for a circular channel of diameter 3 m, the discharge is 2.0 cms. find the critical depth, critical velocity, and minimum specific energy?

(a) The time required to reduce the paratrooper's speed to 5.25 m/s², assuming the acceleration is constant, can be found using the formula `v = u + at`, where `v` is the final velocity, `u` is the initial velocity, `a` is the acceleration, and `t` is the time taken.

Initially, the paratrooper is falling downward at a speed of 30.3 m/s, and after the parachute opens, the upward acceleration is 69 m/s². Therefore, the net acceleration is given by:

Net acceleration = upward acceleration - downward acceleration= 69 - 9.81= 59.19 m/s²

The time taken to reduce the speed to 5.25 m/s can be found by substituting the values into the above formula as shown below:5.25 = 30.3 + 59.19t⇒ t = (5.25 - 30.3)/59.19≈ -0.421 s

Since the time can't be negative, the above estimate is invalid.

(b) The distance fallen during the time interval can be found using the formula `s = ut + 1/2 at²`. If the acceleration is not constant, an easy estimate can be obtained by taking the average of the initial and final speeds, and multiplying by the time taken, which is approximately the same as the actual distance fallen.

The average speed is given by:(30.3 + 5.25)/2 = 17.78 m/s

Therefore, the approximate distance fallen is:s ≈ ut = 17.78 × t

(a), the time taken to reduce the speed to 5.25 m/s is approximately -0.421 s, which can be disregarded since time can't be negative.

Therefore, the actual time taken is:5.25 = 30.3 + at⇒ t = (5.25 - 30.3)/a= 1.435 sSubstituting this into the above formula, the actual distance fallen is:s = 17.78 × 1.435≈ 25.50 m

Therefore, the paratrooper falls a distance of approximately 25.50 m during this time interval.

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yeah i did, hope you understand

Answer:

Chemical energy is energy stored in the bonds of atoms and molecules. ...

Mechanical energy is energy stored in objects by tension. ...

Nuclear energy is energy stored in the nucleus of an atom—the energy that holds the nucleus together. ...

Gravitational energy is energy stored in an object's height.

Answer:

Nuclear power

Electricity

Mechanic

Gravity

Explanation:

Both the assertion and the reason given are true.If the mass of the object is less, the acceleration produced by the force will be more. Hence, the acceleration produced by the force is directly proportional to the magnitude of the force and inversely proportional to the mass of the object.

The given assertion: When astronauts throw something in space, that object would continue moving in the same direction and with the same speed; and the given reason: The acceleration of an object produced by a net applied force is directly related to the magnitude of the force, and inversely related to the mass of the object are both correct.Astronauts are capable of throwing objects in space because they are beyond Earth's gravity and do not have to deal with any significant air resistance. In the absence of other forces like friction or air resistance, the initial velocity will be conserved, and the object will continue to move with the same speed and direction. The object would continue to move in a straight line with the same speed because no external force acts on it to change the object's state of motion.Newton's second law states that the force of an object is directly proportional to its acceleration, but inversely proportional to its mass. F=ma, where F is force, m is mass, and a is acceleration. Therefore, if the mass of the object is less, the acceleration produced by the force will be more. Hence, the acceleration produced by the force is directly proportional to the magnitude of the force and inversely proportional to the mass of the object.

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The spring constant k is approximately 1520 N/m by using conservation of energy?

We can use the conservation of energy to find the spring constant k. Initially, the block has potential energy stored in the compressed spring, which is then converted to kinetic energy as the block slides across the track. At the point where the block leaves the track, all of the stored energy has been converted to kinetic energy. Neglecting air resistance, we can assume that the kinetic energy of the block at this point is equal to the potential energy stored in the spring:

\((1/2)kx² = (1/2)mv²\)

where x is the distance the spring is compressed (0.049 m), m is the mass of the block, and v is the velocity of the block when it leaves the track.

Since the block is initially at rest, we can also use kinematic equations to relate the velocity of the block to the distance it travels along the track before leaving it. The horizontal displacement of the block is unknown, so we'll call it d:

d = (1/2)at²

where a is the acceleration of the block along the track and t is the time it takes to travel that distance. The acceleration of the block is determined by the force applied by the spring:

F = kx

ma = kx

a = kx/m

Now we can substitute this expression for acceleration into the kinematic equation:

\(d = (1/2)(kx/m)t\)²

Since the block leaves the track horizontally, its vertical displacement is given by:

y = (1/2)gt²

where g is the acceleration due to gravity.

Combining these equations, we can eliminate t and solve for k:

\((k/m)(0.049)² = g(2y/g)(2d/(k/mg))²\)

Simplifying, we get:

\(k = (mg²d)/(0.049²(4y + gd))\)

Substituting the given values for m, d, and y, and the acceleration due to gravity g = 9.81 m/s², we get:

\(k = (0.4 kg)(9.81 m/s²)²(2.3 m)/[(0.049 m)²(4(0.8 m) + (9.81 m/s²)(2.3 m))]\)

k ≈ 1520 N/m

Therefore, the spring constant k is approximately 1520 N/m.

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Complete question is;

A cylinder of compressed gas is at a temperature of 23°C. It is cooled until it reaches the pressure of 2000kPa. It has to be cooled to 90K before this happens. Calculate the starting pressure of the gas

Answer:

Starting pressure = 604 KPa

Explanation:

We are given;

Initial temperature; T1 =23°C = 298 K

Final temperature; T2 = 90 K

Final pressure; P2 = 2000 KPa

From gay lussac's law, we know that;

P1•T1 = P2•T2

P1 = (P2•T2)/T1

P1 = (2000 × 90)/298

P1 ≈ 604 KPa

Answer: Often lightning occurs between clouds or inside a cloud. But the lightning we usually care about most is the lightning that goes from clouds to ground.

Explanation:  As the storm moves over the ground, the strong negative charge in the cloud attracts positive charges in the ground.

Answer:

ω = √(2T / (mL))

Explanation:

(a) Draw a free body diagram of the mass.  There are two tension forces, one pulling down and left, the other pulling down and right.

The x-components of the tension forces cancel each other out, so the net force is in the y direction:

∑F = -2T sin θ, where θ is the angle from the horizontal.

For small angles, sin θ ≈ tan θ.

∑F = -2T tan θ

∑F = -2T (Δy / L)

(b) For a spring, the restoring force is F = -kx, and the frequency is ω = √(k/m).  (This is derived by solving a second order differential equation.)

In this case, k = 2T/L, so the frequency is:

ω = √((2T/L) / m)

ω = √(2T / (mL))

Answer:

Larger, because both the Sun and Moon are pulling it.

Explanation:

To determine the normal boiling point of a substance, we need to find the temperature at which its vapor pressure is equal to the standard atmospheric pressure of 760 mmHg.

Given:

Vapor pressure at 35°C = 55.1 mmHg

Heat of Vaporization = 32.1 kJ/mol

To start, we can convert the given temperature from Celsius to Kelvin:

35°C + 273.15 = 308.15 K

Next, we can use the Clausius-Clapeyron equation to relate the vapor pressure, temperature, and heat of vaporization:

ln(P1/P2) = (ΔHvap/R) * (1/T2 - 1/T1)

Where:

P1 = vapor pressure at the known temperature (55.1 mmHg)

P2 = vapor pressure at the boiling point (760 mmHg)

ΔHvap = heat of vaporization (32.1 kJ/mol)

R = ideal gas constant (8.314 J/(mol·K))

T1 = known temperature (308.15 K)

T2 = boiling point temperature (unknown)

Rearranging the equation and solving for T2:

T2 = ΔHvap / [(R * (1/T1 - 1/T2))] + T1

Substituting the known values:

T2 = (32.1 * 10^3) / [(8.314 * (1/308.15 - 1/T2))] + 308.15

We can solve this equation numerically to find the boiling point temperature (T2). After performing the calculation, the closest option to the calculated value is:

c. 368 K

Therefore, the normal boiling point of the substance is approximately 368 K.

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Answer:

the momentum is 50 kg m/s

Explanation:

The computation of the momentum is shown below;

As we know that

Momentum = mass × velocity

where

mass = 5 kg

And, the velocity is 10 m/s

So, the momentum is

= 5 × 10

= 50 kg m/s

Hence, the momentum is 50 kg m/s

Answer:

Fc= 47.363 N

Explanation:

First, you need tangential velocity because they don't give that to you in the problem.

So, the formula for tangential velocity is υ=2πr/t.

For this problem its v=2π4/10= 2.513 m/s

Then we plug this into our equation for centripetal force

Fc= 30*(2.513)^2/4=47.363 N

Fc=47.363 N

The centripetal force acting on Tommy is 47.36 N if Tommy, who has a mass of 30 kg, sits 4.0 meters from the center of a merry-go-round that is rotating for a period of 10 seconds.

A tangible body's mass is the amount of matter it possesses. It's also a metric of inertia or the resistance to velocity when a net force is exerted.

It is given that:

Tommy, who has a mass of 30 kg, sits 4.0 meters from the center of a merry-go-round that is rotating for a period of 10 seconds.

As we know the formula for the centripetal force:

Fc = mv²/r

m = 30 kg

r = 4 meters

First, find the tangential velocity:

The formula for tangential velocity is:

v = 2πr/t

v = 2π4/10

v = 2.513 m/s

Plug the values in the formula:

Fc= 30(2.513)²/4

Fc = 47.36 N

Thus, the centripetal force acting on Tommy is 47.36 N if Tommy, who has a mass of 30 kg, sits 4.0 meters from the center of a merry-go-round that is rotating for a period of 10 seconds.

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The mathematical proportion that relates electrostatic force to the displacement of a pair of charged particles is:

C) inverse square

Why?

The proportion of the electrostatic force (F) between two electric charges is inversely proportional to the square of the distance (d) between them.

The mathematical expression for the force between two charges is:

F (q1q2)/d2, where q1 and q2 are the electric charges of the two charged particles, and d is the distance between them.

As we can see, the force between two electric charges is inversely proportional to the square of the distance between them. Hence, the proportion that relates electrostatic force to the displacement of a pair of charged particles is inverse square.

Option C is the correct answer.

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Answer:

ghittu iihg उह्स उउह्स उग्य्किव जिक्ह्ब

Answer:

A) El componente de aceleración de la aguja en \(t = 0\,s\) es -236,206 centímetros por segundo al cuadrado.

B) Las ecuaciones para la componentes de posición, velocidad y aceleración de la punta en función del tiempo son, respectivamente:

\(x(t) = 1,458\cdot \cos (15,708\cdot t +0,228\pi)\)

\(v(t) = -22,902\cdot \sin (15,708\cdot t + 0,228\pi)\)

\(a(t) = -359,749\cdot \sin (15,708\cdot t + 0,228\pi)\)

Explanation:

El movimiento armónico simple es un movimiento periódico de carácter sinusoidal que está descrito por la siguiente ecuación cinemática:

\(x(t) = A\cdot \cos (\omega\cdot t + \phi )\) (1)

Donde:

\(x(t)\) - Posición actual de la aguja con respecto a la posición de equilibrio, en centímetros.

\(A\) - Amplitud, en centímetros.

\(\omega\) - Frecuencia angular, en radianes por segundo.

\(\phi\) - Ángulo de fase, en radianes.

Por Cálculo Diferencial, obtenemos las fórmulas cinemáticas para la velocidad (\(v(t)\)), en metros por segundo, y la aceleración (\(a(t)\)), en metros por segundo cuadrado, de la aguja:

\(v(t) = -\omega\cdot A \cdot \sin (\omega\cdot t + \phi)\) (2)

\(a(t) = -\omega^{2}\cdot A \cdot \cos (\omega\cdot t + \phi)\) (3)

Por otra parte, la frecuencia angular está descrita por la siguiente fórmula:

\(\omega = 2\pi\cdot f\) (4)

Donde \(f\) es la frecuencia, en hertz.

Ahora, necesitamos calcular la amplitud y el ángulo de fase mediante el sistema de ecuaciones que hemos formado: \(t = 0\,s\), \(x(t) = 1,1\,cm\), \(v(t) = -15\,\frac{cm}{s}\) and \(f = 2,5\,hz\):

Por (4):

\(\omega = 2\pi\cdot f\)

\(\omega = 2\pi\cdot (2,5\,hz)\)

\(\omega \approx 15,708\,\frac{rad}{s}\)

Por (1) y (2):

\(A\cdot \cos \phi = 1,1\) (1b)

\(-15,708\cdot A \cdot \sin \phi = -15\) (2b)

Al dividir (2b) por (1b) y despejar el ángulo de fase tenemos que:

\(-15,708\cdot \tan \phi = -13,636\)

\(\tan \phi = 0,868\)

\(\phi = \tan^{-1} 0.868\)

\(\phi \approx 0,228\pi\,rad\)

Por (1) tenemos el valor de la amplitud: (\(\phi \approx 0,228\pi\,rad\))

\(A = \frac{1,1}{\cos \phi}\)

\(A = \frac{1,1}{\cos 0,228\pi}\)

\(A \approx 1,458\,cm\)

A) El componente de aceleración de la aguja se calcula por (3) evaluada en \(t = 0\,s\):

\(a(t) = -359,749\cdot \sin (15,708\cdot t + 0,228\pi)\)

\(a(0) = -236,206\,\frac{cm}{s^{2}}\)

B) Las ecuaciones para la componentes de posición, velocidad y aceleración de la punta en función del tiempo son, respectivamente:

\(x(t) = 1,458\cdot \cos (15,708\cdot t +0,228\pi)\)

\(v(t) = -22,902\cdot \sin (15,708\cdot t + 0,228\pi)\)

\(a(t) = -359,749\cdot \sin (15,708\cdot t + 0,228\pi)\)

When a wave is transmitted from one substance to another, its refraction will change. Unless it reaches the second substance at a right angle, its direction will also change.

Refraction is the redirection of a wave as it passes from one medium to another medium. The redirection of wave can be caused by the wave's change in speed or by a change in the medium of wave.

The refraction of light or change in the direction of path of light in other medium occurs because the light wave travels with different speeds in different media. When a ray of light passes from one medium to another medium, the direction of the wave changes except for zero degrees because of the change in its speed.

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The pendulum's moment of inertia about an axis perpendicular to the page and passing through G is 4.491 kgm2.

What is the center of mass and moment of inertia of a pendulum made of a slender rod and thin plate?

To determine the location y of the center of mass g of the pendulum, we need to first find the total mass of the pendulum. This can be done by simply adding the masses of the slender rod and the thin plate:

Total mass = mass of rod + mass of plate

Total mass = 2.0 kg + 6.0 kg

Total mass = 8.0 kg

Next, we can use the formula for center of mass to calculate the position of the center of mass. The formula is:

\(y = \frac{m_1 y_1 + m_2 y_2}{m_1 + m_2}\)

where m1 and m2 are the masses of the components (in this case, the mass of the rod and the mass of the plate), and y1 and y2 are their respective distances from a reference point (we can choose any point as a reference, but it's usually convenient to choose the point where the pendulum is suspended).

Let's assume that the slender rod is 1.0 meter long and that the thin plate is attached to the rod at a distance of 0.5 meters from the suspension point. Then we can calculate the distances y1 and y2 as follows:

y1 = 0.5 m (since the center of mass of the rod is at its midpoint)

y2 = 1.0 m + 0.5 m = 1.5 m (since the center of mass of the plate is at its center)

Plugging these values into the formula, we get:

\(y = \frac{m_1 y_1 + m_2 y_2}{m_1 + m_2}\)

y = (2.0 kg x 0.5 m + 6.0 kg x 1.5 m) / 8.0 kg

y = 1.25 m

Therefore, the center of mass of the pendulum is located 1.25 meters from the suspension point.

To calculate the moment of inertia of the pendulum about an axis perpendicular to the page and passing through g, we can use the parallel axis theorem. The formula for moment of inertia about a parallel axis is:

I = Icm + \(md^2\)

where Icm is the moment of inertia about the center of mass, m is the total mass of the system, and d is the distance between the two axes (in this case, the distance between the axis passing through the center of mass and the axis passing through point G).

The moment of inertia of a slender rod about its midpoint is given by:

Irod = (1/12)\(ml^2\)

where l is the length of the rod. Substituting the values given, we get:

\(I_{rod} = (\frac{1}{12} )(2.0 kg)(1.0 m)^2\)

Irod = \(0.1667 kgm^2\)

The moment of inertia of a thin plate about its center is given by:

\(Iplate = (1/12)ml^2 + (1/4)ma^2\)

where a is the half-width of the plate. Since the plate is thin, we can assume that its thickness is negligible compared to its other dimensions, so we can treat it as a two-dimensional object. Substituting the values given, we get:

\(I_{plate} = (1/12)(6.0 kg)(0.5 m)^2 + (1/4)(6.0 kg)(0.5 m)^2\)

\(I_{plate} = 0.375 kgm^2\)

To calculate the moment of inertia of the pendulum about point G, we need to find the distance between the center of mass and point G. Let's assume that point G is located at a distance of 0.8 meters from the suspension point. Then we can calculate the distance d as follows:

d = |y - 0.8|

d = |1.25 m - 0.8 m|

d = 0.45 m

Now we can use the parallel axis theorem to find the moment of inertia about point G:

\(I = I_{cm} + md^2\)

\(I = (0.1667 kgm^2 + 0.375 kgm^2) + 8.0 kg x (0.45 m)^2\)

\(I = 4.491 kgm^2\)

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The color gardener should use to reduce overall light energy, but still maximize plant growth in the greenhouse is blue.

What is greenhouse?

A greenhouse is a structure with walls and a roof mostly made of transparent material, such as glass, where plants that require controlled climatic conditions are grown. It is also referred to as a glasshouse or a hothouse if it has enough heating. These buildings come in a variety of sizes, from modest huts to enormous factories. A cold frame can be compared to a little greenhouse. When a greenhouse is exposed to sunshine, its interior temperature rises noticeably above the ambient temperature, shielding the items inside from cold weather.

The gardener who is concerned that her greenhouse is getting too hot from too much light, and seeks to shade her plants with colored translucent plastic sheets  should use blue color translucent plastic sheets to reduce overall light energy, and still maximize the growth of plants.

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Answer:

Explanation:

First of all we shall calculate mass of copper to be calculated from the formula below.

mass = volume x density

volume = total surface area x thickness of layer

= 12 x 12 x 2 x .01 cm³

= 2.88 cm³

mass = 2.88 x 9 = 25.92 g .

Let time required be t s .  .

charge flowing in time t = 1.5 t coulomb.

Given ,

1 coulomb deposits .00033 g of copper

1.5 t deposits    .00033 x 1.5 t g of copper

So ,

.00033 x 1.5 t = 25.92

t = 52364 s

= 14.54 hours.

Explanation:Lightning can affect radio waves in a number of ways. First, lightning can cause static interference on radio frequencies. This is because the electrical discharge from lightning can create electromagnetic fields that can disrupt radio signals. Second, lightning can also cause physical damage to radio equipment.

The distance d travelled by in object is 68.58 m

What is velocity ?

velocity is defined as rate of change of displacement d of the object with respect to rate of change in time t. In mathematics It is written as :

v = d/t

it should be noted that, velocity is nothing but speed in particular direction. That is velocity is vector quality having both magnitude and direction where as speed is just the magnitude of velocity.

1 feet = 0.3048 m

15 feet = 4.572 m

Now, calculating the distance d travelled by in object :

d = vt

d = 4.572 x 27

d = 68.58 m

Therefore, the distance d travelled by in object is 68.58 m

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Answer:  SEE EXPLANATION!

Explanation:

When waves travel from one medium to another the frequency never changes. As waves travel into the denser medium, they slow down and wavelength decreases. Part of the wave travels faster for longer causing the wave to turn. The wave is slower but the wavelength is shorter meaning frequency remains the same.

I hope this helps you!

The amount of energy consumed in the form of work by the ideal Carnot refrigerator to freeze 2 kg of water at 0°C is approximately 6.05 x 10\(^4 J.\) So the answer is A) 6.1 x 10\(^4 J.\) (rounded to two significant figures).

The Carnot cycle consists of two isothermal and two adiabatic processes. For a refrigerator, the heat is transferred from a low-temperature reservoir (the freezer) to a high-temperature reservoir (the room), and work must be done on the system to accomplish this. The Carnot cycle tells us that the work done by the refrigerator is:

\(W = Q_L (1 - T_H/T_L)\)

where Q_L is the amount of heat transferred from the low-temperature reservoir, T_H is the temperature of the high-temperature reservoir (the room, in this case), and T_L is the temperature of the low-temperature reservoir (the freezer). We can solve for Q_L and then use the heat of transformation for water to find the work done to freeze 2 kg of water.

The temperature of the freezer is 0°C = 273 K. The temperature of the room is 25°C = 298 K. Therefore, we have:

Q_L = W/(1 - T_H/T_L)

= W/(1 - 298 K/273 K)

= W/0.0908

We know that the heat of transformation for water is 333 kJ/kg, so the heat required to freeze 2 kg of water is:

Q_L = (2 kg) * (333 kJ/kg)

= 666 kJ

Substituting this into the equation above, we get:

666 kJ = W/0.0908

Solving for W, we get:

W = 666 kJ * 0.0908

= 60.5 kJ

= 6.05 x 10\(^4 J\)

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The way the flaps are set up for takeoff depends on the type of plane, its weight, the length of the runway, and other things. But most of the time, the takeoff flap setting is somewhere between 15-20 degrees.

With this setup, the flaps can make the wings generate more lift, which shortens the length of the runway needed and lets the plane take off at a slower speed.

The exact flap setting for takeoff is usually written in the aircraft's operating manual or given by the manufacturer.

Pilots will use this information to set the flaps correctly for a safe and efficient takeoff.

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Answer:

The second option

Explanation:

When the elevator comes to a stop, the supporting cable is held at -3000 N of tension.

A force that is transmitted when a rope, cable, or string is pulled tight is tension. The pulling force that an object exerts on a rope, cable, or string transmits along its length to another object that is attached to the other end is known as tension. The force along the length of a rope or cable that is being stretched or pulled is known as tension in physics.

We must determine the elevator's net force in order to determine the supporting cable's tension. The sum of the elevator's acceleration and mass creates this net force. As a result of the elevator's slowdown in this instance, its acceleration is negative (opposing its velocity).

The elevator's acceleration can be determined using the equation for average acceleration:

where a = (v_f - v_i) / t

The elevator's acceleration is denoted by a, the elevator's final velocity is denoted by v_f, and the initial velocity is denoted by v_i, which is 7.0 m/s. The time interval is denoted by t, which is 3.5 seconds.

a = (0 - 7.0) / 3.5

a = -2.0 m/s²

The net force on the elevator is given by the equation:

F_net = m × a

where:

F_net is the net force on the elevator

m is the mass of the elevator (1500 kg)

a is the acceleration of the elevator (-2.0 m/s²)

Substituting the values:

F_net = 1500 × -2.0

F_net = -3000 N

Since the cable is the only force , the tension (T) in the cable must be equal to the net force:

T = F_net

T = -3000 N

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