A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 6 inches below the equilibrium position. (a) Find the position x of the mass at the times t = π/12, π/8, π/6, π/4, and 9π/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.)

Answer:

366 K

Explanation:

T₀ = Constant Temperature of deep lake = 293.0 K

T = Temperature of hot reservoir  connected to carnot engine = ?

η = Efficiency of Carnot engine during the operation

Efficiency of Carnot engine is given as

[tex]\eta = 1-\frac{T_{o}}{T}[/tex]

Inserting the values

[tex]0.200 = 1-\frac{293.0}{T}[/tex]

T = 366 K

Answer:

Part a)

[tex]V = 7.2 \times 10^{11} Volts[/tex]

Part b)

this is a large potential which can not be possible because at this high potential the air will break down and the charge on the sphere will decrease.

Part C)

here we can assume the sphere is placed at vacuum so that there is no break down of air.

Explanation:

Part a)

As we know that the potential near the surface of metal sphere is given by the equation

[tex]V = \frac{kQ}{R}[/tex]

here we have

Q = 8 C

R = 10.0 cm

now we have

[tex]V = \frac{(9\times 10^9)(8 C)}{0.10}[/tex]

[tex]V = 7.2 \times 10^{11} Volts[/tex]

Part b)

this is a large potential which can not be possible because at this high potential the air will break down and the charge on the sphere will decrease.

Part C)

here we can assume the sphere is placed at vacuum so that there is no break down of air.

Final answer:

The voltage near a 10.0 cm diameter metal sphere with 8.00 C of excess charge is calculated to be 1.438 x 10^12 V, which is unreasonable due to the high value leading to inevitable discharge. The assumption of an 8.00 C charge on such a small sphere is responsible for this unrealistic result.

Explanation:

Calculating the Voltage near a Charged Sphere

To find the voltage near a 10.0 cm diameter metal sphere with an excess positive charge of 8.00 C, we use the formula V = kQ/r, where V is the voltage, k is Coulomb's constant (8.99 x 10^9 N m^2/C^2), Q is the charge, and r is the radius of the sphere. For a diameter of 10.0 cm, the radius (r) is 0.05 m. Thus, V = (8.99 x 10^9 N m^2/C^2 * 8.00 C) / 0.05 m = 1.438 x 10^12 V.

Unreasonable Voltage

This voltage is extremely high and unreasonable because a metal sphere of that size could not sustain such a high voltage without discharging. The consequence of such a high voltage would include electric breakdown of the air around the sphere, leading to sparks or lightning-like discharges.

Erroneous Assumptions

The assumption responsible for this unreasonable result is the magnitude of charge being considered. An 8.00 C charge on a small metal sphere is significantly larger than what could realistically accumulate on the surface, given the limits of charge density and material breakdown thresholds.

Answer:

0.94 m/s^2 downwards

Explanation:

m = 70 kg, m g = 70 x 9.8 = 686 N

R = 620 N

Let the acceleration be a, as the apparent weight decreases so the elevator is moving downwards with an acceleration a.

mg - R = ma

686 - 620 = 70 x a

a = 0.94 m/s^2

Answer:

9.82 m/s^2

Explanation:

T = 2 s, g = 9.8 m/s^2

T' = 1.99796 s

Let the acceleration due to gravity at new location is g'.

The formula for the time period of simple pendulum is given by

[tex]T = 2\pi \sqrt{\frac{L}{g}}[/tex]     .... (1)

here, length of the pendulum remains same.

Now at the new location, let the time period be T'.

[tex]T' = 2\pi \sqrt{\frac{L}{g'}}[/tex]    .... (2)

Divide equation (2) by equation (1), we get

[tex]\frac{T'}{T} = \sqrt{\frac{g}{g'}}[/tex]

[tex]\frac{1.99796}{2} = \sqrt{\frac{9.8}{g'}}[/tex]

[tex]0.99796 = {\frac{9.8}{g'}}[/tex]

g' = 9.82 m/s^2

tT9.82 m/s².

Pendulum is the body which is pivoted a point and perform back and forth motion around that point by swinging due to the influence of gravity.

The time period of a pendulum is the time taken by it to complete one cycle of swing left to right and right to left.

It can be given as,

[tex]T=2\pi \sqrt{\dfrac{L}{g}}[/tex]

Here, (g) is the gravitational force of Earth and (L) is the length of the pendulum.

The time period of the pendulum with a period of 2 s in one location g=9.80m/s2 can be given as,

[tex]2=2\pi \sqrt{\dfrac{L}{9.8}}\\L=0.996468\rm m[/tex]      

Now, this pendulum is move to a new location where the period is now 1.99796 s. Thus, put the value in the above formula as,

[tex]1.99796=2\pi \sqrt{\dfrac{0.996468}{g}}\\g=9.82\rm m/s^2[/tex]

Thus, the acceleration due to gravity at its new location for the pendulum is 9.82 m/s².

Learn more about the time period of pendulum here;

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Answer and Explanation:

the electronic devices always have some noises present in the signal

there are some important considerations in optical fiber communications these are.

PRINCIPLE OF POPULATION INVERSION :

The principle of population inversion is defined as for production of high percentage of simulated emission for a laser beam the number of atoms in higher state should be greater than lower energy state

Noise considerations are important in optical fiber communications to maintain the fidelity of the transmitted signal. Population inversion, a critical principle for laser operation, involves achieving more particles in an excited state than in a lower energy state. Single frequency operation and the prevention of multiple transverse modes result in a more focused beam for optimal transmission.

Noise considerations are crucial in optical fiber communications because they can affect the fidelity and integrity of the transmitted signal. Noise can result from a variety of sources, including intrinsic factors within the fiber, like Rayleigh scattering, or from external influences such as electromagnetic interference. Managing noise is essential to maintain a high signal-to-noise ratio (SNR), which enables the clear and accurate transmission of data over long distances.

The principle of population inversion is critical to the functioning of lasers, which are the light sources commonly used in optical fiber communication. Population inversion occurs when a system has more particles in an excited state than in a lower energy state, which is normally the opposite of what happens in thermal equilibrium. It can be achieved by pumping the system with energy, which propels the electrons into a higher energy level. Once the system has achieved population inversion, stimulated emission can occur, leading to the amplification of light and allowing for laser emission.

In laser systems, single frequency operation is often desired, which can be obtained through various methods such as using a monochromatic light source or employing optical filters. Regarding transverse modes, these are the different patterns of light intensity distribution across the cross-section of the beam. Preventing multiple transverse modes ensures that the laser operates in a single spatial mode, providing a cleaner and more focused beam, which is ideal for optical fiber transmissions.

Answer:

846 km

Explanation:

Speed = 47 m/s

time = 5 hours = 5 x 60 x 60 seconds

Distance = speed x time

Distance = 47 x 5 x 60 x 60

Distance = 846000 m

Distance = 846 km

Answer:

(N x π x r^2 x Cosθ) / R x dB(t) / dt

Explanation:

radius = r , Number of turns = N, B = B(t), Angle = θ, Resistance = R

induced emf = rate of change of magnetic flux

e  = - N x dΦ / dt

e = - N x d(B A Cosθ) / dt

e = - N x A x Cosθ x dB(t) / dt

e = - N x π x r^2 x Cosθ x dB(t) / dt

where, negative sign shows the direction of induced emf in the coil.

induced current, i = induced emf / resistance

i = - (N x π x r^2 x Cosθ) / R x dB(t) / dt

Answer:

a) 0.0483 mol

b) 232 °C

Explanation:

Ideal gas law:

PV = nRT

where P is absolute pressure,

V is volume,

n is number of moles,

R is universal gas constant,

and T is absolute temperature.

a) Given:

P = 1.20×10⁵ Pa

V = 1.00 L = 1.00×10⁻³ m³

T = 25.8 °C = 298.95 K

PV = nRT

(1.20×10⁵ Pa) (1.00×10⁻³ m³) = n (8.314 m³ Pa / mol / K) (298.95 K)

n = 0.0483 mol

b) Given:

P = 1.013×10⁵ Pa

V = 2.00 L = 2.00×10⁻³ m³

n = 0.0483 mol

PV = nRT

(1.013×10⁵ Pa) (2.00×10⁻³ m³) = (0.0483 mol) (8.314 m³ Pa / mol / K) T

T = 505.73 K

T = 232 °C

Answer:

4.4 cm

Explanation:

B = 1.98 mT = 1.98 x 10^-3 T, v = 1.53 x 10^7 m/s, m = 9.1 x 10^-31 kg

q = 1.6 x 10^-19 C

(a) The force due to the magnetic field is balanced by the centrpetal force

mv^2 / r = q v B

r = m v / q B

r = (9,1 x 10^-31 x 1.53 x 10^7) / (1.98 x 10^-3 x 1.6 x 10^-19)

r = 0.044 m = 4.4 cm

Answer:

The wavelength of the light is 633 nm.

Explanation:

Given that,

Distance between the two slits d= 0.025 cm

Distance between the screen and slits D = 120 cm

Distance between the slits y= 1.52 cm

We need to calculate the angle

Using formula of double slit

[tex]\tan\theta=\dfrac{y}{D}[/tex]

Where, y = Distance between the slits

D = Distance between the screen and slits

Put the value into the formula

[tex]\tan\theta=\dfrac{1.52}{120}[/tex]

[tex]\theta=\tan^{-1}\dfrac{1.52}{120}[/tex]

[tex]\theta=0.725[/tex]

We need to calculate the wavelength

Using formula of wavelength

[tex]d\sin\theta=n\lambda[/tex]

Put the value into the formula

[tex]0.025\times\sin0.725=5\times\lambda[/tex]

[tex]\lambda=\dfrac{0.025\times10^{-2}\times\sin0.725}{5}[/tex]

[tex]\lambda=6.326\times10^{-7}\ m[/tex]

[tex]\lambda=633\ nm[/tex]

Hence, The wavelength of the light is 633 nm.

The average current passing through a device is given by:

I = Q/Δt

I is the average current

Q is the amount of charge that has passed through the device

Δt is the amount of elapsed time

Given values:

Q = 4.00C

Δt = 4.00hr = 14400s

Plug in the values and solve for I:

I = 4.00/14400

I = 0.000277777778A

I = 0.278mA

Final answer:

The current produced by the solar cells of a pocket calculator through which 4.00 C of charge passes in 4.00 hours is 0.278 milliamperes.

Explanation:

The current produced by the solar cells of a pocket calculator when 4.00 C of charge passes through it in 4.00 hours can be calculated using the formula for electric current I = Q / t, where I is the current in amperes, Q is the charge in coulombs, and t is the time in seconds.

To find the current in milliamperes (mA), first convert the time to seconds:

4.00 hours × 3600 seconds/hour = 14400 seconds.

Next, use the formula to calculate current:

I = 4.00 C / 14400 s = 0.00027778 A,

which is equivalent to 0.278 mA

Answer:

Option D is the correct answer.

Explanation:

Stress is the force per unit area that tend to change the shape of body.

Stress is defined as internal resistive force per unit area.

         [tex]\texttt{Stress}=\frac{\texttt{Internal resistive force}}{\texttt{Area}}[/tex]

         [tex]\sigma =\frac{F}{A}[/tex]

So, so stress distributed over an area is best described as internal resistive force.

Option D is the correct answer.

Final answer:

Stress distributed over an area refers to the internal resistive forces that develop within a material in response to applied external forces. It is best described as an internal force, specifically termed internal resistive force, and is measured as the force per unit area.

Explanation:

Stress distributed over an area is best described as d) Internal resistive force. Stress is a physical quantity that represents the internal forces per unit area within a material that develop as a response to applied external forces or changes in temperature. It is calculated by the ratio of force to area and measured in Newtons per square meter (N/m²). Stress caused by forces perpendicular to the cross-section of the material is called normal stress, which can be tensile or compressive. Similarly, stress caused by forces parallel to the area, such as shear stress, represents deformation through sliding layers.

For example, when a metal rod is pulled from both ends, the internal resistive forces that develop within the material to oppose elongation are a manifestation of tensile stress. In contrast, when a book is pushed down upon by a hand, the internal resistive forces that prevent the book from compressing are an example of compressive stress.

Answer:

[tex]p_2 = 664081 N/m^{2}[/tex]

Explanation:

from the ideal gas law we have

PV = mRT

[tex]P = \rho RT[/tex]

[tex]\rho = \frac{P}{RT}[/tex]

HERE  R is gas constant for dry air  =  287  J K^{-1} kg^{-1}

[tex]\rho = \frac{7.00 10^{5}}{287(18+273)}[/tex]

[tex]\rho = 8.38 kg/m^{3}[/tex]

We know by ideal gas law

[tex]\rho = \frac{m_1}{V_1}[/tex]

[tex]m_1 = \rho V_1 = 8.38 *2*10^{-3}[/tex]

[tex]m_1 = 0.0167 kg[/tex]

for m_2

[tex]m_2 = \rho V_i - V_removed[/tex]

[tex]m_2 = 8.38*(.002 - 10^{-4})[/tex]

[tex]m_2 = 0.0159 kg[/tex]

WE KNOW

PV = mRT

V, R and T are constant therefore we have

P is directly proportional to mass

[tex]\frac{p_2}{p_1}=\frac{m_2}{m_1}[/tex]

[tex]p_2 = p_1 * \frac{m_2}{m_1}[/tex]

[tex]p_2 =7*10^{5} * \frac {.0159}{0.0167}[/tex]

[tex]p_2 = 664081 N/m^{2}[/tex]

This problem can be solved using Boyle's Law, which relates the pressure and volume of a gas at a constant temperature. The question asks for the new pressure of a bicycle tire after letting out a certain volume of air. The answer is approximately 7.37 x 10⁵ Pa.

The subject of this question is gas laws, specifically Boyle's Law which states that the pressure and volume of a gas have an inverse relationship when the temperature is kept constant. Assuming the temperature and volume of the tire remain constant before and after you let out the air, when a volume of 100 cm³ (which we will convert to 0.1 L for consistency) of air is let out, the new total volume of the gas is 1.9 L.

According to Boyle's Law, P1*V1 = P2*V2, where P1 and V1 represent the initial pressure and volume, and P2 and V2 represent the final pressure and volume. Plugging the values into this equation, we get:

(7.00 x 10⁵ Pa)(2.00 L) = P2 * (1.9 L)

Which gives us:

P2 = (7.00 x 10⁵ Pa * 2.00 L) / 1.9 L

Therefore, the pressure in the bike tire after letting out 100 cm³ of gas is approximately 7.37 x 10⁵ Pa.

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Answer:

49.85 V

Explanation:

u = 0, s = 5.62 cm, t = 1.15 x 10^-6 s

Let the electric field is E and voltage is V.

Use second equation of motion

s = ut + 1/2 a t^2

5.62 x 10^-2 = 0 + 0.5 a x (1.15 x 10^-6)^2

a = 8.5 x 10^10 m/s^2

m x a = q x E

E = m x a / q

E = (1.67 x 10^-27 x 8.5 x 10^10) / (1.6 x 10^-19)

E = 887.19 V/m

V = E x s

V = 887.19 x 5.62 x 10^-2 = 49.85 V

Answer:

work =p×v =3.27×10^5×1.5×10^-3 =490.5 joule

efficiency =w/q in

:. qin= w/efficiency =490.5/0.225=2180 joule

qout =q in - work =1689.5 joule

q out is work given as heat

The engine must give up 1689.5 J of heat to the low-temperature reservoir after calculating the total work done by the gas and accounting for the engine's efficiency.

To find the amount of work the engine gives up as heat, we first calculate the total work done by the gas using the formula W = PΔV, where W is work, P is pressure, and ΔV is the change in volume. Given a constant pressure of 3.27 x 105 Pa and a change in volume of 1.50 x 10-3 m3, the work done is:

W = PΔV = 3.27 x 105 Pa x 1.50 x 10-3 m3 = 490.5 J.

The efficiency of the engine is the ratio of the useful work output to the total work input, given by  ext_eta = useful work / total work. The equation that relates efficiency, work done (W), and heat given up (Q) is  ext_eta = W / (Q + W). We rearrange the equation to solve for Q:

Q = W /  ext_eta - W

Substituting the known values:

Q = 490.5 J / 0.225 - 490.5 J = 2180 J - 490.5 J = 1689.5 J.

Therefore, the engine must give up 1689.5 J of heat to the low-temperature reservoir.

Using the principle of continuity for incompressible fluids, if the diameter of a blood vessel is reduced by 59.0% due to plaque, the speed of the blood just as it enters this section will be approximately 2.44 times its initial speed.

The subject of the question falls under the topic of fluid flow in physics, specifically concerning the principle of continuity for incompressible fluids. This principle, often applied in fluid dynamics, suggests that in an area of steadily flowing fluid, the mass passing through one cross-section in a unit of time equals the mass passing through other sections.

Given this principle, if the cross-sectional area of the blood vessel decreases due to plaque buildup, the speed of the blood flow must increase accordingly to maintain a steady flow rate. If the diameter of the vessel decreases by 59.0%, the cross-sectional area A, which is proportional to the square of the diameter (A ~ D²), will be reduced to 0.41 of its original value (because (1 - 59/100)² = 0.41). Therefore, the speed V would be 1/0.41, or approximately 2.44 times the original speed V0.

So, if the blood vessel's diameter is reduced by 59.0%, then just as the blood enters the blocked portion of the vessel, its speed V will be 2.44 times the initial speed V0.

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Answer:

The cylinder’s total kinetic energy is 1.918 J.

Explanation:

Given that,

Mass = 4.1 kg

Radius = 0.057 m

Speed = 0.79 m/s

We need to calculate the linear kinetic energy

Using formula of linear kinetic energy

[tex]K.E_{l}=\dfrac{1}{2}mv^2[/tex]

[tex]K.E_{l}=\dfrac{1}{2}\times4.1\times(0.79)^2[/tex]

[tex]K.E_{l}=1.279\ J[/tex]

We need to calculate the rotational kinetic energy

[tex]K.E_{r}=\dfrac{1}{2}\times I\omega^2[/tex]

[tex]K.E_{r}=\dfrac{1}{2}\times\dfrac{1}{2}\times mr^2\times(\dfrac{v}{r})^2[/tex]

[tex]K.E_{r}=\dfrac{1}{4}\times m\times v^2[/tex]

[tex]K.E_{r}=\dfrac{1}{4}\times4.1\times(0.79)^2[/tex]

[tex]K.E_{r}=0.639\ J[/tex]

The total kinetic energy is given by

[tex]K.E=K.E_{l}+K.E_{r}[/tex]

[tex]K.E=1.279+0.639[/tex]

[tex]K.E=1.918\ J[/tex]

Hence, The cylinder’s total kinetic energy is 1.918 J.

Answer:

880 kg / m^3

Explanation:

height of column of oil = 85 cm = 0.85 m

height of column of mercury = 5.5 cm = 0.055 m

Density of mercury = 13600 kg/m^2

Let teh density of oil is d.

A the height of mercury column is balanced by the height of oil column

So, the pressure due to the mercury column = pressure by teh oil column

height of mercury column x density of mercury x g = height of oil column  

                                                                                       x density of oil x g

0.055 x 13600 x g = 0.85 x d x g

748 = 0.85 d

d = 880 kg / m^3

The owner's velocity, with the same momentum as the combined momentum of the dog and cat, is 1.28 m/s directed 9.46 degrees east of the north.

To solve this problem, we need to calculate the dog's momentum, the cat's momentum, and then use these two results to find the owner's velocity and direction.

First, let's calculate the momentum for each pet. Momentum (p) is defined as mass (m) times velocity (v). For the dog, p = mv = 26.2 kg * 3.21 m/s = 84.042 kg*m/s northward. For the cat, p = mv = 5.30 kg * 2.64 m/s = 13.992 kg*m/s eastward.

To find the combined momentum vector of the two animals, we will use Pythagorean theorem because the vectors are perpendicular to each other. So, resultant momentum = sqrt[(84.042^2) + (13.992^2)] = 85.87 kg*m/s.

The owner's momentum equals the total momentum of the dog and cat, so that's 85.87 kg*m/s. The magnitude of the owner's velocity (v) is therefore the momentum divided by his mass: v = p / m = 85.87 kg*m/s / 67.2 kg = 1.28 m/s. The direction of the owner's velocity can be found using trigonometry. The angle is arctan (cat's momentum / dog's momentum) = arctan (13.992 / 84.042) = 9.46° east from north.

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The magnitude of the owner's velocity is approximately [tex]\( 1.267 \, \text{m/s} \)[/tex], and the direction is [tex]\( 45^\circ \)[/tex] northeast.

To find the direction and magnitude of the owner's velocity, we need to calculate the total momentum of the dog and cat and then equate that to the owner's momentum.

 First, we calculate the momentum of the dog and cat separately using the formula p = mv , where p  is the momentum,  m  is the mass, a v is the velocity.

For the dog:

[tex]\[ p_{\text{dog}} = m_{\text{dog}} \times v_{\text{dog}} \][/tex]

[tex]\[ p_{\text{dog}} = 26.2 \, \text{kg} \times 3.21 \, \text{m/s} \][/tex]

[tex]\[ p_{\text{dog}} = 84.002 \, \text{kg} \cdot \text{m/s} \][/tex]

For the cat:

[tex]\[ p_{\text{cat}} = m_{\text{cat}} \times v_{\text{cat}} \][/tex]

[tex]\[ p_{\text{cat}} = 5.30 \, \text{kg} \times 2.64 \, \text{m/s} \][/tex]

[tex]\[ p_{\text{cat}} = 14.032 \, \text{kg} \cdot \text{m/s} \][/tex]

The total momentum of the dog and cat is the vector sum of their individual momenta. Since they are moving in perpendicular directions (northward and eastward), we can use the Pythagorean theorem to find the magnitude of the total momentum:

[tex]\[ p_{\text{total}} = \sqrt{p_{\text{dog}}^2 + p_{\text{cat}}^2} \][/tex]

[tex]\[ p_{\text{total}} = \sqrt{(84.002)^2 + (14.032)^2} \][/tex]

[tex]\[ p_{\text{total}} = \sqrt{7056.0624 + 196.82784} \][/tex]

[tex]\[ p_{\text{total}} = \sqrt{7252.89} \][/tex]

[tex]\[ p_{\text{total}} \ =85.136 \, \text{kg} \cdot \text{m/s} \][/tex]

The direction of the total momentum vector is northeast, which is [tex]45^\circ \)[/tex] from the northward direction (the direction of the dog's velocity).

Now, we equate the owner's momentum to the total momentum of the pets:

[tex]\[ p_{\text{owner}} = p_{\text{total}} \][/tex]

[tex]\[ m_{\text{owner}} \times v_{\text{owner}} = p_{\text{total}} \][/tex]

[tex]\[ 67.2 \, \text{kg} \times v_{\text{owner}} = 85.136 \, \text{kg} \cdot \text{m/s} \][/tex]

[tex]\[ v_{\text{owner}} = \frac{85.136 \, \text{kg} \cdot \text{m/s}}{67.2 \, \text{kg}} \][/tex]

[tex]\[ v_{\text{owner}} \ = 1.267 \, \text{m/s} \][/tex]

Answer:

[tex]5.32\cdot 10^4 g[/tex]

Explanation:

First of all, we need to find the volume of the room, which is given by

[tex]V=2.50 m \cdot 5.50 m \cdot 3.00 m =41.3 m^3[/tex]

Now we  can find the mass of the air by using

[tex]m=dV[/tex]

where

[tex]d=1.29 g/dm^3[/tex] is the density of the air

[tex]V=41.3 m^3 = 41,300 dm^3[/tex] is the volume of the room

Substituting,

[tex]m=(1.29)(41300)=5.32\cdot 10^4 g[/tex]

Final answer:

The mass of the air in a room with dimensions 2.50 m x 5.50 m x 3.00 m and an air density of 1.29 g/dm³ is calculated to be 53.2 kg.

Explanation:

The mass of the air in the room can be calculated by using the formula for density, which is mass (mass) equals density (density) times volume (volume), or m = ρV. Given that the density of air is 1.29 g/dm³, first we need to convert the measurements of the room to dm³ (decimeters cubed) as the given room dimensions are in meters. The volume of the room is 2.50 m x 5.50 m x 3.00 m which equals 41.25 m³. Converting from cubic meters to cubic decimeters results in 41,250 dm³ (1 m³ = 1,000 dm³). Therefore, the mass of air is calculated as 1.29 g/dm³ * 41,250 dm³, which equals 53,212.5 grams or 53.2 kg.

Answer: The average atomic mass of the given element is 20.169 amu.

Explanation:

Average atomic mass of an element is defined as the sum of masses of the isotopes each multiplied by their natural fractional abundance.

Formula used to calculate average atomic mass follows:

[tex]\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_i[/tex]     .....(1)

We are given:

Mass of isotope 1 = 19.99 amu

Percentage abundance of isotope 1 = 90.92 %

Fractional abundance of isotope 1 = 0.9092

Mass of isotope 2 = 20.99 amu

Percentage abundance of isotope 2 = 0.26%

Fractional abundance of isotope 2 = 0.0026

Mass of isotope 3 = 21.99 amu

Percentage abundance of isotope 3 = 8.82%

Fractional abundance of isotope 3 = 0.0882  

Putting values in equation 1, we get:

[tex]\text{Average atomic mass}=[(19.99\times 0.9092)+(20.99\times 0.0026)+(21.99\times 0.0882)][/tex]

[tex]\text{Average atomic mass}=20.169amu[/tex]

Hence, the average atomic mass of the given element is 20.169 amu.

Answer:

The change in internal energy and efficiency are 10000 J and 5.26%.

Explanation:

Given that,

Work = 500 J

Heat transfer = 9500 J

(a). We need to calculate the decrease in her internal energy

Using equation of internal energy of a system

[tex]\Delta U=Q-W[/tex]

Q = heat

W = work done

Put the value into the formula

She looses her heat -9500 J

[tex]\Delta U=-9500-500[/tex]

[tex]\Delta U=-10000\ J[/tex]

(b). We need to calculate the efficiency

Using formula of efficiency

[tex]e=\dfrac{W}{Q}[/tex]

[tex]e=\dfrac{500}{9500}[/tex]

[tex]e=0.0526\times100[/tex]

[tex]e=5.26\%[/tex]

Hence, The change in internal energy and efficiency are 10000 J and 5.26%.

By using the first law of thermodynamics, we calculate the decrease in the woman's internal energy to be -10000 J as a result of 500 J of work done and 9500 J of heat transfer into the environment. Her efficiency, defined as the ratio of work done to the absolute value of the decrease in internal energy, is found to be 5%.

Part (a), let's calculate the decrease in her internal energy. We'll use the first law of thermodynamics, ΔU = Q - W, which stipulates that the change in internal energy (ΔU) in a system is equal to the heat transferred into the system (Q) minus the work done by the system (W). Here, the heat transferred is -9500 J (it's negative since it's transferred out of her body). The work done is 500 J. Hence, the decrease in internal energy is ΔU = -9500 J - 500 J = -10000 J.

For part (b), efficiency (η) is defined as the ratio of the useful output to the total input. In this case, the useful output is the work done, and the total input is the absolute value of the decrease in internal energy. Thus, her efficiency is η = 500 J / 10000 J = 5%.

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Answer:

Electric field, [tex]E=5.63\times 10^{16}\ N/C[/tex]

Explanation:

Given that,

Charge, [tex]q=1.83\times 10^5\ C[/tex]

We need to find the magnitude of electric field 17.1 cm (0.171 m) above an isolated charge. Electric field at a point is given by :

[tex]E=\dfrac{kq}{r^2}[/tex]

[tex]E=\dfrac{9\times 10^9\times 1.83\times 10^5\ C}{(0.171\ m)^2}[/tex]

[tex]E=5.63\times 10^{16}\ N/C[/tex]

So, the electric field is [tex]5.63\times 10^{16}\ N/C[/tex]. Hence, this is the required solution.

Answer:

The Reynolds number is 5600.

Explanation:

Given that,

Density = 1400 kg/m³

Viscosity = 0.5 Pa's

Length = 2 m

Speed = 1 m/s

We need to calculate the Reynolds number

Using formula of Reynolds number

[tex]R_{e}=\dfrac{\rho V\times L}{\mu}[/tex]

Where, [tex]\rho[/tex] = density of fluid

v = speed of syrup

l = length of a person

[tex]\mu[/tex]=Viscosity

Put the all value into the formula

[tex]R_{e}=\dfrac{1400\times1\times2}{0.5}[/tex]

[tex]R_{e}=5600[/tex]

Hence, The Reynolds number is 5600.

Answer:

F = 15771.6 N

Explanation:

Initial velocity of ball just before it will collide is given as

[tex]v_i = \sqrt{2gh_1}[/tex]

[tex]v_i = \sqrt{2(9.81)(32.2)}[/tex]

[tex]v_i = 25.13 m/s[/tex]

now for final speed of rebound we have

[tex]v_f = \sqrt{2gh_2}[/tex]

[tex]v_f = \sqrt{2(9.81)(22.1)}[/tex]

[tex]v_f = 20.82 m/s[/tex]

now the average force is given as

[tex]F = \frac{mv_f - mv_i}{\Delta t}[/tex]

[tex]F = \frac{0.556(20.82 + 25.13)}{1.62 \times 10^{-3}}[/tex]

[tex]F = 15771.6 N[/tex]

Answer:

Well..

Explanation:

That's impossible. I know because I once weighed 11.1 kN, and I was temporarily immobile. It's probably the same for a car, and therefore it can not be "traveling" anywhere at all.. unless you put the car on an airplane or a boat or something.

Answer:

[tex]\rho = 12580.7 kg/m^3[/tex]

Explanation:

As we know that the satellite revolves around the planet then the centripetal force for the satellite is due to gravitational attraction force of the planet

So here we will have

[tex]F = \frac{GMm}{(r + h)^2}[/tex]

here we have

[tex]F =\frac {mv^2}{(r+ h)}[/tex]

[tex]\frac{mv^2}{r + h} = \frac{GMm}{(r + h)^2}[/tex]

here we have

[tex]v = \sqrt{\frac{GM}{(r + h)}}[/tex]

now we can find time period as

[tex]T = \frac{2\pi (r + h)}{v}[/tex]

[tex]T = \frac{2\pi (2.05 \times 10^6 + 310 \times 10^3)}{\sqrt{\frac{GM}{(r + h)}}}[/tex]

[tex]1.15 \times 3600 = \frac{2\pi (2.05 \times 10^6 + 310 \times 10^3)}{\sqrt{\frac{(6.67 \times 10^{-11})(M)}{(2.05 \times 10^6 + 310 \times 10^3)}}}[/tex]

[tex]M = 4.54 \times 10^{23} kg[/tex]

Now the density is given as

[tex]\rho = \frac{M}{\frac{4}{3}\pi r^3}[/tex]

[tex]\rho = \frac{4.54 \times 10^{23}}{\frac{4}[3}\pi(2.05 \times 10^6)^3}[/tex]

[tex]\rho = 12580.7 kg/m^3[/tex]

Explanation:

In order to solve this problem, the Stefan-Boltzmann law will be useful. This law establishes that a black body (an ideal body that absorbs or emits all the radiation that incides on it) "emits thermal radiation with a total hemispheric emissive power proportional to the fourth power of its temperature":  

[tex]P=\sigma A T^{4}[/tex] (1)  

Where:  

[tex]P[/tex] is the energy radiated by a blackbody radiator per second, per unit area (in Watts).

[tex]\sigma=5.6703(10)^{-18}\frac{W}{m^{2} K^{4}}[/tex] is the Stefan-Boltzmann's constant.  

[tex]A[/tex] is the Surface of the body  

[tex]T[/tex] is the effective temperature of the body (its surface absolute temperature) in Kelvin.

However, there is no ideal black body (although the radiation of stars like our Sun is quite close).   Therefore, we will use the Stefan-Boltzmann law for real radiator bodies:  

[tex]P=\sigma A \epsilon T^{4}[/tex] (2)  

Where [tex]\epsilon[/tex] is the star's emissivity  

Knowing this, let's start with the answer:

We have two stars where the emissivity [tex]\epsilon[/tex]  of both is the same:

Star A with a radius [tex]r_{A}=200000km[/tex] and a surface temperature  [tex]T_{A}=6000K[/tex].

Star B with a radius [tex]r_{B}=400000km[/tex] and a surface temperature  [tex]T_{B}=3000K[/tex].

And we are asked to find the ratio of the rate of energy radiated by both stars:

[tex]\frac{P_{A}}{P_{B}}[/tex]   (3)

Where [tex]P_{A}[/tex]  is the  rate of energy radiated by Star A and [tex]P_{B}[/tex]  is the  rate of energy radiated by Star B.

On the other hand, with the radius of each star we can calculate their surface area, using the formula for tha area of a sphere (assuming both stars have spherical shape):

[tex]A_{A}=4\pi r_{A}^{2}[/tex]   (4)

[tex]A_{B}=4\pi r_{B}^{2}[/tex]   (5)

Writting the Stefan-Boltzmann law for each star, taking into consideration their areas:

[tex]P_{A}=\sigma (4\pi r_{A}^{2}) \epsilon {T_{A}}^{4}[/tex] (6)  

[tex]P_{B}=\sigma (4\pi r_{B}^{2}) \epsilon {T_{b}}^{4}[/tex] (7)  

Substituting (6) and (7) in (3):

[tex]\frac{\sigma (4\pi r_{A}^{2}) \epsilon {T_{A}}^{4}}{\sigma (4\pi r_{B}^{2}) \epsilon {T_{B}}^{4}}[/tex]   (8)

[tex]\frac{P_{A}}{P_{B}}=\frac{{r_{A}}^{2} {T_{A}}^{4}}{{r_{B}}^{2} {T_{B}}^{4}}[/tex]   (9)

[tex]\frac{P_{A}}{P_{B}}=\frac{{(200000km)}^{2} {(6000K)}^{4}}{{(400000km)}^{2} {(3000K)}^{4}}[/tex]   (10)

Finally:

[tex]\frac{P_{A}}{P_{B}}=4[/tex]  

Answer:

d

Explanation:

HOPE THIS HELPS!!

Answer:

The distance between the person and the building is 68.48 meters.

Explanation:

It is given that,

Angle of elevation, θ = 30.6 degrees

Height of building, MP = 42 m

Height of person, AB = 1.5 m

We need to find the distance between person and building. It is given by BP.

Since, MN + NP = 42

So, MN = 40.5 m

Using trigonometric equation as :

[tex]tan\theta=\dfrac{MN}{AN}[/tex]

[tex]tan(30.6)=\dfrac{40.5}{AN}[/tex]

AN = 68.48 meters.

So, the distance between the person and the building is 68.48 meters. Hence, this is the required solution.

To determine the distance from a building, we use trigonometry and the formula adjacent = opposite / tangent(angle), taking into account the height of the building minus your height. The distance is calculated to be approximately 68.88 meters.

To find out how far you are from the building, we need to calculate the horizontal distance from the building's base to the point where you are standing. To do this, we can use trigonometry, specifically the tangent function which relates the angle of elevation to the opposite side and the adjacent side of a right-angle triangle. We need to consider the height of the building minus your height to find the correct opposite side.

Since the building is 42.0 meters tall, and you are 1.50 meters tall, the effective height we are looking at is 42.0 m - 1.50 m = 40.5 m. The angle of elevation you are looking at is 30.6 degrees. By using the formula tangent (angle) = opposite / adjacent, we can rearrange this to find the adjacent side (the distance from you to the building): adjacent = opposite / tangent (angle).

Therefore, the distance from you to the building is approximately adjacent = 40.5 m / tan(30.6°). Plugging in the values, we get:

Distance = 40.5 m / tan(30.6°) ≈ 40.5 m / 0.588 ≈ 68.88 m.

So, you are approximately 68.88 meters away from the building.