Use the information to help you answer this question. Based on the data in the table
above, why do you think gasoline is used as fuel for cars?
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The speed of the object that the point that have been marked as B is 14 m/s

The conservation of mechanical energy is a fundamental principle in physics that states that the total mechanical energy of a system remains constant as long as no external forces do work on the system. This principle applies to systems where only conservative forces are involved, meaning forces that can be derived from a potential energy function.

We know that the kinetic energy is equal to the potential energy thus we have that;

[tex]1/2mv^2 = mgh\\1/2v^2 = gh[/tex]

v = √2gh

v = √2 * 9.8 * 10

v = 14 m/s

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The volumetric flow rate of the oil is 2.37 m³/s.

In order to calculate the volumetric flow rate of the oil, we need to use the formula for volumetric flow rate.Q = vA Where,Q = volumetric flow rate v = velocity of fluid A = cross-sectional area of the pipe

First, we need to calculate the cross-sectional area of the pipe. Since the thickness of the pipe is not given, we will use an approximate value for the inner diameter of the pipe, which is equal to the nominal diameter minus twice the wall thickness.

This is given by:Di = N.D. - 2e

For Schedule 80 pipes, the wall thickness is given by:

e = 0.0153D - 0.0153

For N.D. = 450 mm,

e = 0.0153(450) - 0.0153= 6.885 mm

= 0.006885 m.

Hence,Di = 0.45 - 2(0.006885)= 0.43623 m

Now, we can calculate the cross-sectional area of the pipe:

A = π/4 D²

= π/4 (0.43623)²

= 0.15015 m²

Finally, we can calculate the volumetric flow rate using the formula:

Q = vA

Q= 15.8 × 0.15015

Q= 2.37207 m³/s≈ 2.37 m³/s (to two decimal places).

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Power dissipated in wires during transmission ≈ 1.034 × [tex]10^5[/tex] W.

To find the power used to heat the wires during transmission, we need to calculate the total resistance of the transmission line and then use Ohm's law to determine the power dissipated.

Given:

Power generated = 1.2 ×[tex]10^6[/tex]W

Distance to the town = 7.0 km

Resistance per kilometer = 5.0 × [tex]10^-^2[/tex] Ω/km

Voltage = 1200V

First, let's calculate the total resistance of the transmission line. Since there are two wires, the total resistance will be twice the resistance per kilometer.

Resistance per kilometer = 5.0 × [tex]10^-^2[/tex] Ω/km

Total resistance = 2 × (Resistance per kilometer) × Distance

Total resistance = 2 × (5.0 × [tex]10^-^2[/tex] Ω/km) × 7.0 km

Next, we can use Ohm's law to calculate the power dissipated:

Power dissipated = [tex](Voltage^2)[/tex] / Resistance

Power dissipated =[tex](1200V)^2[/tex] / Total resistance

Now we can substitute the value of the total resistance and calculate the power dissipated:

Power dissipated =[tex](1200V)^2[/tex] / (2 × (5.0 × [tex]10^-^2[/tex] Ω/km) × 7.0 km)

Calculating the expression, we get:

Power dissipated ≈ 1.034 ×[tex]10^5[/tex] W

Therefore, the power used to heat the wires during transmission is approximately 1.034 ×[tex]10^5[/tex]W.

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Answer:

The period of a satellite in a circular orbit around the Earth can be calculated using the formula:

T = 2π√(r³/GM)

where:

T = period of the satellite

r = radius of the orbit

G = gravitational constant (6.67 x 10^-11 Nm^2/kg^2)

M = mass of Earth (5.97 x 10^24 kg)

Substituting the given values:

T = 2π√((4x10^16)^3 / (6.67x10^-11 x 5.97x10^24))

T = 2π√(135168 x 10^22 / 3.98739 x 10^14)

T = 2π√(338828.41)

T = 2 x 3.1416 x 582.3408

T = 3661.6 seconds

Therefore, the period of the satellite is 3661.6 seconds, or approximately 61 minutes.

Answer:

1,680 days

Explanation:

We are given that the satellite revolves in a circular orbit with radius r = 4 x 1016 meters. The unit of 1016 means the radius is 4 trillion meters.

We want to find the period or time taken for one revolution. We can use Kepler's third law to calculate the period.

Kepler's third law relates the period (P) of an orbiting body to the semi-major axis (a) of its orbit:

Where a is equal to the radius r for a circular orbit.

The proportionality constant depends on the large scale gravitational parameter (μ) of the central body (in this case, Earth). The law can be written as:

P2 = (4π2/μ) * a3

Where μ for Earth is 398,600 km3/s2. Converting the radius r in meters to kilometers:

a = 4 x 1016 m = 4 x 109 km

Substituting the values of a and μ in the law, we get:

P2 = (4π2/398600)*(43)*109)^3

P2 = 1.62 x 1024

Taking the square root, we get the period:

P = 1.27 x 1012 seconds

Converting this to hours gives the final answer:

1.27 x 1012 seconds / (60*60 seconds/hour) =

1.48 x 105 hours

Therefore, the period (time for one revolution) of the satellite is around 1.48 x 10^5 hours or 1,680 days.

The ratio of hydrogen atoms to oxygen atoms in a water molecule is 2:1, which means that there are two hydrogen atoms for every one oxygen atom in a water molecule.Water is a molecule made up of two hydrogen atoms and one oxygen atom, with a molecular formula of H2O.

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The initial height H of the boy can be determined by adding the height of the slide h and the horizontal distance d the boy travels after leaving the track: H = h + d.

To determine the initial height H of the boy in terms of h and d, we can use the principle of conservation of energy. The total mechanical energy of the system remains constant throughout the motion.

At the top of the slide, the boy has gravitational potential energy given by mgh, where m is the mass of the boy, g is the acceleration due to gravity, and h is the height of the slide above the ground.

As the boy slides down the slide, there is no friction or other dissipative forces, so there is no change in mechanical energy. At the bottom of the track, the gravitational potential energy is converted entirely into kinetic energy.

Therefore, we can equate the initial potential energy to the final kinetic energy:

mgh = 1/2 m[tex]v^{2}[/tex],

where v is the horizontal velocity of the boy when he leaves the track.

Since the boy leaves the track horizontally, the vertical component of his velocity is zero. Therefore, we can use the relationship between horizontal distance d and horizontal velocity v:

d = vt.

Solving these equations, we can express the initial height H in terms of h and d:

H = h + d.

So the initial height H of the boy can be determined by adding the height of the slide h and the horizontal distance d the boy travels after leaving the track.G

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The base Hellcat variant produces 717 horsepower and 656 pound-feet (888 Newton-meters) of torque.

The Dodge Challenger SRT Hellcat is a high-performance vehicle distinguished by its strong engine. The Hellcat is powered by a supercharged 6.2-liter HEMI V8 engine that generates a lot of horsepower (HP) and torque.

The Hellcat Redeye, on the other hand, is a more powerful model with 797 horsepower and 707 lb-ft (958 Nm) of torque.

Thus, these values may vary significantly based on the model year and any vehicle changes.

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Your question seems incomplete, the probable complete question is:

How much HP and torque does a Hellcat SRT have?

Answer:

The major factors affecting the formation of soil are relief, parent material, climate, vegetation and other life-forms and time. Besides these, human activities also influence it to a large extent. The parent material of soil may be deposited by streams or derived from in-situ weathering.

A form of energy released from the nucleus, the core of atoms, made up of protons and neutrons.

The Florida Graduated Driver License (GDL) program is aimed at reducing accidents caused by inexperienced drivers by limiting the driving privileges of young drivers based on their age and driving experience.The Florida Graduated Driver License (GDL) is a program that seeks to reduce traffic accidents caused by inexperienced drivers.

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Answer:

Explanation:

The refractive index of the glass is 1.73.

When a ray of light strikes a surface, it is either reflected, refracted, or both. The angle of refraction is determined by the refractive index of the two materials, the angle of incidence, and the law of refraction.

The law of refraction states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the refractive index of the second material divided by the refractive index of the first material.

In this problem, the angle of incidence is 60 degrees, and the refracted ray is perpendicular to the reflected ray. This means that the angle of refraction is 30 degrees.

The refractive index of the glass is therefore:

n = sin(i) / sin(r) = sin(60) / sin(30) = √3 / 1/2 = 2 / 1 = 1.73

Answer:

it could possibly be b

Explanation:

quiz

The charge 0.00068 C can be written using the prefix µ as 680 μC.

The prefix "µ" (pronounced "micro") represents a scaling factor of 10⁻⁶ . This means that when you write a value with the prefix µ, it is equal to the value multiplied by 10⁻⁶. I

In this case, 680 μC means 680 times 10⁻⁶ coulombs, which is equal to 0.00068 C.

So, the correct way to express the charge 0.00068 C using the prefix µ is 680 μC.

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The angle between vector A and B is 90 degrees.

Let’s consider the vectors A and B with equal magnitudes of 5.

Thus, we can assume that the angle between A and B is θ.

Now, if the sum of A and B is vector 6j, then we can write the vector equation below:

[tex]A + B = 6j[/tex]

Let's first express vector A and B in terms of their components.

Let’s assume that vector A has components Ax and Ay, while vector B has components Bx and By.

Thus, the vector equation above can be rewritten in terms of components below:

[tex]Ax + Bx = 0[/tex]       ------------(1)

[tex]Ay + By = 6[/tex]       ------------(2)

We know that the magnitudes of vectors A and B are equal to 5, thus we can write the following equations:

[tex]x^2+y^2 = 5^2[/tex]       ------------(3)

[tex]x^2+y^2 = 25[/tex]      ------------(4)

From equation (4), we can write:

[tex]y = \sqrt{(25-x^2)}[/tex]      ------------(5)

By substituting equation (5) into equation (2), we have:

[tex]Ay + By = 6Ay + \sqrt{(25-x^2)} = 6Ay[/tex]

[tex]= 6 - \sqrt{(25-x^2)}[/tex]    ------------(6)

We can now substitute equation (6) into equation (3):

[tex]x^2 + (6-\sqrt{(25-x^2)})^2 = 25[/tex]

Solving for x:

[tex]2x^2 + 12\sqrt{(25-x^2)} = 0x^2 + 6\sqrt{(25-x^2)}[/tex]

[tex]= 0x^4 + 36x^2 - 225[/tex]

[tex]= 0x^2[/tex]

[tex]= 3, -15[/tex]

We choose [tex]x^2 = 3[/tex] since it is positive and obtain:

[tex]y = 4By[/tex]

substituting x and y into the original equations [tex]A = Ax + Ay[/tex] and

[tex]B = Bx + By[/tex], we obtain:

[tex]A = (-\sqrt{3}, 6-\sqrt{3})[/tex]

[tex]B = (\sqrt{3}, -1+\sqrt{3})[/tex]

Thus, the dot product of vectors A and B can be expressed as:

[tex]A \cdot B = |A||B| cos(\theta)[/tex]

Now, we know that

[tex]|A| = |B| = 5[/tex]

thus we can write:

[tex]A \cdot B = 25 cos(\theta)[/tex]

Using the formula above, we can obtain the angle θ between vectors A and B as follows:

[tex]cos(\theta) = \frac{(A \cdot B)}{|A||B|}[/tex]

[tex]cos(\theta) = \frac{[(\sqrt{3}(-\sqrt{3}) + (6-\sqrt{3})(-1+\sqrt{3})] }{(5)(5)}[/tex]

[tex]cos(\theta) = \frac{ [-3 + 3]}{25}[/tex]

[tex]cos(\theta) = 0[/tex]

[tex]\theta= cos^{-1}(0)[/tex]

[tex]\theta =90^{\circ}[/tex]

Therefore, the angle between vector A and B is 90 degrees.

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The distance traveled by the girl to complete half way around the circular track is equal to half of the circumference of the circle, which is:

d = (1/2) * 2πr = πr = π(10.0 m) = 31.4 m

The time taken by the girl to travel this distance is given as 15.0 s. Therefore, her average speed is:

average speed = distance / time = 31.4 m / 15.0 s ≈ 2.09 m/s

To calculate the magnitude of the girl's average velocity, we need to determine her displacement and divide it by the time taken. The girl's displacement is the straight-line distance from her starting point to her ending point, which is a distance of 2r = 20.0 m because she has traveled exactly half way around the circular track. Therefore, the magnitude of her average velocity is:

magnitude of average velocity = displacement / time = 20.0 m / 15.0 s ≈ 1.33 m/s

Note that the magnitude of the girl's average velocity is less than her average speed because her average velocity takes into account the direction of her motion, while her average speed does not.

A particle in a 3 dimensional space (x, y, z axes) that cannot move in the y direction has 2 degrees of freedom. It can still move freely along the x and z axes.

Degrees of freedom refer to the number of independent displacements (or motions) that a particle can make. Since this particle cannot move along the y axis, it only has 2 independent motions it can make:

Displacement along the x axis

Displacement along the z axis

So it has 2 degrees of freedom, one for each independent motion (displacement along x and z).

In general, for an n-dimensional space where m dimensions have constrained or fixed movement, the degrees of freedom will be:

Degrees of freedom = n - m

In this case:

n = 3 (since it's a 3D space - x, y and z axes)

m = 1 (y dimension has constrained movement)

Therefore:

Degrees of freedom = 3 - 1 = 2

So the final answer is that the particle has 2 degrees of freedom.

The independent variable in this experiment is the act of turning the bulb on and off, while the dependent variable is the behavior of the earthworm in response to changes in light. The scientist can analyze the data collected to determine the impact of light on the earthworm's behavior.

In the experiment where a scientist is turning a bulb on and off to check the behavior of an earthworm, the independent variable is the manipulation performed by the scientist, which is the act of turning the bulb on and off.

The independent variable is the variable that the scientist deliberately changes or controls in order to observe its effect on the dependent variable. In this case, the scientist is interested in investigating how the earthworm responds to changes in light. By turning the bulb on and off, the scientist is manipulating the presence or absence of light in the environment of the earthworm.

The behavior of the earthworm, which is the dependent variable, will be observed and measured in response to the changes in light. The scientist may record various behaviors such as movement, burrowing, or changes in activity level exhibited by the earthworm when the light is turned on and off.

By systematically controlling the independent variable (turning the bulb on and off) and observing the dependent variable (behavior of the earthworm), the scientist can analyze the relationship between light exposure and the earthworm's behavior. This allows for drawing conclusions about how the earthworm responds to light stimuli.

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The resultant displacement of the free end of rod B from its present location when the temperature rises from 15°C to 25°C is -0.0012 m.

When a metal is heated, it tends to expand, and when cooled, it tends to contract.

The coefficient of linear expansion for a metal determines how much the metal changes in length per unit of temperature change.

The amount of change in length (L) per unit length (Lo) per unit of temperature change (∆T) is given by

∆L=αL ∆T, where α is the coefficient of linear expansion.

We'll use the following formula to calculate the resulting displacement of the free end of rod B from its present location when the temperature rises from 15°C to 25°C:

ΔL = LαΔT

where L is the length of the metal rod

α is the coefficient of linear expansion

ΔT is the temperature difference.

Let us first calculate the coefficient of linear expansion for aluminum and steel.

ALUMINUM:α (aluminum) = 24 × 10-6 /°C

STEEL:α (steel) = 12 × 10-6 /°C

Now, let's calculate the change in length of the rods as a result of the temperature change.

ΔLA = αA

LΔT= 24 × 10-6/°C × 1.0 m × (25°C − 15°C)

LΔT= 0.0024 m

ΔLB = αB

LΔT= 12 × 10-6/°C × 1.0 m × (25°C − 15°C)

LΔT= 0.0012 m

Now we may calculate the resultant displacement of the free end of rod B from its present location.

ΔLresultant = ΔLB - ΔLA

ΔLresultant = (0.0012 m) - (0.0024 m)

ΔLresultant = -0.0012 m

Therefore, the resultant displacement of the free end of rod B from its present location when the temperature rises from 15°C to 25°C is -0.0012 m.

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The correct expression for the natural frequency of oscillation of a stick of length (l) oscillating around one end is given by :[tex]\sqrt{g/l}[/tex].

The correct answer is option A.

To derive this expression, let's go through the calculation:

The restoring force acting on the stick is provided by the gravitational force, which is proportional to the displacement of the stick. The gravitational force is given by F = mg, where m is the mass of the stick and g is the acceleration due to gravity.

For a stick oscillating around one end, the effective length of the pendulum is l. The torque acting on the stick is given by τ = Iα, where I is the moment of inertia of the stick about the pivot point and α is the angular acceleration.

For small angular displacements, we can use the approximation α = θ'', where θ'' is the second derivative of the angular displacement with respect to time.

Using the torque equation, we have Iθ'' = mglθ, where θ represents the angular displacement.

Dividing both sides of the equation by θ and rearranging, we get θ'' + (g/l)θ = 0, which is a differential equation for simple harmonic motion.

The solution to this differential equation is of the form θ = A sin(ωt), where A is the amplitude and ω is the angular frequency.

Comparing this solution to the differential equation, we find that ω² = g/l.

The natural frequency of oscillation is given by f = ω/(2π), so substituting the value of ω, we have f = [tex]\sqrt{(g/l)/(2}[/tex]π).

Therefore, the correct expression for the natural frequency of oscillation is [tex]\sqrt{g/l}[/tex] which corresponds to option A.

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Answer:

It is incredibly difficult to sustain fusion reaction.

Explanation:

Answer: So, just as the blood enters the blocked portion of the vessel, its speed is approximately 7.31 times its initial speed v0

Explanation: The flow rate of a fluid is given by the equation Q = A * v, where Q is the flow rate, A is the cross-sectional area of the vessel, and v is the speed of the fluid. Since the blood is incompressible, its flow rate must remain constant. Therefore, if the cross-sectional area of the vessel decreases, the speed of the blood must increase to maintain a constant flow rate.

The cross-sectional area of a cylinder is given by the equation A = πr^2, where r is the radius of the cylinder. If the diameter of the vessel decreases by 63.0%, then its radius decreases by 63.0% as well. Therefore, the new radius of the vessel is r_new = r_old * (1 - 0.63) = 0.37 * r_old.

Substituting this into the equation for the cross-sectional area, we get:

A_new = π * (0.37 * r_old)^2

A_new = (0.37^2) * π * r_old^2

A_new = 0.1369 * A_old

Since the flow rate must remain constant, we have:

Q = A_old * v0 = A_new * v_new

Substituting in the values for A_old and A_new, we get:

v_new = (A_old / A_new) * v0

v_new = (1 / 0.1369) * v0

v_new ≈ 7.31 * v0

So, just as the blood enters the blocked portion of the vessel, its speed is approximately 7.31 times its initial speed v0.

Answer:

The answer is approximately 350.4J to 1d.p

Explanation:

W=F×S

F=F cosø

W=Fcosø×S

W=71.5cos27×5.5

W=63.7×5.5

W=350.35J

W≈350.4J

Answer:

The electrostatic force is a vector quantity, which means that it has both magnitude and direction. Coulomb's law tells you the the magnitude of the electrostatic force. To determine the direction of the force, you can draw a diagram using force vectors.

Additional Information:

Coulomb's law states that the magnitude of the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, Coulomb's law is expressed as:

[tex]\vec F_e=\dfrac{k_e||q_1||||q_2||}{r^2}[/tex]

Where:

Coulomb's law helps quantify the strength of the electrostatic force and provides a mathematical relationship to calculate the force between charged objects based on their charges and distance.

[tex]\hrulefill[/tex]

A vector is a mathematical object that has both magnitude and direction. It is used to represent physical quantities that require both of these components to be fully described, such as displacement, velocity, force (in this case it's the electrostatic force), and acceleration.

In a vector, the magnitude represents the size or length of the vector, while the direction indicates the orientation or angle of the vector in space. Vectors are typically represented by arrows, where the length of the arrow corresponds to the magnitude, and the direction of the arrow indicates the direction of the vector.

[tex]\hrulefill[/tex]

To determine the direction of an electrostatic force between charged objects, you need to consider the following principles:

In general, you can determine the direction of the electrostatic force by considering the signs of the charges and applying the principles of attraction and repulsion.

**Noting what I said in principle #3: I like to use a different form of Coulomb's Law when dealing with multiple charges. Although I won't get in too much detail about this, as I am assuming you are just learning about electrostatic physics.  

The third force should have a magnitude of 0.16 g N and be directed at an angle of approximately 30.96° above the positive x-axis (positive y-direction).

To balance the system, the third force should be applied in such a way that the net force on the system becomes zero. In other words, the magnitudes and directions of the three forces should cancel each other out.

First, let's convert the masses from grams to kilograms:

Mass 1 = 100.0 grams = 0.1 kg

Mass 2 = 200.0 grams = 0.2 kg

Now, let's calculate the x-component and y-component of each force:

Force 1:

x-component = 0.6 * 0.1 kg * g = 0.06 g N (in the positive x-direction)

y-component = 0 N (no y-component)

Force 2:

x-component = -0.2 kg * g * cos(120°) = -0.2 g * (-0.5) = 0.1 g N (in the positive x-direction)

y-component = -0.2 kg * g * sin(120°) = -0.2 g * (-sqrt(3)/2) = 0.1 sqrt(3) g N (in the positive y-direction)

To balance the system, the x-component of the third force should be equal to the sum of the x-components of Force 1 and Force 2:

Third Force (x-component) = 0.06 g N + 0.1 g N = 0.16 g N (in the positive x-direction)

Similarly, the y-component of the third force should be equal to the sum of the y-components of Force 1 and Force 2:

Third Force (y-component) = 0 N + 0.1 sqrt(3) g N = 0.1 sqrt(3) g N (in the positive y-direction)

Therefore, the third force should have a magnitude of 0.16 g N and be directed at an angle of approximately 30.96° above the positive x-axis (positive y-direction).

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Answer:

[tex]s_{avg}= \dfrac{2 \pi}{3} \approx 2.09 \ m/s[/tex]

[tex]v_{avg}=\frac{4}{3} \approx 1.33 \ m/s[/tex]

Explanation:

To find the girl's average speed and average velocity, we can use the following formulas:

[tex]s_{avg}= \dfrac{\pi r}{t} \\\\ \\v_{avg}= \dfrac{2r}{t}\\\\\\ \hrule[/tex]

(A) - Finding the average speed.

[tex]\Longrightarrow s_{avg}= \dfrac{\pi(10.0)}{15.0}\\\\\\\therefore \boxed{s_{avg}= \dfrac{2 \pi}{3} \approx 2.09 \ m/s}[/tex]

(B) - Finding the average velocity.

[tex]\Longrightarrow v_{avg}= \dfrac{2(10.0)}{15.0}\\\\\\\therefore \boxed{v_{avg}=\frac{4}{3} \approx 1.33 \ m/s }[/tex]

Thus, the problem is solved.

To find the mass of the object, we can use the formula for kinetic energy:

Kinetic energy (KE) = (1/2) * mass * velocity^2

Given that the kinetic energy is 426 J and the velocity is 13 m/s, we can rearrange the equation to solve for the mass:

mass = (2 * KE) / (velocity^2)

Substituting the given values:

mass = (2 * 426 J) / (13 m/s)^2

mass = (2 * 426 J) / (169 m^2/s^2)

mass = 852 J / 169 m^2/s^2

mass = 5.04 kg

Therefore, the mass of the object is 5.04 kg.

The moment of inertia of the object about the dash line is 2.1316 kg·[tex]m^2[/tex].

To calculate the moment of inertia of an object about a given axis, we need to know the mass of the object and its distribution of mass around the axis.

Given that the mass of the object is 4 kg and the distance from the axis of rotation (dash line) is 73 cm, we can calculate the moment of inertia using the formula:

Moment of inertia (I) = m * [tex]r^2[/tex]

Where m is the mass of the object and r is the perpendicular distance from the axis of rotation to the mass element.

Converting the distance from centimeters to meters:

r = 73 cm = 0.73 m

Substituting the values into the formula:

I = 4 kg * (0.73 [tex]m^2[/tex]

Calculating:

I = 4 kg * 0.5329[tex]m^2[/tex]

Simplifying:

I = 2.1316 kg·[tex]m^2[/tex]

Therefore, the moment of inertia of the object about the dash line is approximately 2.1316 kg·.[tex]m^2[/tex]

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The given scenario describes an experiment involving an electroscope, a glass bottle, a cardboard lid, a bolt or nail, a light wire, and an aluminum foil strip.

The purpose of the experiment is to demonstrate the behavior of electrons and their effect on the electroscope. Initially, when the electroscope is neutral, it means that there are equal numbers of protons and electrons on the foil leaves, causing them to hang down straight. The glass bottle and the cardboard lid act as insulators, preventing the rapid escape of electrons and maintaining equilibrium.

When the head of the bolt is touched with a plastic ruler that has been rubbed with fur or wool, the ruler gains excess electrons due to the process of friction. These excess electrons are transferred to the bolt since metal is a good conductor. The electrons then move down the bolt and accumulate on the foil leaves.

As the foil receives the additional electrons, the repulsive force between the like charges (electrons) causes the foil leaves to separate or fly apart from one another. This is a result of the electrostatic repulsion between the negatively charged leaves.

The purpose of using the glass bottle is to provide a protective barrier against air currents that could interfere with the experiment. It also allows observation of the behavior of the foil leaves as they move apart, indicating the presence of excess electrons.

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Counselling skills are crucial in both professional and personal relationships because they aid in the development of a supportive environment. It includes the creation of a helping relationship, the promotion of efficient interaction, and the establishment of a secure therapeutic relationship. Core counseling skills help to create a positive atmosphere and are used to maintain a supportive relationship with the patient.

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We can calculate the time taken by the compass to hit the ground by using kinematic equations of motion. The motion of the compass is a free-fall motion since it is only under the influence of gravity. When the compass is dropped, it is initially at rest.

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Answer:

3,600 years old

Explanation:

To determine the age of the object based on the remaining radioactive atoms, we can use the concept of half-life.

The half-life is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life of the radioactive element is 1,200 years. This means that after 1,200 years, half of the radioactive atoms will have decayed, and the remaining half will still be radioactive.

Half-life formula

[tex]\boxed{N(t)=N_0\left(\dfrac{1}{2}\right)^{\frac{t}{t_{1/2}}}}[/tex]

where:

The initial quantity is 100% and the quantity remaining is 12.5%. The half-life is 1,200 years. Therefore, the values to substitute into the half-life formula are:

Substitute the values into the half-life formula:

[tex]0.125=1\left(\dfrac{1}{2}\right)^{\dfrac{t}{1200}}[/tex]

Solve for t:

[tex]\begin{aligned}0.125&=\left(\dfrac{1}{2}\right)^{\dfrac{t}{1200}}\\\\\dfrac{1}{8}&=\left(\dfrac{1}{2}\right)^{\dfrac{t}{1200}}\\\\\ln \left(\dfrac{1}{8}\right)&=\ln \left(\dfrac{1}{2}\right)^{\dfrac{t}{1200}}\\\\\ln \left(\dfrac{1}{8}\right)&=\dfrac{t}{1200}\ln \left(\dfrac{1}{2}\right)\\\\1200\ln \left(\dfrac{1}{8}\right)&=t\ln \left(\dfrac{1}{2}\right)\\\\1200(\ln1-\ln8)&=t(\ln1-\ln 2)\\\\1200(-\ln8)&=t(-\ln 2)\\\\1200(-\ln2^3)&=t(-\ln 2)\\\\1200(-3\ln2)&=t(-\ln 2)\\\\-3600\ln2&=-t\ln 2\\\\\end{aligned}[/tex]

                  [tex]\begin{aligned}t\ln 2&=3600\ln2\\\\t&=3600\end{aligned}[/tex]

Therefore, if only 12.5% of the radioactive atoms remain, the object is approximately 3,600 years old.