L = [(2/5) * (5.97 x 10²⁴ kg) * (6.37 x 10⁶ m)²] * [2π/(8.64 x 10⁴ s)] = 7.07 x 10³³ kg·m²/s.

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If lens 1 from part d were placed in exactly the same location as lens 2, the image produced by lens 1 would be larger than the image produced by lens 2.

The reason is that the magnification produced by a lens depends on the ratio of the image distance to the object distance.

The larger the ratio, the larger the magnification.

Therefore, if lens 1 were placed in the same location as lens 2, it would produce a larger image because lens 1 has a shorter focal length and will bring the image closer to the lens than lens 2.

This will result in a larger image than that produced by lens 2.

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Answer:

The difference is that water is an incompressible fluid — its density is almost constant as the pressure changes — while air is a compressible fluid — its density changes with pressure. ... Atmospheric pressure is the pressure exerted on a surface by the weight of the atmosphere (a compressible fluid) above it

Explanation:

change some words

The statement "Snell's law gives the change in intensity of a beam of light when it travels from one medium to another" will be evaluated to determine its truthfulness. Option A is correct answer.

Snell's law, also known as the law of refraction, relates the angles of incidence and refraction of a light beam as it passes from one medium to another. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two media.

However, Snell's law does not directly give information about the change in intensity of the light beam. Intensity refers to the amount of power carried by the light per unit area and is related to the square of the amplitude of the electric field. The change in intensity of a light beam when it passes through different media is influenced by factors such as absorption, scattering, and reflection, which are not explicitly described by Snell's law.

Therefore, the statement "Snell's law gives the change in intensity of a beam of light when it travels from one medium to another" is false. Snell's law primarily relates the angles of incidence and refraction, providing information about the direction of the light beam but not directly addressing changes in intensity.

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The complete question is

Snell’s law gives the change in intensity of a beam of light when it travels from one medium to another. group of answer choices true false

A. The higher the index of refraction of a medium

B. The slower light moves within it.

Answer:

the correct one is 2

Explanation:

The emission and arcion spectra are similar, in the emission spectra a heated material emits photons for the internal transitions of the electrons, in the absorption spectrum the continuous emission of a lamp is absorbed at the energies that the material has transitions.

In our case the material is low early, so all the electrons are in their base states.

As the light beam has all wavelengths, those corresponding to the first emission of the material will be observed.

When reviewing the answers, the correct one is 2

Consider increasing the mass vibrating on a spring's oscillation's amplitude. The claims (A) and (D) regarding this mass are true.

A. Its maximum speed increases.

D. Its maximum kinetic energy increases.

Here is the explanation :

When you increase the amplitude of oscillation of a mass vibrating on a spring, two correct statements about the mass are:

A. Its maximum speed increases: The maximum speed of the mass occurs at the amplitude of the oscillation. Increasing the amplitude means the mass travels a greater distance from the equilibrium position, leading to a higher maximum speed during its oscillation.

D. Its maximum kinetic energy increases: The kinetic energy of the mass is directly proportional to the square of its speed. As the maximum speed increases, the maximum kinetic energy also increases because kinetic energy is dependent on the square of the speed.

The other two statements are incorrect:

B. Its period of oscillation does not change: The period of oscillation is determined by the properties of the spring and the mass and is independent of the amplitude. Increasing the amplitude does not affect the period of oscillation.

C. Its maximum acceleration does not change: The maximum acceleration of the mass occurs at the extreme points of its motion, which are determined by the properties of the spring and the mass. Increasing the amplitude does not change the maximum acceleration.

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Complete question :

Suppose you increase the amplitude of oscillation of a mass vibrating on a spring. Which of the following statements about this mass are correct? (There may be more than one correct choice.)

A. Its maximum speed increases.

B. Its period of oscillation increases.

C. Its maximum acceleration increases.

D. Its maximum kinetic energy increases.

To achieve a 3.6-times magnified virtual image, you will need a concave mirror with a radius of curvature (R) of approximately -1.067 cm.

To achieve a 3.6-times magnified virtual image, you will need a concave mirror. Concave mirrors have the ability to create magnified virtual images.

To determine the radius of curvature of the mirror (R), we can use the mirror formula

1/f = 1/v - 1/u

where f is the focal length of the mirror, v is the image distance (negative for virtual images), and u is the object distance.

Given that the magnification (m) is equal to -v/u, and the desired magnification is 3.6, we can write

m = -v/u

3.6 = -v/u

Since the image is virtual, the image distance (v) will be negative. Also, the object distance (u) is given as 4.9 cm.

Plugging in the values into the magnification equation, we get

3.6 = -v/4.9

Solving for v, we find

v = -4.9/3.6

v ≈ -1.3611 cm

Now, substituting the values of v and u into the mirror formula, we have

1/f = 1/(-1.3611) - 1/4.9

Simplifying the equation, we get

1/f ≈ -0.7335 - 0.2041

1/f ≈ -0.9376

Taking the reciprocal of both sides, we find

f ≈ -1.067 cm

The negative sign indicates that the mirror has a concave shape.

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The permeability of the iron is approximately 1.26 x 10^(-3) Tm/A. If the current through the solenoid is turned off and then restored to 10 A, the magnetic field inside the solenoid will not necessarily return to exactly 2.0 T.

The magnetic field inside a solenoid with an iron core can be calculated using the formula:

B = μ₀ * μᵣ * (N * I) / L

Where:

B is the magnetic field (2.0 T)

μ₀ is the permeability of free space (4π x 10^(-7) Tm/A)

μᵣ is the relative permeability of iron (unknown)

N is the number of turns of wire (100)

I is the current through the solenoid (10 A)

L is the length of the solenoid (25 cm = 0.25 m)

To find the relative permeability of iron (μᵣ), we rearrange the formula:

μᵣ = (B * L) / (μ₀ * N * I)

Plugging in the given values:

μᵣ = (2.0 T * 0.25 m) / (4π x 10^(-7) Tm/A * 100 * 10 A)

   ≈ 1.26 x 10^(-3) Tm/A

Therefore, the permeability of the iron is approximately 1.26 x 10^(-3) Tm/A.

If the current through the solenoid is turned off and then restored to 10 A, the magnetic field inside the solenoid will not necessarily return to exactly 2.0 T.

The relationship between the magnetic field and the current is given by the formula mentioned earlier, and it depends on the permeability of the iron.

If the permeability changes or if there are other factors affecting the magnetic field, the value may vary.

However, if the iron remains unchanged and no other factors significantly affect the magnetic field, it is reasonable to expect that the field will return close to 2.0 T when the current is restored.

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The resonance angular frequency (ω0) of the circuit is approximately 3615 radians per second. The maximum voltage amplitude (Vmax) that the source can have without exceeding the maximum capacitor voltage is 570 volts.

Part A:

The resonance angular frequency ω0 of the circuit can be calculated using the formula:

ω0 = 1 / √(LC)

Inductance (L) = 0.380 H

Capacitance (C) = 2.00×10^(-2) μF = 2.00×10^(-8) F

Converting the capacitance to farads:

C = 2.00×10^(-8) F

Plugging the values into the formula, we get:

ω0 = 1 / √(0.380 * 2.00×10^(-8))

   = 1 / √(7.6×10^(-9))

   = 1 / (2.76×10^(-4))

   ≈ 3615 rad/s

Therefore, the resonance angular frequency ω0 of the circuit is approximately 3615 radians per second.

Part B:

To determine the maximum voltage amplitude Vmax that the source can have without exceeding the maximum capacitor voltage, we need to consider the relationship between the voltage across the capacitor (Vc) and the voltage across the source (Vs) in an L-R-C series circuit.

At resonance, the voltage across the capacitor (Vc) is maximum, and the voltage across the inductor (VL) and resistor (VR) is minimum.

In this case, the maximum voltage across the capacitor is equal to the maximum voltage across the source.

Peak voltage withstand by the capacitor = 570 V

Therefore, the maximum voltage amplitude (Vmax) that the source can have without exceeding the maximum capacitor voltage is 570 V.

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(a) To find the force that will stretch a similar piece of wire to 1.87 cm, we can use the concept of Hooke's Law. Hooke's Law states that the force required to stretch or compress a spring (or wire) is directly proportional to the displacement or change in length.

Given that the original force is 17.0 N and it stretches the wire by 0.650 cm, we can set up a proportion to find the force required for a 1.87 cm stretch.

Let F1 be the original force, x1 be the original displacement, F2 be the unknown force, and x2 be the desired displacement. The proportion can be expressed as:

F1 / x1 = F2 / x2

Substituting the given values, we have:

17.0 N / 0.650 cm = F2 / 1.87 cm

Now we can solve for F2:

F2 = (17.0 N / 0.650 cm) * 1.87 cm

F2 ≈ 48.8 N

Therefore, a force of approximately 48.8 N will stretch a similar piece of wire to 1.87 cm.

(b) To determine how far a similar piece of wire will stretch when a force of 21.3 N is applied, we can use Hooke's Law again.

Using the same variables as before, the proportion can be set up as:

F1 / x1 = F2 / x2

Substituting the given values:

17.0 N / 0.650 cm = 21.3 N / x2

Solving for x2:

x2 = (21.3 N / 17.0 N) * 0.650 cm

x2 ≈ 0.815 cm

Therefore, a force of 21.3 N will cause the wire to stretch approximately 0.815 cm.

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hello! it is velocity.

i say this because, Inertia is the tendency of an object to resist changes in its state of motion. ... The state of motion of an object is defined by its velocity - the speed with a direction.

The image of the object moves towards the mirror as the object approaches the mirror and its focal point.

When an object moves along the optical axis of a concave spherical mirror and approaches the mirror's focal point, the image formed by the mirror undergoes a change in position. This change is characterized by the image moving towards the mirror.

In a concave mirror, the focal point is located on the same side as the object, but at a distance determined by the mirror's curvature. As the object moves closer to the focal point, the reflected rays converge and the image position changes. The image moves towards the mirror as a result.

To understand this phenomenon, we can consider the ray diagram for a concave mirror. As the object approaches the focal point, the rays of light from different points on the object converge towards the focal point after reflection. This convergence leads to the image moving towards the mirror.

When a luminous object moves along the optical axis of a concave spherical mirror and approaches the mirror's focal point, the image of the object moves towards the mirror. This is due to the convergence of reflected rays as the object approaches the focal point, resulting in a change in the image position.

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The maximum tοrque exerted by the persοn is 86.6 Nm.

Tοrque is a measure οf the tendency οf a fοrce tο rοtate an οbject arοund a specific axis. It is alsο referred tο as the mοment οf fοrce.

Given:

Mass οf the persοn (m) = 52 kg

Radius οf the circle fοrmed by the pedals (r) = 17 cm = 0.17 m

Weight οf the persοn (W) = m * g, where g is the acceleratiοn due tο gravity (apprοximately 9.8 m/s²)

Tο find the fοrce exerted by the persοn οn each pedal, we can use the equatiοn:

Fοrce (F) = Weight (W)

The weight οf the persοn is given by:

W = m * g

Substituting the given values:

W = 52 kg * 9.8 m/s²

W ≈ 509.6 N

Nοw, the maximum tοrque (τ) can be calculated using the equatiοn:

Tοrque (τ) = Fοrce (F) * Lever Arm (r)

τ = F * r

Substituting the values:

τ = 509.6 N * 0.17 m

τ ≈ 86.6 N·m

Therefοre, the maximum tοrque exerted by the persοn is apprοximately 86.6 N·m.

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The statement "foxconn retrofitted the empire state building with led lighting, cutting down on energy consumption by 73 percent." is false as Foxconn did not retrofit the Empire State Building with LED lighting

There is no record or evidence to support the claim that Foxconn, a multinational electronics contract manufacturing company, retrofitted the Empire State Building with LED lighting resulting in a 73 percent reduction in energy consumption. Foxconn is primarily known for its manufacturing operations, particularly in the field of electronics and technology.

The retrofitting of the Empire State Building with LED lighting did occur, but the company responsible for this project was Philips Lighting (now known as Signify). The retrofitting project, completed in 2012, involved replacing the building's traditional lighting fixtures with energy-efficient LED lights, resulting in significant energy savings. However, the reported energy reduction was approximately 38 percent, not 73 percent.

Therefore, the statement claiming that Foxconn retrofitted the Empire State Building with LED lighting, reducing energy consumption by 73 percent, is false.

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The average and instantaneous velocities in m/s at 8.0 seconds would be 0.5 m/s and  0 m/s respectively, therefore the correct answer is option D.

What is Velocity?

The total displacement covered by any object per unit of time is known as velocity. It depends on the magnitude as well as the direction of the moving object.

As given in the problem, this object was moving at a velocity of 1.0 m/s east at the end of 4.0 seconds.

The average velocity of the object = ( 4 - 0 ) / (8 -0)

The instantaneous velocity of the object = 0 m/s

Thus, the average and instantaneous velocities in m/s at 8.0 seconds would be 0.5 m/s and  0 m/s respectively, therefore the correct answer is option D.

Answer:

Explanation:

Answer:

Average = 0.67 m/s east; instantaneous = 0 m/s

Explanation:

took the test

The pulley must rotate at a speed of approximately 1.99 radians per second for the cable car to make the trip in 12 minutes.

To determine the rotational speed of the pulley, we need to calculate the angular velocity (ω) in radians per second.

Distance traveled by the cable car = 6.8 km

Time taken to make the trip = 12 minutes

First, let's convert the distance to meters:

Distance = 6.8 km = 6,800 meters

Next, let's convert the time to seconds:

Time = 12 minutes = 12 * 60 seconds = 720 seconds

The linear speed (v) of the cable car can be calculated using the formula:

v = distance / time

v = 6,800 meters / 720 seconds

v ≈ 9.44 m/s

The linear speed of the cable car is equal to the circumference of the pulley multiplied by its angular velocity:

v = 2πrω

where r is the radius of the pulley (half of its diameter).

Given the diameter of the pulley is 3.0 m, the radius is:

r = 3.0 m / 2 = 1.5 m

Substituting the values into the equation:

9.44 m/s = 2π(1.5 m)ω

To solve for ω, divide both sides by 2π(1.5 m):

ω = 9.44 m/s / (2π(1.5 m))

ω ≈ 1.99 rad/s

Therefore, the pulley must rotate at a speed of approximately 1.99 radians per second for the cable car to make the trip in 12 minutes.

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Answer:

[tex]0.025\ \text{m}[/tex]

Yes

Explanation:

[tex]m_8[/tex] = Mass of uranium 238 ion = [tex]3.95\times 10^{-25}\ \text{kg}[/tex]

[tex]m_5[/tex] = Mass of uranium 235 ion = [tex]3.9\times 10^{-25}\ \text{kg}[/tex]

v = Velocity of ions = [tex]3\times 10^5\ \text{m/s}[/tex]

q = Charge of triply charged ions = [tex]3\times 1.6\times 10^{-19}\ \text{C}[/tex]

B = Magnetic field = 0.25 T

The force balance is

[tex]\dfrac{mv^2}{r}=qvB\\\Rightarrow r=\dfrac{mv}{qB}[/tex]

The difference between the radius of the ions are

[tex]\Delta r=(m_8-m_5)\dfrac{v}{qB}\\\Rightarrow \Delta r=\dfrac{(3.95\times 10^{-25}-3.9\times 10^{-25})\times 3\times 10^5}{3\times 1.6\times 10^{-19}\times 0.25}\\\Rightarrow \Delta r=0.0125\ \text{m}[/tex]

Separation is given by

[tex]\Delta d=2\Delta r=2\times 0.0125\\\Rightarrow \Delta d=0.025\ \text{m}[/tex]

The separation between their paths when they hit a target after traversing a semicircle is [tex]0.025\ \text{m}[/tex].

Yes, the distance between the paths is 2.5 cm is a practical separation between as it is easily measurable.

The resistance of the wire is 0.6 ohms. The magnitude of the electric field in the wire is 0.75 V/m.

To find the resistance of the wire, we can use Ohm's Law, which states that the resistance (R) is equal to the ratio of the potential difference (V) across a conductor to the current (I) flowing through it:

R = V / I

Given that the potential difference V is 1.5 V and the current I is 2.5 A, we can calculate the resistance:

R = 1.5 V / 2.5 A = 0.6 Ω

Therefore, the resistance of the wire is 0.6 ohms.

To find the magnitude of the electric field in the wire, we can use the relationship between the electric field (E), potential difference (V), and distance (d). For a uniform electric field in a straight wire, the electric field is given by:

E = V / d

Given that the potential difference V is 1.5 V and the length of the wire (distance) d is 2.0 m, we can calculate the magnitude of the electric field:

E = 1.5 V / 2.0 m = 0.75 V/m

Therefore, the magnitude of the electric field in the wire is 0.75 V/m.

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The most liquid asset among the given options is likely to be a traveler's check. Option C is the correct answer.

Among the given options, the most liquid asset is a traveler's check (option C). Liquidity refers to how quickly and easily an asset can be converted into cash without significant loss in value. An automobile (option A) can take time and effort to sell, and its value can depreciate.

A U.S. savings bond (option B) has a fixed maturity date and may require time to redeem. 50 shares of Microsoft stock (option D) can be sold relatively quickly, but the liquidity depends on market conditions and trading volume. A traveler's check (option C) can be easily exchanged for cash at various locations, making it the most liquid asset in this context.

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The question is -

Which of the following assets is the most liquid?

A. an automobile.

B. a u.s. savings bond.

C. a traveler's check.

D. 50 shares of Microsoft stock.

Answer:

did you find the answer please answer back

Answer:a

Explanation:ap ex verified

Answer:

the number of times the crest of a wave hits a certain point

the more waves, the higher the frequency

Explanation:

Answer:

The first law, also known as Law of Conservation of Energy, states that energy cannot be created or destroyed in an isolated system.  The second law of thermodynamics states that the entropy of any isolated system always increases.  The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero.

Explanation:

The option that is NOT correct for a simple magnifying glass is:

d) The lens is diverging.

A simple magnifying glass consists of a converging lens, not a diverging lens. The purpose of a magnifying glass is to create a magnified virtual image of an object.

When an object is placed closer to the converging lens than its focal point, a virtual and erect image is formed on the opposite side of the lens.

This image appears larger than the object and is located at a distance farther away from the lens than the object itself. The converging lens bends the light rays in such a way that they appear to diverge from a point behind the lens, creating a virtual image.

Therefore, the statement that the lens is diverging is incorrect for a simple magnifying glass.

To clarify further, a diverging lens would cause the light rays to spread out, resulting in a diminished, virtual image. A converging lens, on the other hand, causes the light rays to converge, allowing for magnification and the formation of a virtual image.

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The types of telescopes that will be able to detect flux from objects when located on Earth include optical telescopes, radio telescopes, and infrared telescopes.

Optical Telescopes: Optical telescopes are specifically designed to gather and focus visible light, enabling the detection of flux from astronomical objects. They come in two main types: refracting telescopes, which use lenses to gather and focus light, and reflecting telescopes, which use mirrors to capture and direct light to a detector or eyepiece.

Radio Telescopes: Radio telescopes detect and analyze radio waves emitted by astronomical objects. They are designed to capture a wide range of radio frequencies and are crucial for studying celestial sources that emit primarily in the radio part of the electromagnetic spectrum. By analyzing the received signals, astronomers can study phenomena such as pulsars, quasars, and cosmic microwave background radiation.

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The length of the copper wire must be approximately 44.2 meters for it to have a resistance of 0.128 ohms, assuming a 14-gauge wire with a diameter of 1.63 mm and using the resistivity of copper.

To find the length of the wire, we can use Ohm's Law, which states that the resistance (R) is equal to the product of the resistivity (ρ), the length (L), and the cross-sectional area (A) of the wire, divided by the diameter (d) of the wire squared.

The formula can be written as:

R = ρ * (L / A)

Resistance (R) = 0.128 ohms

Resistivity of copper (ρ) = (1.68 × 10^-8) ohm-meter (at 20°C)

Diameter (d) = 1.63 mm = 0.00163 meters (converted from millimeters to meters)

We need to find the length (L) of the wire.

To calculate the cross-sectional area (A) of the wire, we can use the formula for the area of a circle:

A = π * (d/2)^2

Plugging in the values, we have:

A = 3.14159 * (0.00163 / 2)^2

A  ≈ 2.08 x 10^-6 square meters

Rearranging Ohm's Law to solve for the length (L), we get:

L = (R * A) / ρ

Substituting the given values:

L = (0.128 * 2.08 x 10^-6) / (1.68 x 10^-8)

L  ≈ 44.2 meters

The length of the copper wire must be approximately 44.2 meters for it to have a resistance of 0.128 ohms, assuming a 14-gauge wire with a diameter of 1.63 mm and using the resistivity of copper.

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a) The angular acceleration of the wheels is approximately 0.861 rad/s². b) The angular velocity of the wheels after 18.0 s is approximately 15.5 rad/s. c) The cyclist has traveled approximately 201.06 meters in 18.0 seconds.

Time (t) = 18.0 s

Number of revolutions (N) = 89

Radius of the wheel (r) = 36.0 cm = 0.36 m

a) The angular acceleration (α) can be calculated using the formula

α = (2πN) / t²

where N is the number of revolutions and t is the time.

α = (2πN) / t²

α = (2π × 89) / (18.0²)

α ≈ 0.861 rad/s²

b) The angular velocity (ω) can be calculated using the formula

ω = αt

ω = αt

ω = 0.861 * 18.0

ω ≈ 15.5 rad/s

c) The distance traveled by the cyclist can be calculated using the formula:

distance = circumference of the wheel × N

where N is the number of revolutions and the circumference of the wheel can be calculated as 2πr, where r is the radius of the wheel.

Distance = circumference of the wheel × N

Distance = (2π × 0.36) × 89

Distance ≈ 201.06 m

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The temperature to which you would have to heat a brass rod for it to be 2.5% longer than it is at 30°C is 218°C (two significant figures).

Explanation: Let's begin with the formula for linear thermal expansion.

ΔL = αLΔT

Here, ΔL is the change in length,α is the coefficient of linear expansion, L is the original length, andΔT is the change in temperature.

The equation can be rearranged as follows:

α = ΔL/LΔT

The coefficient of linear expansion is the change in length per degree Celsius per unit length.

The value of α for brass is given as 1.9 × 10^-5/°C.

So, to solve for the change in temperature required to achieve a 2.5% increase in length,

substitute the values into the formula above:

α = ΔL/L

ΔT1.9 × 10^-5/°C

α= (2.5/100)L/ΔT

The L value can be taken as 1 cm for this problem,

giving:

1.9 × 10^-5/°C = (2.5/100)(1 cm)/ΔT

ΔT = 1 cm/(2.5/100)(1.9 × 10^-5/°C)

ΔT = 218°C  (two significant figures).

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Answer:

The increase in gravitational potential energy is the same in both cases

Explanation:

It is easier to climb a mountain in a zigzag way rather than climbing on a straight line but since the distance is the same ( vertical height ) , mass and gravity is the same. Hence the increase in gravitational potential energy is the same in both cases.

gravitational potential energy = mgh ( same in both cases )

m = mass

g = acceleration due to gravity

h = distance ( vertical height )