A bullet moving with an initial speed of vo strikes and embeds itself in a block of wood which is suspended by a string, causing the bullet and block to rise to a maximum height h. Which of the following statements is true of the collision? o The initial momentum of the bullet before the collision is equal to the momentum of the bullet and block at the instant they reach the maximum height h. the bullet immediately after the collision the potential energy of the bullet and block at the instant they reach the maximum O The initial momentum of the bullet before the collision is equal to the momentum of o The kinetic energy of the bullet and block immediately after the collision is equal to height h. energy of the bullet and block when they reach the maximum heighth energy of the bullet and block immediately after the colision O The initial kinetic energy of the bullet before the collision is equal to the potential o The initial kinetic energy of the bullet before the collision is equal to the kinetic

Answer:

 In a circuit with parallelresistors, the smaller resistance dominates; in a circuit with resistors inseries, the larger one dominates. Make some specific examples of resistorsin parallel and in series to explain this rule of thumb.

Explanation:

Lets start with Resistors in series:

Suppose a 12v battery is connected in a circuit with 3 resistors in series.

Voltage = 12 V

R1          = 1 ohm

R2         = 6 ohm

R3         = 13 ohm

Total resistance is simply sum of all resistors connected in series as following:

Rs   = R1 + R2 + R3

Rs   = 1 + 6 + 13

Rs   = 20 ohm

Here Rs = Total Resistance in series circuit

Now total current can be found by using ohm's law V = IR

I = V/R

Here R = R total

I = 12/20 = 0.6 Ampere

In series circuit current remains same.

so I1 = I2 = I3 = I

Now we can find Power dissipation across every resistor to show the dominant Resistor as:

P1 = I² R1 = (0.6 A)² ( 1 ohm) = 0.36 watt.          (a)

P2 = I² R2 = (0.6 A)² ( 6 ohm) = 2.16 watt.        (b)

P3 = I² R3 = (0.6 A)² ( 13 ohm) = 4.68 watt.      (c)

From equation a, b and c  we can conclude that more power is dissipated across R3 which is the Larger than both other resistors R1 and R2.

Now lets take the case of Parallel Circuit with same Values of Voltage and resistors But now in parallel.

In parallel circuit Total resistance is calculated as following:

1/Rp = 1/R1 + 1/R2 + 1/R3

1/Rp = 1/1 + 1/6 + 1/13 = 1 + 0.1667 + 0.0769

1/Rp = 1.2436

Rp   = 0.8041 ohm

Now total current is as following:

I = V/R

I = 12/0.8041 = 14.92 A

Now we calculate individual currents :

In parallel circuit Voltage remains same.

I1 = V/R1

I1 = 12/1 = 12 A

Similarly,

I2 = V/R2

I2 = 12/ 6 = 2 A

and

I3 = V/R3

I3 = 12/13 = 0.92 A

Now Power dissipation can be calculated as :

P1 = I1² * R1

P1 = 12² * 1 = 144 * 1

P1 = 144 Watt            (1)

Similarly,

P2 = I2² * R2

P2 = 2² * 6 = 4 * 6

P2 = 24 Watt            (2)

And

P3 = I3² * R3

P3 = (0.92)² * 13 = 0.8464 * 13

P3 = 11 Watt.              (3)

Now from Equation 1, 2 and 3 we can conclude that More power is dissipated across Lower resistor .

Hence in a circuit with parallel resistors, the smaller resistance dominates; in a circuit with resistors in series, the larger one dominates.

The speed of sound in air increases with temperature. By taking the difference between the given temperature and 0°C, then multiplying by the rate of speed increase per degree Celsius, you can find the speed of sound. This comes out to approximately 365.8 m/s at 58.0°C.

The speed of sound in air varies depending on the temperature of the air. In general, the speed of sound increases by approximately 0.6 m/s for each degree Celsius increase in temperature. Therefore, we need to find the difference between the given temperature (58.0°C) and 0°C, which is 58, and then multiply that by 0.6 to find the increase in speed due to temperature.

Step 1: Find the temperature difference = 58.0°C - 0°C = 58°C

Step 2: Multiply the temperature difference by the rate of speed increase, which is 0.6 m/s/°C. We get: (58°C) x (0.6 m/s/°C) = 34.8 m/s.

Step 3: To find the speed of sound at the higher temperature, add this increase to the speed of sound at 0°C, which is 331 m/s.

Step 4: So, the speed of sound in air at 58.0°C is 331 m/s + 34.8 m/s = 365.8 m/s (approximately).

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Answer:

+Q

Explanation:

As no electric field can exist (in electrostatic condition) inside a conductor, if we apply Gauss 'Law to a spherical gaussian surface with a radius just a bit larger than the distance of the inner surface to the center (but less tah the distance of the outer surface), the net flux through this surface must be zero, due to E=0 at any point of the gaussian surface.

Therefore, as the net flux must  be proportional to the  charge enclosed  by the surface, it follows that Qenc = 0.

⇒ Qenc = Qc + Qin = -2Q + Qin = 0 ⇒ Qin = +2Q

So, if the net charge of  the conductor is + 3Q (which must remain the same due to the conservation of charge principle) and no charge can exist within the conductor (in electrostatic conditions), we have the following equation:

Qnet = Qin + Qou = +3Q ⇒ +2Q + Qou = +3Q

⇒ Qou = +Q

Answer:

V = 6.23 cm³

Explanation:

given,

Length of the cylinder, h = 5 cm

Diameter of the cylinder, d = 1.26 cm

                                          r = 0.63 cm

Volume of the cylinder = ?

We know,

  [tex]V = \pi r^2 h[/tex]

  [tex]V = \pi \times 0.63^2\times 5[/tex]

        V = 6.23 cm³

Volume of the cylinder is equal to V = 6.23 cm³

The volume of a metal cylinder with a length of 5.0 cm and a diameter of 1.26 cm (-approximately 4.9 cm^3- when calculated using the formula: Volume = π * (d/2)^2 * h.

To calculate the volume of a cylinder, you use the formula: Volume = π * (d/2)^2 * h. Here, d represents the diameter of the cylinder, h represents the height, and π (pi) is a constant approximately equal to 3.14159. Plugging the values into the formula, we get:
Volume = π * (1.26 cm/2)^2 * 5.0 cm
After performing the above computations, the volume of the metal cylinder is approximately 4.9 cm^3 when rounded to two significant figures.

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Answer: °C = 4.44°C

Explanation: The centigrade scale and Fahrenheit scale are related by the formulae below

9 *°C = 5(°F - 32)

Where °C = measurement of temperature in centigrade scale.

°F = measurement of temperature in Fahrenheit scale =40°F

By substituting the parameters, we have that

9 * °C = 5 (40 - 32)

9* °C = 5(8)

9 * °C = 40

°C = 40/9

°C = 4.44°C

Temperature decreases by approximately 3.5°F for every 1000 feet increase in altitude. Given the altitude difference of 3130 feet from Boulder to Bear Peak and Boulder's temperature of 40°F, we can calculate that the temperature at Bear Peak is expected to be approximately 29°F.

The question asks for the temperature at a higher altitude given the temperature at a lower one. This involves understanding how temperature changes with altitude. It is stated that, on average, temperature decreases by about 3.5°F for every 1000 feet you climb in altitude, a phenomenon known as the lapse rate.

Given that, if the starting temperature in Boulder (altitude: 5330’) is 40F, and we need to find the temperature on Bear Peak (altitude: 8460’), we need to calculate the difference in altitude and the corresponding temperature decrease.

The altitude difference is 8460 - 5330 = 3130 feet. From this height difference, we can determine the corresponding temperature change by multiplying 3130 feet by 3.5°F per 1000 feet, yielding a temperature decrease of about 11°F.

To find the temperature at the higher altitude (Bear Peak), we then subtract this temperature change from the starting temperature. Thus,  40°F - 11°F gives 29°F as the expected temperature on Bear Peak.

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Answer:

It's true. Potential energy is actually the concentrations of different elements. Diffusion is the process of moving the elements or materials from the area of high concentration (high potential energy) to the low concentration. So in bot facilitated and simple types of diffusion the level of potential energy decreases across the membrane.

Explanation:

Answer:

Please see below as the answer is self - explanatory

Explanation:

a) 10³ = kilo (kilogram = 10³ grams, kilometer= 10³ meters)

Symbol : k.

b) 10⁻² = centi (it is the 100th part of a unit, like centimeter, or centigram) Symbol:  c.

c) .1 = deci (it is the tenth part (deci comes from the word that means "ten"in latin) of a unit: decimeter, decigram)

Symbol: d.

d) 10⁻3 = mili (it is a 1000th part of a unit: milimeter, miligram), the name comes from the word used in latin to mean "one thousand".

Symbol: m

e) 1,000,000 = 10⁶ = mega (megawatt)

Symbol: M

f= 0.000001 = 10⁻6 = micro (micrometer, microsecond),

Symbol: μ.

Answer:

Explanation:

Given

Wavelength of first timpani [tex]\lambda _1=2.2\ m[/tex]

Frequency corresponding to this Wavelength

[tex]f_1=\frac{v}{\lambda _1}[/tex]

where [tex]v=velocity\ of\ sound (343 m/s)[/tex]

[tex]f_1=\frac{343}{2.2}[/tex]

[tex]f_1=155.9\ Hz[/tex]

Wavelength of Second timpani [tex]\lambda _2=2.1\ m[/tex]

Frequency corresponding to this Wavelength

[tex]f_2=\frac{v}{\lambda _2}[/tex]

[tex]f_2=\frac{343}{2.1}=163.33\ Hz[/tex]

Beat frequency [tex]=f_2-f_1[/tex]

Beat frequency [tex]=163.33-155.9=7.43[/tex]

so approximately 7 beats per second

Final answer:

The beat frequency heard when two timpani are played together, with wavelengths of 2.20 m and 2.10 m and the speed of sound being 343 m/s, is 7.42 Hz.

Explanation:

When two timpani (tunable drums) are played at the same time with wavelengths of 2.20 m and 2.10 m, respectively, and the speed of sound is 343 m/s, we can calculate the frequencies of these sounds and subsequently determine the beat frequency heard.

The frequency of a wave is given by the formula f = v / λ (where f is the frequency, v is the speed of sound, and λ is the wavelength).

For the first timpani, the frequency is 343 m/s / 2.20 m = 155.91 Hz; for the second, it is 343 m/s / 2.10 m = 163.33 Hz.

The beat frequency, which is the absolute difference between these two frequencies, will be -

= 163.33 Hz - 155.91 Hz

= 7.42 Hz.

Final answer:

The charge enclosed by the cubical box with a total electric flux of 1840 N·m2/C is calculated using Gauss's law and is found to be 16.29 nC.

Explanation:

The question deals with the concept of electric flux and its relation to the enclosed charge using Gauss's law, which is a fundamental principle in electromagnetism. According to Gauss's law, the total electric flux through a closed surface is equal to the charge enclosed by the surface divided by the permittivity of free space (ε0).

The formula for Gauss's law in integral form is Φ = Q / ε0, where Φ is the electric flux, Q is the charge enclosed, and ε0 is the electric constant (approximately 8.854 x 10-12 C2/N·m2). Given that the total electric flux from a cubical box is 1840 N·m2/C, and using the value of ε0, the enclosed charge (Q) can be calculated.

To find the charge, we rearrange the equation as Q = Φ·ε0 and substitute the given values to get Q = 1840 N·m2/C × 8.854 x 10-12 C2/N·m2, resulting in Q = 1.629 x 10-8 C or 16.29 nC (nanocoulombs).

The charge enclosed by the cubical box,is approximately 1.63 × 10⁻⁸ C .

To determine the charge enclosed by a cubical box, we can use Gauss's Law. According to Gauss's Law, the electric flux (Φ) through a closed surface is given by:

Φ = Q / ε₀

where:

Rearranging this formula to solve for Q, we get:

Q = Φ × ε₀

Substitute the given values:

Q = 1840 N·m²/C × 8.854 × 10⁻¹² C²/N·m²

Q ≈ 1.63 × 10⁻⁸ C

Therefore, the charge enclosed by the cubical box is approximately 1.63 × 10⁻⁸ C.

To solve this problem it will be necessary to apply the interference principle. Under this principle interference is understood as a phenomenon in which two or more waves overlap to form a resulting wave of greater, lesser or equal amplitude. In this case, if both are at the same point, the result of the total displacement will be the sum of the individual displacements, therefore

[tex]x = \sum h_i[/tex]

[tex]x = 60cm + 80cm[/tex]

[tex]x =140cm[/tex]

Therefore the resulting displacement above equilibrium is 140cm

Final answer:

When two water waves meet at the same point, the resulting displacement above equilibrium can be calculated by adding the individual displacements together. In this case, the resulting displacement above equilibrium is 140 cm.

Explanation:

The resulting displacement above equilibrium when two water waves meet at the same point can be determined by adding the individual displacements together. In this case, one wave has a displacement above equilibrium of 60 cm and the other wave has a displacement above equilibrium of 80 cm. The resulting displacement is found by adding 60 cm and 80 cm, which gives a resulting displacement above equilibrium of 140 cm.

Answer:

unit (v) = [ -0.199 i - 0.8955 j + 0.39801 k ]

Explanation:

Given:

                            v =  (-23.2, -104.4, 46.4) m/s

Above expression describes spacecraft's velocity vector v.

Find:

Find unit vector in the direction of spacecraft velocity v.

Solution:

Step 1: Compute magnitude of velocity vector.

                            mag (v) = sqrt ( 23.2^2 + 104.4^2 + 46.4^2)

                            mag (v) = 116.58 m/s

Step 2: Compute unit vector unit (v)

                            unit (v) = vec (v) / mag (v)

                            unit (v) = [ -23.2 i -104.4 j + 46.4 k ] / 116.58

                            unit (v) = [ -0.199 i - 0.8955 j + 0.39801 k ]

The unit vector in the direction of the spacecraft’s velocity is found by dividing the velocity vector by its magnitude. Accordingly, if one knows the component values of the spacecraft's velocity, one can calculate the components for the unit vector by dividing each component by the magnitude of the velocity.

The unit vector in the direction of the spacecraft's velocity can be determined from its velocity vector. The unit vector is a vector of length 1 that points in the same direction as the given vector. It can be found by dividing the velocity vector of the spacecraft by its magnitude. If V represents the velocity vector, then the unit vector U is calculated as U = V / |V| where |V| is the magnitude of the vector V. Thus, if you know the component values of the spacecraft's velocity, you can calculate the respective components for the unit vector by dividing each component of the velocity vector by the velocity's magnitude.

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Explanation:

The given data is as follows.

    Inner wheel Radius = 20 m,

   Distance between left and right wheel = 1.5m,

Let us assume speed of drive shaft is N rpm.

Formula to calculate angular velocity is as follows.

    Angular velocity of automobile = w = [tex]\frac{V}{R}[/tex]

where,   V = linear velocity of automobile m/min,

              R = turning radius from automobile center in meter

In the given case, angular velocity remains same for inner and outer wheel but there is change in linear velocity of inner wheel and outer wheel.

Now, we assume that

         u = linear velocity of inner wheel

and,   u' = linear velocity of outer wheel.

Formula for angular velocity of inner wheel w = ,

Formula for angular velocity of outer wheel w =

Now, for inner wheels

                   w =

                      = [tex]\frac{u}{(R - d)}[/tex]

                  u = [tex]V \times \frac{(R - d)}{R}[/tex]

                    = [tex]V \times (1 - \frac{d}{R})[/tex]

If radius of wheel is r it will cover  distance in one min.

Since, velocity of wheel is u it will cover distance u in unit time(min)

Thus,             u = [tex]2\pi rn[/tex] = [tex]V \times (1 - \frac{d}{R})[/tex]

Now, rotation per minute of inner wheel is calculated as follows.

         n = [tex]\frac{V}{2 \pi r \times (1 - \frac{d}{R})}[/tex]

            = [tex]\frac{V}{2 \pi r \times (1 - \frac{0.75}{20})}[/tex] (since 2d = 1.5m given, d = 0.75m),

             = [tex]\frac{V}{r} \times 0.1532[/tex]

So, rotation per minute of outer wheel; n' =  

                   = [tex]\frac{V}{2 \pi r \times (1 + \frac{0.75}{20})}[/tex]

                   = [tex]\frac{V}{r} \times 0.1651[/tex]

In a sharp left turn, the car's right wheel rotates 1.0375 times the speed of the drive shaft, while the left wheel rotates at the speed of the drive shaft. This difference is due to the right wheel covering a larger distance than the left wheel.

The principle in operation here is that in a sharp turn, the outer wheel (in this case, the right wheel) has to cover a larger distance than the inner wheel (left wheel). Therefore, the right wheel will rotate faster than the left one.

Now, calculating the difference in rotation speeds of the wheels, we consider the radii of the paths of the two wheels. For the left wheel, the radius is 20 m and for the right wheel, the radius is greater by half the wheelbase distance, that is, 20.75 m.

The ratio of the speeds is equal to the ratio of the radii of the two paths. Therefore, the speed of the right wheel as a fraction of the drive shaft speed is 20.75/20 = 1.0375 and the speed of the left wheel as a fraction of the drive shaft speed is 20/20 = 1.

So, in conclusion, during a sharp turn to the left, the right wheel rotates 1.0375 times the speed of the drive shaft, while the left wheel rotates at the same speed as the drive shaft.

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Answer:

[tex]m=1864.68\ g[/tex]

Explanation:

Given:

volume of air in the room, [tex]V=410\ m^3[/tex]

temperature of the room, [tex]T=25+273=298\ K[/tex]

Saturation water vapor pressure at any temperature T K is given as:

[tex]p_{sw}=\frac{e^{(77.3450 + 0.0057\times T - \frac{ 7235}{T} )}}{T^{8.2}}[/tex]

putting T=298 K we have

[tex]p_{sw}=3130\ Pa[/tex]

The no. of moles of water molecules that this volume of air can hold is:

Using Ideal gas law,

[tex]P.V=n.R.T[/tex]

[tex]n=\frac{P_{sw}.V}{R.T}[/tex]

[tex]n=\frac{3130\times 410}{8.314\times 298}[/tex]

[tex]n=518\ moles[/tex] is the maximum capacity of the given volume of air to hold the moisture.

Currently we have 80% of n, so the mass of 20% of n:

[tex]m=(20\%\ of\ n)\times M}[/tex]

where;

M= molecular mass of water

[tex]m=0.2\times 518\times 18[/tex]

[tex]m=1864.68\ g[/tex] is the mass of water that can vaporize further.

Q: How much heat must be absorbed by 125 g of ethanol to change its temperature from 21.5 oC to 34.8 oC?  The specific heat of ethanol is 2.44 J/(gC).

Answer:

4056.5 J

Explanation:

The formula for the specific heat capacity of ethanol is given as

Q = cm(t₂-t₁)..................... Equation 1

Where q = quantity of heat, c = specific heat capacity of ethanol, m = mass of ethanol, t₁ = initial temperature of ethanol, t₂ = final temperature of ethanol.

Given: m = 125 g, t₁ = 25.5 °C, t₂ = 34.8 °C

Constant; c = 2.44 J/g.°C

Substitute into equation 1

Q = 125(2.44)(34.8-21.5)

Q = 125(2.44)(13.3)

Q = 4056.5 J.

Hence the amount of heat absorbed = 4056.5 J

Answer: Option (b) is the correct answer.

Explanation:

Since, there is a negative charge present on the ball and a positive charge present on the rod. So, when the negatively charged metal ball will come in contact with the rod then positive charges from rod get conducted towards the metal ball.

Hence, the rod gets neutralized. But towards the metal ball there is a continuous supply of negative charges. Therefore, after the neutralization of positive charge from the rod there will be flow of negative charges from the metal ball towards the rod.

Thus, we can conclude that negative charge spread evenly on both ends.

Option (b) is the correct answer.

b. There is negative charge spread evenly on both ends.

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Answer:

f = 735 Hz

Explanation:

given,

Person distance from speakers

r₁ = 4.1 m      r₂ = 4.8 m

Path difference

d = r₂ - r₁ = 4.8 - 4.1 = 0.7 m

For destructive interference

[tex]d = \dfrac{n\lambda}{2}[/tex]

where, n = 1, 3,5..

we know, λ = v/f

[tex]d = \dfrac{n v}{2f}[/tex]

v is the speed of the sound = 343 m/s

f is the frequency

[tex]f = \dfrac{n v}{2d}[/tex]

for n = 1

[tex]f = \dfrac{343}{2\times 0.7}[/tex]

     f = 245 Hz

for n = 3

[tex]f = \dfrac{3\times 343}{2\times 0.7}[/tex]

     f = 735 Hz

Hence,the second lowest frequency of the destructive interference is 735 Hz.

Answer:

Q= 835J

Explanation:

Specific heat capacity of Helium=5.193J/gk

Q=msΔT

ΔT=T2-T1

Q=change in energy

m=mass of substance

S= Specific heat capacity

Q= Change in energy

T2= 38.3 degrees Celsius =(38.3+273)k= 311.3k

T1=24.2 degree Celsius =24.2+273k

T1=297.2k

ΔT=T2-T1=(311.3-297.2)k=14.1K

Q=(11.4g)*(5.193J/gk)*(14.1k)

Q=834.72282J

Approximately, Q= 835J

Answer:

[tex]\omega = \frac{mv\frac{L}{2}\sin(29^\circ)}{\frac{1}{3}ML^2 + m(\frac{L}{2})^2} = 0.91~{\rm rad/s}[/tex]

Explanation:

The angular speed of the system can be found by conservation of angular momentum. Since the ball and the rod are stick together, the collision is completely inelastic, ergo kinetic energy is not conserved.

[tex]L_{initial} = L_{final}\\m\vec{v}\times \vec{r} = I\omega[/tex]

The moment of inertia of the combined objects is equal to the sum of moment of inertia of the separate objects.

[tex]I = \frac{1}{3}ML^2 + m(\frac{L}{2})^2[/tex]

The cross product in the left-hand side can be written as a sine of the angle.

Therefore;

[tex]mv\frac{L}{2}\sin(29^\circ) = (\frac{1}{3}ML^2 + m(\frac{L}{2})^2)\omega\\(19\times 10^{-3})(5)(\frac{47\times 10^{-2}}{2})\sin(29^\circ) = (\frac{1}{3}(146\times 10^{-3})(47\times 10^{-2})^2 + (19\times 10^{-3})(\frac{47\times 10^{-2}}{2})^2)\omega\\\omega = 0.91~{\rm rad/s}[/tex]In terms of system parameters:

[tex]\omega = \frac{mv\frac{L}{2}\sin(29^\circ)}{\frac{1}{3}ML^2 + m(\frac{L}{2})^2}[/tex]

Answer:

a. 11.5kv/m

b.102nC/m^2

c.3.363pF

d. 77.3pC

Explanation:

Data given

[tex]area=7.60cm^{2}\\ distance,d=2mm\\voltage,v=23v[/tex]

to calculate the electric field, we use the equation below

V=Ed

where v=voltage, d= distance and E=electric field.

Hence we have

[tex]E=v/d\\E=\frac{23}{2*10^{-3}} \\E=11.5*10^{3} v/m\\E=11.5Kv/m[/tex]

b.the expression for the charge density is expressed as

σ=ξE

where ξ is the permitivity of air with a value of 8.85*10^-12C^2/N.m^2

If we insert the values we have

[tex]8.85*10^{-12} *11500\\1.02*10^{-7}C/m^{2} \\102nC/m^{2}[/tex]

c.

from the expression for the capacitance

[tex]C=eA/d[/tex]

if we substitute values we arrive at

[tex]C=\frac{8.85*10^{-12}*7.6*10^{-4}}{2*10^{-3} } \\C=\frac{6.726*10^{-15} }{2*10^{-3} } \\C=3.363*10^{-12}F\\C=3.363pF[/tex]

d. To calculate the charge on each plate, we use the formula below

[tex]Q=CV\\Q=23*3.363*10^{-12}\\ Q=7.73*10^{-12}\\ Q=77.3pC[/tex]

For the air-filled capacitor:

(a) The electric field is 11.5 kV/m

(b) The surface charge density is 1.02×10⁻⁷C/m²

(c) The capacitance is 3.36pF

(d) Charge on the plate: 76pC

Given that an air-filled capacitor consists of two parallel plates such that the:

Area of the plates, A = 7.6 cm² = 7.6×10⁻⁴ m²

distance between the plates, d = 2mm = 2×10⁻³m

voltage applied, V = 23V

(a) Electric field is given by:

E = V\d

E = 23/2×10⁻³

E = 11.5 kV/m

(b) The electric field for a parallel plate capacitor in terms of the surface charge density is given by:

E = σ/ε₀

where σ is the surface charge density:

σ = ε₀E

σ = 8.85×10⁻¹²×11.5×10³

σ = 1.02×10⁻⁷C/m²

(c) the capacitance is given by:

C = ε₀A/d

C = (8.85×10⁻¹²)×(7.6×10⁻⁴)/2×10⁻³

C = 3.36×10⁻¹²F

C = 3.36 pF

(d) The charge (Q) on the plate is given by:

Q = σA

Q = 1.02×10⁻⁷× 7.6×10⁻⁴

Q = 76 pC

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Answer:

Explanation:

The experiment confirm the inverse square law which relates the force between two charged particles to the product of the charges and the distance between the charges.

From the general equation, we notice the force is inversely related to the distance between the charges, when the distance is halved, the force increase by a factor of 4, hence a decrease in distance leads to a corresponding increase in the force value.

Also the electric field intensity a charge exert on another charge within the region of its field is independent on the distance because distance has no effect on electric field strength.

Answer:

(a)  104 N

(b) 52 N

Explanation:

Given Data

Angle of inclination of the ramp: 20°

F makes an angle of 30° with the ramp

The component of F parallel to the ramp is Fx = 90 N.  

The component of F perpendicular to the ramp is Fy.

(a)  

Let the +x-direction be up the incline and the +y-direction by the perpendicular to the surface of the incline.  

Resolve F into its x-component from Pythagorean theorem:  

Fx=Fcos30°

Solve for F:  

F= Fx/cos30°  

Substitute for Fx from given data:  

Fx=90 N/cos30°

   =104 N

(b) Resolve r into its y-component from Pythagorean theorem:

     Fy = Fsin 30°

   Substitute for F from part (a):

     Fy = (104 N) (sin 30°)  

          = 52 N  

To find the force FS necessary for the component Fx parallel to the ramp to be 90.0 N, we can use the equation Fx = FS * cos(30°) = 90.0 N. To find the component Fy perpendicular to the ramp, we can use the equation Fy = FS * sin(30°).

To find the force FS necessary for the component Fx parallel to the ramp to be 90.0 N, we can use the equation Fx = FS * cos(30°) = 90.0 N. Rearranging the equation, FS = 90.0 N / cos(30°). Therefore, FS ≈ 103.9 N.

To find the component Fy perpendicular to the ramp, we can use the equation Fy = FS * sin(30°). Substituting the value of FS, Fy ≈ 103.9 N * sin(30°). Therefore, Fy ≈ 51.9 N.

Answer:

T2=336K

Explanation:

Clausius-Clapeyron equation is used to determine the vapour pressure at different temperatures:

where:

In(P2/P1) = ΔvapH/R(1/T1 - 1/T2)

p1 and p2 are the vapour pressures at temperatures 

T1 and T2

ΔvapH = the enthalpy  of vaporization of the liquid

R = the Universal Gas Constant

p1=p1, T1=307K

p2=3.50p1; T2=?

ΔvapH=37.51kJ/mol=37510J/mol

R=8.314J.K^-1moL^-1

In(3.50P1/P1)= (37510J/mol)/(8.314J.K^-1)*(1/307 - 1/T2)

P1 and P1 cancelled out:

In(3.50)=4511.667(T2 - 307/307T2)

1.253=14.696(T2 - 307/T2)

1.253=(14.696T2) - (14.696*307)/T2

1.253T2=14.696T2 - 4511.672

Therefore,

4511.672=14.696T2 - 1.253T2

4511.672=13.443T2

So therefore, T2=4511.672/13.443=335.61

Approximately, T2=336K

Answer:

8.07 m/s, 81.7º NE.

Explanation:

        [tex]vocx = voc* cos 40 = 1.53 m/s * 0.766 = 1.17 m/s\\vocy = voc* sin 40 = 1.53 m/s * 0.643 = 0.98 m/s[/tex]

        [tex]vshy = vsw + vwy = 7.00 m/s + 0.98 m/s = 7.98 m/s[/tex]

        vshx = 1.17 m/s

        [tex]v = \sqrt{vshx^{2} + vshy^{2} } =\sqrt{(7.98m/s)^{2} +(1.17m/s)^{2} } =8.07 m/s[/tex]

        [tex]tg \theta = \frac{vshy}{vshx} = \frac{7.98}{1.17} = 6.82 \\ \theta = tg^{-1} (6.82)\\ \theta= 81.7\deg[/tex]

To solve this problem we will apply the linear motion kinematic equations.

The equation that describes the position as a function of the initial velocity, acceleration and time is given by the relation

[tex]s = v_0 t +\frac{1}{2} at^2[/tex]

Here,

[tex]v_0 =[/tex] Initial velocity

t = Time

a = Acceleration, at this case due to gravity

There is not initial velocity then we have that the equation to the given time is

[tex]s = \frac{1}{2} (9.8)(6.8)^2[/tex]

[tex]s = 226.8m[/tex]

If the ball is held at a height of 1m before it is dropped, we have that the Building height is

[tex]h = 226.8-1[/tex]

[tex]h = 225.8m[/tex]

Answer:

Explanation:

If u is the initial velocity at an angle \theta with horizontal then

Horizontal range of Frog can be given by

[tex]R=ut+\frac{1}{2}at^2[/tex]

where u=initial velocity

a=acceleration

t=time

Here initial horizontal velocity

[tex]u_x=u\cos \theta [/tex]

and there is no acceleration in the horizontal motion

Therefore

[tex]R=u\cos \theta \times t+0[/tex]

Considering vertical motion

[tex]Y=ut+\frac{1}{2}at^2[/tex]

here Initial vertical velocity [tex]u_y=u\sin \theta [/tex]

acceleration [tex]a=g[/tex]

for complete motion Y=0 i.e.displacement is zero

[tex]0=u\sin \theta \times t-\frac{1}{2}gt^2[/tex]

[tex]t=\frac{2u\sin \theta }{g}[/tex]

Therefore Range is

[tex]R=\frac{u^2\sin 2\theta }{g}[/tex]

Range will be maximum when [tex]\theta =45[/tex]

[tex]R=\frac{u^2}{g}----1[/tex]

and Maximum height [tex]h_{max}=\frac{u^2\sin ^2 \theta }{2g}[/tex]

for [tex]\theta =45[/tex]

[tex]h_{max}=\frac{u^2}{4g}----2[/tex]

Divide 1 and 2

[tex]\frac{R_{max}}{h_{max}}=\frac{\frac{u^2}{g}}{\frac{u^2}{4g}}[/tex]

[tex]\frac{R_{max}}{h_{max}}=4[/tex]

Final answer:

To raise the boiling point of 2.85 kg of water by 2°C, one needs to add approximately 320.41 grams of sodium chloride (NaCl), calculated based on the boiling point elevation formula and considering NaCl's dissociation into ions.

Explanation:

To calculate how much NaCl is needed to increase the boiling point of 2.85 kg of water by 2°C, we use the boiling point elevation formula: ΔT = i*Kb*m, where ΔT is the change in boiling point, i is the van 't Hoff factor (which is 2 for NaCl because it dissociates into Na+ and Cl- ions), Kb is the ebullioscopic constant of water (0.52 °C kg/mole), and m is the molality of the solution. First, we solve for m knowing that we want to increase the boiling point by 2°C. With Kb = 0.52 °C kg/mole and i=2, we have 2°C = (2)*(0.52 °C kg/mol)*m. From here, m = 1.923 mol/kg.

Next, to find the mass of NaCl needed, we convert molality to moles of solute needed using the mass of the solvent (water) in kg, then multiply by the molar mass of NaCl. Since molality = moles of solute / kg of solvent, moles of NaCl = molality * kg of solvent = 1.923 mol/kg * 2.85 kg = 5.48 moles. The mass of NaCl required = moles * molar mass = 5.48 mol * 58.44 g/mol = 320.41 g.

Therefore, to increase the temperature of the boiling water by 2°C, we need to add approximately 320.41 grams of NaCl.

Answer

given,

Mean of temperature in Celsius = 37    Standard deviation in Celsius = 0.5

relation between Fahrenheit and Celsius

[tex]F = \dfrac{9}{5}C + 32[/tex]

Mean of temperature in Fahrenheit

[tex]Mean_F =\dfrac{9}{5}\times Mean_C + 32[/tex]

[tex]Mean_F =\dfrac{9}{5}\times 37 + 32[/tex]

[tex]Mean_F = 98.6\ F[/tex]

Standard deviation of Fahrenheit.

[tex]SD_F = \dfrac{9}{5}\times SD_C [/tex]

addition of 32 will not change the Standard deviation.

[tex]SD_F = \dfrac{9}{5}\times 0.5[/tex]

[tex]SD_F = 0.9[/tex]

The electric flux through a spherical shell in a uniform electric field is calculated using Gauss's Law. The physical principles of uniform electric fields and spherical symmetry are applied to determine the flux, emphasizing the concept of electric flux through closed surfaces.

The question involves calculating the electric flux through a spherical shell placed in a uniform electric field. According to Gauss's Law, the electric flux (ΦE) through a closed surface surrounding a charge is proportional to the enclosed charge (ΦE = q/ε0), regardless of the shape of the surface. In a uniform electric field, the electric flux through a closed surface, like a spherical shell, can be derived from the formula ΦE = E⋅A, where E is the electric field strength and A is the area of the spherical shell.

For a spherical shell of radius 9.7 m in a uniform electric field of 1310 N/C, the area of the shell (A) is 4πr2, resulting in A = 4π(9.72) square meters. Substituting the values into ΦE = E⋅A gives us the total electric flux through the shell.

Answer:

(c) more than 500

Explanation:

Until 2019, more than 3000 planetary systems have been discovered that contain more than 4000 exoplanets, since some of these systems contain multiple planets. Most known extrasolar planets are gas giants equal to or more massive than the planet Jupiter, with orbits very close to its star.

Final answer:

The number of confirmed exoplanets is more than 5000. Through missions like Kepler, the catalog of exoplanets includes systems with a variety of planet arrangements and types, indicating an incredibly diverse universe with potentially billions of Earth-size planets. The correct answer is option is d) more than 5000.

Explanation:

The number of confirmed exoplanets is (d) more than 5000. As of July 2015, NASA's Kepler mission had detected a total of 4,696 possible exoplanets, and 1,030 of those candidates had been confirmed as planets. Advancing to 2018, astronomers had data on nearly 3,000 exoplanet systems.

By 2022, this knowledge expanded to include data on over 800 systems, many with multiple planets, and an understanding that one quarter of stars may have exoplanet systems. This implies the existence of at least 50 billion planets in our Galaxy alone. Recent studies have shown that planets like Earth are the most common type of planet, leading to an estimated 100 billion Earth-size planets around Sun-like stars in the Galaxy.

It's important to note that detections have been made possible using the Doppler and transit techniques, and while most of the exoplanets found are more massive than Earth, the shortage of small rocky planets detected is an observational bias, as they are more difficult to detect.

The ensemble of exoplanets discovered is incredibly diverse, suggesting a variety of planet formations and arrangements in these systems. Some systems have been observed to have rocky planets closer to their stars than in our solar system, and others have large gas giants, known as 'hot Jupiters', very close to their stars.

Answer:

Explanation:

Given

Wavelength of incoming light [tex]\lambda =425\ nm[/tex]

We know

[tex]speed\ of\ wave=frequency\times wavelength[/tex]

[tex]frequency=\frac{speed}{wavelength}[/tex]

[tex]\mu =\frac{3\times 10^8}{425\times 10^{-9}}[/tex]

[tex]\mu =7.058\times 10^{14}\ Hz[/tex]

Energy associated with this frequency

[tex]E=h\mu [/tex]

where h=Planck's constant

[tex]E=6.626\times 10^{-34}\times 7.058\times 10^{14}[/tex]

[tex]E=46.76\times 10^{-20}\ Hz[/tex]

Energy of one mole of Photon[tex]=N_a\times E[/tex]

[tex]=6.022\times 10^{23}\times 46.76\times 10^{-20}[/tex]

[tex]=281.58\times 10^{3}[/tex]

[tex]=281.58\ kJ[/tex]

To calculate the energy of a mole of photons of the emission at 425 nm, use the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. Convert the wavelength to meters, substitute the values into the equation, and calculate to find the energy of a single photon. Multiply this by Avogadro's number to find the energy of a mole of photons.

To calculate the energy of a mole of photons of the emission at 425 nm, we can use the equation E = hc/λ, where E is the energy, h is Planck's constant (6.63 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength (in meters).

Converting the wavelength to meters, we have 425 nm = 425 x 10^-9 m.

Substituting the values into the equation, we get E = (6.63 x 10^-34 J·s)(3.00 x 10^8 m/s) / (425 x 10^-9 m). Calculating this gives us the energy of a single photon of this emission. To find the energy of a mole of photons, we can multiply this value by Avogadro's number (6.02 x 10^23 photons/mol).

Therefore, the energy of a mole of photons of this emission is (6.63 x 10^-34 J·s)(3.00 x 10^8 m/s) / (425 x 10^-9 m) x (6.02 x 10^23 photons/mol).

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