Physics High School

## Answers

**Answer 1**

The radius of the **copper cable** is approximately 0.004 m.

The resistance of the copper cable can be calculated using **Ohm's law**: R = V/I, where V is the potential difference and I is the current. Thus, R = (1.6 x 10^-2 V) / (1200 A) = 1.33 x 10^-5 ohms.

The resistance of a cylindrical conductor is given by R = (ρL) / A, where ρ is the** resistivity **of the material, L is the length of the** conductor**, and A is its cross-sectional area. Solving for the area, we get A = (ρL) / R.

Assuming the cable is made of pure copper with a resistivity of 1.68 x 10^-8 ohm-meters, and using the length of the two points on the cable, which is 0.24 m, we can calculate the** area** of the cross-section of the cable. A = (1.68 x 10^-8 ohm-meters x 0.24 m) / (1.33 x 10^-5 ohms) = 0.0000757 m^2.

Finally, we can solve for the radius using the formula for the area of a circle, A = πr^2. The radius of the cable is approximately 0.004 m.

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## Related Questions

A soap bubble has an index of refraction of 1.33. What minimum thickness of this bubble will ensure the maximum reflection of normal incident 530 nm wavelength light? What color deviates the most when shining a white light through a prism?

### Answers

To ensure maximum reflection of normal incident light, we need to consider the conditions for **constructive** interference in a thin film. For the condition for constructive interference is given by:

2t = mλ/n

2t = m * (530 × 10^-9 m) / 1.33

where t is the **thickness** of the film, λ is the wavelength of the incident light, n is the refractive index of the film, and m is an integer representing the order of the interference.

In this case, we want the maximum **reflection** of light with a wavelength of 530 nm (or 530 × 10^-9 m) and a refractive index of 1.33.

Plugging these values into the equation, we have:

2t = m * (530 × 10^-9 m) / 1.33

To ensure **maximum** reflection, we want the minimum thickness, which occurs when m = 0 (zeroth order).

2t = 0 * (530 × 10^-9 m) / 1.33

t = 0

Therefore, the minimum thickness of the soap bubble that ensures maximum reflection of 530 nm light is zero. This means that any thickness of the bubble will result in some **degree** of reflection.

When shining white light through a prism, the color that deviates the most is violet. This is because **violet** light has the shortest wavelength among the visible light spectrum, and it experiences the greatest change in direction (deviation) when passing through the **prism** due to its higher refractive index compared to other colors.

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What determines the direction that ions will move through ion channels?

- Both the ion's concentration gradient and the electrical gradient across the plasma membrane !!!

- Only the ion's concentration gradient across the plasma membrane

- Only the electrical gradient across the plasma membrane

### Answers

The correct answer is: Both the ion's concentration gradient and the electrical gradient across the **plasma membrane.**

The movement of ions through ion channels is influenced by both the ion's concentration **gradient **and the electrical gradient across the plasma membrane.

The concentration gradient refers to the difference in ion concentration on either side of the membrane. If there is a higher concentration of a particular ion on one side of the membrane** compared **to the other, the ion will tend to move from an area of higher concentration to an area of lower concentration.

The electrical gradient, also known as the membrane potential, is the difference in electrical charge across the plasma membrane. This gradient can be established by **various factors, **including the distribution of ions and the activity of ion pumps and channels. The electrical gradient can influence the movement of ions by attracting or repelling them based on their charge.

Therefore, the direction that ions will move through ion channels is determined by the** combined** influence of both the ion's concentration gradient and the electrical gradient across the plasma membrane.

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read each question carefully. write your response in the space provided for each part of each question. answers must be written out in paragraph form. outlines, bulleted lists, or diagrams alone are not acceptable and will not be scored. researchers tested the effect of light on the rate of photosynthesis by a species of shrub growing under conditions that differ widely in the amount of available light but where the availability of water and soil nutrients is fairly constant. under constant temperature, relative humidity, and leaf surface area, the researchers used increasing illumination (measured as photosynthetic photon flux density, the number of photons of wavelengths between 400 and 700 nanometers per unit surface area and unit time) and determined the net photosynthesis (measured by the amount of carbon dioxide fixed per unit surface area and unit time at each illumination) of the shrubs growing in full sun, partial sun, or in shade (table 1).

### Answers

The researchers conducted an experiment to investigate the effect of light on the rate of **photosynthesis** in a species of shrub. They specifically focused on the impact of varying levels of available light while keeping the conditions of water availability and soil nutrients constant. The experiment maintained a consistent temperature, relative humidity, and leaf surface area throughout.

To measure the **effect** of light, the researchers used increasing illumination, quantified as photosynthetic photon flux density. This measure represents the number of photons within the wavelength range of 400 to 700 nanometers per unit surface area and unit time. By manipulating the illumination levels, the researchers created different light conditions for the shrubs, including full sun, partial sun, and shade.

The researchers then measured the net photosynthesis of the shrubs under each **illumination **condition. Net photosynthesis was assessed by quantifying the amount of carbon dioxide fixed per unit surface area and unit time at each level of illumination.

The **experiment **aimed to determine how the rate of photosynthesis in the shrubs is influenced by varying light conditions. By subjecting the shrubs to different levels of illumination, ranging from full sun to partial sun and shade, the researchers could assess how the availability of light affects the process of photosynthesis.

To measure the effect, the researchers utilized photosynthetic **photon** flux density, which is a standardized measure of light intensity within the photosynthetically active range. This measure allowed them to precisely control and quantify the illumination levels experienced by the shrubs.

To assess the rate of photosynthesis, the researchers focused on net photosynthesis, which represents the amount of carbon dioxide that is fixed (converted to organic compounds) per unit surface area and unit time. This measurement provides insights into the productivity and **efficiency **of the shrubs' photosynthetic process under different light conditions.

By conducting this experiment and analyzing the data obtained, the researchers were able to explore the relationship between light availability and the rate of photosynthesis in the studied shrub species. The results of the experiment will contribute to our understanding of how light influences plant growth, **productivity**, and adaptation strategies. Additionally, the findings can have implications for agricultural practices, forestry, and ecological studies where light availability plays a crucial role in plant performance and ecosystem dynamics.

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schoolyard teeter-totter with a total length of 6.4 m and a mass of 41 kg is pivoted at its center. a 21-kg child sits on one end of the teeter-totter. (a) where should a parent push vertically downward with a force of 210 n in order to hold the teeter-totter level? (b) where should the parent push with a force of 310 n? (c) how would your answers to parts (a) and (b) change if the mass of the teeter-totter were doubled? explain.

### Answers

The parent should push (a) vertically downward with a **force **of 210 N (b) The parent should push vertically downward with a force (c) If the mass of the teeter-totter were doubled

**What is force?**

In physics, force is a fundamental concept that describes the interaction between objects or **particles**, resulting in a change in their motion or deformation. Force is a vector quantity, meaning it has both magnitude and direction.

The most common definition of force is given by Isaac Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its **acceleration**. Mathematically, it is represented as F = m × a, where F is the force, m is the mass of the object, and a is its acceleration.

(a) The parent should push vertically downward with a force of 210 N at a distance of 2.2 m from the center of the teeter-totter to hold it level.

In order to hold the teeter-totter level, the sum of the torques acting on it must be zero. Torque is calculated by multiplying the force applied by the distance from the pivot point. Since the teeter-totter is balanced, the torque exerted by the child sitting on one end is equal to the torque exerted by the parent pushing **downward**. Therefore, we can set up an equation:

**Torque_child **= Torque_parent

(mass_child) × (gravity) × (distance_child) = (force_parent) × (distance_parent)

(21 kg) × (9.8 m/s²) × (3.2 m) = (force_parent) × (2.2 m)

Solving for force_parent, we find:

force_parent = [(21 kg) × (9.8 m/s²) × (3.2 m)] / (2.2 m) ≈ 210 N

(b) The parent should push vertically downward with a force of 310 N at a distance of 1.4 m from the center of the **teeter**-totter to hold it level.

Following the same logic as in part (a), we set up the **equation**:

(mass_child) × (gravity) × (distance_child) = (force_parent) × (distance_parent)

(21 kg) × (9.8 m/s²) × (3.2 m) = (force_parent) × (1.4 m)

Solving for **force_parent**, we find:

force_parent = [(21 kg) × (9.8 m/s²) × (3.2 m)] / (1.4 m) ≈ 310 N

(c) If the mass of the teeter-totter were doubled, the answers to parts (a) and (b) would remain the same. This is because the mass of the teeter-totter does not affect the **balance **when it is pivoted at the center.

The torque exerted by the child and the torque exerted by the parent will still be equal, and the teeter-totter will remain level. Doubling the mass would increase the overall weight of the teeter-totter, but it would not change the forces and distances needed to maintain **balance**.

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Determine the activation overpotential due to a cathode reaction at 80ºC and a current density of 0.85 A/cm2. The exchange current density = 1.2x10-3 A/cm2, and alpha = 0.4. a)0.132 volts. b)0.269 c)1.183 volts. d)0.250 volts. e)0.057 volts.

### Answers

The activation **overpotential **due to the cathode reaction at 80ºC and a current density of 0.85 A/cm² is approximately 0.269 volts.

To determine the activation overpotential (η) due to a cathode reaction, we can use the **Tafel equation**:

[tex]\eta = (\frac {RT}{\alpha F}) \times ln(\frac {j}{j_{0}})[/tex]

where:

η = activation overpotential

R = gas constant (8.314 J/(mol·K))

T = temperature in Kelvin

α = **transfer coefficient **(also known as symmetry factor)

F = Faraday's constant (96485 C/mol)

j = actual current density

[tex]j_{0}[/tex] = exchange current density

Given:

T = 80ºC = 353 K

j = 0.85 A/cm²

[tex]j_{0} = 1.2\times10^{-3} A/cm^{2}[/tex]

α = 0.4

Substituting the values into the equation:

η

=[tex](\frac {RT}{\alpha F}) \times ln(\frac {j}{j_{0}})[/tex]

= [tex](\frac { (8.314 J/(mol \cdot K) \times 353 K}{0.4 \times 96485 C/mol}) \times ln(\frac {0.85 A/cm^{2}}{1.2 \times 10^{-3} A/cm^{2}})[/tex]

Calculating this expression:

[tex]\eta \approx 0.269 volts[/tex]

Therefore, the activation overpotential due to the **cathode **reaction at 80ºC and a current density of 0.85 A/cm² is approximately 0.269 volts.

The correct answer is (b) 0.269 volts.

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By what factor will the intensity change when the corresponding sound level increases by 3 dB? (a) 3 (b) 0.5 (c) 2 (d) 4

### Answers

The factor by which the **intensity **will change when the sound level increases by 3 dB is approximately 2.

When the sound level increases by 3 dB, we can determine the corresponding change in intensity using the relationship:

[tex]\triangle L = 10log10\frac {I_2}{I_1}[/tex]

where ΔL is the change in **sound level** in decibels, I₁ is the initial intensity, and I₂ is the final intensity.

Given that the sound level **increases **by 3 dB, we have:

ΔL = 3 dB

To find the corresponding change in intensity, we rearrange the equation as:

[tex]\frac {I_2}{I_1} = 10^{(\triangle L/10)}[/tex]

Substituting **ΔL = 3 dB**:

[tex]\frac {I_2}{I_1} = 10^{(3/10)}[/tex]

[tex]\frac {I_2}{I_1} \approx 1.995[/tex]

Therefore, the factor by which the intensity will change when the sound level increases by 3 dB is approximately 1.995. We can select the closest option, which is (c) 2.

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Certain cancers of the liver can be treated by injecting microscopic glass spheres containing radioactive 90Y into the blood vessels that supply the tumor. The spheres become lodged in the small capillaries of the tumor, both cutting off its blood supply and delivering a high dose of radiation. 90Y has a half-life of 64 h and emits a beta particle with an average energy of 0.89 MeV.

What is the total dose equivalent for an injection with an initial activity of 4.0×107Bq if all the energy is deposited in a 46 g tumor?

Express your answer with the appropriate units.

### Answers

The total **dose** equivalent for an **injection **with an initial activity of 4.0×10^7 Bq, depositing all energy in a 46 g tumor, is 193.6 Gy.

To calculate the total dose equivalent, follow these steps:

1. Determine the total **energy** emitted: Initial activity (4.0×10^7 Bq) * average energy per** decay** (0.89 MeV) * **half-life** (64 h) * 3600 s/h * 1.602×10^-13 J/MeV = 3.31×10^4 J

2. Convert the **tumor **mass to kg: 46 g * 1 kg/1000 g = 0.046 kg

3. Calculate the absorbed dose: Total energy (3.31×10^4 J) / tumor mass (0.046 kg) = 719.6 J/kg

4. Convert the absorbed dose to Gy: 719.6 J/kg * 1 Gy/J/kg = 719.6 Gy

5. Since all energy is deposited in the tumor, the total dose equivalent is equal to the absorbed dose, which is 193.6 Gy.

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200 kPa when its temperature is 20 °C (Gauge pressure is the difference between the actual pressure and atmospheric pressure). After the car has been driven at high speeds, the tire temperature increases to 50 °C. a) Assuming that the volume of the tyre does not change, and that air behaves as an ideal gas, find the gauge pressure of the air in the tire. b) Calculate the gauge pressure if the volume of the tyre expands by 10 % .

### Answers

a) The ** gauge pressure** of the air in the tire after it has been driven at high speeds and the temperature increased to 50 °C is approximately 228.7 kPa.

b) If the volume of the tire expands by 10%, the gauge pressure of the air in the tire would be approximately 231.8 kPa.

To calculate the gauge pressure of the air in the tire, we need to use the ideal gas law, which states that the **pressure **of a gas is directly proportional to its temperature when the volume is constant.

The ideal gas law is given by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

a) Assuming the volume of the tire remains constant, we can use the ideal gas law to solve for the gauge pressure. First, let's convert the given temperatures to Kelvin:

Initial temperature (T1) = 20 °C + 273.15 = 293.15 K

Final temperature (T2) = 50 °C + 273.15 = 323.15 K

The initial gauge pressure (P1) is given as 200 kPa. To find the final gauge pressure (P2), we can set up the following equation using the ideal gas law:

(P1 + Patm) / T1 = (P2 + Patm) / T2

Where Patm is the atmospheric pressure (which we assume remains constant). Rearranging the equation and solving for P2, we get:

P2 = (P1 + Patm) * (T2 / T1) - Patm

Substituting the values, P1 = 200 kPa, T1 = 293.15 K, T2 = 323.15 K, and assuming Patm is 101.3 kPa, we can calculate P2:

P2 = (200 + 101.3) * (323.15 / 293.15) - 101.3

P2 ≈ 228.7 kPa

Therefore, the gauge pressure of the air in the tire after it has been driven at high speeds and the temperature increased to 50 °C is approximately 228.7 kPa.

b) If the volume of the tire expands by 10%, we need to account for this change in volume when calculating the gauge pressure. We can use the combined gas law to incorporate the **volume change**. The combined gas law is given by the equation PV/T = constant.

Let's denote the initial volume as V1 and the final volume as V2, where V2 = V1 + 0.1V1 = 1.1V1 (10% **expansion**).

Using the combined gas law, we can set up the following equation:

(P1 + Patm) / T1 = (P2 + Patm) / T2

Now, we need to consider the volume change:

(P1 + Patm) * (V1 / T1) = (P2 + Patm) * (V2 / T2)

Substituting V2 = 1.1V1, we get:

(P1 + Patm) * (V1 / T1) = (P2 + Patm) * (1.1V1 / T2)

Simplifying and solving for P2:

P2 = ((P1 + Patm) * (V1 / T1) * T2) / (1.1V1) - Patm

Substituting the values, P1 = 200 kPa, T1 = 293.15 K, T2 = 323.15 K, V1 = 1 (as it's a relative volume), and assuming Patm is 101.3 kPa, we can calculate P2:

P2 = ((200 + 101.3) * (1 / 293.15) * 323.15) / (1.1) - 101.3

P2 ≈ 231.8 kPa

Therefore, if the volume of the tire expands by 10%, the gauge pressure of the air in the tire would be approximately 231.8 kPa.

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the standard hydrogen peroxide volume used with permanent haircolor is

### Answers

The** standard volume of hydrogen peroxide** used with permanent hair color is typically 20 volume (6%).

The** standard volume of hydrogen peroxide** used with permanent hair color is typically 20 volume (6%). It is important to note that different **hair color **brands or formulations may offer different volumes of hydrogen peroxide options, so it is always advisable to refer to the specific instructions and recommendations provided by the hair color manufacturer.

The percentage value, in this case, 6%, indicates the weight of hydrogen peroxide present in the formulation. In a 20 volume hydrogen peroxide solution, 6% of the total weight is hydrogen peroxide, while the remaining 94% consists of other components, such as water, stabilizers, and conditioners.

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A solid sphere of weight 36.0 N

rolls up an incline at an angle of 30.0O At the bottom of the incline the center of mass of the sphere has a translational speed of 4.90 m/s. (a) What is the kinetic energy of the sphere at the bottom of the incline? (b) How far does the sphere travel up along the incline? (c) Does the answer to (b) depend on the sphere's mass?

### Answers

**Kinetic energy **is 1/2 mv2. The** kinetic energy** of the sphere at the bottom of the incline is** 61.7 J** and **velocity.**

Thus, An object's** kinetic energy **is the kind of power it has as a result of motion. It is described as the effort required to move a mass-determined body from rest to the indicated** velocity. **

The body holds onto the **kinetic energy** it acquired during its acceleration until its speed changes. The body exerts the same amount of effort when slowing down from its current pace to a condition of rest.

Formally, **kinetic energy i**s the second term in a Taylor expansion of a particle's relativistic **energy** and any term in a system's Lagrangian that includes a derivative with respect to time.

Thus, **Kinetic energy **is 1/2 mv2. The** kinetic energy** of the sphere at the bottom of the incline is** 61.7 J** and **velocity.**

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.Find the fundamental frequency and the frequency of the first three overtones of the pipe 60.0cm long, if the pipe is open at both ends.

Ffund,Fov1,Fov2,Fov3=______Hz

Find the funaemental freuency and the frequency of the first three overtones of the pipe 60.0cm long, if the pipe is closed at one end.

Ffund,Fov1,Fov2,Fov3=________Hz

If the pipe is open at both ends, what is the number of the highest harmonic that may be heard by a person who can hear frequencies from 20.0Hz to 2.00x10^4Hz?

n=____

If the pipe is closed at one end, what is the number of the highest harmonic that may be heard by a person who can hear frequencies from 20.0Hz to 2.00x10^4Hz?

n=____

### Answers

For a pipe 60.0 cm long, open at both ends: Fₐₒᵥ₁ = 282.8 Hz, Fₐₒᵥ₂ = 848.4 Hz, Fₐₒᵥ₃ = 1414 Hz. For a pipe **closed **at one end: Fᶜₗₒ₁ = 94.3 Hz, Fᶜₗₒ₂ = 282.8 Hz, Fᶜₗₒ₃ = 471.4 Hz.

Determine what are the fundamental frequency?

Fundamental **frequency **and the frequency of the first three overtones of a pipe 60.0 cm long, open at both ends:

Fₐₒᵥ₁, Fₐₒᵥ₂, Fₐₒᵥ₃ = 282.8 Hz, 848.4 Hz, 1414 Hz

Fundamental frequency and the frequency of the first three overtones of a pipe 60.0 cm long, closed at one end:

Fᶜₗₒ₁, Fᶜₗₒ₂, Fᶜₗₒ₃ = 94.3 Hz, 282.8 Hz, 471.4 Hz

Number of the highest **harmonic **that may be heard by a person who can hear frequencies from 20.0 Hz to 2.00x10⁴ Hz in a pipe open at both ends:

n = 99

Number of the highest harmonic that may be heard by a person who can hear frequencies from 20.0 Hz to 2.00x10⁴ Hz in a **pipe **closed at one end:

n = 198

For a pipe open at both ends, the fundamental frequency (Fₐₒᵥ₁) can be calculated using the formula Fₐₒᵥ₁ = v / 2L, where v is the **speed **of sound and L is the length of the pipe. In this case, the length of the pipe is 60.0 cm (or 0.60 m).

Using the known speed of **sound **(approximately 343 m/s), we can substitute these values into the formula to find Fₐₒᵥ₁ = 343 / (2 * 0.60) = 282.8 Hz.

The frequencies of the first three overtones can be calculated by multiplying the fundamental frequency by the harmonic number (1, 2, 3). Therefore, Fₐₒᵥ₂ = 2 * Fₐₒᵥ₁ = 2 * 282.8 Hz = 565.6 Hz, and Fₐₒᵥ₃ = 3 * Fₐₒᵥ₁ = 3 * 282.8 Hz = 848.4 Hz.

For a pipe closed at one end, the fundamental frequency (Fᶜₗₒ₁) can be calculated using the formula Fᶜₗₒ₁ = v / 4L, where v is the speed of sound and L is the length of the pipe. Substituting the values, we find Fᶜₗₒ₁ = 343 / (4 * 0.60) = 94.3 Hz.

The frequencies of the first three overtones for a closed pipe can be calculated using the formula Fᶜₗₒₙ = (2n - 1) * Fᶜₗₒ₁, where n is the harmonic number. Thus, Fᶜₗₒ₂ = (2 * 2 - 1) * Fᶜₗₒ₁ = 3 * 94.3 Hz = 282.8 Hz, and Fᶜₗₒ₃ = (2 * 3 - 1) * Fᶜₗₒ₁ = 5 * 94.3 Hz = 471.4 Hz.

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Consider the simple model of the zoom lens shown in Fig.34.43a in the textbook. The converging lens has focal length f1=12cm, and the diverging lens has focal length f2=−12cm. The lenses are separated by 4 cm as shown in Fig.34.43a. A)Now consider the model of the zoom lens shown in Fig.34.43b, in which the lenses are separated by 8 cm. For a distant object, where is the image of the converging lens shown in Fig.34.43b, in which the lenses are separated by 8 cm? B)The image of the converging lens serves as the object for the diverging lens. What is the object distance for the diverging lens? C)Where is the final image?

### Answers

In the given setup, the image of the **converging lens** is formed 12 cm behind it, and the final image is formed 144/13 cm behind the diverging lens.

A) In the model shown in Fig.34.43b, where the lenses are separated by 8 cm, the image of the converging lens (f1=12 cm) is formed at a distance behind the converging lens. This distance can be determined using the **lens formula**:

1/f1 = 1/v1 - 1/u1,

where f1 is the focal length of the converging lens and u1 is the object distance.

Since the object is assumed to be at infinity (distant object), the object distance u1 is equal to infinity. Plugging these values into the lens formula, we get:

1/f1 = 1/v1 - 1/infinity.

As 1/infinity approaches zero, the equation simplifies to:

1/f1 = 1/v1.

Rearranging the equation, we find:

v1 = f1 = 12 cm.

Therefore, the image of the converging lens is formed at a **distance **of 12 cm behind the lens.

B) The image formed by the converging lens (v1 = 12 cm) serves as the object for the diverging lens. The object distance for the diverging lens (f2 = -12 cm) is equal to the image distance of the converging lens, which is 12 cm.

C) To determine the position of the final image, we can use the lens formula for the diverging lens:

1/f2 = 1/v2 - 1/u2,

where f2 is the focal length of the diverging lens and u2 is the object distance.

Substituting the given values, we have:

1/-12 = 1/v2 - 1/12.

Simplifying the equation, we find:

-1/12 = 1/v2 - 1/12.

Combining the fractions, we get:

-1/12 = (12 - v2) / (12v2).

Cross-multiplying and rearranging the equation, we find:

v2 = 144/13 cm.

Therefore, the **final image** is formed at a distance of 144/13 cm behind the diverging lens.

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a balloon is rising at a rate of 4 meters per second from a point on the ground 56 meters from an observer. find the rate of change of the angle of elevation from the observer to the balloon when the balloon is 40 meters above the ground.

### Answers

The **rate **of change of the angle of **elevation **from the observer to the balloon when it is 40 meters above the ground is approximately 0.0026 radians per second.

Let x be the horizontal distance from the observer to the point on the ground below the balloon, y be the **height** of the balloon, and θ be the **angle** of elevation. Given x = 56 meters, dy/dt = 4 meters per second, and y = 40 meters. We need to find dθ/dt.

Step 1: Use the tangent function: tan(θ) = y/x.

Step 2: **Differentiate** both sides with respect to time: sec²(θ) * dθ/dt = (dy/dt * x - y * dx/dt) / x².

Step 3: Solve for dθ/dt: dθ/dt = (dy/dt * x - y * dx/dt) / (x² * sec²(θ)).

Step 4: Plug in the given values and calculate dθ/dt: dθ/dt ≈ 0.0026** radians** per second.

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If the wavelength of a particular beam of light in vacuum is 500 nm, and the index refraction of a material is 2.66, what is the wavelength of the light in the material? a. 94 nm b. 500 nm c. None. d. 188 nm e. 1330 nm

### Answers

the is d. 188 nm that the wavelength of light in a material can be found using the formula λ = λ₀/n, where λ₀ is the wavelength in vacuum and n is the refractive index of the material. So, in this case, the **wavelength **in the material be calculated as λ = 500 nm / 2.66 = 188 nm.

the **refractive **index of a material is the ratio of the speed of light in a vacuum to its speed in the material. So, when light enters a material, its speed decreases, and its wavelength also decreases according to the formula above. This **phenomenon **is what causes the bending of light when it passes through a prism or lens.

The given wavelength of **light **in vacuum is 500 nm. The index of refraction of the material is 2.66. To find the wavelength of light in the material, we use the formula Wavelength in material = (Wavelength in vacuum) (Index of refraction) Plug in the given values: Wavelength in material = (500 nm) / (2.66) **Wavelength **in material = 188 n the wavelength of the light in the material is 188 nm.

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Metals are often used for making designer jewelry because they

A) conduct electricity

B) do not conduct heat well

C) are shiny

D) are strong but can be bent

E) c and d

### Answers

**Answer:**

E

**Explanation:**

Metals (the ones used to make jewelry) are valuable, Resistant to corrosion, and retain their appearance well over long periods of time.

(Pls mark me brainliest)

**Metals** are often used for making designer jewelry because they have a **combination** of properties that make them suitable for this purpose. One important property is their ability to be shaped and bent without breaking, which makes them ideal for creating intricate designs.

This property is due to their strength and flexibility, which allows them to be manipulated into various shapes and forms. Additionally, metals are often shiny and can be polished to a high gloss, which adds to their **aesthetic** appeal. While some metals such as gold and silver are good conductors of electricity, their conductivity is not the primary reason for their use in jewelry making. Similarly, while metals do conduct heat, their thermal conductivity is not a major factor in their use for making jewelry. Therefore, option E, which includes both C and D, is the most appropriate answer.

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Coherent light with wavelength 500 nm passes through two narrow slits separated by 0.340 mm. At a distance from the slits large compared to their separation, what is the phase difference (in radians) in the light from the two slits at an angle of 23.0

### Answers

To calculate the phase difference in the **light** from the two slits, we can use the formula:

Δϕ = (2π / λ) * d * sin(θ)

λ = 500 nm = 500 × 10^(-9) m

d = 0.340 mm = 0.340 × 10^(-3) m

θ = 23.0 degrees = 23.0 × (π / 180) radians

Where:

Δϕ is the **phase** difference

λ is the wavelength of the light

d is the **separation** between the slits

θ is the angle at which we are observing the **interference** pattern

Given:

λ = 500 nm = 500 × 10^(-9) m

d = 0.340 mm = 0.340 × 10^(-3) m

θ = 23.0 degrees = 23.0 × (π / 180) radians

Substituting these values into the formula:

Δϕ = (2π / (500 × 10^(-9) m)) * (0.340 × 10^(-3) m) * sin(23.0 × (π / 180) radians)

Δϕ ≈ 0.161 radians

Therefore, the phase difference in the light from the two slits at an angle of 23.0 degrees is approximately 0.161 **radians**.

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at what temperature will 1.30 mole of an ideal gas in a 2.40 l container exert a pressure of 1.30 atm?

### Answers

**Answer:**

[tex]T=29.2326 \ K[/tex]

**Explanation:**

We can use the **ideal gas law** to answer this question. The **ideal gas law **relates a gasses pressure, volume, and temperature and is written as follows.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{The Ideal Gas Law:}}\\\\PV=nRT\end{array}\right}[/tex]

"n" is the number of moles present in the gas and "R" is referred to as the universal gas constant.

[tex]R=0.0821 \ \frac{atm \cdot L}{mol \cdot K} \ \text{or} \ 8.31 \ \frac{J}{mol \cdot K}[/tex]

Be careful when using the** ideal gas law**, make sure to use the appropriate R value and remember that T is measured in kelvin.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Given:

[tex]P=1.30 \ atm\\V=2.40 \ L\\n=1.30 \ mol\\R=0.0821 \ \frac{atm \cdot L}{mol \cdot K} \[/tex]

Find:

[tex]T= \ ?? \ K[/tex]

(1) - Solve the **ideal gas law** for "T"

[tex]PV=nRT\\\\\Longrightarrow T=\frac{PV}{nR}[/tex]

(2) - Plug the known values into the equation

[tex]T=\frac{PV}{nR} \\\\\Longrightarrow T=\frac{(1.30)(2.40)}{(1.30)(0.0821)} \\\\\therefore \boxed{\boxed{T=29.2326 \ K}}[/tex]

Thus, the gasses **temperature **is found.

To determine the **temperature** at which 1.30 mole of an ideal gas in a 2.40 L container exerts a pressure of 1.30 atm, we can use the ideal gas law equation: PV = nRT

P = **pressure**

V = volume

n = number of moles

R = ideal gas constant

T = temperature

We can rearrange the equation to solve for temperature (T):

T = PV / (nR)

Given:

P = 1.30 atm

V = 2.40 L

n = 1.30 mole

R = ideal **gas** constant (8.314 J/(mol·K))

Substituting the values into the equation:

T = (1.30 atm) * (2.40 L) / (1.30 mole * 8.314 J/(mol·K))

T ≈ 2.56 K

Therefore, at approximately 2.56 **Kelvin**, 1.30 mole of the ideal gas in a 2.40 L container will exert a pressure of 1.30 atm.

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atmosphere has low air pressure and is mostly carbon dioxide

### Answers

The **atmosphere **on Mars has a low air pressure and is mostly composed of carbon dioxide. This means that the air is thinner and less dense than on Earth, which can make it difficult for humans to breathe without the assistance of specialized equipment.

Additionally, the high levels of **carbon dioxide **in the atmosphere make it difficult for humans to grow crops and sustain life on the planet without the use of advanced **technologies**. It sounds like you're describing some characteristics of an atmosphere that has low air pressure and is mostly composed of carbon dioxide.

Here's an explanation using the terms you provided: An atmosphere with low air pressure typically has a lower density of air molecules, meaning there are fewer air **molecules **in a given volume compared to an atmosphere with higher pressure.

In this case, the atmosphere is primarily composed of carbon dioxide, which is a greenhouse gas. This means that the carbon dioxide in the atmosphere can trap heat, potentially causing a greenhouse effect and impacting the **climate** of the planet.

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2.a transverse wave is traveling down a rope with mass, m = 10 kg, and length, l = 50 m. if the rope is under a tension force of 2000 n, what is the wave speed of the transverse wave?

### Answers

**The wave speed **of a transverse wave traveling down a rope can be determined using the **formula v = √(T/μ)**, where v represents the wave speed, T is the tension force, and μ is the linear mass density of the rope.

To find the** linear mass density**, we divide the mass of the rope (m) by its length (l): μ = m/l.

Given that the mass of the rope is 10 kg and the length is 50 m, the linear mass density is μ = 10 kg / 50 m = 0.2 kg/m.

Substituting the values of T = 2000 N and μ = 0.2 kg/m into the formula for wave speed, we have:

**v = √(2000 N / 0.2 kg/m)**

= √(10000 m^2/s^2 / kg/m)

= √(10000 m^2/s^2) (canceling out the units)

** = 100 m/s**

Therefore, the wave speed of the transverse wave traveling down the rope is **100 m/s.**

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Consider a circular tube of diameter D and length L, with a mass flow rate of m_dot. (a) For constant heat flux conditions, derive an expression for the ratio of the temperature difference between the tube wall at the tube ext and the inlet temperature, Ts(x=L) - Tm,i, to the total heat transfer rate to the fluid q. Express your result in terms of m_dot, L, the local Nusselt number at the tube exit NuD(x=L), and relevant fluid properties. (b) Repeat part (a) for constant surface temperature conditions. Express your result in temrs of m_dot, L, the average Nusselt number from the tube inlet to the tube exit NuD, and relevant fluid properties.

### Answers

(a) For constant** heat flux** conditions, the expression for the ratio of the temperature difference between the** tube wall **at the tube exit (Ts(x=L)) and the inlet temperature (Tm,i) to the **total heat transfer** rate to the fluid (q) can be derived using the following steps:

1. Apply the **energy balance **equation to the tube segment of length L:

q = m_dot * Cp * (Ts(x=L) - Tm,i)

where q is the total heat transfer rate, m_dot is the **mass flow rate,** Cp is the specific heat capacity of the fluid, Ts(x=L) is the temperature at the tube exit, and Tm,i is the **inlet temperature.**

2. Substitute the heat transfer rate with the **Nusselt number:**

q = NuD(x=L) * k * A * (Ts(x=L) - Tm,i) / L

where NuD(x=L) is the local Nusselt number at the tube exit, k is the **thermal conductivity** of the fluid, and A is the** cross-sectional area** of the tube.

3. Rearrange the equation to solve for the desired ratio:

(Ts(x=L) - Tm,i) / q = L / (NuD(x=L) * k * A)

The** right-hand side** of the equation represents the thermal resistance of the tube.

Therefore, the expression for the ratio of the temperature difference between the tube wall at the tube exit and the inlet temperature to the total** heat transfer rate** to the fluid, under constant heat flux conditions, is L / (NuD(x=L) * k * A).

(b) For** constant surface temperature** conditions, the expression for the ratio can be derived similarly. However, instead of using the local Nusselt number at the tube exit, we use the average Nusselt number from the tube inlet to the tube exit (NuD). The expression becomes:

(Ts(x=L) - Tm,i) / q = L / (NuD * k * A)

The only difference is the use of the** average Nusselt number** (NuD) instead of the local Nusselt number (NuD(x=L)).

Therefore, the expression for the ratio of the temperature difference between the** tube wall **at the tube exit and the inlet temperature to the total heat transfer rate to the fluid, under** constant surface temperature **conditions, is L / (NuD * k * A).

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what is the net gravitational force fout on a unit mass located on the outer surface of the dyson sphere described in part a? express your answer in newtons.

### Answers

The net **gravitational force** on a unit** mass** located on the outer surface of a Dyson sphere would be zero.

As I don't have the information from part A of your question, I will provide a general explanation using the terms you provided.

The net gravitational force (Fout) on a unit mass located on the **outer surface** of a Dyson Sphere can be calculated using Newton's Law of** Universal Gravitation**. The formula is:

Fout = (G * M * m) / r^2

Where:

- Fout is the net gravitational force in Newtons (N)

- G is the gravitational constant (6.674 × 10^-11 N m²/kg²)

- M is the mass of the Dyson Sphere in kilograms (kg)

- m is the unit mass in kilograms (kg) placed on the outer surface of the Dyson Sphere

- r is the **radius** of the Dyson Sphere in meters (m)

However, without the specific values from part A, I cannot provide a numerical answer. Please provide the details from part A, and I will gladly help you calculate the net gravitational force.

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what is the length of a box in which the minimum energy of an electron is 1.4×10−18 jj ? express your answer in nanometers.

### Answers

The length of the box is approximately 0.528 nanometers. To determine the length of a box in which the minimum energy of an **electron **is given,

we can use the equation for the minimum energy of a particle in a one-dimensional box: E_min = (h^2 * n^2) / (8 * m * L^2)

where:

E_min is the minimum **energy **(given as 1.4×10^(-18) J)

h is Planck's **constant **(6.626 x 10^(-34) J·s)

n is the **quantum **number (1 for the ground state)

m is the mass of the electron (9.109 x 10^(-31) kg)

L is the **length **of the box (to be determined)

Rearranging the equation to solve for L, we have:

L = sqrt((h^2 * n^2) / (8 * m * E_min))

Plugging in the given values, we get:

L = sqrt((6.626 x 10^(-34) J·s)^2 * (1^2) / (8 * (9.109 x 10^(-31) kg) * (1.4×10^(-18) J)))

Calculating this expression gives:

L ≈ 0.528 nm (rounded to three decimal places)

Therefore, the length of the box is approximately 0.528 nanometers.

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Which of the following statements are correct regarding preservation of the earth's magnetic field signature within magnetite crystals contained in a basalt flow erupted and solidified at the earth's Equator today?

1. The magnetite crystals will possess a reversed (south) polarity

2. The magnetite crystals will possess a normal (north) polarity

3. the magnetite crystals will have a steep inclination

4. The magnetite crystals will have a low inclination

5. Magnetite crystals will be arranged haphazardly within the crystallized basalt flow

### Answers

The **magnetite crystals **will possess a normal (north) polarity.

Option **2 **is correct.

This is because the earth's magnetic field has a **predominantly **north polarity at the equator, so magnetite crystals formed there would align with that polarity.

1. The magnetite crystals will possess a reversed (south) **polarity **is incorrect because this would only occur during times of magnetic field reversal, which has not occurred in the past few hundred thousand years.

3. The magnetite crystals will have a steep inclination and** 4**. The magnetite crystals will have a low inclination are also incorrect because the inclination of the magnetite crystals would depend on the **latitude **at which they were formed, not just the fact that they were formed at the equator.

5. Magnetite crystals will be arranged haphazardly within the crystallized basalt flow is also incorrect because magnetite crystals would **align **with the earth's magnetic field while they are forming, so they would have a certain orientation within the **basalt flow**.

Your answer: The correct statements regarding the preservation of the earth's magnetic field signature within magnetite crystals contained in a basalt flow erupted and solidified at the **earth's Equator **today are:

2. The magnetite crystals will possess a normal (north) polarity, as the current magnetic field is in the normal polarity state.

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a car is negotiating a flat circular curve of radius 50m with a speed of 20m/s. what is the centripetal accelaration of the car?

### Answers

The **centripetal acceleration** of an object moving in a circular path is given by the formula:

Centripetal acceleration (a) =** (v^2) / r,**

where v is the velocity of the object and r is the radius of the** circular path.**

In this case, the velocity of the car is given as 20 m/s and the radius of the** circular curve i**s 50 m.

Using the formula, we can calculate the centripetal acceleration:

**a = (20^2) / 50.**

Simplifying the expression, we have:

a = 400 / 50.

Calculating this expression, we find:

a = 8 m/s^2.

Therefore, the centripetal acceleration of the car is** 8 m/s^2.**

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a balloon that contains 0.500 l of helium at 25 °c is cooled to 11 °c, at a constant pressure. what volume does the balloon now occupy?

### Answers

To solve this problem, we can use the combined **gas** law, which states that the ratio of initial and final volumes of a gas is equal to the ratio of initial and final temperatures, assuming constant pressure.

(P1 * V1) / T1 = (P2 * V2) / T2

(V1 / T1) = (V2 / T2)

V1 = 0.500 L

T1 = 25 °C = 25 + 273.15 K = 298.15 K

T2 = 11 °C = 11 + 273.15 K = 284.15 K

The combined gas **law** equation is:

(P1 * V1) / T1 = (P2 * V2) / T2

Where P1 and P2 are the initial and final **pressures**, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final **temperatures**.

In this case, the pressure is constant, so we can rewrite the equation as:

(V1 / T1) = (V2 / T2)

Let's plug in the given values:

V1 = 0.500 L

T1 = 25 °C = 25 + 273.15 K = 298.15 K

T2 = 11 °C = 11 + 273.15 K = 284.15 K

Now we can solve for V2:

(V1 / T1) = (V2 / T2)

(0.500 L / 298.15 K) = (V2 / 284.15 K)

V2 = (0.500 L * 284.15 K) / 298.15 K

V2 ≈ 0.477 L

Therefore, the **balloon** now occupies approximately 0.477 liters of volume after being cooled to 11 °C at a constant pressure.

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A ball is released from rest at a height of 10. 0 m and free falls to the ground. When the same mass is released from rest at a height of 40. 0 m, how much more kinetic energy will it have just before reaching the ground?

### Answers

The ball released from a height of 40.0 m will have 293.9 J more **kinetic energy** than the ball released from a height of 10.0 m.

We can solve this using the equation for **gravitational **potential energy:

GPE = mgh

where GPE is gravitational potential energy, m is mass, g is the acceleration due to gravity, and h is height. We know that the ball has the same mass in both scenarios, so we can simplify the equation to:

GPE = gh

Now, we can solve for the gravitational **potential **energy at each height and find the difference between them. For the first scenario where the ball is released from a height of 10.0 m:

GPE = (9.81 m/s²)(10.0 m) = 98.1 J

For the second scenario where the ball is released from a height of 40.0 m:

GPE = (9.81 m/s²)(40.0 m) = 392 J

The difference in gravitational potential energy is:ΔGPE = (392 J) - (98.1 J) = 293.9 J

This is the amount of kinetic energy the ball will gain as it falls from a greater **height**.

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When an object moves in uniform circular motion, the direction of its acceleration is 3 A) is directed away from the center of its circular path. B) is directed toward the center of its circular path. 6 C) depends on the speed of the object. D) in the same direction as its velocity vector. E) in the opposite direction of its velocity vector.

### Answers

When an object moves in uniform circular motion, the direction of its **acceleration** is directed toward the center of its circular path. This means that option B) is the correct answer.

In uniform circular motion, the object moves along a circular path with a constant speed. Even though the **speed** is constant, the object is continuously changing its direction due to the centripetal acceleration, which is always directed toward the center of the circular path. This **acceleration** is responsible for keeping the object moving in a curved path instead of a **straight** line.

The centripetal acceleration is given by the equation:

a = (v^2) / r

Where:

a is the **centripetal** acceleration,

v is the velocity of the object,

r is the radius of the circular path.

Since the centripetal acceleration is directed toward the center of the circle, it is perpendicular to the velocity vector. Therefore, the acceleration and velocity vectors are **orthogonal** to each other. This rules out options D) and E).

Hence, the correct answer is B) is directed toward the center of its circular path.

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more nations have gravitated toward the market-based model because

### Answers

More nations have gravitated toward the** model** because it offers several advantages and has proven to be a successful approach in promoting economic growth and development.

Efficiency: The market-based model, characterized by free markets and competition, allows for efficient allocation of resources. It enables individuals and businesses to make decisions based on market forces, such as supply and **demand**, which leads to the optimal allocation of goods and services. This efficiency promotes productivity and economic growth.

Innovation and Entrepreneurship: The market-based model encourages innovation and **entrepreneurship**. In a competitive market, businesses are incentivized to develop new products and services to meet consumer demands. This drive for innovation fosters technological advancements, job creation, and economic dynamism.

Individual Freedom: Market-based economies prioritize individual freedom and choice. Individuals have the freedom to make decisions regarding their consumption, **production**, and employment. This freedom allows for personal initiative, economic mobility, and the pursuit of individual aspirations.

International Trade: Market-based economies promote international trade and globalization. By opening up to international markets, countries can benefit from the exchange of goods, services, and ideas, leading to increased economic opportunities and access to a wider range of resources.

Economic Stability: Market-based economies tend to be more resilient and adaptable to changing circumstances. The **decentralized **nature of markets allows for self-correction mechanisms, such as price adjustments, in response to economic shocks.

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Final answer:

Nations have gravitated toward the **market-based **model because it promotes economic growth and efficiency, encourages innovation and investment, and allows for flexibility and adaptation to global trends and demands.

Explanation:

More **nations **have gravitated toward the market-based model because it has been proven to promote economic growth and increase efficiency. The market-based model is based on the principles of supply and demand, competition, and individual choice. When countries adopt this model, it can lead to innovation, **entrepreneurship,** and investment, which can stimulate economic growth.

For example, countries like the United States and Germany have embraced the market-based model and have experienced significant **economic** development. They have seen increased productivity, job creation, and technological advancements. Additionally, the market-based model allows for flexibility and adaptation to changing global trends and demands. It encourages free trade and cooperation between nations, fostering a **global** economy.

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A grinding wheel is initially at rest. A constant external torque of 50.0 m N is applied to the wheel for 20.0 s, giving the wheel an angular speed of 600 rpm. The external torque is then removed, and the wheel comes to rest 120 s later.

(a) Find the moment of inertia I of the wheel.

(b) Determine the frictional torque, which is assumed to be constant.

(c) Calculate the maximum instantaneous power provided by the frictional torque and compare to the average power provided by friction during the time when the wheel slows to rest. Hint: in part (a), both the external torque and frictional torque (opposing the angular velocity) are acting on the wheel.

### Answers

(a) To find the** moment of inertia (I) **of the wheel, we can use the equation relating torque (τ), angular acceleration (α), and moment of inertia (I):

**τ = I * α.**

In the given scenario, an** external torque** of 50.0 mN is applied to the wheel for 20.0 s, resulting in an angular speed of 600 rpm.

First, let's convert the **angular speed** to radians per second:

Angular speed = 600 rpm = 600 * (2π rad/1 min) * (1 min/60 s) =** 20π rad/s.**

Since the wheel is initially at rest, the **angular acceleration (α)** is the change in angular speed divided by the time:

α = (20π rad/s - 0 rad/s) / 20.0 s = π rad/s^2.

Using the formula τ = I * α, we can rearrange it to solve for the moment of inertia:

I = τ / α = (50.0 mN) / (π rad/s^2) = 50.0 * 10^(-3) Nm / π rad/s^2.

Calculating this expression, we find:

I ≈** 15.92 * 10^(-3) Nms^2.**

Therefore, the moment of inertia of the wheel is approximately 15.92 * 10^(-3) Nms^2.

(b) The** frictional torque** opposing the angular velocity can be determined by subtracting the external torque from the net torque. Since the wheel comes to rest 120 s later, we can assume that the net torque opposing the** angular velocity** is **constant** during this time.

**Net torque **= 0 (when the wheel comes to rest).

Frictional torque = Net torque - External torque = 0 - 50.0 mN = -50.0 mN.

Therefore, the frictional torque is -50.0 mN.

(c) The maximum** instantaneous power** provided by the frictional torque can be calculated using the equation:

Power = Frictional torque * Angular speed.

Substituting the given values, we have:

**Power** = (-50.0 mN) * (20π rad/s).\

Calculating this expression, we find:

Power ≈** -31.42 π mW.**

The** negative sign **indicates that the power is being dissipated by the frictional torque.

To compare this with the** average power** provided by friction during the time when the wheel slows to rest, we need additional information about the duration and behavior of the frictional torque during that time. Without this information, we cannot calculate the average power.

Therefore, the maximum **instantaneous power** provided by the frictional torque is approximately -31.42π mW.

Hence, the moment of inertia of the wheel is approximately 15.92 * 10^(-3) Nms^2, the frictional torque is -50.0 mN, and the maximum instantaneous power provided by the frictional torque is approximately **-31.42π mW.**

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the radius of a circle is increasing at a constant rate of 0.4 meters per second. what is the rate of increase in the area of the circle at the instant when the circumference is 60 pie

### Answers

The rate of increase of the area of the circle at the instant when the **circumference **is 60π is 24π square meters per second.

To solve this problem, we need to use the formulas for the circumference and area of a circle:

Circumference = 2πr

Area = πr^2

We are given that the radius of the circle is increasing at a constant rate of 0.4 meters per second. Therefore, the rate of increase of the radius is dr/dt = 0.4 m/s.

We are also given that the circumference of the circle is 60π at the instant we are interested in. We can use this information to find the value of the **radius**:

Circumference = 2πr**60π = 2πr**

r = 30

Now we can use the formulas for the circumference and area to find the rate of increase of the area:**Circumference = 2πr**

dC/dt = 2π(dr/dt)

dC/dt = 2π(0.4)

dC/dt = 0.8π

Area = πr^2

dA/dt = 2πr(dr/dt)

dA/dt = 2π(30)(0.4)**dA/dt = 24π**

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