You are on an airplane that is landing. The plane in front of your plane blows a tire. The pilot of your plane is advised to abort the landing, so he pulls up, moving in a semicircular upward-bending path. The path has a radius of 450m with a radial acceleration of 17m/s2. What is the plane’s speed?

Answer:

Explanation:

velocity of ship with respect to water = 6.5 m/s due north

[tex]\overrightarrow{v}_{s,w}=6.5 \widehat{j}[/tex]

velocity of water with respect to earth = 1.5 m/s at 40° north of east

[tex]\overrightarrow{v}_{w,e}=1.5\left ( Cos40\widehat{i} +Sin40\widehat{j}\right)[/tex]

velocity of ship with respect to water = velocity of ship with respect to earth - velocity of water with respect to earth

[tex]\overrightarrow{v}_{s,w} = \overrightarrow{v}_{s,e} - \overrightarrow{v}_{w,e}[/tex]

[tex]\overrightarrow{v}_{s,e} = 6.5 \widehat{j}- 1.5\left (Cos40\widehat{i} +Sin40\widehat{j} \right )[/tex]

[tex]\overrightarrow{v}_{s,e} = - 1.15 \widehat{i}+5.54\widehat{j}[/tex]

The magnitude of the velocity of ship relative to earth is [tex]\sqrt{1.15^{2}+5.54^{2}}[/tex] = 5.66 m/s

Answer:

Emission spectrum

Explanation:

The emmison spectrum is unique to every elements

Light consists of electromagnetic radiation of different wavelengths. Therefore, when the elements or their compounds are heated either on a flame or by an electric arc they emit energy in the form of light.

The color band indicate the amount of energy emitted in form of electromagnetic radiation.

When electrons in an atom gain energy, the become excited, on falling and losing their energy, they return to their ground state releasing the measure of energy they absorbed in transitioning.

The characteristic color bands emitted by an element when heated are called line spectra, which act as a unique fingerprint for the element and are important for identifying various physical properties.

The characteristic color bands that represent the range of radiations emitted by an element when it is heated are known as the line spectra. When elements are heated to incandescence, like in Bunsen and Kirchhoff's experiments, they emit light with a series of sharp wavelengths characteristic of that element's atomic composition.

This light, when analyzed using a spectrometer or a simple prism, results in visible narrow bands of colors, each corresponding to a specific wavelength. For instance, hydrogen emits a red light with a strong line at 656 nm, and sodium is known to emit in the yellow portion of the spectrum at about 589 nm.

The line spectra serve as a unique fingerprint for each element and are crucial for understanding not only the chemical composition but also various physical properties such as temperature and density of the radiant gas. In terms of non-visible bands, color palettes are often chosen to represent different levels of brightness, energies of photons, and inferred physical properties from data modeling, which are essential in the study of astronomy and spectroscopy.

Answer:

Solid cylinder

Explanation:

Solid cylinder will reach first

If radius of each cylinder is r

mass is m

then,

Moment of inertia I= dm[tex]r^{2}[/tex]

Here d = measure as how close the mass is to the edge

Velocity of rolling cylinder is given by

v= [tex]\sqrt} \frac{2gh}{1+d}[/tex]

where,

g= 9.8 m/s2

h= height from ground

So from formula of  velocity we can say that velocity will be maximum if denominator is minimum i-e if k is of small value -- or in other word if mass is away from edge i-e if mass is closer to the center !

As all the mass in hollow cylinder is near the edge so k value will be higher for it and hence it will have low velocity value. So it will reach later  as compared to the solid cylinder in which mass is closer to the center and hence k is greater for solid cylinder.

Answer:

823.46 kgm/s

Explanation:

At 9 m above the water before he jumps, Henri LaMothe has a potential energy change, mgh which equals his kinetic energy 1/2mv² just as he reaches the surface of the water.

So, mgh = 1/2mv²

From here, his velocity just as he reaches the surface of the water is

v = √2gh

h = 9 m and g = 9.8 m/s²

v = √(2 × 9 × 9.8) m/s

v = √176.4 m/s

v₁ = 13.28 m/s

So his velocity just as he reaches the surface of the water is 13.28 m/s.

Now he dives into 32 cm = 0.32 m of water and stops so his final velocity v₂ = 0.

So, if we take the upward direction as positive, his initial momentum at the surface of the water is p₁ = -mv₁. His final momentum is p₂ = mv₂.

His momentum change or impulse, J = p₂ - p₁ = mv₂ - (-mv₁) = mv₂ + mv₁. Since m = Henri LaMothe's mass = 62 kg,

J = (62 × 0 + 62 × 13.28) kgm/s = 0 +  823.46 kgm/s = 823.46 kgm/s

So the magnitude of the impulse J of the water on him is 823.46 kgm/s

Answer:

[tex]2.72\times 10^{6} J[/tex]

Explanation:

Molar mass of isooctane will be 12*8+8=114 g/mole

Combustion of 21.8 gal yields energy of

21.8*3780*0.692*-5440/114=-2721124.6484210 J

In scientific notation, this is [tex]2.72\times 10^{6} J[/tex]

Answer:

The distance the bungee cord that would be stretched 0.602 m, should be selected when pulled by a force of 380 N.

Explanation:

As from the given data

the length of the rope is given as l=30 m

the stretched length is given as l'=41m

the stretched length required is give as  y=l'-l=41-30=11m

the mass is m=95 kg

the  force is  F=380 N

the gravitational acceleration is g=9.8 m/s2

The equation of  k is given by equating the energy at the equilibrium point which is given as

[tex]U_{potential}=U_{elastic}\\mgh=\dfrac{1}{2} k y^2\\k=\dfrac{2mgh}{y^2}[/tex]

Here

m=95 kg, g=9.8 m/s2, h=41 m, y=11 m so

[tex]k=\dfrac{2mgh}{y^2}\\k=\dfrac{2\times 95\times 9.8\times 41}{11^2}\\k=630.92 N/m[/tex]

Now the force is

[tex]F=kx\\[/tex] or

[tex]x=\dfrac{F}{k}\\[/tex]

So here F=380 N, k=630.92 N/m

[tex]x=\dfrac{F}{k}\\x=\dfrac{380}{630.92}\\x=0.602 m[/tex]

So the distance is 0.602 m

The student requires help to calculate the stretch distance of a bungee cord when a force is applied, which is determined using Hooke's Law, F = kx, where F is the applied force and k is the spring constant.

The student is asking about the properties of a bungee cord that would be suitable for their father-in-law's jump so that he will fall safely without hitting the ground. Specifically, the question involves calculating the amount by which the bungee cord would stretch when a force of 380.0 N is applied to it. The restoring force that the bungee cord exerts is given as kx, where k is the spring constant and x is the stretch distance.

To find the correct bungee cord, one must solve for x in the equation F = kx given that F (the force applied) is 380.0 N. The spring constant k is the unknown in this problem and must be determined based on the requirement that the maximum fall before the cord stops the father-in-law is 41 m, factoring in his weight and the initial unstretched length of the bungee cord (30 m).

This problem requires knowledge in the area of Hooke's Law and the work-energy principle, as it deals with forces and the properties of elastic materials. The actual calculation is not provided because it would require additional information about the bungee cords the student has access to, such as their specific spring constants.

Answer: 800N

Explanation:

Given :

Mass of ball =0.8kg

Contact time = 0.05 sec

Final velocity = initial velocity = 25m/s

Magnitude of the average force exerted on the wall by the ball is can be calculated using the relation;

Force(F) = mass(m) * average acceleration(a)

a= (initial velocity(u) + final velocity(v))/t

m = 0.8kg

u = v = 25m/s

t = contact time of the ball = 0.05s

Therefore,

a = (25 + 25) ÷ 0.05 = 1000m/s^2

Therefore,

Magnitude of average force (F)

F=ma

m = mass of ball = 0.8

a = 1000m/s^2

F = 0.8 * 1000

F = 800N

Meselson and Stahl

Explanation:

The classic experiment that supported the semiconservative model of dna replication was performed by Matthew Meselson and Franklin W. Stahl. In this model, the two strands of DNA unwind from each other, and each acts as a template for synthesis of a new, complementary strand. This results in two DNA molecules with one original strand and one new strand. They used E. coli bacteria as a model system.

Answer:

Explanation:

Given

Person travel 180 km with [tex]v_1=95\ km/h[/tex]

and slow down to [tex]v_2=65\ km/h[/tex] due to rain

time taken to cover 180 km is

[tex]t_1=\dfrac{180}{95}[/tex]

[tex]t_1=1.89\ hr[/tex]

total time [tex]T=4.5\ hr[/tex]

suppose [tex]t_2[/tex] is the time for which it travels with [tex]v_2=65\ km/h[/tex]

[tex]t_2=T-t_1[/tex]

[tex]t_2=4.5-1.89[/tex]

[tex]t_2=2.61\ hr[/tex]

so distance travel during this time [tex]d_2=v_2\times t_2[/tex]

[tex]d_2=65\times 2.61[/tex]

[tex]d_2=169.65\ km[/tex]

total distance [tex]d=180+d_2[/tex]

[tex]d=180+169.65[/tex]

[tex]d=349.65\ km[/tex]

(b)Average speed

[tex]v_{avg}=\dfrac{Distance}{time}[/tex]

[tex]v_{avg}=\dfrac{349.65}{4.5}[/tex]

[tex]v_{avg}=77.7\ km/h[/tex]

Answer:

The correct option is false

Explanation:

Awning windows are easy to open windows (made of glass) that are hinged at the top and are opened from the bottom. These windows form a slant (of about 45 degree) after opening hence do not open 100%; this slant opening is advantageous in preventing rain from entering the building.

The windows can also be tightly sealed (from the inside) during extreme/cold weather conditions but are not commonly used everywhere in the world because of there limitations (slight openings) which can prevent proper ventilation in hot regions.

Answer:

The current in R₁ is 0.0816 A.

The current at H point is 0.0243 A.

Explanation:

Given that,

Voltage = 64.5

Resistance is

[tex]R_{1}=711\ \Omega[/tex]

[tex]R_{2}=182\ \Omega[/tex]

[tex]R_{3}=663\ \Omega[/tex]

[tex]R_{4}=534\ \Omega[/tex]

[tex]R_{5}=265\ \Omega[/tex]

Suppose, The specified points are R₁ and H.

According to figure,

R₂,R₃,R₄ and R₅ are connected in parallel

We need to calculate the resistance

Using parallel formula

[tex]\dfrac{1}{R}=\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}}+\dfrac{1}{R_{4}}+\dfrac{1}{R_{5}}[/tex]

Put the value into the formula

[tex]\dfrac{1}{R}=\dfrac{1}{182}+\dfrac{1}{663}+\dfrac{1}{534}+\dfrac{1}{265}[/tex]

[tex]\dfrac{1}{R}=\dfrac{35501}{2806615}[/tex]

[tex]R=79.05\ \Omega[/tex]

R and R₁ are connected in series

We need to calculate the equilibrium resistance

Using series formula

[tex]R_{eq}=R_{1}+R[/tex]

[tex]R_{eq}=711+79.05[/tex]

[tex]R_{eq}=790.05\ \Omega[/tex]

We need to calculate the equivalent current

Using ohm's law

[tex]i_{eq}=\dfrac{V}{R_{eq}}[/tex]

Put the value into the formula

[tex]i_{eq}=\dfrac{64.5}{790.05}[/tex]

[tex]i_{eq}=0.0816\ A[/tex]

We know that,

In series combination current distribution in each resistor will be same.

So, Current in R and R₁ will be equal to [tex]i_{eq}[/tex].

The current at h point will be equal to current in R₅

We need to calculate the voltage in R

Using ohm's law

[tex]V=I_{eq}\timesR[/tex]

Put the value into the formula

[tex]V=0.0816\times79.05[/tex]

[tex]V=6.45\ Volt[/tex]

In resistors parallel combination voltage distribution in each part will be same.

So, [tex]V_{2}=V_{3}=V_{4}=V_{5}=6.45 V[/tex]

We need to calculate the current at H point  

Using ohm's law

[tex]i_{h}=\dfrac{V_{5}}{R_{5}}[/tex]

Put the value into the formula

[tex]i_{h}=\dfrac{6.45}{265}[/tex]

[tex]i_{h}=0.0243\ A[/tex]

Hence, The current in R₁ is 0.0816 A.

The current at H point is 0.0243 A.

Answer:

Maximum altitude above the ground = 1,540,224 m = 1540.2 km

Explanation:

Using the equations of motion

u = initial velocity of the projectile = 5.5 km/s = 5500 m/s

v = final velocity of the projectile at maximum height reached = 0 m/s

g = acceleration due to gravity = (GM/R²) (from the gravitational law)

g = (6.674 × 10⁻¹¹ × 5.97 × 10²⁴)/(6370000²)

g = -9.82 m/s² (minus because of the direction in which it is directed)

y = vertical distance covered by the projectile = ?

v² = u² + 2gy

0² = 5500² + 2(-9.82)(y)

19.64y = 5500²

y = 1,540,224 m = 1540.2 km

Hope this Helps!!!

Answer:

242.85 Hz

Explanation:

For maximum intensity of sound, the path difference,ΔL = (n + 1/2)λ/2 where n = 0,1,2...

Since Abby is standing perpendicular to one speaker, the path length for the sound from the other speaker to him is L₁ = √(2.00² + 5.50²) = √(4.00 + 30.25) = √34.25 = 5.85 m.

The path difference to him is thus ΔL = 5.85 m - 5.50 m = 0.35 m.

Since ΔL = (n + 1/2)λ/2 and for lowest frequency n = 0,

ΔL = (n + 1/2)λ/2 = (0 + 1/2)λ/2 = λ/4

ΔL = λ = v/f and f = v/4ΔL where f = frequency of wave and v = velocity of sound wave = 340 m/s.

f = 340/(4 × 0.35) = 242.85 Hz

The condition of constructive interference and the speed of a wave allows finding the frequency for the first constructive interference that Abby hears is:

         f = 971.4 Hz

The interference of the coherent sound wave occurs when two wave fronts are added at a point and the intensity depends on the path difference of these waves, we have two extreme cases:

          Δr = [tex]2n \ \frac{\lambda}{2}[/tex]

Where Δr is the path difference, λ is the wavelength and n is an integer.

In the attachment we can see the distance from Abby is to the speakers for the closest y = 5.50 m, the distance to the furthest speaker.

Let's use the Pythagoras' theorem,

             r =[tex]\sqrt{x^2 + y^2}[/tex]  

Let's calculate.

            r = [tex]\sqrt{2^2 + 5.5^2}[/tex]  

            r = 5.85 m

The difference in path is:

           Δr = r-y

           Δr = 5.85 - 5.5

           Δr = 0.35 m

let's find the wavelength.

          Δr = 2n [tex]\frac{\lambda}{2}[/tex]  

          λ = [tex]\frac{\Delta r}{n}[/tex]

The first constructive interference occurs for n = 1

           λ= Δr

           λ = 0.35 m

Wave speed is proportional to wavelength and frequency.

          v = λ f

          f = [tex]\frac{v}{\lambda }[/tex]

Let's calculate.

          f = [tex]\frac{340}{0.35}[/tex]  

          f = 971.4 Hz

In conclusion using the condition of constructive interference and the speed of a wave we can find the frequency for the first constructive interference that Abby hears is:

          f = 971.4 Hz

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Answer:

Work done = 87.5 J

Explanation:

Given:

Force required to stretch the spring (F) = 250 N

Extension of the spring (x) = 30 cm = 0.30 m     [1 cm = 0.01 m]

So, spring constant (k) of the spring is given as:

[tex]k=\frac{F}{x}\\\\k=\frac{250\ N}{0.30\ m}=833.33\ N/m[/tex]

Also given:

Initial length of the spring (x₁) = 20 cm = 0.20 m

Final length of the spring (x₂) = 50 cm = 0.50 m

Now, work done in stretching the spring from an initial length (x₁) to final length (x₂) is given as:

[tex]W=\frac{1}{2}k(x_2^2-x_1^2)[/tex]

Plug in the given values and solve for 'W. This gives,

[tex]W=\frac{1}{2}\times \frac{250}{0.3}\times (0.50^2-0.20^2)\\\\W=\frac{1250}{3}\times (0.25-0.04)\\\\W=\frac{1250\times 0.21}{3}=87.5\ J[/tex]

Therefore, work is done in stretching the spring from 20 centimeters to 50 centimeters is 87.5 J

The work done in stretching a spring can be calculated using Hooke's law. Here, to find the work done in stretching a spring from 20 centimeters to 50 centimeters, we first find the spring constant using the given force and distance, then compute the work using the difference in the squares of the final and initial stretching distances. The work done is 104.1 Joules.

The subject of this question pertains to the physics concept of work done on an object, in this case, a spring. When a force is applied to a spring, it stretches, and in doing so, work is done. The work done can be calculated using Hooke's Law, which states that the force (F) needed to extend or compress a spring by some distance X is proportional to that distance. This is represented by the equation F = kX, where k is the spring constant.

First, we need to find the spring constant k using the provided force (250 newtons) and the initial stretching distance (30 centimeters or 0.3 meters), so k = F/X = 250/0.3 = 833.33 N/m.

Next, we compute the work done in stretching the spring from 20 centimeters (0.20 meters) to 50 centimeters (0.50 meters). The work done (W) on a spring is given by the equation W =1/2*k*(X2^2-X1^2), where X2 and X1 are the final and initial stretching distances respectively. So, W = 1/2 * 833.33 * ((0.5)^2 - (0.2)^2) = 104.1 Joules.

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Answer:Friction force

Explanation:

The frictional force is responsible for stopping the moving object.

The friction force is provided by nature in the form of air resistance, fluid resistance, Surface resistance.

For surface resistance, the friction force is of two types namely kinetic friction force and static friction force.

Static friction acts when the object is stationary and a force is applied to cause the motion while kinetic friction acts when the body starts moving.

kinetic friction is lesser is in magnitude as compared to static friction.

The misunderstood force that causes objects to seem to stop on their own is known as friction. This force opposes the motion of objects. The misconception was fixed with Newton's first law of motion.

The force that people did not understand before they realized that objects have a tendency to maintain their velocity in a straight line unless acted upon by a net force is friction. Friction is a force that opposes movement. It's the reason why objects seem to stop on their own when in contact with other objects or surfaces. The perception that an object moves and then eventually stops due to its own 'nature' occurs because friction was at play, causing it to slow down and finally stop. It was Sir Isaac Newton who, in his first law of motion, clarified this misperception by stating that an object in motion stays in motion unless acted upon by an external force.

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Answer:

Unusually large moons form in giant impacts, which are relatively rare events

Explanation:

Solution:

- Finding large moons comparable in size to their planets result from impacts of two astro-bodies. The probability of such an event occurring is very rare.

- Even at the best luck, one moon can be made from the result of giant impact. While the probability of 6 planets having moons of comparable sizes is close to impossible. The transition from an undifferentiated cloud to a star system complete with planets and moons takes about 100 million years.

Answer:

The total work done by the mover is 2.81 kJ.

Explanation:

Given the 46 kg crate is displaced by 10.4 meters.

And the acceleration is zero. Also, [tex]\mu_k=0.60[/tex]

let [tex]P[/tex] is applied force, [tex]F_N[/tex] is the net force, [tex]m[/tex] is the mass and [tex]g=9.81\ m/s^2[/tex]

and [tex]\mu_k=0.60[/tex]

[tex]F_N=P- \mu_k\times mg[/tex]

As the acceleration is zero, the net force will also be zero.

[tex]0=P- \mu_k\times mg\\P=\mu_k\times mg[/tex].

[tex]P=0.6\times 46\times 9.81=270.76\ N[/tex]

Now, we know the work done is force times displacement.

So,

[tex]W=P\times d\\W=270.76\times 10.4=2815.90\ J\\W=2.81\ kJ[/tex]

So, the total work done by the mover to displace 46 kg crate by 10.4 meters 2.81 kJ.

Answer:

ΔPE= -4.8×10⁻²⁰J

Explanation:

Given data

Electric field of strength E=3.0 N/C

Charge of proton q=1.60×10⁻¹⁹C

Proton moves distance d=10 cm=0.10 m

To find

Change in electrical potential energy ΔPE

Solution

As we know that:

ΔPE= -qEd

[tex]=-(1.60*10^{-19}C )(3.0N/C)(0.10m)\\=-4.8*10^{-20}J[/tex]

ΔPE= -4.8×10⁻²⁰J

Answer:

Explanation:

Given:

D = 10 cm

= 0.1 m

E = 3.0 N/C

Qp = 1.602 × 10^-19 C

U = Q × V

But,

V = E × D

= 3 × 0.1

= 0.3 V

U = 1.602 × 10-19 × 0.3

= 4.806 × 10^-20 J.

The HCP structure has the fewest slip directions, making HCP metals like Mg and Zn more difficult to deform at room temperature compared to those with BCC or FCC structures.

The crystal structure that has the fewest slip directions and is thus generally more difficult to deform at room temperature is the hexagonal close-packed (HCP) structure. Metals with the HCP structure include Cd, Co, Li, Mg, Na, and Zn. The nature of HCP's stacking arrangement, with alternating type A and type B close-packed layers (ABABAB...), results in fewer slip systems compared to body-centered cubic (BCC) and face-centered cubic (FCC) structures. BCC structures, found in metals like K, Ba, Cr, Mo, W, and Fe, have a coordination number of 8, whereas FCC structures have a coordination number of 12 and include metals like Ag, Al, Ca, Cu, Ni, Pb, and Pt. The closer atomic packing found in FCC, identified as CCP or cubic close-packed, is reflected in the ABCABCABC... stacking sequence, which affords a higher number of slip directions.

Answer:

The required torque is 1.17 N-m.

Explanation:

The given data :-

The magnitude of force ( F ) = 4.5 N.

The length of arm ( r ) = 0.26 m.

Here given that force is applied at perpendicular means ( ∅ ) = 90°.

The torque ( T ) is given by

T = F * r * sin∅

T = 4.5 * 0.26 * sin 90°

T = 4.5 * 0.26 * 1

T = 1.17 N-m.

The magnitude of the torque produced by the given force perpendicular to the lever is 1.17N.m.

Given the data in the question;

Torque; [tex]T = \ ?[/tex]

Torque simply the measure of the force that can cause an object to rotate about an axis. It is expressed as:

[tex]T = rFsin\theta[/tex]

Where r is radius, F is force applied and θ is the angle between the force and the lever arm.

We substitute our given values into the equation;

[tex]T = 0.26m * 4.5N * sin90^o\\\\T = 0.26m * 4.5N * 1\\\\T = 1.17N.m[/tex]

Therefore, the magnitude of the torque produced by the given force perpendicular to the lever is 1.17N.m.

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Answer:

64.59kpa

Explanation:

See attachment

Answer:

the equilibrium constant is equal to 1 (i.e., the reactant and product concentrations are always equal).

Explanation:

ΔG is a symbol related to Gibbs free energy, which is a physical quantity related to thermodynamics. ΔG refers to the difference between the change in enthalpy (and sometimes entropy) and the temperature of a chemical reaction.

Gibbs free energy is very useful for measuring the work done between the reactants in a reaction. It is calculated using the formula: ΔG = change in enthalpy - (temperature x change in entropy).

The ΔG of a reaction would have a minimum value (zero), if the equilibrium constant is equal to 1 (that is, the concentrations of the reagent and the product are always equal).

the equilibrium constant should be equal to 1 (i.e., the reactant and product concentrations are always equal).

ΔG refers to a symbol that should be related to Gibbs free energy, i.e. physical quantity related to thermodynamics. ΔG means the difference between the change in enthalpy and the temperature of a chemical reaction. Now it is determined using the formula:

ΔG = change in enthalpy - (temperature x change in entropy).

In the case when the ΔG of a reaction would have a minimum value (zero), so if the equilibrium constant is equivalent to 1 i.e. the concentrations of the reagent and the product should always equal.

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Answer:

fail to reject the null hypothesis; there is not sufficient evidence to support the claim that the songs are from a population with a standard deviation less than one minute  

Explanation:

Answer:

1.9 s

Explanation:

We are given that

Length of cable=l=15 m

We have to find the time you have to move out of the way.

We know that

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

Where g=[tex]9.8m/s^2[/tex]

By using the formula

[tex]T=2\pi\sqrt{\frac{15}{9.8}}[/tex]

[tex]T=2\times 3.14\times \sqrt{\frac{15}{9.8}}=7.77 s[/tex]

Time you have to move out

[tex]t=\frac{T}{4}=\frac{7.77}{4}=1.9 s[/tex]

Hence,time you have to move out of the way=7.77 s

The tangential speed v that the bob must have is: v = [tex]\sqrt{gLsin(\theta)tan(\theta)[/tex]

And the time for one full revolution is: T = [tex]\frac{2\pi \sqrt{Lsin(\theta)}}{\sqrt{g tan(\theta)}}[/tex]

To solve this problem, we need to find the tangential speed, v, that the bob must have to move in a horizontal circle and the time, T, it takes to make one complete revolution. Here’s a step-by-step approach to the solution:

Determine the radius of the circular motion (R):

Given that the string length is L and the angle from the vertical is θ, the radius of the horizontal circle can be expressed as:

R = L sin(θ)

Analyze the forces acting on the bob:

The forces acting on the bob are:

Equations of motion:

In the vertical direction, since there is no vertical acceleration, the vertical component of the tension must balance the weight of the bob:

Tcos(θ) = mg

In the horizontal direction, the horizontal component of the tension provides the centripetal force necessary for the circular motion:

Tsin(θ) = mv²/R

Solve for the tension (T):

From the vertical force balance equation:

T = mg ​/cos(θ)

Substitute T into the horizontal force equation and solve for v:

mgsin(θ) /cos(θ) ​= mv²/R

Simplifying, we get:

gtan(θ) = v² /R​

Substitute R = L sin(θ):

gtan(θ) = Lsin(θ)v²

Solving for v, we get:

v = [tex]\sqrt{gLsin(\theta)tan(\theta)}[/tex]

Determine the period of the motion (T):

The time for one complete revolution (T) is the circumference of the circle divided by the tangential speed v:

T = 2πR /v​

Substitute R and v:

T = [tex]\frac{2\pi Lsin(\theta)}{\sqrt{gLsin(\theta)tan(\theta)}}[/tex]

Simplifying further:

T = [tex]\frac{2\pi \sqrt{Lsin(\theta)}}{\sqrt{g tan(\theta)}}[/tex]

Therefore, the tangential speed v:  v = [tex]\sqrt{gLsin(\theta)tan(\theta)[/tex]  ,and the period of revolution is: T = [tex]\frac{2\pi \sqrt{Lsin(\theta)}}{\sqrt{g tan(\theta)}}[/tex].

Answer:

The three lowest possible values for d are 0.85 m, 2.55 m and 4.25 m.

Explanation:

Given that,

Distance = d

Frequency = 200 Hz

Speed of sound = 340 m/s

We need to calculate the wave length

Using formula of frequency

[tex]f= \dfrac{v}{\lambda}[/tex]

[tex]\lambda=\dfrac{v}{f}[/tex]

Put the value into the formula

[tex]\lambda=\dfrac{340}{200}[/tex]

[tex]\lambda=1.7\ m[/tex]

We need to calculate the three lowest possible values for d

Using formula of destructive interference

[tex]\Delta\phi=2\pi\dfrac{\Delta x}{\lambda}[/tex]

[tex]2\pi\dfrac{\Delta x}{\lambda}=(m+\dfrac{1}{2})2\pi[/tex]

Where, [tex]\Delta x[/tex] = distance

Put the value into the formula

For m = 0,

[tex]\dfrac{\Delta x}{1.7}=(0+\dfrac{1}{2})[/tex]

[tex]\Delta x=\dfrac{1.7}{2}[/tex]

[tex]\Delta x=0.85\ m[/tex]

For m =1 ,

[tex]\dfrac{\Delta x}{1.7}=(1+\dfrac{1}{2})[/tex]

[tex]\Delta x=\dfrac{1.7\times3}{2}[/tex]

[tex]\Delta x=2.55\ m[/tex]

For m=2,

[tex]\dfrac{\Delta x}{1.7}=(2+\dfrac{1}{2})[/tex]

[tex]\Delta x=\dfrac{1.7\times5}{2}[/tex]

[tex]\Delta x=4.25\ m[/tex]

Hence, The three lowest possible values for d are 0.85 m, 2.55 m and 4.25 m.

The three lowest possible values for d are 0.85 m, 2.55 m and 4.25 m.

Since we are looking for the points of no sound, these are points of destructive interference. So, the path difference, ΔL which is the distance between the two speakers, d is

ΔL = d = (n + 1/2)λ where

So, d = (n + 1/2)v/f

d = (n + 1/2)340m/s ÷ 200 Hz

d = (n + 1/2)1.7 m

The lowest possible values of d are when n = 0, 1 and 2.

So,

d = (n + 1/2)1.7 m

d = (0 + 1/2)1.7 m

d = (1/2)1.7 m

d = 0.85 m

d = (n + 1/2)1.7 m

d = (1 + 1/2)1.7 m

d = (3/2)1.7 m

d = (1.5)1.7 m

d = 2.55 m

d = (n + 1/2)1.7 m

d = (2 + 1/2)1.7 m

d = (5/2)1.7 m

d = 2.5 × 1.7 m

d = 4.25 m

So, the three lowest possible values for d are 0.85 m, 2.55 m and 4.25 m.

Learn more about destructive interference here:

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Answer:

Average power = 0.240Watts

Explanation:

The insect requires double the force on its wings to counteract the gravitational force pulling it down.it generates upward force as below

Upward Force=2Gravitational force

force =2x(mass x gravitational pull)

F=(0.007x9,8)x 2

F=0.137 Nm

Power generated is =work/time

power =force *displacement/time

convert 1.5cm to SI units meters=0.015meters

displacement in one second is=0.015 x number of strokes

displacement =0.015*117

displacement =1.755 meters

power=(0.137*1.755)/1second

power=0.240 Watts

Answer:

The final pressure of the whole system is 34.80 atm.

Explanation:

Given that,

Volume = 45.0 ml

Volume of first bulb = 77.0 mL

Pressure  = 8.89 atm

Volume of second  bulb = 250 mL

Pressure = 2.82 atm

Volume of third  bulb = 21.0 mL

Pressure = 8.42 atm

We need to calculate the final pressure of the whole system

Using formula of pressure

[tex]P_{1}V_{1}+P_{2}V_{2}+P_{3}V_{3}+P_{t}V_{t}=P_{f}V_{f}[/tex]

Where, [tex]P_{1}[/tex]= pressure of first bulb

[tex]P_{2}[/tex]= pressure of second bulb

[tex]P_{3}[/tex]= pressure of third bulb

[tex]P_{4}[/tex]= initial pressure of tube

[tex]V_{1}[/tex]= Volume of first bulb

[tex]V_{2}[/tex]=Volume of second bulb

[tex]V_{3}[/tex]= Volume of third bulb

[tex]V_{4}[/tex]= Initial volume of tube

Put the value into the formula

[tex]8.89\times77.0+250\times2.82+21.0\times8.42+0=P_{f}\times45[/tex]

[tex]P_{f}=\dfrac{1566.35}{45}[/tex]

[tex]P_{f}=34.80\ atm[/tex]

Hence, The final pressure of the whole system is 34.80 atm.

Answer:

THE ANSWER IS: TRUE

Explanation:

Strategic planning is indeed long-range and formulated by top management but not under the assumption that the company operates in a vacuum. Effective strategic planning acknowledges and incorporates external factors.

The statement is partially true and partially false. It is accurate that strategic planning is long-range and formulated by top management. These types of plans typically look several years into the future to set comprehensive goals for the company. However, the statement is false in suggesting that strategic planning is done as if a company operates in a vacuum. In truth, effective strategic planning must incorporate external influences like market trends, competitive activities, and regulatory changes.

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Answer:

Explanation:

Imagine that current runs in all the 5 sides . In that case the pentagon will have a magnetic moment directed in z- direction . So in the magnetic field it will experience a torque equal to MB where M is magnetic moment and B is magnetic field. But net force on it will be zero.

So , force on four sides due to magnetic field will be equal and opposite to force on fifth side if current runs through it.

force on fifth side if current runs through it

= BIL

= .222 x 3.33 x .0555

= 41.03 x 10⁻³ N .