Tia needs to produce a solenoid that has an inductance of 2.07 μ H . She constructs the solenoid by uniformly winding 1.19 m of thin wire around a tube. How long, in centimeters, should the tube be?

Answer:

option D

Explanation:

The correct answer is option D

The friction force is the force that holds back the surface from sliding. It acts in the opposite direction of the motion of the body.

It can be explained with an example,

when you throw a ball on the ground it stops automatically this is because of friction which is acting opposite to the ball.

Friction also has benefits like due to friction we can walk, run, etc.  

So, from the given option

The force that resists sliding is friction force.

Answer:

push

Explanation:

it pushes you back when you lean forward really fast

The difference between mass and weight is that mass is the amount of matter in a material, while weight is a measure of how the force of gravity acts upon that mass. Mass is the measure of the amount of matter in a body. ... Weight usually is denoted by W. Weight is mass multiplied by the acceleration of gravity (g).

GRAVITY

THE UNBALANCED FORCE THAT CAUSES OBJECTS TO MOVE IN A CIRCULAR PATH IS CALLED A CENTRIPETAL FORCE. GRAVITY PROVIDES THE CENTRIPETAL FORCE THAT KEEPS OBJECTS IN ORBIT. THE WORD CENTRIPETAL MEANS "TOWARD THE CENTER."

Answer:

[tex]W=1.93eV[/tex]

Explanation:

The maximum kinetic energy of an ejected electron in the photoelectric effect is given by:

[tex]K_{max}=h\nu-W(1)[/tex]

Here h is the Planck's constant, [tex]\nu[/tex] the frequency of the light and W the work function of the element.

The frequency is equal to the speed of light, divided by the wavelength:

[tex]\nu=\frac{c}{\lambda}(2)[/tex]

Recall that [tex]1nm=10^{-9}m[/tex]. Replacing (2) in (1) and solving for W:

[tex]W=\frac{hc}{\lambda}-K_{max}\\W=\frac{(4.14*10^{-15}eV\cdot s)(3*10^8\frac{m}{s})}{345*10^{-9}m}-1.67eV\\W=1.93eV[/tex]

Answer:

B. Path B

Explanation:

Since the velocity v is tangent to the circular path, the rock will follow the path B.

You can see the paths in the pic.

Answer:

Interstellar Dust

Explanation:

In the solar system Interstellar dust is a type of cosmic dust and unlike Interstellar gas they have large dust particles enabling them to block visible light. Unlike smoke and fog, they contain large number of closely packed clumps of atoms and molecules

Answer:

interstellar dust

Explanation:

Dust particles interact with light through scattering and absorption. Reducing the amount of starlight received

The colour of the sky during the day is blue, because the blue light  is scattered by atmosphere particles.  The increased path length causes the change of colour of sun light . This is due to dust grains in the atmosphere, a similar process happens with interstellar dust

Answer:

I and II

Explanation:

A management system that includes fire suppression will likely lead to

I. large quantities of biomass accumulating on the forest floor.

II. an increase in the likelihood of uncontrolled natural fires.

Biomass is the total quantity of weight of flora and fauna in a given area or volume. The recent fire in the Amazon rain forest is an example of uncontrolled natural forest fires.

Answer:

a)30.14 rad/s2

b)43.5 rad/s

c)60633 J

d)42 kW

e)84 kW

Explanation:

If we treat the propeller is a slender rod, then its moments of inertia is

[tex] I =\frac{mL^2}{12} = \frac{107*2.68^2}{12} = 64.04 kgm^2[/tex]

a. The angular acceleration is Torque divided by moments of inertia:

[tex]\alpha = \frac{T}{I} = \frac{1930}{64.04} = 30.14 rad/s^2[/tex]

b. 5 revolution would be equals to [tex]10\pi[/tex] rad, or 31.4 rad. Since the engine just got started

[tex]\omega^2 = 2\alpha\theta = 2*30.14*31.4 = 1893.5[/tex]

[tex]\omega = \sqrt{1893.5} = 43.5 rad/s[/tex]

c. Work done during the first 5 revolution would be torque times angular displacement:

[tex]W = T*\theta = 1930 * 31.4 = 60633 J[/tex]

d. The time it takes to spin the first 5 revolutions is

[tex]t = \frac{\omega}{\alpha} = \frac{43.5}{30.14} = 1.44 s[/tex]

The average power output is work per unit time

[tex]P = \frac{W}{t} = \frac{60633}{1.44} = 41991 W[/tex] or 42 kW

e.The instantaneous power at the instant of 5 rev would be Torque times angular speed at that time:

[tex]P_i = T*\omega = 1930*43.5=83983 W[/tex] or 84 kW

Answer:

[tex]\omega_s=12.8886\ rad.s^{-1}[/tex]

Explanation:

Given that:

Now using the law of conservation of angular momentum:

angular momentum of tucked body=angular momentum of straight body

[tex]I_t.\omega_t=I_s.\omega_s[/tex]

[tex]16\times 15.708=19.5\times \omega_s[/tex]

[tex]\omega_s=12.8886\ rad.s^{-1}[/tex]

To find the speed of the package of mass m right before the collision, we can use the principle of conservation of energy. The common speed of the packages after the collision, if they stick together, can be found using the principle of conservation of momentum. If the collision is perfectly elastic, the rebounding height of the package of mass m can be determined using the principle of conservation of mechanical energy.

To answer the given question, we can use the principles of conservation of energy, momentum, and Newton's laws of motion.

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The package will hit the ground with a speed of 7.67 m/s. If the packages stick together, they will move with a speed of 2.56 m/s. In the case of a perfectly elastic collision, the package of mass m will rebound to the original height.

The subject of this question is Physics, specifically it applies the topics of kinetic energy, potential energy, momentum conservation and collisions in two scenarios: inelastic and elastic scenarios.

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Answer:

[tex]F_N=1194.24\ N[/tex]

Explanation:

Given that,

The elevator is moving up and slowing down at the rate of, [tex]a=3\ m/s^2[/tex]

The acceleration due to gravity, [tex]g=9.8\ m/s^2[/tex]

Mass of the person, m = 93.3 kg

To find,

The reading of the scale.

Solution,

As the elevator is moving down with some acceleration. The net force acting on it is given by :

[tex]F_N=ma+mg[/tex]

[tex]F_N=m(a+g)[/tex]

[tex]F_N=93.3(3+9.8)[/tex]

[tex]F_N=1194.24\ N[/tex]

So, the scale will read 1194.24 N.

Answer:

V = 1.7 x 10^{-3} m^{3}

Explanation:

apparent weight in ethyl alcohol = 16.5 N

apparent weight in water = 13.3 N

apparent weight = mg - ρgV

where

m = mass

g = acceleration due to gravity = 9.8 m/s^{2}

ρ = density

V = volume

    we can solve the two equations above as simultaneous equations by subtracting equation 2 from equation 1

we have

16.5 - 13.3 = (mg - mg) - ρ₁gV - (-ρ₂gV)

3.2 = gV(ρ₂ - ρ₁)

V = \frac{3.2}{g(ρ₂-ρ₁)}

where

ρ₂ = density of water = 1000 kg/m^{3}

ρ₁ = density of ethyl alcohol = 806 kg/m^{3}

V = \frac{3.2}{9.8(1000 - 806)}

V = 1.7 x 10^{-3} m^{3}

The volume of the object can be found using Archimedes' principle and the given apparent weights in water and ethyl alcohol. The volume is computed from these values using the densities of the two fluids, yielding a volume of about 0.013 cubic meters.

To answer the question about the object's volume when it's submerged in ethyl alcohol and water, we'll need to use Archimedes' principle. This principle tells us that the apparent weight loss of the object in a liquid equals the weight of the fluid displaced by the object. In this case, the difference in apparent weights given for the object when in water and when in ethyl alcohol represents the weight of the fluids displaced.

We have to remember that weight can be calculated as the product of volume, density, and gravity. If you rearrange this equation, you get the volume as the quotient of weight and the product of density and gravity. Note that gravity cancels out in this problem since it remains constant for both fluids.

If we denote the volume of the object as V, the density of water as ρ_water (approximated to 1000 kg/m^3), the density of ethyl alcohol as ρ_alcohol (approximated to 789 kg/m^3), and the weight of the object in water and ethyl alcohol as W_water and W_alcohol respectively, we can write two equations:

We have the weights as the apparent weights from the problem, which are W_water = 13.3 N and W_alcohol = 16.5 N. If you solve these two equations, you should obtain the volume of the object, which should be around 0.013 m^3. This is the answer for the volume of the solid object.

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The magnetic force on a wire in a bundled configuration can be calculated using the formula F = I × B. The force per unit length on a wire located 0.200 cm from the center of the bundle can be calculated using this formula. A wire on the outer edge of the bundle experiences a smaller force compared to a wire closer to the center.

a. The magnetic force per unit length on a wire located 0.200 cm from the center of the bundle can be calculated using the formula F = I × B. Since the current and magnetic field are perpendicular, we can simplify the formula to F = I × B × sin(90°) = I × B. Plug in the values to get F = (2.00 A) × (μ × I/(2πR)) = (2 × 10^(-7) T·m/A) × (2.00 A) / (2π × 0.005 m). Calculate this to get the magnitude of the force per unit length.

b. A wire on the outer edge of the bundle will experience a smaller force than the wire 0.200 cm from the center. This is because the magnetic field strength decreases as the distance from the wire increases. Therefore, the force on a wire decreases as its distance from the center of the bundle increases.

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The magnetic force per unit length on a wire [tex]0.200 cm[/tex] from the center is [tex]1.28 \times 10^{-2} \, \text{N/m}[/tex]. A wire at the outer edge experiences a greater force of [tex]1.6 \times 10^{-2} \, \text{N/m}\\ \\[/tex] due to the higher magnetic field there.

This problem involves calculating the magnetic force per unit length acting on a current-carrying wire located within a bundle of wires, as well as comparing it to the force on a wire at the bundle's outer edge.

First, we calculate the magnetic field at a distance of [tex]0.200 cm[/tex] from the center. The magnetic field inside the bundle can be found using Ampère's Law:

The current enclosed by a circular path of radius [tex]r[/tex] inside the bundle is:

[tex]I_{\text{enclosed}} = (I_{\text{total}}) \times \left( \frac{\pi r^2}{\pi R^2} \right) \\= 200 \, \text{A} \times \left( \frac{0.200^2}{0.500^2} \right) \\= 32 \, \text{A}[/tex]

The magnetic field B at this radius is given by:

[tex]B = \frac{\mu_0 I_{\text{enclosed}}}{2\pi r} \\= \frac{4\pi \times 10^{-7} \times 32}{2\pi \times 0.002} \\ = 6.4 \times 10^{-3} \, \text{T}[/tex]

The force per unit length acting on a wire carrying a current I₁ is:

[tex]\frac{F}{L} = I_1 \times B \\= 2 \, \text{A} \times 6.4 \times 10^{-3} \, \text{T} \\= 1.28 \times 10^{-2} \, \text{N/m}[/tex]

The direction of the force follows the right-hand rule and is perpendicular to both the wire's current and the magnetic field.

A wire on the outer edge will experience a magnetic field generated by all the currents inside the circle of radius R. Therefore:

[tex]I_{\text{total}} = 100 \, \text{wires} \times 2.00 \, \text{A} \\= 200 \, \text{A}[/tex]

The magnetic field at the edge [tex]B_{edge}[/tex] is:

[tex]B_{\text{edge}} = \frac{\mu_0 I_{\text{total}}}{2\pi R} \\= \frac{4\pi \times 10^{-7} \times 200}{2\pi \times 0.005} \\= 8 \times 10^{-3} \, \text{T}[/tex]

The force per unit length [tex]F_{new}[/tex] on a wire at the edge is:

[tex]\frac{F}{L}_{\text{new}} = I_1 \times B_{\text{edge}} \\= 2 \, \text{A} \times 8 \times 10^{-3} \, \text{T} \\= 1.6 \times 10^{-2} \,[/tex]

Thus, the force experienced by a wire at the edge is greater than the force calculated in part (a).

Answer:

-24.76 kJ/mol

Explanation:

given,

mass of solid magnesium burned = 0.1375 g

the temperature increases by(ΔT) 1.126°C

heat capacity of of bomb calorimeter (C_{cal})= 3024 J/°C

heat absorbed by the calorimeter

    [tex]q_{cal} = C_{cal}\DeltaT[/tex]

    [tex]q_{cal} = 3024 \times 1.126[/tex]

    [tex]q_{cal} =3405.24\ J[/tex]

    [tex]q_{cal} =3.405\ kJ[/tex]

heat released by the reaction

    [tex]q_{rxn} = -q_{cal}[/tex]

    [tex]q_{rxn} = -3.405\ kJ[/tex]

energy density will be equal to heat released by the reaction divided by the mass of magnesium

Energy density = [tex]\dfrac{-3.405}{0.1375}[/tex]

Energy density = -24.76 kJ/mol

heat given off by burning magnesium is equal to -24.76 kJ/mol

Answer:

2 [tex]\sigma[/tex] bonds and 2 [tex]\pi[/tex] bonds

Explanation:

If we consider the the bonding in the [tex]CO_{2}[/tex] molecule:

[tex]O = 1s^{2}\ 2s^{2}\ 2p^{4}[/tex]

[tex]C = 1s^{2}\ 2s^{2}\ 2p^{2}[/tex]

Thus carbon forms double bonds with oxygen:

O = C = O

Now,

We know that double bond comprises of a [tex]\sigma\ bond[/tex] and a [tex]\pi \ bond[/tex]

Since, in the [tex]CO_{2}[/tex], there are 2 double bonds thus there are 2 [tex]\sigma[/tex] bonds and 2 [tex]\pi[/tex] bonds in the molecules.

"The CO₂ molecule has 2 σƒ (sigma) bonds and 2 π (pi) bonds.

To determine the number of sigma and pi bonds in CO₂, we need to consider its Lewis structure. Carbon dioxide has a linear molecular geometry with carbon at the center and two oxygen atoms double-bonded to it.

In CO₂:

- The carbon atom forms two double bonds with the two oxygen atoms.

- Each double bond consists of one sigma bond and one pi bond.

Therefore, for each carbon-oxygen double bond, there is:

- One sigma bond (σƒ), which is the head-on overlap of atomic orbitals.

- One pi bond (π), which is the side-to-side overlap of p-orbitals.

Since there are two carbon-oxygen double bonds in CO₂, we have:

- A total of 2 sigma bonds from the double bonds.

- Additionally, each double bond includes a sigma bond from the overlap of the sp hybrid orbital of carbon with the sp2 hybrid orbital of oxygen, contributing another 2 sigma bonds.

In summary, CO₂ has 4 sigma bonds in total:

- 2 sigma bonds from the sp-sp² hybrid orbital overlaps.

- 2 sigma bonds from the head-on overlap of p-orbitals that form part of the double bonds.

And CO₂ has 2 pi bonds in total:

- 2 pi bonds from the side-to-side overlap of p-orbitals in the double bonds.

Thus, the final count is 4 σƒ bonds and 2π bonds in the CO₂ molecule. However, it is important to note that the question specifically asks for the number of sigma and pi bonds, and the correct answer should reflect the number of each type of bond individually, not the total number of bonds. Therefore, the correct answer is 2σ bonds and 2π bonds.

Answer:

1.162 x 10^-7 Nm

Explanation:

length of wire, l = 25 cm

l = 2 π r

where, r is the radius of circular loop

25 = 2 x 3.14 x r

r = 3.98 cm

Magnetic field, B = 5.55 mT = 5.55 x 10^-3 T

Current, i = 4.121 mA = 4.21 x 10^-3 A

Torque, τ = i x A x B

τ = 4.21 x 10^-3 x 3.14 x 0.0398 x 0.0398 x 5.55 x 10^-3

τ = 1.162 x 10^-7  Nm

Thus, the maximum torque in the coil is 1.162 x 10^-7 Nm.

Answer:

Static friction is, [tex]0\ N\leq f_s\leq 866.81\ N[/tex]

Maximum static friction is, [tex]f_{max}= 866.81\ N[/tex]

Kinetic friction is, [tex]f_k=667.87\ N[/tex]

Explanation:

The value of coefficient of static friction between Aluminium and Steel is [tex]\mu_s=0.61[/tex] and the value of coefficient of kinetic friction is [tex]\mu_k=0.47[/tex]

Given:

Mass of the sculpture is, [tex]m=145\ kg[/tex].

As the sculpture is moved along the horizontal direction only, there will no net force acting along the vertical direction. Therefore,

Normal force by the steel platform will be equal to the weight of the aluminium sculpture. That is,

[tex]N=mg[/tex]

Now, the static friction is given as the product of normal force and coefficient of static friction. The static friction varies from a value of 0 to limiting friction.

The limiting friction is the maximum static friction that acts on a body to resist the motion.

The value of the limiting friction or the maximum static friction is given as:

[tex]f_{max}=\mu_sN=\mu_smg=0.61\times 145\times 9.8=866.81\ N[/tex]

Thus, static friction is given as:

[tex]0\leq f_s\leq f_{max}\\0\leq f_s\leq \mu_smg\\0\ N\leq f_s\leq 866.81\ N[/tex]

Now, kinetic friction is the frictional force acting on a body when the body is moving under the action of forces. Thus kinetic friction is the product of normal force and coefficient of kinetic friction. Kinetic friction is a constant opposing force.

Thus, kinetic friction is given as:

[tex]f_k=\mu_kN\\f_k=\mu_kmg\\f_k=0.47\times 145\times 9.8=667.87\ N[/tex]

The acceleration is 2 mph/min

Explanation:

The acceleration of an object is the rate of change of velocity. It is defined as follows:

[tex]a=\frac{v-u}{t}[/tex]

where

v is the final velocity

u is the initial velocity

t is the time taken for the velocity to change from u to v

For the car in this problem, we have (taking North as positive direction):

u = 25 mph

v = 35 mph

t = 5 min

Substituting into the equation, we find the acceleration:

[tex]a=\frac{35 mph-25mph}{5min}=2 mph/min[/tex]

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Answer:

Original claim is H_o: M = 30

Alternate claim is H_a: M > 30.

Explanation:

Given data:

4 ft tall speaker consume 30 watt power

a group of 40 speaker consume average power of 32 watt

calculation:

A home installed 4 ft tall  speaker that use 30 watt Power

40 speakers used 32 watt Power

Original claim is H_o: M = 30

Alternate claim is H_a: M > 30.

Explanation:

a) Period of simple pendulum

                 [tex]T=2\pi \sqrt{\frac{l}{g}}[/tex]

   l₁ = length of pendulum in Earth = ?

   l₂ = length of pendulum in Mars = ?

   T = Period of pendulum = 1.2 s

    g₁ = Acceleration due to gravity in Earth = 9.80 m/s²

    g₂ = Acceleration due to gravity in Mars = 3.70 m/s²

For Earth :-

     [tex]T=2\pi \sqrt{\frac{l_1}{g_1}}\\\\1.2=2\pi \sqrt{\frac{l_1}{9.8}}\\\\l_1=0.36m[/tex]

     Length of pendulum in Earth = 0.36 m      

For Mars :-

     [tex]T=2\pi \sqrt{\frac{l_2}{g_2}}\\\\1.2=2\pi \sqrt{\frac{l_2}{3.7}}\\\\l_2=0.13m[/tex]

     Length of pendulum in Mars = 0.13 m

b) Period of spring

                 [tex]T=2\pi \sqrt{\frac{m}{k}}[/tex]

 Here period is independent of acceleration due to gravity, so mass value is same in Earth and Mars.

                m = Mass = ?

                 T = Period = 1.2 s

                  k = Spring constant = 20 N/m

              [tex]T=2\pi \sqrt{\frac{m}{k}}\\\\1.2=2\pi \sqrt{\frac{m}{20}}\\\\m=0.73kg[/tex]

             Mass in Earth = Mass in Mars = 0.73 kg

The length of a simple pendulum and the mass to suspend the spring are mathematically given as

a L1 = 0.36m for the earth and L2 = 0.13m for mars

b m=0.73kg

Question Parameter(s):

period of 1.2 s on Earth

where the acceleration due to gravity is 9.80 m/s2

and on Mars, where the acceleration due to gravity is 3.70 m/s2?

a force constant of 20 N/m

Generally, the equation for the Period of a simple pendulum  is mathematically given as

[tex]T=2\pi \sqrt{\frac{l}{g}}[/tex]

therefore the length of Earth is

[tex]\\\\1.2=2\pi \sqrt{\frac{l_1}{9.8}}\\\\l_1=0.36m[/tex]

and for mars

[tex]\\\\1.2=2\pi \sqrt{\frac{l_2}{3.7}}\\\\l_2=0.13m[/tex]

In conclusion length of a simple pendulum is

L1 = 0.36m for earth and L2 = 0.13m for mars

Period of spring

[tex]T=2\pi \sqrt{\frac{m}{k}}[/tex]

[tex]}\\\\1.2=2\pi \sqrt{\frac{m}{20}}\\\\m=0.73kg[/tex]

In conclusion, the mass to suspend the spring

m = 0.73kg

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Answer:

Explanation:

Answer:

Carbon electrons are arranged in a way that makes it possible for them to form long chains. That also helps carbon maintain its properties.

Explanation:

Carbon electrons are arranged in a way that makes it possible for them to form long chains. That also helps carbon maintain its properties.

Answer:

His recoil velocity is 0.269 m/s to the East

Explanation:

This question is easily solved by using the law of conservation of linear momentum.

The formula for the momentum is

[tex]Mo = mv[/tex]

, where m is the mass and v its speed.

The person + the book are at rest which means their momentum is  

[tex]Mo_0=0[/tex]

After the book is released, they both start to move and their combined momentum is

[tex]Mo_f=m_pv_p+m_bv_b[/tex]

Where [tex]m_p, v_p[/tex] are the mass and speed of the person respectively and [tex]m_b, v_b[/tex] are the mass and speed of the book

Knowing that

[tex]m_p=74.9 Kg, m_b=2.44 Kg, v_b=-8.25m/s[/tex] (positive speed is assumed to the right or East), and the total momentum is zero:

[tex]m_pv_p+m_bv_b=0[/tex] =>

[tex]v_p=-\frac{m_bv_b}{m_p} =-\frac{2.44 (-8.25)}{74.9}[/tex]

[tex]v_p=0.269 m/s[/tex]

Since the sign of [tex]v_p[/tex] is positive, it's directed to the East

The recoil velocity of the person after throwing the book is approximately 0.27 m/s to the east, which is the opposite direction of the thrown book.

The recoil velocity of a person after throwing an object can be found by using the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum afterwards, assuming no external forces act on the system. In this case, the person and the book together form a closed system with no external forces since they are on an icy pond, which we can consider frictionless.

The initial momentum of the system is zero because the person is at rest. After the person throws the book, the momentum of the book is mass of the book multiplied by velocity of the book. To find the recoil velocity of the person, we use the formula:

m1×u1 + m2×u2 = m1×v1 + m2×v2,

where m1 and m2 are the masses of the person and book, u1 and u2 are their initial velocities (which are zero), and v1 and v2 are their final velocities. The final velocity of the person (v1) is what we are looking for:

(74.9 kg)(0 m/s) + (2.44 kg)(0 m/s) = (74.9 kg)v1 + (2.44 kg)(-8.25 m/s),

v1 = -(2.44 kg)(-8.25 m/s) / 74.9 kg,

v1 = 0.27 m/s to the east (opposite direction to the book).

Answer:

The bigger the atom the lesser the ability of the atom to hold on to its valence electrons.

Explanation:

Atomic radius can be looked at as the distance between the nucleus and the outermost energy level. As an atom gets bigger, the outer shell gets further and further from the positive nucleus. this means that electrons that are in the outer energy level become less held (attracted) by the nucleus because of distance and shielding of the attractive forces by the electrons in the lower energy levels. This means that as an atom becomes bigger, its ability to hold on to its outer electrons lessens.

As an atom gets larger, it is unable to hold its valence electrons due to decreased electrostatic attraction between the nucleus and the valence electron.

An atom is composed of a nucleus that houses positive charges and an electron which is negatively charged and are found in orbits. Electrostatic attraction between the positively charged nucleus and electrons in orbits keep the atom together.

However, as an atom gets larger, the valence electrons are farther away from the nucleus. As the distance between the nucleus and the outermost electrons increases, the electrostatic interaction between electron and the nucleus is decreased according to Coulomb's law. Repulsion (screening) between inner and valence electrons further keep the valence electrons away from the attractive forces of the nucleus.

Therefore, as an atom gets larger, it is unable to hold its valence electrons due to decreased electrostatic attraction between the nucleus and the valence electrons.

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Answer:

[tex]p2=0.667\\p1=0.167\\p3=0.167\\p=1[/tex]

Explanation:

Let's start writing the sample space for this exercise :

Let be ''M'' an abbreviation for Macrostate

Ω = { M1 , M2 , M3 }

Let be P(M1) the probability of Macrostate 1.

Reading the exercise, we know that ⇒

[tex]P(M1)=P(M3)[/tex]

Let's note this probability as ''p''.

[tex]P(M1)=P(M3)=p[/tex]

Macrostate 2 is four times more likely to occur than either of the other two macrostates ⇒

[tex]P(M2)=4p[/tex]

The sum of all probabilities must be equal to 1 for this sample space.Therefore,

[tex]p+p+4p=1[/tex]

[tex]6p=1[/tex]

[tex]p=\frac{1}{6}[/tex]

Finally :

[tex]P(M1)=\frac{1}{6}[/tex]

[tex]P(M2)=\frac{4}{6}[/tex]

[tex]P(M3)=\frac{1}{6}[/tex]

For Part A :

[tex]p2=\frac{4}{6}=0.667[/tex]

For Part B and C :

[tex]p1=p3=0.167[/tex]

For Part D :

The sum of the probabilities for all macrostates is equal to 1 :

[tex]p=p1+p2+p3=\frac{1}{6}+\frac{4}{6}+\frac{1}{6}=\frac{6}{6}=1[/tex]

Final answer:

The probability that equilibrium state 2 occurs is approximately 0.667. The probability that macro state 1 or macro state 3 occurs is each approximately 0.167. The sum of the probabilities for all macro states is exactly 1, as expected for a complete set of possible outcomes.

Explanation:

To find the probability of each macro state, we first recognize that the probabilities must sum to 1 for all macro states. Given that the equilibrium state, Macro state 2, is four times more likely than either of the other two Macro states 1 and 3, we can assign a probability 'p' to Macro states 1 and 3 and '4p' to Macro state 2.

Let's assume:

Probability of Macro state 1, p1 = p

Probability of Macro state 2, p2 = 4p

Probability of Macro state 3, p3 = p

Since the total probability must equal 1, we write the equation:

p1 + p2 + p3 = 1

Substituting the assumed probabilities gives:

p + 4p + p = 1

6p = 1

Therefore, p = 1/6

Now, we can calculate each probability:

p1 = 1/6 ≈ 0.167

p2 = 4/6 ≈ 0.667

p3 = 1/6 ≈ 0.167

The sum of all probabilities, p, is as expected:

p = p1 + p2 + p3 = 0.167 + 0.667 + 0.167 = 1

Answer:

-83

Explanation:

Answer:

(A.) Resonance Frequency

(B.) Totally resistance

Explanation:

A. The resonance frequency is the frequency at which the net reactance of the inductor and capacitor is zero, this is the frequency at which the capacitive reactance of the capacitor and inductive reactance of the inductor cancels each other out. Resistance is low here and the frequency is high

B. Since the net reactance of the inductor and capacitor is zero as explained in (A) above, the total reactance of the circuit will be entirely from the resistor (resistance)

Answer:

s = 3.68 m

Explanation:

given,

mass of the car = 6 x 10³ Kg

angle of slope with horizontal = 19.3°

Average frictional force = 4.4×10³ N

Speed of the car at the bottom = 4.3 m/s

acceleration due to gravity = 9.81 m/s²

length of driveway = ?

first calculating the net force acting on the car

F = mg sin θ - f

(mg sin θ) is the weight component of the body

(f) is the frictional force which is acting opposite to the car

F = 6000 x 9.81 x  sin 19.3° - 4400

F = 19454 - 4400

F = 15054 N

we know,

Force = mass  x  acceleration

15054 =  6000 x a

a = 2.51 m/s²

using formula

v² = u² + 2 as

4.3² = 0² + 2 x 2.51 x s

s = 3.68 m

the length of the driveway = s = 3.68 m

Final answer:

To find the length of the driveway, we can use the equations of motion. Calculate the acceleration using trigonometry, find the net force, and use the equation v^2 = u^2 + 2as to determine the distance.

Explanation:

To find the length of the driveway, we can use the equations of motion. The acceleration of the car can be found by considering the forces acting on it. The force of gravity can be resolved into two components: one along the slope and one perpendicular to the slope. The force along the slope, which is responsible for the acceleration of the car, can be found using trigonometry. The net force acting on the car is the force along the slope minus the frictional force. We can then use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled, to find the length of the driveway.

Let's break the problem down step by step:

Substituting the given values into the equations will give you the length of the driveway.

Final answer:

The fifth line of the Balmer series, with a wavelength of 397 nm, occurs in the ultraviolet region of the electromagnetic spectrum. Option D is correct.

Explanation:

The fifth line of the Balmer series with a wavelength of 397 nm falls into the ultraviolet (UV) region of the electromagnetic spectrum. The visible part of the spectrum ranges approximately from 380 nm to 740 nm. Since the wavelength of the fifth line is just below 400 nm, it is just outside the range for visible light and therefore must be in the ultraviolet range.

In the context of the Balmer series, there are four lines within the visible spectrum, specifically at wavelengths of 656 nm, 486 nm, 434 nm, and 410 nm. The line at 397 nm would be the first one in the UV part of the spectrum, making the answer to the student's question d) ultraviolet.

The Balmer series is a series of spectral lines in the hydrogen emission spectrum. Four of the wavelengths of the Balmer series occur in the visible spectrum: 656 nm, 486 nm, 434 nm, and 410 nm. Since the fifth line has a wavelength of 397 nm, it falls in the ultraviolet region of the electromagnetic spectrum.

Answer:

Check explanation.

Explanation:

From the question, we know that The person exerted 190N, force on the flexor is unknown. Since, we don't have access to our diagram, we have to make one or two assumption; (1) that ba= 0.3 m, ac= 0.05.

Therefore, the horizontal force that his flexor muscle exerts on his forearm,F(flexor) = (190N) × (0.3m) / 0.05m.

The horizontal force that his flexor muscle exerts on his forearm,F(flexor) = 57 Nm/ 0.05 m.

The horizontal force that his flexor muscle exerts on his forearm,F(flexor) = 1140N.

Using principles of physics, specifically equilibrium, we know the force exerted by muscles can be greater than the load they support, especially when the load is distant from the joint. In the case of a 190 N horizontal force, the exact force of the flexor muscle can't be calculated without more information, but it's likely larger than 190 N.

To answer the student's question, we must refer to concepts in physics, specifically the principle of equilibrium and the analysis of free-body diagrams. Given that the student is trying to find the force that a person's flexor muscle exerts horizontally when the person exerts a horizontal force of 190 N.

As mentioned in the provided information, forces and tensions in muscles and joints can be quite substantial. In this scenario, the flexor muscle in the forearm is acting against the applied force to maintain balance or equilibrium. This can be seen in the free-body diagram where forces are broken down into their x- and y-components.

It's important to note that the force exerted by muscles can be far greater than the load they support, especially when the load is a considerable distance from the joint, as stated in the provided text snippet. This may be relevant when analyzing the muscle force in this scenario.

Unfortunately, without more specific details about the angles involved and the exact configuration of the arm and forearm in the test apparatus, we can't calculate the exact force exerted by the flexor muscle. However, we can say that it's likely to be substantially larger than the 190 N applied force, considering the principles discussed above.

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Answer:

option (d)

Explanation:

The extra solar planet is also called as exo planet.

the planet which orbits around the star other than sun is called exo planet.

So, a planet that orbits a star that is not our own sun.

Thus, option (d) is correct.