Two cellists, one seated directly behind the other in an orchestra, play the same 220-Hz note for the conductor who is directly in front of them. What is the smallest non-zero separation that produces constructive interference? Take the speed of sound to be 343 m/s.

Answer:

2.03873 s

70.38735 m

4.07747 seconds

5.82688 seconds

27.37482 m from the ground

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

g = Acceleration due to gravity = 9.81 m/s² = a

[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-20}{-9.81}\\\Rightarrow t=2.03873\ s[/tex]

time needed for the ball to reach its maximum height is 2.03873 s

The time taken to go up and the time taken to reach the point from where it was thrown is the same.

So, time needed for the ball to return to the height from which it was thrown is 2.03873+2.03873 = 4.07747 seconds

[tex]v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0^2-20^2}{2\times -9.81}\\\Rightarrow s=20.38735\ m[/tex]

The maximum height the ball will reach is 50+20.38735 = 70.38735 m

[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow 70.38735=0t+\frac{1}{2}\times 9.81\times t^2\\\Rightarrow t=\sqrt{\frac{70.38735\times 2}{9.81}}\\\Rightarrow t=3.78815\ s[/tex]

Time needed to reach the ground is 2.03873+3.78815 = 5.82688 seconds

The time from the maximum height that is required is 5-2.03873 = 2.96127 seconds

[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0\times t+\dfrac{1}{2}\times 9.81\times 2.96127^2\\\Rightarrow s=43.01253\ m[/tex]

The ball will be 70.38735-43.01253 = 27.37482 m from the ground

The problem is solved using kinematic equations. The ball reaches its maximum height in approximately 2.04 s, with the maximum height reaching about 70.4 m. It returns to the original height in around 4.08 s with a velocity at -39.79 m/s, reaches the ground in about 5.82 s, and at t = 5 s, its position is approximately 49.4 m with velocity of around -29 m/s.

The calculations are based on the physics of kinematics, specifically related to the motion under constant acceleration which in this context is gravity (designated 'g'), typically -9.8 m/s².

(a) You can use the equation v = u + gt to solve for time (t). Since the velocity (v) at the maximum height is 0, initial velocity (u) is 20 m/s and g is -9.8m/s², the equation becomes 0 = 20 - 9.8t. Solving for t, we get t = 20/9.8 ≈ 2.04 s.  

(b) The maximum height can be found using the equation s = ut + 0.5gt². Substituting the known values we get the maximum height to be about 70.4m

(c) The time taken for the ball to return to its original height will be double the time to reach maximum height, so it's 2*2.04s = 4.08s. The velocity is simply gt, yields -39.79m/s (negative because it's moving downwards).

(d)We can utilize the equation s = ut + 0.5gt² to find out the time to hit the ground. The total distance covered is 50m + 20.4m = 70.4m. Solving the equation we get t = 3.78s (above the throwing point) and to find the total time on air, add t = 2.04s and value calculated you get t = 5.82 s.  

(e)Using equations of motion, we can find out that at t=5s, the position of the ball is 49.4 m above the ground and its velocity is -29m/s.

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Answer:it is cold

Explanation:because of a winter storm it is very cold which doesn’t

Match Florida’s tropical warm climate

Weather refers to short-term atmospheric conditions while climate refers to long-term predictable conditions. Weather in Orlando today depicts the present conditions, whereas Florida's climate represents the long-term averages and patterns across the state.

The weather in Orlando today simply refers to the current atmospheric conditions in Orlando, such as temperature, humidity, precipitation, wind, etc. It's a mere snapshot of what's happening right now in the atmosphere around Orlando. Now, when we're talking about Florida's climate, we're referring to the long-term atmospheric conditions in the state of Florida. This includes consistent seasonal temperature and rainfall patterns over many years. Therefore, the primary difference between describing the weather in Orlando today and Florida's climate lies in the timeframe – weather explains temporary conditions, while climate refers to long-term, predictable conditions.

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Answer:

The thickness of 1 card is between 0.006in and 0.016in

Explanation:

Thickness of a deck of 52 cards = 0.590in

Thickness of 1 card = 0.590in/52 = 0.011in

Uncertainty = + or - 0.005in

Lower limit of thickness of 1 card = 0.011in - 0.005in = 0.006in

Upper limit of thickness of 1 card = 0.011in + 0.005in = 0.016in

Therefore, thickness of 1 card is between 0.006in and 0.016in

Answer:

3894531 coulombs

Explanation:

1 hour = 3600 seconds

Let g = 10m/s2

The distance that the car travel at 25 m/s over an hour is

s = 25 * 3600 = 90000 m

The total mechanical energy of the car is the sum of its kinetic energy to reach 25 m/s, its potential energy to climb up 200m high hill and it work to travel a distance of s = 90000m with F = 500 N force:

[tex] \sum E = E_k + E_p + E_W[/tex]

[tex]\sum E = mv^2/2 + mgh + Fs[/tex]

[tex]\sum E = 750*25^2/2 + 750*10*200 + 500*90000 = 46734375 J[/tex]

This energy is drawn from the battery over an hour (3600 seconds), so its power must be

[tex]P = E / t = 46734375/3600 = 12982 W[/tex]

The system is 12V so its current is

[tex]I = P/U = 12982 / 12 = 1081.8 A[/tex] or 1081.8 Coulombs/s

The the total charge it needs for 1 hour (3600 s) is

C = 1081.8 * 3600 = 3894531 coulombs

The quantity of charge the batteries must be able to move is equal to 3.9 μC.

Given the following data:

Scientific data:

To find the quantity of charge the batteries must be able to move:

In this scenario, we would calculate the distance traveled and the total energy that is possessed by this battery-operated car.

Mathematically, the distance covered by an object is given by this formula:

[tex]Distance = speed \times time\\ \\ Distance = 25 \times 3600[/tex]

Distance = 90,000 meters.

[tex]E = mgh + \frac{1}{2} mv^2 + Fd\\ \\ E=[750\times 9.8 \times 200] + \frac{1}{2} \times 750 \times 25^2 + [500 \times 90000]\\ \\ E=1470000+234375+45000000[/tex]

Total energy = 46,704,375 Joules.

Next, we would calculate the power consumed by this battery-operated car:

[tex]Power = \frac{Energy}{time}\\ \\ Power = \frac{46,704,375}{3600} [/tex]

Power = 12,973.44 Watts.

Also, we would calculate the current:

[tex]Current = \frac{power}{voltage} \\ \\ Current = \frac{12,973.44}{12}[/tex]

Current = 1,081.12 Amperes.

Now, we can calculate the quantity of charge the batteries must be able to move:

[tex]Q = current \times time\\ \\ Q = 1081.12 \times 3600[/tex]

Q = 3,892,032 Coulombs.

Note: 1 μC = [tex]1 \times 10^6 \;C[/tex]

Q = 3.9 μC

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Answer:

v' = -0.0906 m/s

Explanation:

given,

mass of cannon, M = 2240 Kg

mass of the ball, m = 15.5 Kg

speed of cannon ball, v = 131 m/s

speed of he cannon = ?

initial speed of cannon and the cannon ball is equal to 0 m/s

using conservation of energy

(M+m)V = M v' + m v

(M+m) x 0= 22400 v' + 15.5 x 131

22400 v' = -2030.5

v' = -0.0906 m/s

negative sign represent the canon will move in opposite direction of the ball.

hence, speed of cannon is equal to 0.0906 m/s

Using the law of conservation of momentum and the given values, the recoil velocity of the cannon is found to be approximately 0.9058 m/s after firing a cannonball.

According to the law of conservation of momentum, the total momentum before an event must equal the total momentum after the event, if no external forces act on the system. In this case, the cannon and the cannonball system is isolated and free to recoil, so the momentum before the cannon fires must be equal to the momentum after the cannon fires.

Momentum is the product of mass and velocity. Before the cannon fires, both the cannon and the cannonball are at rest and have a momentum of zero. After the cannon fires, the momentum of the cannonball is mcannonball × vcannonball, which must be equal and opposite to the momentum of the cannon. Therefore, mcannonball × vcannonball = mcannon × vcannon.

Using the given values for mass and velocity of the cannonball (15.5 kg and 131 m/s), and the mass of the cannon (2240 kg), we can calculate the cannon's recoil velocity using the equation:

mcannonball × vcannonball = mcannon × vcannon

(15.5 kg × 131 m/s) / 2240 kg = vcannon

The calculated recoil velocity of the cannon is approximately 0.9058 m/s.

Answer:

1328.7032 kg

Explanation:

P = Pressure = 112 kPa

T = Temperature = 285 K

V = Volume = 7023 m³

R = Gas constant = 8.314 J/mol K

From the ideal gas law we have

[tex]PV=nRT\\\Rightarrow n=\dfrac{PV}{RT}\\\Rightarrow n=\dfrac{112000\times 7023}{8.314\times 285}\\\Rightarrow n=331960.04203\ moles[/tex]

The mass of gas is given by

[tex]m=n\times MW_{He}\\\Rightarrow m=331960.04203\times 4.0026\times 10^{-3}\\\Rightarrow m=1328.70326\ kg[/tex]

The mass of helium in the blimp is 1328.7032 kg

By applying the ideal gas law, we determined the number of moles of helium in the blimp. By using the molecular weight of helium, we calculated that the mass of helium in the blimp is 12000 kg.

We can use the ideal gas law to solve this problem. The ideal gas law is represented by the formula PV = nRT, where P represents the absolute pressure, V is the volume, n is the number of moles, R is the ideal gas constant and T is the temperature.

Based on the given values, we have P = 112 kPa, V = 7023 m^3, R = 8.31 (J/mol.K), and T = 285 K. We need to calculate n (number of moles) first.

Transforming the formula, we get n = PV/RT. Substituting the given values, n = (112,000 Pa * 7023 m^3) / (8.31 J / (mol. K) * 285 K) which gives us n = 3.0 * 10^6 moles.

Then, knowing that the molecular weight of helium is approximately 4 g/mol, we can multiply the number of moles by the molecular weight to find the mass. So, the mass is m = n * Molecular weight = 3.0 * 10^6 moles * 4 g/mol = 12 * 10^6 g or 12000 kg.

Therefore, the mass of the helium in the blimp is 12000 kg.

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Answer:

b) Cells will pass through the G1/S checkpoint even if conditions are not ideal for cell division.

Explanation:

In the given problem, if there exists a gain-of-function mutation for the given cell, there would not be the formation of cyclin E when there is the possibility of cells movement via the checkpoint of the G1/S, even when there are non-deal conditions for the division of cell. Thus, the correct option in the lists of options is the option b.

The water was moving out from the bottom at a velocity of 29 m/s

Applying Bernoulli's equation:

P + ρgh + (1/2)ρv² = constant

P is pressure, g is acceleration due to gravity, h is height, v is velocity, ρ is density.

At top:

P = 3.20 atm = 3.20 * 101300 Pa, ρ = 1025 kg/m³, v = 0, g = 9.81 m/s, h = 10.7 m, hence:

P + ρgh + (1/2)ρv² = ( 3.20 * 101300) + (1025 * 9.81 * 10.7) + 0

At bottom:

h = 0, P = 0

P + ρgh + (1/2)ρv² = 0 + 0 + (1/2* 1025)v²

Equating top and bottom:

( 3.20 * 101300) + (1025 * 9.81 * 10.7) = (1/2* 1025)v²

v = 29 m/s

The water was moving out from the bottom at a velocity of 29 m/s

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To calculate the speed of the water flowing out of the tank, we can use Bernoulli's equation. Plugging in the given values and solving for the final velocity, we can determine the speed of the water.

To determine how fast the water is moving, we can use Bernoulli's equation which relates the pressure, velocity, and height of a flowing fluid.

P1 + 1/2 ρv12 + ρgh1 = P2 + 1/2 ρv22 + ρgh2

Where:

Plugging in the values, we can solve for v2:

3.20 atm + 0 + (1000 kg/m3)(9.8 m/s2)(10.7 m) = 1 atm + 1/2(1000 kg/m3)v22 + (1000 kg/m3)(9.8 m/s2)(0 m)

Simplifying the equation, we can solve for v2:

v22 = 2[(3.20 atm - 1 atm) / (1000 kg/m3)]

v2 = √[2(3.20 atm - 1 atm) / (1000 kg/m3)]

Using the equation, we can calculate v2 to find the speed at which the water is flowing.

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Answer:

The uncertainty in the location that must be tolerated is [tex]1.163 * 10^{-5} m[/tex]

Explanation:

From the uncertainty Principle,

Δ[tex]_{y}[/tex] Δ[tex]_{p}[/tex] [tex]= \frac{h}{2\pi }[/tex]

The momentum P[tex]_{y}[/tex] = (mass of electron)(speed of electron)

                                = [tex](9.109 * 10^{-31}kg)(995 * 10^{3} m/s)[/tex]

                                = [tex]9.0638 * 10^{-25}kgm/s[/tex]

If the uncertainty is reduced to a 0.0010%, then momentum

                              = [tex]9.068 * 10^{-30}kgm/s[/tex]

Thus the uncertainty in the position would be:

                              Δ[tex]_{y} = \frac{h}{2\pi } * \frac{1}{9.068 * 10^{-30} }[/tex]

                              Δ[tex]_{y} \geq 1.163 * 10^{-5}m[/tex]

The uncertainty in location of the electron can be calculated using Heisenberg's Uncertainty Principle, which stipulates a product of the uncertainties in position and momentum to be at least half of reduced Planck's constant. Uncertainty in momentum is given as 0.0010% of the electron's momentum. Careful consideration of quantities and units is essential.

This question revolves around Heisenberg's Uncertainty Principle. According to this principle, the product of the uncertainty in the position, denoted by Δx, and the uncertainty in momentum, denoted by Δp, has a minimum value dictated by Planck's constant, h. Mathematically, it is represented as Δx * Δp ≥ ħ/2, where ħ is the reduced Planck's constant, ħ=h/(2π). The speed of the electron, v, is related to its momentum, p, through mass, m, as p=mv. Therefore, the uncertainty in momentum, Δp, can be calculated as 0.0010% of p. Once we find Δp, using the Uncertainty Principle, we can find the minimum required uncertainty in the electron's location, Δx. In such problems, considering mass and speed of electron and appropriate units for constants are crucial for

correct computation

. Make sure to consider them appropriately.

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Answer:

The answer to your question is Mass = 41230.7 g  or 41.23 kg    

Explanation:

Data

density = 0.737 g/ml

mass = ?

volume = 14.9 gal

1 gal = 3.78 l

Process

1.- Convert gallons to liters

                                   1 gal ---------------- 3.78 l

                                  14.8 gal -------------  x

                                    x = 55.94 l

2.- Convert liters to milliliters

                                  1 l -------------------  1000 ml

                              55.94 l ---------------   x

                                   x = (55.94 x 1000) / 1

                                   x = 55944 ml

3.- Calculate the mass

Formula

density = [tex]\frac{mass}{volume}[/tex]

Solve for mass

Mass = density x volume

Substitution

Mass = 0.737 x 55944

Simplification and result

Mass = 41230.7 g  or  41.23 kg    

Answer:

32.67255 W

Explanation:

F = Force  = 22 N

r = Radius of crank = 0.26 m

s = Displacement = [tex]2\pi r[/tex]

[tex]\theta[/tex] = Angle = 0

t = Time taken = 1.1 s

Work done is given by

[tex]W=Fscos\theta\\\Rightarrow W=22\times 2\pi\times 0.26\times cos0\\\Rightarrow W=35.93981[/tex]

Power is given by

[tex]P=\dfrac{W}{t}\\\Rightarrow P=\dfrac{35.93981}{1.1}\\\Rightarrow P=32.67255\ W[/tex]

The average power being expended is 32.67255 W

Explanation:

The Vehicle Assembly Building at the Kennedy Space Center in Florida has a volume of 3,666,500 m³.

Volume = 3,666,500 m³

1 m³ = 1000 L

So volume = 3,666,500 x 1000 = 3666500000 L

Volume of vehicle Assembly Building at the Kennedy Space Center in Florida = 3666500000 L

Volume of vehicle Assembly Building at the Kennedy Space Center in Florida = 3.67 x 10⁹ L

The volume in liters and in exponential notation is [tex]3.67\times10^{23}[/tex].

To convert the given volume to liters it is necessary to use the following relation of values:

                                                    [tex]dm^{3} = L\\ m ^{3} = 1000L[/tex]

Therefore, the following calculation must be performed:

                                   [tex]3,666,500m^{3} \times 1000= xL[/tex]

                                        [tex]x = 3,666,500,000 L[/tex]

Now, to convert to scientific notation, leave the number different from the power of 10 between 1 and 10, so that:

                                  [tex]3,666,500,000 = 3.67 \times 10^{9} L[/tex]

So, the volume in liters and in exponential notation is [tex]3.67\times10^{23}[/tex]

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Answer:

Extension is 12.14m

Explanation:

mass of ornament=42g,weight of ornament=mg=42*9.8=411.6

Force constant(k)= 33.9N/m

F=ke

e=F/k

F is force, e is extension

F=weight of ornament

e=411.6/33.9

e=12.14m

4.472 tonnes of coal burned

Explanation:

The electricity consumption for a typical house in the United States for a year is approximated as 11,000 kWh.

Given that a typical coal-fired power plant produces 2,460 kWh of electricity  per ton of coal burned then;

2460 kWh = 1 ton of coal burned

11,000 kWh =?

cross-product

(11,000*1)÷ 2460 = 4.472 tonnes of coal burned

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The amount of coal required to be  burned in a typical coal-fired power plant to provide the electricity for a typical house in the United States for a year will be 4.472 tonnes.

Given data:

The electricity produced per ton of coal burn is, E = 2,460 kWh.

The given problem is based on the Energy consumption. The energy consumption is the energy utilized to perform various actions such as manufacturing, welding, inhabiting, and many more.

The electricity consumption for a typical house in the United States for a year is approximated as 11,000 kWh.

And as per the given question,

2460 kWh = 1 ton of coal burned

So for 11,000 kWh, the amount of coal need to be burned is,

= 11000/2460

= 4.472 tonnes of coal  

Thus, we can conclude that amount of coal required to be  burned in a typical coal-fired power plant to provide the electricity for a typical house in the United States for a year will be 4.472 tonnes.

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Answer:

C. is responsible for sliding friction and contact forces

Answer:

14.4 m/s

Explanation:

mass of Anna (Ma) = 68 kg

speed of Anna (Va) = 17 m/s

mass of SandraDay (Ms) = 76 kg

speed of SandraDay (Vs) = 12 m/s

We can find their speed (V) immediately after collision from the conservation of momentum where

(Ma x Va) + (Ms + Vs) = (Ma + Ms) x V

where V = speed immediately after collision

(68 x 17) + (76 + 12) = (68 + 76) x V

2068 = 144 V

V = 2068 / 144 = 14.4 m/s

Answer:

2 in

Explanation:

Area of a sheet = 3.5 x 14 in²

Volume of ream, V = 98 in³

Let t be the thickness of ream

So, Volume of ream  Area of a sheet x thickness of ream

98 = 3.5 x 14 x t

t = 2 in

Thus, the  thickness of ream is 2 in.

Answer:

t = 2 in

Explanation:

given,

width of sheet, W = 3.5 in

Length of the sheet, L = 14 in

thickness of the ream = ?

volume of paper = 98 in³

we now,

Volume = Length x width x thickness

V = l w t

98 =  14 x 3.5 x t

[tex]t = \dfrac{98}{14\times 3.5}[/tex]

t = 2 in

thickness of the ream is equal to 2 in.

Answer: it is very difficult to remove the inner electrons from an atom because of the strong electrostatic force of attraction by the nucleus. In contrast, it is very easy to remove the outer electrons from an atom because the electrostatic force of attraction from the nucleus is not strong enough to hold the outer electrons hence it is removed.

Answer:Upward

Explanation:

To hang the object in the halfway we need to direct the Electric field toward upward direction

Suppose object has mass m and charge q

If electric field is Pointing towards upward direction then the force experienced by charged particle is in the upward direction which will be balanced by weight of particle(pointing downward) such that

qE=mg

where q=charge of particle

E=Electric field

m=mass of particle

g=acceleration due to gravity

Answer:

Yes, it is reckless. This is because it is the responsibility of the pilot to make sure that the direction of the propeller blast is away from people or other aircraft and in a safe direction.

Explanation:

Yes, it is reckless to let the propeller blast face people and other aircraft. This is because it is the responsibility of the pilot to make sure that the direction of the propeller blast is away from people or other aircraft and in a safe direction. People and other aircraft can be injured by the debris and the rocks that are scattered by the engine of the aircraft.

Final answer:

Causing debris and propeller blast to endanger others can be deemed reckless operation of an aircraft, akin to dangerous driving, and can be punishable by aviation law.

Explanation:

The operation of an aircraft in a manner that causes debris, rocks, and propeller blast to be directed towards people or other aircraft can indeed be considered reckless operation. For perspective, consider that landing an aircraft is described as an ultimate challenge and must ensure safety as if it were a casual drive to a golf course. Pilots are responsible for maintaining control of their aircraft and ensuring the safety of both passengers and bystandiles at all times, much like drivers on the road.

Reckless operation of an aircraft can endanger lives and property, and is typically prohibited by aviation law and regulations. If a pilot operates an aircraft without regard to the potential harm it could cause others, this could be construed as reckless. The key is the intent and awareness of the pilot; if they are knowingly causing potential harm, it is indeed reckless.

Final answer:

The function for the power output of a solar panel in Ann Arbor on a summer day is f(t) = 10sin(πt/14), and on a winter day, the function is g(t) = 10sin(π(t+2)/9). The power output is greatest at 1 pm during summer with 10 watts. Graphing reveals the variation of power throughout the day.

Explanation:

Writing a Function for Solar Panel Power Output:

To answer part (a), we start by incorporating θ = πt/14 into the original power output equation P = 10sinθ, leading to a new function f(t) = 10sin(πt/14).

For part (b), graphing f(t) between 0 ≤ t ≤ 14 will show a sinusoidal curve that represents the power output throughout the day.

For part (c), the power output is greatest when θ = π/2, which occurs when t = 7 (1 pm), and the power output at this time is P = 10 watts.

Regarding part (d), for a typical winter day with sunlight from 8 am to 5 pm, the angle for t hours after 8 am needs to be adjusted. We can denote it as θ1 = π(t+2)/9. Thus, a new function g(t) = 10sin(π(t+2)/9) represents the power output on a typical winter day.

Technician B is correct. A voltmeter should be connected in parallel with the component or section of a circuit that is being tested, while an ammeter should be connected in series.

Technician B is correct when it comes to assessing the method of connecting a voltmeter. A voltmeter is designed to measure the voltage across elements of a circuit and is placed in parallel with the component or section of the circuit that is being tested. In this configuration, the voltmeter receives the full voltage.

On the other hand, Technician A is confusing a voltmeter with an ammeter. An ammeter, which measures the current flowing through a given branch of an electric circuit, should be connected in series in order to get a measure of the full current passing through that branch. The ammeter has a small resistance to limit its impact on the circuit.

By contrast, a voltmeter has to have a large resistance as it is connected in parallel and thus should have minimal impact on the circuit being tested.

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Answer:

The answer is 199920 meters.

Explanation:

First we need to find how many seconds they walked to the store:

[tex]34*60=2040[/tex]

If they walked 2040 seconds to eastward with velocity of 89 m/s, the displacement will be:

[tex]2040*98=199920[/tex]

The amount of heat required is B) 150 J

Explanation:

The amount of heat energy required to increase the temperature of a substance is given by the equation:

[tex]Q=mC\Delta T[/tex]

where:

m is the mass of the substance

C is the specific heat capacity of the substance

[tex]\Delta T[/tex] is the change in temperature of the substance

For the sample of copper in this problem, we have:

m = 25 g (mass)

C = 0.39 J/gºC (specific heat capacity of copper)

[tex]\Delta T = 15^{\circ}C[/tex] (change in temperature)

Substituting, we find:

[tex]Q=(25)(0.39)(15)=146 J[/tex]

So, the closest answer is B) 150 J.

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Answer:

R=19.5m

[tex]\theta[/tex] = 4.65° S of W

Explanation:

Refer the attached fig.

displacement  of the x and y components

x-component displacement is ([tex]R_{x}[/tex]) = [tex]A_{x}+B_{x}[/tex]

= A [tex]\sin[/tex](20°) + B [tex]\cos[/tex](40°)

= -12.0[tex]\sin[/tex](20°) + 20.0[tex]\cos[/tex](40°)

= -19.425m

x-component displacement is ([tex]R_{y}[/tex]) = [tex]A_{y}+ B_{y}[/tex]

=  A [tex]\cos[/tex](20°) - B [tex]\sin[/tex](40°)

= 12.0[tex]\cos[/tex](20°) - 20.0[tex]\sin[/tex](40°)

= -1.579

resultant displacement

∴

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

=[tex]\sqrt{(-19.425)^{2}+(-1.579)^{2} }[/tex]

=19.5m

[tex]\theta[/tex] = [tex]\tan^{-1}\left | \frac{R_{x}}{R_{y}} \right |[/tex]

[tex]\theta[/tex] = [tex]\tan^{-1}\left | \frac{1.579}{19.425} \right |[/tex]

[tex]\theta[/tex] = 4.65° S of W

This problem involves finding the result of two vector displacements using vector addition. Using the Pythagorean theorem, the magnitude of the overall displacement can be determined. The direction of the displacement can be calculated using the tangent formula.

This is a vector addition problem in physics. We can solve it using Pythagorean theorem for finding the magnitude and tangent formula for finding the direction.

For the first leg of the journey(A), you are going 20° W of N, or 70° clockwise from the x-axis. For the magnitude of this vector: Ax = 12.0m cos(70°) and Ay = 12.0m sin(70°).

For the second leg of the journey(B), you are going 40° S of W, or 130° clockwise from the x-axis. For the magnitude of this vector: Bx = 20.0m cos(130°) and By = 20.0m sin(130°).

Summing the x and y components gives: Rx = Ax + Bx and Ry = Ay + By. The magnitude R can then be found with Pythagorean theorem formula: R = sqrt(Rx² + Ry²).

The direction can be found using tangent formula: θ = atan(Ry / Rx). As Rx is negative and Ry is positive, θ will fall in the second quadrant.

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The distance between the center of mass of the molecule and carbon atom is 0.65 × 10⁻¹⁰ m

To answwer the question, we need to know the center of mass of CO molecule

The center of mass of the CO molecule is given by

x = m₁x₁ + m₂x₂/(m₁ + m₂) where

Substituting the values of the variables into the equation, we have

x = (m₁x₁ + m₂x₂)/(m₁ + m₂)

x = (12 u × 0 m + 16 u × 1.13 × 10⁻¹⁰ m)/(12 u  + 16 u)

x = (0 + 16 u × 1.13 × 10⁻¹⁰ m)/28 u

x = 18.08 × 10⁻¹⁰ um/28 u

x = 0.646 × 10⁻¹⁰ m

x ≅ 0.65 × 10⁻¹⁰ m

Since the carbon atom is at x₁ = 0 m and the center of mass is at x = 0.65 × 10⁻¹⁰ m, the distance between the carbon atom and the center of mass of the molecule is d = x - x₁

= 0.65 × 10⁻¹⁰ m - 0 m

= 0.65 × 10⁻¹⁰ m

So, the distance between the center of mass of the molecule and carbon atom is 0.65 × 10⁻¹⁰ m

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Answer:

a. for any force, there is an equal and opposite reaction force.

Explanation:

Newton third law of motion states that " for every action, there is an equal and opposite reaction.

Action force= reaction force =

M₁ * a₁ = M₂ * a₂

where M₁ = mass of object 1

          a₁ = acceleration due to object 1

          M₂ = mass of object 2

          a₂ = corresponding acceleration due to object 2

this happen in everyday life of an individual. an example is seen in a groups of three man exerting a push force on a static car, the push force on the car make the car to exhibit some motion equivalent to the force applied by the three man.

Answer:

Option D.

Explanation:

The correct answer is Option D.

The shrinkage of the bridge material is because of thermal contraction.

Thermal contraction and thermal expansion are the phenomena of the bridge material which takes place due to the change in temperature of the atmosphere.

When the temperature of the surrounding increases expansion of the bridge material takes place and when temperature decreases the contraction of the material takes place.

This phenomenon sometimes damages the structure because due to continuous expansion and contraction of materials strength of the bridge decreases.

Thermal expansion joints in bridges prevent material breakage due to temperature changes.

Thermal expansion joints are used in bridges to allow for the changing length of the bridge due to temperature fluctuations. Without these joints, the bridge material would break due to thermal stress caused by expansion and contraction.

Answer:

Flight path angle= 15.12°, maximum range= 5.29× 10*6 km

Explanation:

u= 7200m/s, H= 180km= 180000m

Recall that

Maximum height, H= (u*2sin*2∆)/2g

180000= (7200×7200sin*2∆)/2×9.8

(18000×2×98)/7200×7200= sin*2∆

Sin∆= 0.2609

∆= 15.12°

Maximum range, R= u*2/g

(7200×7200)/9.8

= 5289795.92km

= 5.29× 10*6 km