A one-dimensional particle-in-a-box may be used to illustrate the import kinetic energy quantization in covalent bond formation. For example, the electronic energy change associated with the reaction H+H H2 may be modeled by treating each reactant H atom as an electron in a one-dimensional box of length LH 5a0 (the 99% electron density diameter of hydrogen), and treating he diatomic H2 as a one-dimensional box of length LH2 RB+5ao (where ao is the Bohr radius of hydrogen and Re 0.74 Å is the experimental bond length of H2). (a) Use the above particle-in-a-box model to model ance of predict the bond formation energy of H2, and compare your result with the experi- mental value of -436 kJ/mol. (b) What interactions have been neglected in the above calculation and what does your result imply with regard to the importance of kinetic energy quantization in covalent bond formation?

Answer:

q₁  = -2.92 nC

Explanation:

Given;

first point charge, q₁ = ?

second point charge, q₂ = 10 nC

net flux through the surface of the sphere, Φ =  800 N.m²/C

According to Gauss’s law, the flux through any closed surface (Gaussian surface), is equal to the net charge enclosed divided by the permittivity of free space.

[tex]\phi = \frac{q_{enc.}}{\epsilon_o}[/tex]

where;

Φ is net flux

[tex]q_{enc.}[/tex] net charge enclosed

ε₀ is permittivity of free space.

[tex]q_{enc.}[/tex] = Φε₀

       = 800 x 8.85 x 10⁻¹²

       = 7.08 x 10⁻⁹ C

[tex]q_{enc.}[/tex] = 7.08 nC

q₁ + q₂ = [tex]q_{enc.}[/tex]

q₁ = [tex]q_{enc.}[/tex] - q₂

q₁  = 7.08nC -  10 nC

q₁  = -2.92 nC

Answer:

3.83*10^7 m

Explanation:

Assume that the distance at which gravitational force due to both Earth and moon is zero and it l is given by force force balance

F(moon) = F(earth)

F(moon) = GM(moon) / r²

F(earth) = GM(earth) / (d - r)²

If F(moon) = F(earth), then

GM(moon) / r² = GM(earth) / (d - r)²

7.35*10^22 / r² = 5.97*10^24 / (3.84*10^8 - r)²

now, we take the square root of both sides, we have

2.71*10^11 / r² = 24.4*10^11 / (3.84*10^8 - r) =>

2.71 / r² = 24.4 / (3.84*10^8 - r)

if we cross multiply, we have

24.4r = 1.04064*10^9 - 2.71r

24.4r + 2.71r = 1.04064*10^9

27.11r = 1.04064*10^9

r = 1.04064*10^9 / 27.11

r = 3.83*10^7 m

Answer:

Explanation:

The solution to the problem is given in the pictures attached below; the three pictures explains the problem fully and I hope it helps you. Thank you

Answer:

i need some explanation

Explanation:

The correct statements are D, C, and E. Blood flows from the heart to the lungs to pick up oxygen and then to the rest of the body to deliver oxygen, sugar, and nutrients while collecting carbon dioxide.

Understanding the flow of blood in the body is essential. Here are the correct statements regarding blood circulation:

The heart pumps oxygen-poor blood to the lungs through the pulmonary circuit where it releases carbon dioxide and picks up oxygen.

The oxygen-rich blood is then pumped through the systemic circuit to the rest of the body, delivering oxygen, sugar, and nutrients to the cells and collecting carbon dioxide to be expelled during the next circulation.

Therefore, the correct statements are D, C, and E.

Complete Question

Which statements are true about the flow of blood in the body? Check all that apply.

A. Blood picks up oxygen from the cells of the body.

B. Blood delivers carbon dioxide to cells in the body.

C. Blood picks up carbon dioxide from the cells of the body.

D. Blood flows from the heart to the lungs to pick up oxygen.

E. Blood delivers sugar and nutrients to cells in the body.

F. Blood flows from the lungs to the heart to pick up oxygen.

Answer:

28 grams

Explanation:

The equation for the reaction is

3H(2) + N(2) -> 2NH(3)

Then we have.

The molar mass, M of ammonia is 17 g/mol.

34 grams of ammonia, NH3 then would be

34 g / 17 g/mol

= 2 moles

2 moles of ammonia will be obtained from

(2 * 1) / 2

​= 1 mole of nitrogen

The molar masses of nitrogen is 28 g/mol

2 moles of nitrogen corresponds to 1 * 28 = 28 grams.

Answer:

fR = f(c + v)/c

Explanation:

The speed of a wave is its frequency x wavelenght. Therefore,

Frequency is speed of wave over the wavelength.

Since the source (ultrasound machine) is stationary, and the receiver red blood cell is moving towards it. The wavelenght of the wave sent out towards the observer is c/f

The speed of the reflected sound wave is (c + v), so that the reflected frequency fR is given by

fR = f(c + v)/c

The measured reflected frequency (  fR) in Doppler-shifted ultrasound, when blood cells move towards the source, is calculated using the formula  fR = f * (c + v) / c, where f is the original frequency, c is the speed of sound in blood, and v is the velocity of blood cells.

The question relates to the principle of the Doppler effect and its application in calculating the velocity of blood flow using Doppler-shifted ultrasound. The Doppler effect occurs when a wave source and an observer are in relative motion, resulting in a change in the observed frequency. Specifically, when the blood cells move towards the ultrasound source, the frequency of the reflected ultrasound increases. This change in frequency can be measured for diagnostic purposes.

To find the measured reflected frequency fR when blood cells are moving towards the source, you can use the formula:

fR = f * (c + v) / c

Where,

f = original frequency of the ultrasound

c = speed of sound in blood (or human tissue)

v = velocity of blood cells relative to the ultrasound source

Answer:

The magnetic field required required for the beam not to be deflected  is [tex]B = 0.0036T[/tex]

Explanation:

From the question we are told that

    The charge on the particle is [tex]q = +2e[/tex]

    The mass of the particle is  [tex]m = 6.64 *10^{-27} kg[/tex]

    The potential difference is [tex]V_a = 1.8 kV = 1.8 *10^{3} V[/tex]

    The potential difference between the two parallel plate is  [tex]V_b = 120 V[/tex]

    The separation between the plate is  [tex]d = 8 mm = \frac{8}{1000} = 8*10^{-3}m[/tex]

The Kinetic energy experienced by the beam before entering the region of the parallel plate is equivalent to the potential energy of the beam  after the region having a potential difference of 1.8kV

               [tex]KE_b = PE_b[/tex]

Generelly

              [tex]KE_b = \frac{1}{2} m v^2[/tex]

And      [tex]PE_b = q V_a[/tex]

 Equating this two formulas

              [tex]\frac{1}{2} mv^2 = q V_a[/tex]

making v the subject

           [tex]v = \sqrt{\frac{q V_a}{2 m} }[/tex]

Substituting value  

           [tex]v = \sqrt{\frac{ 2* 1.602 *10^{-19} * 1.8 *10^{3}}{2 * 6.64 *10^{-27}} }[/tex]

           [tex]v = 41.65*10^4 m/s[/tex]

Generally the electric field between the plates is mathematically represented as

                 [tex]E = \frac{V_b}{d}[/tex]  

Substituting value  

                 [tex]E = \frac{120}{8*10^{-3}}[/tex]              

                [tex]E = 15 *10^3 NC^{-1}[/tex]

the magnetic field  is mathematically evaluate    

                     [tex]B = \frac{E}{v}[/tex]

                   [tex]B = \frac{15 *10^{3}}{41.65 *10^4}[/tex]

                    [tex]B = 0.0036T[/tex]

Answer:

1.3*10^14 J

Explanation:

The energy of the satellite that orbits the earth is given by the second Newton law:

[tex]F=ma_c\\\\-G\frac{mM_s}{r^2}=m\frac{v^2}{r}\\\\v^2=\frac{GM}{r}\\\\E_T=K+U=G\frac{mM_s}{2r}-G\frac{mM}{r}=-G\frac{mM}{2r}[/tex]

where you have taken into account the centripetal acceleration of the satellite.

m: mass of the satellite

M_s: mass of the sun = 1.98*10^30 kg

G: Cavendish's constant = 6.67*10^-11 m^3/kg s^2

r: distance to the center of the Earth = Earth radius + distance satellite-Earth surface

To find the needed energy, you first compute the energy for a constant altitude of 99km:

r = 6.371*10^6m + 99*10^3m = 6.47*10^6 m

[tex]E_T=-(6.67*10^-11 m^3 /kg.s^2)\frac{(969kg)(1.98*10^{30}kg)}{2(6.47*10^6)}\\\\E_T=-9.88*10^{15} \ J[/tex]

Next, you calculate the energy for an altitude of 195km:

r = 6.371*10^6m + 195*10^{3}m = 6.56*10^6 m

[tex]E_T=-(6.67*10^-11 m^3 /kg.s^2)\frac{(969kg)(1.98*10^{30}kg)}{2(6.56*10^6)}\\\\E_T=-9.75*10^{15} \ J[/tex]

Finally, the energy required to put the satellite in the new orbit is:

-9.75*10^15 J - (-9.88*10^15 J) = 1.3*10^14 J

Answer:

Magnetic field is in south west direction .

Explanation:

Let us represent various direction by  i , j, k . i representing east , j representing north and k representing vertically upward direction .

magnetic field is represented vectorially as follows

B = B₀ ( - i - j )

In the first case velocity of electron

v = v k

Force = q ( v x B )

= -e [ vk x B₀ ( - i - j ) ]

= evB₀ ( j -i )

Direction of force is north -west .

In the second case velocity of electron

v = vj

Force = -e [ vj x B₀ ( - i - j ) ]

= - evB₀ k

force is downward

In the third case, velocity of electron

v = v( -j +i )

Force = -e [ v( -j +i ) x B₀ ( - i - j ) ]

= 2 evB₀ k

Force is upward.

Find the given attachment for solution

The electric flux trough x = 0 plane is = - EL² and the electric flux trough x = l plane is = EL².

Although an electric field cannot flow by itself, electric flux in electromagnetism is a measure of the electric field passing through a specific surface.

An electric field surrounds an electric charge, such as a solitary electron in space. Field lines have no physical significance and are merely a graphic representation of field strength and direction.

The number of "lines" per unit area, also known as the electric flux density, is inversely proportional to the electric field strength. The total number of electric field lines passing through a surface determines the amount of electric flux.

Hence, electric flux trough x = 0 plane is = - EL² and the electric flux trough x = l plane is = EL².

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Answer:

The question above is repeated twice.

Removing the repetition, we have:  A plane flies toward a stationary siren at 1/4 the speed of sound. Then the plane stands still on the ground and the siren is driven toward it at 1/4 the speed of sound. In both cases, a person sitting in the plane will hear the same frequency of sound from the siren. True or False?

The correct answer to the question is "False"

Explanation:

The question above, illustrates a phenomenon referred to as "Doppler effect"

The Doppler effect only changes the frequency of the sound which explains how wavelength changes when a wave source is moving toward or away from an object. The Doppler effect occurs when a source of waves and/or observer move relative to each other.

When a sound source is moving toward the observer (a person sitting in the plane) in the case above,  the observer will hear a higher pitch as the source approaches. That is, the plane stands still on the ground and the siren is driven toward it.This is due to a decrease in the amplitude of the sound wave.

However, If the observer moves toward the stationary source, the observed frequency is higher than the source frequency. In this case, A plane flies toward a stationary siren.

λ = v/f = vT,

where T is the period,

The relationship  between frequency, speed, and wavelength is:

f = v/λ

v represents the speed of sound through the medium.

Doppler effect depends on things moving, as the observer moves, the frequency becomes higher as the distance decreases. If the observer moves and the distance becomes larger, it means that the sound frequency becomes lower.

Final answer:

The Doppler effect explains why a person sitting in a plane moving toward or away from a stationary siren at 1/4 the speed of sound perceives the same frequency of sound. This phenomenon is true due to the relative motion between the source of sound and the observer.

Explanation:

True

The phenomenon described in the question is related to the Doppler effect in physics. When a source of sound and an observer are in motion relative to each other, the frequency of the sound waves changes due to this motion. In this case, when the plane is moving toward or away from the siren at 1/4 the speed of sound, the observer perceives the same frequency of sound from the siren.

Answer:

Find the given attachments for complete solution

Answer:

10n to the right

Explanation:

Answer:

When they are approaching each other

    [tex]f_a = 2228.7 \ Hz[/tex]

When they are passing  each other

    [tex]f_a = 2100Hz[/tex]

 When they are retreating  from each other

     [tex]f_a = 1980.7 Hz[/tex]

Explanation:

From the question we are told that

     The velocity of car one is  [tex]v_1 = 13.0 m/s[/tex]

      The velocity of car two is  [tex]v_2 = 7.22 m/s[/tex]

     The frequency of sound from car one is  [tex]f_e = 2.10 kHz[/tex]

Generally the speed of sound at normal temperature is  [tex]v = 343 m/s[/tex]

  Now as the cars move relative to each other doppler effect is created and this  can be represented  mathematically  as

              [tex]f_a = f_o [\frac{v \pm v_o}{v \pm v_s} ][/tex]

Where [tex]v_s[/tex] is the velocity of the source of sound

            [tex]v_o[/tex] is the velocity of the observer of the sound

            [tex]f_o[/tex] is the actual frequence

             [tex]f_a[/tex]  is the apparent frequency

Considering the case when they are approaching each other

        [tex]f_a = f_o [\frac{v + v_o}{v - v_s} ][/tex]

          [tex]v_o = v_2[/tex]  

         [tex]v_s = v_1[/tex]

         [tex]f_o = f_e[/tex]

Substituting value

            [tex]f_a = 2100 [\frac{343 + 7.22}{ 343 - 13} ][/tex]

              [tex]f_a = 2228.7 \ Hz[/tex]

Considering the case when they are passing  each other    

At that instant

                  [tex]v_o = v_s = 0m/s[/tex]

                   [tex]f_o = f_e[/tex]

               [tex]f_a = f_o [\frac{v }{v } ][/tex]

              [tex]f_a = f_o[/tex]

Substituting value

             [tex]f_a = 2100Hz[/tex]

Considering the case when they are retreating  from each other    

                [tex]f_a = f_o [\frac{v - v_o}{v + v_s} ][/tex]

          [tex]v_o = v_2[/tex]  

         [tex]v_s = v_1[/tex]

         [tex]f_o = f_e[/tex]      

Substituting value

         [tex]f_a = 2100 [\frac{343 - 7.22}{343 + 13} ][/tex]    

          [tex]f_a = 1980.7 Hz[/tex]    

Answer:

f = 687.85 Hz

Explanation:

Given that,

The wavelength of sound wave, [tex]\lambda=0.75\ m[/tex]

We need to find the frequency of the sound wave. The relation between wavelength and frequency is given by :

[tex]v=f\lambda[/tex]

v is speed of sound at T = 35°C = 308.15 K

[tex]v=331+0.6T\\\\v=331+0.6\times 308.15 \\\\v=515.89\ m/s[/tex]

So,

[tex]f=\dfrac{v}{\lambda}\\\\f=\dfrac{515.89}{0.75}\\\\f=687.85\ Hz[/tex]

So, the frequency of the sound is 687.85 Hz.

Final answer:

To calculate the frequency of a sound wave, use the formula frequency = speed of sound / wavelength. For this specific scenario, the frequency of the sound wave is 3400 Hz.

Explanation:

The frequency of the sound wave can be calculated using the formula:

frequency = speed of sound / wavelength

Given that the speed of sound in air is 340 m/s and the wavelength is 0.10 m, we can plug in the values to find the frequency:

frequency = 340 m/s / 0.10 m = 3400 Hz

Therefore, the frequency of the sound wave is 3400 Hz.

Answer:

26.64°

Explanation:

Given:

a = 16.3 cm

b = 32.5 cm

Angle when laser beam reflects off the mirror and strike the wall =

θ [tex] = tan^-^1(\frac{b}{a}) [/tex]

[tex] = tan^-^1(\frac{32.5}{16.3}) [/tex]

= 63. 36°

For angle of reflection, we have:

θr = 90° - 63.36°

θr = 26.64°

Since angle of incidence, θi is equal to angle of reflection θr, the angle of incidence θi at which the laser beam strikes the mirror is =

θi = θr = 26.64°

Answer:

true

Explanation:

Answer:true

Explanation:

Acceleration is measured in meters per second squared

Answer:

c. electric attraction is a force that can act at a distance.

Explanation:

stuisland

Final answer:

A negatively charged balloon attracting positively charged hair strands without contact illustrates that c. electric attraction can act at a distance.

Explanation:

When Katie rubs the balloon against her hair, electrons move from her hair to the balloon, resulting in the balloon having a negative charge and her hair having a positive charge. If the negatively charged balloon is brought near Katie's hair and the hair strands move toward it without direct contact, this demonstrates electric attraction as a force that can act at a distance.

Therefore, electric attraction is a force that can act at a distance. This example, similar to the effect observed when someone touches a Van de Graaff generator, shows charge separation and induction. It validates the scientific concept that electric forces can operate between charged objects even when they are not in physical contact.

Answer:

239.55 KJ

Explanation:

Given:

Mass 'm' = 106 g

Latent heat of vaporization'L'= 2260 J/g.

Molecular weight of water'M' = 18 g/mol

Pressure 'P' = 101325 Pa

Temperature 'T' = 373.15 K

Using the formula of phase change, in order to determine the amount of heat required, we have

Q = mL

Q = 106 x 2260

Q = 239560J = 239.55 KJ

Answer:

the maximum velocity of the mass v (max) = 2 ft/s

the amount of time it takes for the mass to move from its lowest position to its highest position∆t = 1/3 seconds = 0.33 seconds

Explanation:

Given the velocity equation;

v=−2 cos(3πt)

The maximum velocity would be at cos(3πt) = 1 or cos(3πt) = -1

v (max) = -2 × -1 = 2 ft/s

The time taken for the mass to move from lowest position to highest position

At Lowest position, vertical velocity equals zero.

At highest position, vertical velocity equals zero.

The time taken for the mass to move from one v = 0 to the next v = 0

Cos(π/2) = 0 and

Cos(3π/2) = 0

For the first;

Cos(3πt) = cos(π/2)

3πt1 = π/2

t1 = π/2(3π)

t1 = 1/6 second

For the second;

Cos(3πt) = cos(3π/2)

3πt2 = 3π/2

t2 = 3π/2(3π)

t2 = 1/2 second

∆t = t2 - t1 = 1/2 - 1/6 = 3/6 - 1/6 = 2/6 = 1/3 seconds

∆t = 1/3 seconds

Answer:

C

Explanation:

i took the test

A small, positively charged ball is moved close to a large, positively charged ball. "It will move away from the large ball because like charges repel." The correct option is A.

Charge Interaction: The behavior of charged objects is governed by the fundamental principle that opposite charges attract each other, and like charges repel each other.

Coulomb's Law: Coulomb's Law describes the electrostatic force between two charged objects. It states that the force of attraction or repulsion between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Repulsion: Because both the small and large balls have a positive charge, they will exert a repulsive force on each other when they are in close proximity.

Movement Away: When the small ball is released near the large ball, it will experience this repulsive force, causing it to move away from the large ball.

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Answer:

t = 10 minutes

Emma’s scarf will be longer than tish scarf after 10 minutes

Explanation:

Given;

The length of tish scarf after t minutes can be written as;

L1 = 17.75 + 2 3/8 ×t

L1 = 17.75 + 2.375t

The length of emma scarf after t minutes can be written as;

L2 = 4 + 3 3/4 × t

L2 = 4 + 3.75t

For emma scarf to be longer than tish;

L2 >/= L1

At L2 = L1

4+3.75t = 17.75 + 2.375t

Solving for t

3.75t - 2.375t = 17.75 - 4

1.375t = 13.75

t = 13.75/1.375

t = 10 minutes

Emma’s scarf will be longer than tish scarf after 10 minutes

Answer:

8 minutes sooner

Explanation:

Average speed of snail= 4cm/min

Distance to be covered = 160cm

Time taken for the journey = distance/speed

Time taken for the journey = 160/4

Time taken for the journey = 40 min

If it crawed an average speed of 5cm/min

Distance = 160 cm

Time for the journey = distance/speed

Time for the journey = 160/5

Time for the journey = 32 min

Its going to take the snail 40 min - 32 min to Kno how sooner it will taje it if the average speed is 5cm/min

40 min - 32 min = 8 min

Answer:

741 J/kg°C

Explanation:

Given that

Initial temperature of glass, T(g) = 72° C

Specific heat capacity of glass, c(g) = 840 J/kg°C

Temperature of liquid, T(l)= 40° C

Final temperature, T(2) = 57° C

Specific heat capacity of the liquid, c(l) = ?

Using the relation

Heat gained by the liquid = Heat lost by the glass

m(l).C(l).ΔT(l) = m(g).C(g).ΔT(g)

Since their mass are the same, then

C(l)ΔT(l) = C(g)ΔT(g)

C(l) = C(g)ΔT(g) / ΔT(l)

C(l) = 840 * (72 - 57) / (57 - 40)

C(l) = 12600 / 17

C(l) = 741 J/kg°C

A) the item required for the experiment is a stopwatch.

B) You are looking for time savings. To get this, divide the time by 10. The result is the period. The formula is given as

F  =  [tex]\frac{1}{T}[/tex] Where F is the frequency i.e. the number of cycles per second and T is the number of seconds per cycle.

C) One parameter of the pendulum that can be altered in order to affect the frequency of the pendulum is its length.  A pendulum with a longer string will have a lower frequency.

The one with a shorter length will have a higher frequency

D) In an environment that is thermally insulated perfectly, it means that any heat generated within the room is trapped within it. As the pendulum comes to rest, the room will experience a slight increase in temperature due to the conversion of mechanical energy to thermal energy.

Understanding the physics of pendulums helps one to get a better grasp of gravity, inertia, and centripetal force.

Pendulums are used for the construction or engineering of clocks, metronomes, sismometers, amusement park rides.

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The simple pendulum above consists of a bob hanging from a light string the experiments is :

A. Stopwatch

B. You are looking for time savings. To get this, divide the time by 10.

C. The one parameter of the pendulum that can be modified in arrange to influence the recurrence of the pendulum is its length.

D. In an environment that's thermally protects superbly

Answer A:

Answer B:

The experimental procedure that you would use is :

Where :

Answer C:

Answer D:

Uses of the pendulum experiments :

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Answer:1960j

Explanation:

total input energy=2000j

98% of total input energy is useful

98% of 2000

98/100 x 2000

(98 x 2000) ➗ 100

196000 ➗ 100=1960

1960j is useful

The amount of useful transferred energy is  1960 J.

A body's capacity for work is measured in terms of energy. It cannot be produced or eliminated. There are numerous types of energy, including thermal, electrical, fusion, electrical, and nuclear. Energy has the ability to change its forms.

Efficiency is essentially a measurement of the amount of labour or energy that can be saved throughout a process. In other words, it's similar to comparing the energy input and output in any particular system. For instance, we observe that many processes result in the loss of effort or energy like vibration or waste heat.

Given parameters:

Total input energy; I =2000 Joule.

efficiency of the kettle; η = 98%.

We have to find useful output energy of the kettle: O = ?

We know that: output energy = efficiency × input energy

= 98% ×  2000 J.

 = 98/100 x 2000 J.

= (98 x 2000) ÷ 100 J.

= 196000 ÷ 100 J

= 1960 J.

Hence, the useful transferred energy is  1960 J.

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Ball 1 floats with half exposed above water level. Tension on rope holding Ball 2 is calculated using weight and buoyant force. Tension on rope holding Ball 3 is equal to buoyant force.

A. Ball 1 is floating with half of it exposed above the water level.

This means that the buoyant force on the ball is equal to the weight of the ball.

Since the buoyant force is greater than the weight of the ball, the ball floats.

B. The tension on the rope holding Ball 2 can be found using the equation:

Tension = Weight - Buoyant force.

The weight of the ball is calculated by multiplying its volume by its density and acceleration due to gravity.

The buoyant force can be found by multiplying the volume of the ball submerged in water by the density of water and acceleration due to gravity.

C. The tension on the rope holding Ball 3 is the same as the buoyant force acting on it.

The buoyant force can be found by multiplying the volume of the ball submerged in water by the density of water and acceleration due to gravity.

Ball 1's density is 500 kg/m³. The tension on the rope holding Ball 2 is 41.15 N. The tension on the rope holding Ball 3 is 121.24 N.

Let's solve this problem step-by-step to better understand floating and submerged objects in water.

A.) Which is true for Ball 1?

Ball 1 floats with half of it exposed above the water level. This means the density of Ball 1 must be half the density of water. Since the density of water is 1000 kg/m³, the density of Ball 1 is:

B.) What is the tension on the rope holding the second ball, in newtons?

Ball 2 has a density of 893 kg/m³ and is held below the surface of water. The buoyant force is equal to the weight of the volume of water displaced by Ball 2.

Calculate the volume of Ball 2: (Volume of a sphere = 4/3 π r³)

Calculate the buoyant force:

Calculate the weight of Ball 2:

Calculate the tension in the rope:

C.) What is the tension on the rope holding the third ball in N?

Ball 3 has a density of 1320 kg/m³ and is also fully submerged, suspended by a rope.

Calculate the weight of Ball 3:

Calculate the tension in the rope:

This example shows how to calculate buoyant forces and tensions for submerged and floating objects.

The unit vector forms of the given vectors is required.

The required vectors are [tex]A=-8.93\hat{i}+15.16\hat{j}[/tex] and [tex]B=-10.75\hat{i}-18.84\hat{j}[/tex]

Magnitude of vector A = [tex]|A|=17.6[/tex]

Angle vector A makes with positive x axis counter clockwise = [tex]\theta_1=120.5^{\circ}[/tex]

Magnitude of vector B = [tex]|B|=21.7[/tex]

Angle vector B makes with positive x axis counter clockwise = [tex]\theta_2=240.3^{\circ}[/tex]

The vectors need to be resolved in order to write in the unit vector forms.

The vectors are

[tex]A=|A|(\cos\theta_1\hat{i}+\sin\theta_1\hat{j})\\\Rightarrow A=17.6(\cos120.5\hat{i}+\sin120.5\hat{j})\\\Rightarrow A=-8.93\hat{i}+15.16\hat{j}[/tex]

[tex]B=|B|(\cos\theta_2\hat{i}+\sin\theta_2\hat{j})\\\Rightarrow B=21.7(\cos240.3\hat{i}+\sin240.3\hat{j})\\\Rightarrow B=-10.75\hat{i}-18.84\hat{j}[/tex]

Learn more about vectors:

https://brainly.com/question/25811261

Final answer:

To resolve the vectors into components, apply trigonometric functions -- cosine for x components and sine for y components -- to their magnitudes and angles, then express them in unit vector form with i and j.

Explanation:

When resolving vectors A and B into their components in the x-y plane, the general method involves using trigonometry, specifically, the cosine and sine functions for the x and y components, respectively. Given that vector A has a magnitude of 17.6 and an angle of 120.5° from the x-axis, its components can be calculated as follows:

Ax = A * cos(θ) = 17.6 * cos(120.5°)

Ay = A * sin(θ) = 17.6 * sin(120.5°)

Similarly, vector B with a magnitude of 21.7 and an angle of 240.3° from the x-axis has components:

Bx = B * cos(θ) = 21.7 * cos(240.3°)

By = B * sin(θ) = 21.7 * sin(240.3°)

The resulting components should then be written in unit vector form by attaching the unit vectors i (for the x-axis) and j (for the y-axis) to the respective components.

Correct question is;

To regulate the intensity of light reaching our retinas, our pupils1 change diameter anywhere from 2 mm in bright light to 8 mm in dim light. Find the angular resolution of the eye for 550 nm wavelength light at those extremes. In which light can you see more sharply, dim or bright?

Answer:

We'll see more sharply in dim light

Explanation:

If we consider diffraction through a circular aperture, then angular resolution is given by;

θ = 1.22λ/D

where:

θ is the angular resolution (radians) λ is the wavelength of light

D is the diameter of the lens' aperture.

Thus,

at diameter = 2mm = 2 x 10^(-3) m = 2 x 10^(6) nm

θ = (1.22 * 550)/(2 x 10^(6))

θ = 335.5 x 10^(-6) radians

Now, we need to convert this to arc seconds.

Thus;

1 arc second = 4.85 x 10^(-6) radians

So,θ = 335.5 x 10^(-6) radians = [335.5 x 10^(-6)]/[4.85 x 10^(-6)]

= 69.18 arc seconds

at diameter = 8mm = 8 x 10^(-3) m = 8 x 10^(6) nm

θ = (1.22 * 550)/(8 x 10^(6))

θ = 83.875 x 10^(-6) radians

Now, we need to convert this to arc seconds.

Thus;

1 arc second = 4.85 x 10^(-6) radians

So,θ = 83.875 x 10^(-6) radians = [83.875 x 10^(-6)]/[4.85 x 10^(-6)]

= 17.3 arc seconds

From the values of angular resolution gotten, we see that sharpness of image increases with increasing angular resolution. Thus, objects are sharper in dim light.

Answer:

Wavelength of the incident wave in air = 1 m

Wavelength of the incident wave in medium 2 = 0.33 m

Intrinsic impedance of media 1 = 377 ohms

Intrinsic impedance of media 2 = 125.68 ohms

Check the explanation section for a better understanding

Explanation:

a) Wavelength of the incident wave in air

The frequency of the electromagnetic wave in air, f = 300 MHz = 3 * 10⁸ Hz

Speed of light in air, c =  3 * 10⁸ Hz

Wavelength of the incident wave in air:

[tex]\lambda_{air} = \frac{c}{f} \\\lambda_{air} = \frac{3 * 10^{8} }{3 * 10^{8}} \\\lambda_{air} = 1 m[/tex]

Wavelength of the incident wave in medium 2

The refractive index of air in the lossless dielectric medium:

[tex]n = \sqrt{\epsilon_{r} } \\n = \sqrt{9 }\\n =3[/tex]

[tex]\lambda_{2} = \frac{c}{nf}\\\lambda_{2} = \frac{3 * 10^{6} }{3 * 3 * 10^{6}}\\\lambda_{2} = 1/3\\\lambda_{2} = 0.33 m[/tex]

b) Intrinsic impedances of media 1 and media 2

The intrinsic impedance of media 1 is given as:

[tex]n_1 = \sqrt{\frac{\mu_0}{\epsilon_{0} } }[/tex]

Permeability of free space, [tex]\mu_{0} = 4 \pi * 10^{-7} H/m[/tex]

Permittivity for air, [tex]\epsilon_{0} = 8.84 * 10^{-12} F/m[/tex]

[tex]n_1 = \sqrt{\frac{4\pi * 10^{-7} }{8.84 * 10^{-12} } }[/tex]

[tex]n_1 = 377 \Omega[/tex]

The intrinsic impedance of media 2 is given as:

[tex]n_2 = \sqrt{\frac{\mu_r \mu_0}{\epsilon_r \epsilon_{0} } }[/tex]

Permeability of free space, [tex]\mu_{0} = 4 \pi * 10^{-7} H/m[/tex]

Permittivity for air, [tex]\epsilon_{0} = 8.84 * 10^{-12} F/m[/tex]

ϵr = 9

[tex]n_2 = \sqrt{\frac{4\pi * 10^{-7} *1 }{8.84 * 10^{-12} *9 } }[/tex]

[tex]n_2 = 125.68 \Omega[/tex]

c) The reflection coefficient,r  and the transmission coefficient,t at the boundary.

Reflection coefficient, [tex]r = \frac{n - n_{0} }{n + n_{0} }[/tex]

You didn't put the refractive index at the boundary in the question, you can substitute it into the formula above to find it.

[tex]r = \frac{3 - n_{0} }{3 + n_{0} }[/tex]

Transmission coefficient at the boundary, t = r -1

d) The amplitude of the incident electric field is [tex]E_{0} = 10 V/m[/tex]

Maximum amplitudes in the total field is given by:

[tex]E = tE_{0}[/tex] and [tex]E = r E_{0}[/tex]

E = 10r, E = 10t