If a marathon runner averages 8.6 mi/h, how long does it take him or her to run a 26.22-mi marathon?

Final answer:

Vesna Vulovic's fall of 6 miles and 551 yards converts to approximately 10,159.8324 meters, combining both conversions of miles and yards to meters.

Explanation:

The question asks for the conversion of the distance Vesna Vulovic survived falling without a parachute from miles and yards into meters. To convert 6 miles and 551 yards to meters, we first note that 1 mile equals 1,609.34 meters, and 1 yard equals 0.9144 meters. Therefore, 6 miles convert to 9,656.04 meters (6 x 1,609.34) and 551 yards convert to 503.7924 meters (551 x 0.9144). Adding these two distances together yields a total fall of 10,159.8324 meters.

Answer:

In second time period will be [tex]1.4\times 10^{-6}sec[/tex]

Explanation:

We have given the time period  of wave [tex]T=1.4microsecond[/tex]

We have to change this time period in unit of second

We know that 1 micro sec [tex]10^{-6}sec[/tex]

We have to change 1.4 micro second

To change the time period from micro second to second we have to multiply with [tex]10^{-6}[/tex]

So [tex]1.4microsecond =1.4\times 10^{-6}sec[/tex]

Answer:

370.6 nm

Explanation:

wavelength in vacuum = 494 nm

refractive index of water with respect to air = 1.333

Let the wavelength of light in water is λ.

The frequency of the light remains same but the speed and the wavelength is changed as the light passes from one medium to another.

By using the definition of refractive index

[tex]n = \frac{wavelength in air}{wavelength in water}[/tex]

where, n be the refractive index of water with respect to air

By substituting the values, we get

[tex]1.333 = \frac{494}{\lambda }[/tex]

λ = 370.6 nm

Thus, the wavelength of light in water is 370.6 nm.

Answer:

for red light     e = -30 Degree

for Blue light e = 12.67 degree

Explanation:

given data:

using prism formula for red light

[tex]n =\frac{sin90}{sin r}[/tex]

[tex]sin r = \frac{1}{n}[/tex]

[tex]r =sin^{-1}\times \frac{1}{n}[/tex]

[tex]r =sin^{-1}\times \frac{1}{1} = 90 Degree[/tex]

from figure

r+ r' = A

where A is 60 degree

r' = 60 - 90 = -30 degree

angle of emergence will be

[tex]\mu = \frac{sin e}{sin r'}[/tex]

[tex]sin e =\mu \times sin r'[/tex]

[tex]e = sin^{-1} [-0.5\times 1][/tex]

e = -30 Degree

using prism formula for Blue light

[tex]n =\frac{sin90}{sin r}[/tex]

[tex]sin r = \frac{1}{n}[/tex]

[tex]r =sin^{-1}\times \frac{1}{n}[/tex]

[tex]r =sin^{-1}\times \frac{1}{1.3} = 50.28 Degree[/tex]

from figure

r+ r' = A

where A is 60 degree

r' = 60 - 50.28 = 9.72 degree

angle of emergence will be

[tex]\mu = \frac{sin e}{sin r'}[/tex]

[tex]sin e =\mu \times sin r'[/tex]

[tex]e = sin^{-1} [sin(9.72)\times 1.3][/tex]

e =  12.67 Degree

Answer:

Net charge,[tex]Q=7.84\times 10^{-6}\ C[/tex]

Explanation:

Number of protons, [tex]n_p=9\times 10^{13}[/tex]

Number of electrons, [tex]n_e=4.1\times 10^{13}[/tex]

Charge on electron, [tex]q_e=-1.6\times 10^{-19}\ C[/tex]

Charge on proton, [tex]q_p=1.6\times 10^{-19}\ C[/tex]

Net charge acting on the substance is :

[tex]Q=n_eq_e+n_pq_p[/tex]

[tex]Q=4.1\times 10^{13}\times (-1.6\times 10^{-19})+9\times 10^{13}\times 1.6\times 10^{-19}[/tex]

[tex]Q=0.00000784\ C[/tex]

or

[tex]Q=7.84\times 10^{-6}\ C[/tex]

So, the net charge on the substance is [tex]7.84\times 10^{-6}\ C[/tex]. Hence, this is the required solution.

Answer:

speed of the car at the bottom of the driveway is 3.8 m/s

Explanation:

given data

mass = 2.1× 10³ kg

distance = 5 m

angle = 20 degree

average friction force = 4 × 10³ N

to find out

find the speed of the car at the bottom of the driveway

solution

we find acceleration a by  force equation that is

force = mg×sin20 - friction force

ma = mg×sin20 - friction force

put here value

2100a = 2100 ( 9.8)×sin20 - 4000

a = 1.447 m/s²

so from motion of equation

v²-u² = 2as

here u is 0 by initial speed and v is velocity and a is acceleration and s is distance

v²-0 = 2(1.447)(5)

v = 3.8

speed of the car at the bottom of the driveway is 3.8 m/s

Answer:D

Explanation:

A secondary battery or rechargeable battery is a battery that can be discharged and recharged.

It is an elcetrochemical cell which involve redox reaction i.e. oxidation and reduction. Oxidation is a process of loosing the electrons while reduction involves gaining of electron.

During discharging battery act as galvanic cell in which Chemical energy is converted into Electrical energy.

During Charging battery act as Electrolytic cell in which Electrical energy is converted in to chemical energy.

Answer:

The reulting electric field at x = 4.0 and y = 0.0 from the dipole is 0.5612 N/C

Solution:

As per the question:

Charges of the dipole, q = [tex]\pm 2\mu C[/tex]

Separation distance between the charges, d = 0.0010 m

Separation distance between the center and the charge, d' = [tex]\frac{d}{2} = 5\times 10^{- 4} m[/tex]

x = 4.0 m

y = 0.0 m

Now,

The electric field due to the positive charge on the right of the origin:

E = [tex]k\frac{q}{(d' + x)^{2}}[/tex]

where

k = Coulomb's constant = [tex]9\times 10^{9} Nm^{2}C^{- 2}[/tex]

Now,

E = [tex](9\times 10^{9})\frac{2\times 10^{- 6}}{(5\times 10^{- 4} + 4)^{2}} = 1124.72\ N/C[/tex]

Similarly, electric field due to the negative charge:

E' = [tex]k\frac{q}{(x - d')^{2}}[/tex]

E' = [tex](9\times 10^{9})\frac{2\times 10^{- 6}}{(4 - 5\times 10^{4})^{2}} = - 1125.28\ N/C[/tex]

Thus

[tex]E_{total} = E' - E = 0.5612 N/C[/tex]

The electric field due to the dipole at the point x = 4.0 m, y = 0.0 m is -0.56 N/C. Option b

In this problem, we will use the formula for the electric field due to a dipole, E = k * 2p / r^3. Here, k is the Coulomb constant, p is the dipole moment, and r is the distance from the center of the dipole to the point where we want to find the electric field.

First, we need to find the dipole moment, p. The dipole moment is the product of the charge and the separation between the charges, so p = q * d = 2 * 10^-6 C * 0.0010 m = 2 * 10^-9 C.m.

The distance to the point where we want to find the electric field is 4.0 m, so r = 4.0 m. Plugging these values into the formula for the electric field gives us E = (9 * 10^9 N.m^2/C^2) * 2 * 2 * 10^-9 C.m / (4.0 m)^3 = 0.56 N/C.

Because the charges are aligned along the x axis with the positive charge to the right of the origin and we are considering a point to the right of both charges, the electric field will point in the negative x direction. Therefore, the correct answer is (B) -.56 i N/C.

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Answer:

Second drop: 1.04 m

First drop: 1.66 m

Explanation:

Assuming the droplets are not affected by aerodynamic drag.

They are in free fall, affected only by gravity.

I set a frame of reference with the origin at the nozzle and the positive X axis pointing down.

We can use the equation for position under constant acceleration.

X(t) = x0 + v0 * t + 1/2 * a *t^2

x0 = 0

a = 9.81 m/s^2

v0 = 0

Then:

X(t) = 4.9 * t^2

The drop will hit the floor when X(t) = 1.9

1.9 = 4.9 * t^2

t^2 = 1.9 / 4.9

[tex]t = \sqrt{0.388} = 0.62 s[/tex]

That is the moment when the 4th drop begins falling.

Assuming they fall at constant interval,

Δt = 0.62 / 3 = 0.2 s (approximately)

The second drop will be at:

X2(0.62) = 4.9 * (0.62 - 1*0.2)^2 = 0.86 m

And the third at:

X3(0.62) = 4.9 * (0.62 - 2*0.2)^2 = 0.24 m

The positions are:

1.9 - 0.86 = 1.04 m

1.9 - 0.24 = 1.66 m

above the floor

Answer:

Explanation: This is done using the equation:

[tex]\frac{4}{3} π R^{3}[/tex]

Because the Radius is a know value. We have the following.

[tex]\frac{4}{3} π (10mm)^{3}[/tex]

Which is:

4188.7902 mm

Explanation:

Given that,

Initial speed of the missile u = 0

Final speed of the missile, v = 4.5 km/s = 4500 m/s

Time taken by the missile, t = 90 s

Let a is the acceleration of the sports car.  It can be calculated using first equation of motion as :

[tex]v=u+at[/tex]

[tex]v=at[/tex]

[tex]a=\dfrac{v}{t}[/tex]

[tex]a=\dfrac{4500\ m/s}{90\ s}[/tex]

[tex]a=50\ m/s^2[/tex]

Value of g, [tex]g=9.8\ m/s^2[/tex]

[tex]a=\dfrac{50}{9.8}\ m/s^2[/tex]

[tex]a=(5.10)\ g\ m/s^2[/tex]

So, the acceleration of the missile is [tex](5.10)\ g\ m/s^2[/tex]. Hence, this is required solution.

Final answer:

The average acceleration of the missile is 50 m/s², and the acceleration in multiples of gravity is approximately 5.10 g.

Explanation:

To calculate the average acceleration of an intercontinental ballistic missile (ICBM) given it goes from rest to a suborbital speed of 4.50 km/s (or 4500 m/s) in 90.0 seconds, you can use the formula for average acceleration, which is the change in velocity (Δ v) divided by the change in time (Δ t). The formula is:

a =  Δv / Δt

Using the given information:
Δ v is (final velocity - initial velocity)
Δ v = 4500 m/s - 0 m/s = 4500 m/s
Δ t = 90.0 s

So the average acceleration, a, is:

a = 4500 m/s / 90.0 s = 50 m/s²

To find the acceleration in multiples of g (9.80 m/s²), divide the average acceleration by the acceleration due to gravity:

Acceleration in multiples of g = a / g

Acceleration in multiples of g = 50 m/s² / 9.80 m/s² ≈ 5.10 g

Therefore, the average acceleration of the missile is 50 m/s² and in multiples of gravity it is approximately 5.10 g.

Answer: [tex]V_{0,x } = 297.7 \frac{m}{s}\\V_{0,y } = 637 \frac{m}{s}[/tex]

Explanation:

Hi!

We define the point (0,0) as the intial position of the ball. The initial velocity is [tex](V_{0,x}, V_{0,y})[/tex]

The motion of the ball in the horizontal direction (x) has constant velocity, because there is no force in that direction. :

[tex]x(t) = V_{0,x}t[/tex]

In the vertical direction (y), there is the downward acceleration g of gravity:

[tex]y(t) = -gt^2 + V_{0,y}t[/tex]

(note the minus sign of acceleration, because it points in the negative y-direction)

When the ball hits the ground, at t = 65s,  y(t = 65 s) = 0. We use this to find the value of the initial vertical velocity:

[tex]0 = t(-gt + V_{0,y})\\V_{0,y} = gt = 9.8 \frac{m}{s^2} 65 s = 637 \frac{m}{s}[/tex]

We used that g = 9.8 m/s²

To find the horizonttal component we use the angle:

[tex]\tan(65\º) = \frac{V_{y,0}}{V_{x,0}} = 2.14\\V_{x,0} = 297.7\frac{m}{s}[/tex]

Answer:

[tex]t = \sqrt{L / ( sin(\theta) * (-1/2) * g * tg(\theta) )}[/tex]

Explanation:

The mass will have a weight, and since it is on a surface it will have a normal reaction.

The vertical component of the normal reaction will be equal and opposite to the weight.

w = g * m

Nv = N * sin(θ)

N is the normal reaction and Nh its vertical component

Nv = -w

N * sin(θ) = -g * m

The horizontal component of the normal will be

Nh = N * cos(θ)

N = Nh / cos(θ)

Then:

Nh / cos(θ) * sin(θ) = -g * m

sin/cos = tg

Nh * tg(θ) = -g * m

The horizontal component of the normal force will be the only force in the horizontal direction

It will cause an acceleration

Nh = ah * m

Then

ah * m * tg(θ) = -g * m

Simplifying the mass on each side

ah * tg(θ) = -g

ah = -g * tg(θ)

The mass will slide from a height related to the lenght of the ramp

L = D * sin(θ)

D = L / sin(θ) This is the distance it will slide

We set up a reference system with origin at the top of the ramp and the positive X axis pointing down the ramp in the direction of the slope.

In this reference system:

X(t) = X0 + V0*t + 1/2 * a * t^2

X0 = 0

V0 = 0

Then

X(t) = -1/2 * g * tg(θ) * t^2

It will move the distance D

L / sin(θ) = -1/2 * g * tg(θ) * t^2

t^2 = L / ( sin(θ) * (-1/2) * g * tg(θ) )

[tex]t = \sqrt{L / ( sin(\theta) * (-1/2) * g * tg(\theta) )}[/tex]

The negative sign will dissapear because gravity has a negative sign too.

Answer:[tex]h=160.84 W/m^2-K[/tex]

Explanation:

Given

mass flow rate=0.3 kg/s

diameter of pipe=5 cm

length of pipe=10 m

Inside temperature=22

Pipe surface =100

Temperature drop=30

specific heat of vapor(c)=2190 J/kg.k

heat supplied [tex]Q=mc\Delta T=0.3\times 2190\times (30)[/tex]

Heat due to convection =hA(100-30)

[tex]A=\pi d\cdot L[/tex]

[tex]A=\pi 0.05\times 10=1.571 m^2[/tex]

[tex]Q_{convection}=h\times 1.571\times (100-22)=122.538 h[/tex]

[tex]Q=Q_{convection}[/tex]

19,710=122.538 h

[tex]h=160.84 W/m^2-K[/tex]

The maximum theoretical efficiency for a heat engine operating between a high temperature of 300°C (573.15 K) and a low temperature of 27°C (300.15 K) is 47.63%, calculated using the Carnot efficiency formula.

To calculate the maximum theoretical efficiency for a heat engine operating between two temperatures, we can use the efficiency formula derived from the Carnot cycle, which is given by:

\(\eta = 1 - \frac{T_{cold}}{T_{hot}}\)

Where \(\eta\) is the efficiency, \(T_{cold}\) is the cold reservoir temperature, and \(T_{hot}\) is the hot reservoir temperature. Temperatures must be in Kelvin.

First, convert the temperatures from Celsius to Kelvin:

\(T_{cold} = 27 \degree C + 273.15 = 300.15 K\)

\(T_{hot} = 300 \degree C + 273.15 = 573.15 K\)

Now, substitute these values into the efficiency formula:

\(\eta = 1 - \frac{300.15}{573.15}\)

\(\eta = 1 - 0.5237\)

So, the maximum theoretical efficiency is:

\(\eta = 0.4763\)

Or in percentage:

\(\eta = 47.63\%\)

This calculation assumes an ideal Carnot engine, which is a theoretical limit and cannot be achieved in practical engines; the actual efficiency will be lower due to various inefficiencies.

Answer:

44.1 m

Explanation:

initial velocity of ball, u = 0

height of building, H = 106 m

g = 9.8 m/s^2

t = 3 second

Let the ball travels a distance of h in first 3 seconds.

Use second equation of motion

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

h = 0 + 0.5 x 9.8 x 3 x 3

h = 44.1 m

Thus, the distance traveled by the ball in first 3 seconds is 44.1 m.

Answer:

[tex]9.375\times 10^{13}electron[/tex] leave out with a charge of [tex]1.5\times 10^{-5}C[/tex]

Explanation:

We have given total charge [tex]Q=1.5\times 10^{-5}C[/tex]

We know that charge on one electron = [tex]1.6\times 10^{-19}C[/tex]

We have to find the total number of electron in total charge

So [tex]q=ne[/tex], here q is total charge, n is number of electron and e is charge on one electron

So [tex]1.5\times 10^{-5}=n\times 1.6\times 10^{-19}[/tex]

[tex]n=0.9375\times 10^{14}=9.375\times 10^{13}electron[/tex]

So [tex]9.375\times 10^{13}electron[/tex] leave out with a charge of [tex]1.5\times 10^{-5}C[/tex]

Answer:

effeciency n = = 49%

Explanation:

given data:

mass of aircraft 3250 kg

power P = 1500 hp = 1118549.81 watt

time = 12.5 min

h = 10 km = 10,000 m

v =85 km/h = 236.11 m/s

[tex]n = \frac{P_0}{P}[/tex]

[tex]P_o = \frac{total\ energy}{t} = \frac{ kinetic \energy + gravitational\ energy}{t}[/tex]

kinetic energy[tex] = \frac{1}{2} mv^2  =\frac{1}{2} 3250* 236 = 90590389.66 kg m^2/s^2[/tex]

kinetic energy [tex]= 90590389.66 kg m^2/s^2[/tex]

gravitational energy [tex]= mgh = 3250*9.8*10000 = 315500000.00  kg m^2/s^2[/tex]

total energy [tex]= 90590389.66 +315500000.00 = 409091242.28 kg m^2/s^2[/tex]

[tex]P_o =\frac{409091242.28}{750} = 545454.99 j/s[/tex]

[tex]effeciency\ n = \frac{P_o}{P} = \frac{545454.99}{1118549.81} = 0.49[/tex]

effeciency n = = 49%

To calculate the efficiency of an aircraft engine, we calculate the work done by the aircraft in climbing to its cruising altitude and reaching its cruising speed, then compare it to the total energy input from the engines. Using the aircraft's mass, altitude, speed, and power output in the efficiency formula allows us to determine its efficiency. Real-world factors like air resistance would normally be considered, but are omitted in this scenario.

Calculating Aircraft Engine Efficiency

The efficiency of an aircraft's engines can be determined by comparing the actual mechanical work done to the energy input as power from the engines. For the given aircraft scenario, we can calculate the work done by the aircraft in reaching both its cruising altitude and speed, and then determine efficiency using the average power output of the engines.

Work Done by the Aircraft

We start by calculating the work done against gravity to reach the cruising altitude (also known as potential energy, PE) and the kinetic energy (KE) gained by the aircraft to reach cruising speed:

PE = m * g * h

KE = 0.5 * m * v²

Where m is the mass of the aircraft, g is the acceleration due to gravity (9.81 m/s²), h is the altitude (10,000 meters), and v is the speed (converted to m/s).

Average Power and Efficiency

Next, we convert the aircraft's average power output from horsepower to watts:

1 horsepower = 745.7 watts

Average Power = 1500 hp * 745.7 W/hp

Now, we'll calculate efficiency:

Efficiency (η) = (Work done / Energy input) * 100%

The total work done is the sum of PE and KE. Energy input is the power multiplied by the time in seconds the power is delivered.

Let's apply these steps using the provided data:

Convert 12.5 minutes to seconds.

Calculate the work done based on mass, speed, and altitude.

Calculate the total energy input from the engines.

Finally, use these values to find the engine efficiency.

Please note, in a real-world scenario, additional factors like air resistance and variations in engine power output would affect these calculations.

The question deals with the Doppler effect which occurs with the relative motion between the source of the wave and the observer. The observed change in frequency, as the police car with a siren sounding at 500 Hz passes the truck moving in the opposite direction, is calculated to be approximately 67.5 Hz.

The question you're asking involves the concept of the Doppler effect, which is observed when the frequency of a wave changes because of relative movement between the source of the wave and the observer.

Here, I will explain how to use the formula for the Doppler effect when the source is moving towards the observer:

f' = f0 * (v + v0) / v

And here is the formula when the source is moving away from the observer:

f' = f0 * v / (v + vs)

In these formulae, f' is the observed frequency, f0 is the source frequency (500 Hz), v is the speed of sound (343 m/s), v0 is the observer's speed towards the source (truck's speed = 36 m/s), and vs is the source's speed away from the observer (police car's speed = 45 m/s).

Firstly, as the police car approaches the stationary observer (which is the truck), the formula becomes :

f' = 500 * (343 + 36) / 343

Calculating this gives us an observed frequency of approximately 530.5 Hz.

Then, as the police car moves away from the truck, we use the second formula:

f' = 500 * 343 / (343 + 45)

This gives us an observed frequency of about 463 Hz.

Therefore, the total change in frequency, as heard by the observer in the truck, is approximately 530.5 Hz - 463 Hz, which gives us a change in frequency of approximately 67.5 Hz.

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Final answer:

Using the Doppler effect equation for sound with both the observer and the source moving towards each other, the observed frequency is calculated as 636 Hz. The change in frequency heard by the observer in the truck is 136 Hz.

Explanation:

The scenario described involves the application of the Doppler effect, which is an increase or decrease in the frequency of sound, light, or other waves as the source and observer move toward or away from each other. To solve this problem, we will use the Doppler equation for sound when source and observer are moving in opposite directions towards each other:

f' = f((v + vo) / (v - vs))

where:
f' is the observed frequency,
f is the emitted frequency (500 Hz in this case),
v is the speed of sound in air (343 m/s),
vo is the observer's velocity towards the source (36 m/s, as the truck moves in the opposite direction to the police car),
vs is the source's velocity towards the observer (45 m/s).

Plugging in the values:

f' = 500 Hz ((343 m/s + 36 m/s) / (343 m/s - 45 m/s))
  = 500 Hz ((379 m/s) / (298 m/s))
  = 500 Hz * 1.272
  = 636 Hz

The observed frequency is 636 Hz, so the change in frequency is the observed frequency minus the emitted frequency:

Change in frequency = 636 Hz - 500 Hz = 136 Hz.

Answer:

Linear mass density,[tex]\lambda=2\times 10^{-4}\ kg/m[/tex]

Explanation:

Given that,

Mass of the string, m = 0.3 g = 0.0003 kg

Length of the string, l = 1.5 m

The linear mass density of a string is defined as the mass of the string per unit length. Mathematically, it is given by :

[tex]\lambda=\dfrac{m}{l}[/tex]

[tex]\lambda=\dfrac{0.0003\ kg}{1.5\ m}[/tex]

[tex]\lambda=0.0002\ kg/m[/tex]

or

[tex]\lambda=2\times 10^{-4}\ kg/m[/tex]

So, the linear mass density of a string is [tex]2\times 10^{-4}\ kg/m[/tex]. Hence, this is the required solution.

To calculate the linear mass density of the string, you divide the mass in kilograms by the length in meters. For a 0.3g and 1.5m string, this yields a linear mass density of 0.0002 kg/m.

The student asks how to calculate the linear mass density (μ) of a string. The linear mass density is defined as mass per unit length. To calculate it for a given string, you divide the mass of the string by its length. The provided string has a mass of 0.3g, which should be converted to kilograms (0.0003 kg), and a length of 1.5m.

The formula to calculate linear mass density is:
μ = mass/length.

Therefore, the linear mass density of the string is:
μ = 0.0003 kg / 1.5 m = 0.0002 kg/m.

Final answer:

The acceleration of gravity on the Moon is 1.67 m/s².

Explanation:

The weight of an object is determined by the acceleration due to gravity. On Earth, a 60.0 kg person weighs 588 N (60.0 kg × 9.8 m/s²). However, on the Moon, the person weighs 100.0 N. To find the acceleration of gravity on the Moon, we can rearrange the weight formula:

weight = mass × acceleration due to gravity

Using this formula, we can solve for the acceleration due to gravity on the Moon:

acceleration due to gravity = weight / mass = 100.0 N / 60.0 kg = 1.67 m/s²

The acceleration of gravity on the Moon is approximately 1.625 m/s².

To find the acceleration of gravity on the Moon, we use Newton's second law of motion, which states that force (F) is equal to mass (m) times acceleration (a), or F = m * a.

In this case, the force is the weight of the person on the Moon, which is given as 100.0 N, and the mass of the person is 60.0 kg.

We can rearrange the equation to solve for the acceleration due to gravity on the Moon:

[tex]\[ g_{\text{moon}} = \frac{F}{m} \][/tex]

Substituting the given values:

[tex]\[ g_{\text{moon}} = \frac{100.0 \, \text{N}}{60.0 \, \text{kg}} \] \[ g_{\text{moon}} = \frac{100.0}{60.0} \, \text{m/s}^2 \] \[ g_{\text{moon}} = 1.666\ldots \, \text{m/s}^2 \][/tex]

Therefore, the acceleration of gravity on the Moon is approximately 1.625 m/s².

Explanation:

Given that,

Frequency in the string, f = 110 Hz

Tension, T = 602 N

Tension, T' = 564 N

We know that frequency in a string is given by :

[tex]f=\dfrac{1}{2L}\sqrt{\dfrac{T}{m/L}}[/tex], T is the tension in the string

i.e.

[tex]f\propto\sqrt{T}[/tex]

[tex]\dfrac{f}{f'}=\sqrt{\dfrac{T}{T'}}[/tex], f' is the another frequency

[tex]{f'}=f\times \sqrt{\dfrac{T'}{T}}[/tex]

[tex]{f'}=110\times \sqrt{\dfrac{564}{602}}[/tex]

f' =106.47 Hz

We need to find the beat frequency when the hammer strikes the two strings simultaneously. The difference in frequency is called its beat frequency as :

[tex]f_b=|f-f'|[/tex]

[tex]f_b=|110-106.47|[/tex]

[tex]f_b=3.53\ beats/s[/tex]

So, the beat frequency when the hammer strikes the two strings simultaneously is 3.53 beats per second.

Final answer:

To calculate the beat frequency between two piano strings where one string's tension changes, it involves understanding sound production in instruments and the phenomenon of beats. However, without the length and mass of the strings, determining the beat frequency directly from the tension change is not straightforward.

Explanation:

The question involves calculating the beat frequency heard when a piano hammer strikes two strings tuned to the same note, where one string's tension has been altered. Beat frequency is the difference between the frequencies of two sounds. When two similar frequencies are played together, they produce beats that can be heard as a pulsation. However, to calculate the beat frequency from the given tensions, we first need to know the frequencies of the strings based on their tensions. Unfortunately, without specific information about the length and mass of the strings, calculating the exact frequencies and thus the beat frequency directly from the change in tension (602 N to 564 N) is not straightforward in this context. Normally, frequency can be related to tension in a string using the formula for the fundamental frequency of a vibrating string, which depends on the tension, length, and mass per unit length of the string. The question implies an understanding of the physical principles behind the production of sound in stringed instruments and the phenomenon of beats.

Answer:

option  B

Explanation:

The correct answer is option  B

From the option given option B describes law of conservation of energy which is total amount of energy is constant for closed system.

law of conservation of energy stated that energy cannot be created nor be destroyed but it can transformed from one form to another.

rest options are not correct as they does not follow the statement of the energy conservation.

Final answer:

The law of conservation of energy states that energy cannot be created or destroyed but only transformed or transferred within an isolated system. Thus, the total energy within a closed system remains constant.

Explanation:

The law of conservation of energy states that in any physical or chemical process, energy is neither created nor destroyed. This foundational concept in physics implies that the total amount of energy in an isolated system is constant despite the possibility of energy changing forms or being transferred from one part of the system to another.

Applying this principle, the correct statement from the options given to the student would be that the total amount of energy is constant for a closed system. This is because within such a system, energy can only be transformed from one type to another, such as from potential energy to kinetic energy, or transferred between objects or fields, but the overall energy balance does not change.

Answer:

Force, F = −229.72 N

Explanation:

Given that,

First charge particle, [tex]q_1=-6.29\times 10^{-6}\ C[/tex]

Second charged particle, [tex]q_2=5.23\times 10^{-6}\ C[/tex]

Distance between charges, d = 0.0359 m

The electric force between the two charged particles is given by :

[tex]F=k\dfrac{q_1q_2}{d^2}[/tex]

[tex]F=9\times 10^9\times \dfrac{-6.29\times 10^{-6}\times 5.23\times 10^{-6}}{(0.0359)^2}[/tex]

F = −229.72 N

So, the magnitude of force that one particle exerts on the other is 229.72 N. Hence, this is the required solution.

Explanation:

Let i, j and k represents east, north and upward direction respectively.

Velocity due north, [tex]v_a=44j\ mi/hr[/tex]

Velocity of the crosswind, [tex]v_w=44i\ mi/hr[/tex]

Velocity of downdraft, [tex]v_d=-22k\ mi/hr[/tex] (downward direction)

(a) Let v is the position vector that represents the velocity of the plane relative to the ground. It is given by :

[tex]v=44i+44j-22k[/tex]

(b) The speed of the plane relative to the ground can be calculated as :

[tex]v=\sqrt{44^2+44^2+22^2}[/tex]

v = 66 m/s

Hence, this is the required solution.

The speed of the plane relative to the ground is computed as 66 mi/hr by taking the square root of the sum of squares of the components of the velocity vector.

The plane's velocity north is given as 44 mi/hr, eastward crosswind as 44 mi/hr, and downdraft velocity as 22 mi/hr downwards.

We can represent these vectors using a coordinate system where north is the positive y-axis, east is the positive x-axis, and down is the negative z-axis. The position vector V (velocity relative to the ground) can be represented as:

V = vnorthi + veastj + vdownk,

where i, j, and k are the unit vectors in the x, y, and z directions respectively. Substituting the given values, we have:

V = 44j + 44i - 22k

The speed of the plane relative to the ground is the magnitude of this vector, which can be calculated using the Pythagorean theorem:

Speed = √(vnorth^2 + veast^2 + vdown^2),

Substituting the given values results in:

Speed = √(44^2 + 44^2 + (-22)^2)

= √(1936 + 1936 + 484)

= √(4356)

= 66 mi/hr.

Answer:

The car overtakes the truck at a distance d = 3266.2ft from the starting point

Explanation:

Problem Analysis

When car catches truck:

dc = dt = d

dc: car displacement

dt: truck displacement

tc = tt = t

tc: car time

tt : truck time

car kinematics :

car moves with uniformly accelerated movement:

d = vi*t + (1/2)a*t²

vi = 0 : initial speed

d = (1/2)*a*t² Equation (1)

Truck kinematics:

Truck moves with constant speed:

d = v*t Equation (2)

Data

We know that the acceleration of the car is 3.00 ft / s² and the speed of the truck is 70.0 ft / s .

Development problem

Since the distance traveled by the car is equal to the distance traveled by the truck and the time elapsed is the same for both, then we equate equations (1 ) and (2)

Equation (1) = Equation (2)

(1/2)*a*t² = v*t

(1/2)*3*t² = 70*t  (We divide both sides by t)

1.5*t = 70

t = 70 ÷ 1.5

t = 46.66 s

We replace t = 46.66 s in equation (2) to calculate d:

d = 70*46.66 = 3266.2ft

d = 3266.2 ft

Answer:

n = 3

Solution:

Since, the slit used is same and hence slit distance 'x' will also be same.

Also, the wavelengths coincide, [tex]\theta [/tex] will also be same.

Using Bragg's eqn for both the wavelengths:

[tex]xsin\theta = n\lambda[/tex]

[tex]xsin\theta = n\times 680.0\times 10^{- 9}[/tex]           (1)

[tex]xsin\theta = (n + 1)\lambda[/tex]

[tex]xsin\theta = (n + 1)\times 510.0\times 10^{- 9}[/tex]         (2)

equate eqn (1) and (2):

[tex] n\times 680.0\times 10^{- 9} = (n + 1)\times 510.0\times 10^{- 9}[/tex]

[tex]n = \frac{510.0\times 10^{- 9}}{680.0\times 10^{- 9} - 510.0\times 10^{- 9}}[/tex]

n = 3

Final answer:

Using the formula for the location of maxima in a double slit interference pattern and equating the equations for the two different wavelengths, we find that the value of n is 3 for this Young's two-slit experiment scenario.

Explanation:

To determine the value of n such that an nth-order maximum for a wavelength of 680.0 nm coincides with the (n+1)th maximum of light of wavelength 510.0 nm in a Young's two-slit experiment, we can use the formula for the location of maxima in a double slit interference pattern:

dsinθ = mλ, where d is the separation of the slits, sinθ is the sine of the angle of the maxima, m is the order of the maximum, and λ is the wavelength of the light.

For two wavelengths to coincide, we equate the two equations:

nλ1 = (n+1)λ2

Substituting the given wavelengths:

n(680.0 nm) = (n+1)(510.0 nm)

Solving for n gives:

n = 510.0 / (680.0 - 510.0) = 3

Answer:

area is  131.9223168 square meters

Explanation:

given data

we have given 1420 square feet

to find out

area in square meters

solution

we know that 1 square feet is equal to  0.09290304 square meter

so for 1420 square feet we will multiply 1420 by  0.09290304 square meter

and we get 1420 square feet will be = 1420 × 0.09290304  square meter

1420 square feet  = 131.9223168 square meter

so area is  131.9223168 square meters

After the battery is disconnected, the potential difference between the capacitor plates remains at 9.00V. After a sheet of Teflon is inserted between the plates, the potential difference decreases due to increased capacitance.

Part A: When a parallel-plate capacitor is charged by a battery and then the battery is disconnected, the potential difference between the plates remains the same as it was before disconnecting the battery. In this case, the potential difference would remain 9.00V, as this potential difference is determined by the charge on the capacitor and the capacitance, neither of which changes when the battery is disconnected.

Part B: When a dielectric (in this case Teflon) is inserted between the plates of a charged capacitor without a connected battery, the potential difference between the plates decreases. This is because the dielectric increases the capacitance of the capacitor, causing the potential difference to decrease for a fixed charge. The exact amount of the decrease would depend on the dielectric constant of Teflon.

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The potential difference between the capacitor plates remains 9.00 V after disconnecting the battery. After inserting Teflon, the potential difference decreases to around 4.29 V.

A) The potential difference between the plates will remain at 9.00 V after the battery is disconnected as no charge can leave the plates.

B) Introducing a dielectric such as Teflon with a dielectric constant K will reduce the potential difference.

The formula to calculate the new potential difference (V') is given by [tex]V' = V/K[/tex], where

Thus, the new potential difference will be [tex]V' = 9.00\left V / 2.1 \approx 4.29\left V[/tex]. This occurs because Teflon inserts a dielectric constant that reduces the voltage.

Answer:

The answer is [tex] -9.239 \times 10^{-8}\ N = [/tex]

Explanation:

The definition of electric force between two puntual charges is

[tex]F_e = \frac{K q_1 q_2}{d^2}[/tex]

where

[tex]K = 9 \times 10^9\ Nm^2/C^2[/tex].

In this case,

[tex]q_1 = e = 1.602\times 10^{-19}\ C[/tex],

[tex]q_2 = -e = -1.602\times 10^{-19}\ C[/tex]

and

[tex]d = 5 \times 10^{-11}\ m[/tex].

So the force is

[tex]F_e = -9.239 \times 10^{-8}\ N [/tex]

where the negative sign implies force of attraction.

Answer:

distance between object and screen is 2 m

Explanation:

given data

focal length = 0.18 m

magnification = 9.0 x

to find out

distance from the object

solution

we know that magnification is express as

magnification m = [tex]\frac{v}{u}[/tex]   .............1

here u is distance of object from lens

and v is distance of image from lens

so here

9 = [tex]\frac{v}{u}[/tex]

v = 9 u   ..................2

now we will apply here lens formula that is

[tex]\frac{1}{f} = \frac{1}{u} + \frac{1}{v}[/tex]        ....................3

put here value f is focal length and v = 9 u

[tex]\frac{1}{0.18} = \frac{1}{u} + \frac{1}{9u}[/tex]  

solve it we get

u = 0.2

so v = 9 (0.2 )

v = 1.8

so here distance between object and screen is v +u

distance between object and screen = 1.8 + 0.2

distance between object and screen is 2 m