The first time that astronomers observed both gravitational waves and electromagnetic waves from the same event, what they were observing was:_____

Answer:

2.59 ms^2

Explanation:

Radius, r= 17m

Velocity,v = 6.64m/s

Ac= V^2/r

Ac= (6.64)^2/17

Ac= 2.59 m/s^2

The angle of attack of airfoil with a 2m chord in an airstream with a velocity of 50m/s, and the lift per unit span is 1353n/m will be 4 degrees.

To find the answer, we have to know more about the dynamic pressure.

                        [tex]l=2m\\v=50m/s\\L=1353N/m\\d_{infinity}=1.233Kg/m^3[/tex]

                  [tex]P_d=\frac{1}{2} dv^2=\frac{1}{2}*1.233*50^2=1541.25 Pascals.[/tex]

                          [tex]k=\frac{L}{P*l} =\frac{1353}{1541.25*2}=0.438[/tex]

                                  [tex]\alpha =sin^{-1}(\frac{k}{2\pi } )\\\alpha =sin^{-1}(\frac{0.438}{2\pi } )\\\alpha =4.007 degrees.[/tex]

Thus, we can conclude that, the angle of attack of airfoil with a 2m chord in an airstream with a velocity of 50m/s, and the lift per unit span is 1353n/m will be 4 degrees.

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According to the Newton's law of universal gravitation 2.4, the force between any more than two or three types of heavier mass which really involves with mass falling to the ground is proved by the distance, the mass's rotational speed and the rotating direction. It happens the changes in space and time, and also in the diameter of it's own mass.

-3.90, 1.83 are the component form of the vector u v.

What is magnitude of vector?

We have vector u = 5 ( cos 75 i + sin 75 j )

                              = 1.294 i + 4.830 j

Vector v = 6 ( cos 210 i + sin 210 j )  

              = -5.19 i - 3 j

Now we add both component

u + v =  1.294 i + 4.830 j + (-5.19 i - 3 j)

        = -3.90 i + 1.83 j

        = < -3.90, 1.83>

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The correct option is (D). < -3.90, 1.83>

Vector is a quantity with both magnitude and direction. It is often represented by an arrow whose length is proportional to the magnitude of the quantity and whose direction is the same as that of the quantity.

What are vectors?

Given, vector u = 5 ( cos 75 i + sin 75 j ) = 1.294 i + 4.830 j

Vector v = 6 ( cos 210 i + sin 210 j ) = -5.19 i - 3 j

u + v =  1.294 i + 4.830 j + (-5.19 i - 3 j) = -3.90 i + 1.83 j

        = < -3.90, 1.83>

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Weight of the mass is the tension in the string if the turntable is held fixed, with the mass hanging from the pulley

Weight is a force that acts at all times on all objects near Earth. The Earth pulls on all objects with a force of gravity downward toward the center of the Earth. Weight (symbolized w ) is a quantity representing the force exerted on a particle or object by an acceleration field, particularly the gravitational field of the Earth at the surface.

The tension force is defined as the force that is transmitted through a rope, string or wire when pulled by forces acting from opposite sides. The tension force is directed over the length of the wire and pulls energy equally on the bodies at the ends.

The direction of tension is the pull which is given the name tension. Thus, the tension will point away from the mass in the direction of the string/rope. In case of the hanging mass, the string pulls it upwards, so the string/rope exerts an upper force on the mass and the tension will be in the upper side.

Tension will act opposite the the weight of the mass attached in order to maintain equilibrium .

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On connecting a 9V  battery to a Capacitor consisting of two circular plates of radius 0.066 m separated by an air gap of 2. 0 mm. The charge on the positive plate is 544.7 ×10⁻¹² C.

Capacitance of the capacitor is determined by the area of the plate of Capacitor and distance between the plates of capacitor.

Let the area of the Capacitor be A , radius of circular plates be r and distance between the plates of capacitor be d.

Given, Voltage, V = 9V

           Radius, r = 0.066m

           Distance, d = 2mm = 0.002m

Area of the Capacitor, A = πr²

                                     A = π(0.066)²

                                     A = 0.013m²

Capacitance, C = ε₀A / d

                      C = 8.85×10⁻¹²×0.013/0.002

                       C = 60.5 ×10⁻¹² F

                        C = 60.5 pF

We know that Q = CV where Q is the charge on capacitor.

Q = 60.5 ×10⁻¹² × 9

Q= 544.7 ×10⁻¹² C

Since, both plates of a capacitor acquire equal and opposite charge.

Hence the charge on the positive plate of the capacitor is 544.7 ×10⁻¹² C.

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The ecosystem refers to all of the living and nonliving things on earth that sustain life.

Ecosystem

An ecosystem, also known as an ecological system, is made up of all the organisms and the physical setting in which they live. The nutrition cycles and energy flows connect these biotic and abiotic elements. Photosynthesis is how energy enters the system and is absorbed by plant tissue. Animals play a significant part in the transfer of materials and energy through the system by eating plants and one another. They also have an impact on the biomass levels of the microbial and plant communities. In addition to facilitating nutrient cycling by transforming nutrients held in dead biomass back into a form that can be easily utilised by plants and microorganisms, decomposers also release carbon into the atmosphere through the breakdown of dead organic matter.

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High-frequency waves are (more-less) likely to ionize an atom because of their greater (energy speed) for low- radiofrequency is generally considered to be non-ionizing, while high- radiofrequency is generally considered to be ionizing.

Microwaves and radio waves are examples of radiofrequency (RF) radiation, which is at the low-energy end of the electromagnetic spectrum. It belongs to the non-ionizing radiation class. Non-ionizing radiation lacks the energy to expel an atom's electrons.

A minimally invasive procedure known as radiofrequency ablation, or RFA, reduces the size of tumors, nodules, and other growths in the body. RFA is used to treat a variety of ailments, such as benign and cancerous tumors, chronic venous insufficiency in the legs, and persistent back and neck pain.

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The Kinetic energy per unit volume appears in total energy equation of a flowing fluid, that does not appear in the total energy equation for a non-flowing fluid.

Kinetic Energy per unit volume is defined as the Kinetic energy of the flowing fluid per unit volume.

Bernoulli Equation is a equation that remains constant for a given fluid which comprises of Potential energy per volume, Kinetic energy per volume and Pressure.

It is given by:

P + ρgh + ρv²/2 = constant

where, P is the Pressure

            ρ is the density of fluid

            g is acceleration due to gravity

            h is the height

            v is the velocity

∴ ρgh is called as Potential energy per volume

∴ ρv²/2 is called as Kinetic energy per volume

In a Flowing Fluid:

In a Non-Flowing Fluid:

Hence, Kinetic Energy per unit volume does not appear in the total energy equation for a non-flowing fluid but appears in total energy equation for a flowing fluid.

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As additional resistors are included lined up across a consistent voltage source, there are more ways for current to take.

So more current spills out of the source, and the all out current provided by the source increments.

The power supplied by the battery is (voltage) x (current).  So if the voltage is constant and the current increases, the power being supplied must also increase.

A resistor is an electrical part that cutoff points or manages the progression of electrical flow in an electronic circuit. Resistors can likewise be utilized to give a particular voltage to a functioning gadget like a semiconductor.

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A low partial pressure of oxygen promotes hemoglobin binding to carbon dioxide. This is an example of the  Haldane effect

The less saturated hemoglobin is and the lower the partial pressure of oxygen in the blood is, the more readily hemoglobin binds to carbon dioxide. This is an example of the Haldane effect.

The Haldane effect is a property of hemoglobin first described by John Scott Haldane, within which oxygenation of blood in the lungs displaces carbon dioxide from hemoglobin, increasing the removal of carbon dioxide. Consequently, oxygenated blood has a reduced affinity for carbon dioxide.

The Haldane effect is a property of hemoglobin first described by John Scott Haldane, within which oxygenation of blood in the lungs displaces carbon dioxide from hemoglobin, increasing the removal of carbon dioxide. Consequently, oxygenated blood has a reduced affinity for carbon dioxide.

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The recommended range from which a temperature should be selected and maintained constantly to achieve targeted temperature manage is 32ºC-36ºC.

In most centers, the patient is actively cooled by using an induced hypothermia protocol for 24 hours to a goal temperature of 32ºC-36ºC. The goal is to achieve the target temperature as quickly as possible. In most cases, this can be achieved within 3-4 hours of initiating cooling.

Targeted temperature management (TTM), previously known as mild therapeutic hypothermia, in selected patients surviving out-of-hospital sudden cardiac arrest (OHCA) can significantly improve rates of long-term neurologically intact survival, [1] and it may prove to be one of the most important clinical advancements in the science of resuscitation.

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Zinc metal (Zn) reacts with sulfur (S) to create zinc sulfide (ZnS), and the chemical reaction is: Zn (s) + S (s) = ZnS (s).

Importance of Zinc (Zn) and sulfur (S):

Chemical reaction -

In this experiment, heating a zinc(Zn) and sulfur(S) combination causes an interesting chemical reaction. A blinding flash of light, hot sparks, a hissing sound, and a cloud of white smoke in the shape of a mushroom are produced.

Therefore, the following chemical processes are taking place in the reaction: Zn (s) + S (s) = ZnS (s).

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A car starts from rest and constantly accelerates at a rate of 10 [m/s2 ] during a 402 [m] race. At the finish line, the speed of the car is [tex]\mathbf{89}.\mathbf{6660}\ \mathbit{m}/\mathbit{s}[/tex].

The initial velocity of the car [tex]u = 0[/tex]

Constant acceleration [tex]a = 10~ m/s^2[/tex]

Distance of the Race [tex]d = 402~ m[/tex]

The car is accelerating with a constant acceleration [tex]a[/tex] , so the car's velocity will change with time as it approaches the finish point which is at a distance [tex]d[/tex] from the initial point.

Newton's equation is the backbone of Classical Mechanics. Let's say the velocity of the car at the finish line is [tex]v[/tex].  We know that displacement is the product of average velocity and time.

Or  [tex]s=\frac{u+v}{2}\times t[/tex]

Using Newton’s first equation [tex]v\ =\ u\ +\ at[/tex]

Newton's equation of motion turns out to be,

[tex]v^2 = u^2+2ad[/tex]

[tex]v^2 = 2\times 10 \times 402[/tex]

so, [tex]v = \sqrt{8040} = 89.6667 ~m/s[/tex]

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The radius is increasing at a rate of  0.31cm/sec.

We know the volume of the balloon is increasing at a rate of 3.3 [tex]ft^{3} min[/tex]

This is expressed as:

[tex]\frac{dV}{dT}[/tex] = 3.3

The volume of a sphere is given by:

V = [tex]\frac{4}{3}[/tex]π[tex]r^{3}[/tex]

The question asks to find the rate of which the radius is increasing when the radius is 0.65 feet.

We need to find:

[tex]\frac{dr}{dt}[/tex]

Since we don't have t in our equation, we will be differentiating implicitly. We can use the chain rule for this:

[tex]\frac{dV}{dT}[/tex] = [tex]\frac{dV}{dR}[/tex].[tex]\frac{dr}{dt}[/tex]

We already know  

[tex]\frac{dV}{dT}[/tex] = 3.3

∴

3.3 =  [tex]\frac{dV}{dR}[/tex].[tex]\frac{dr}{dt}[/tex]

To find [tex]\frac{dV}{dR}[/tex]  we differentiate  V = [tex]\frac{4}{3}[/tex]π[tex]r^{3}[/tex]

∴

3.3 = 4[tex]\frac{3.3}{5.30}[/tex][tex]r^{2}[/tex].[tex]\frac{dr}{dt}[/tex]

Dividing ,

[tex]\frac{3.3}{5.30}[/tex] = [tex]\frac{dr}{dt}[/tex] = 0.622 ft/min = 0.31 cm/sec

The radius is increasing at a rate of  0.31cm/sec.

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9.87 seconds

The time required for this system to come to rest is equal to 9.87 seconds.

We have the following data:

Mass of gear A = 675 g to kg = 0.675 kg.

Radius of gear A = 40 mm to m = 0.04 m.

Mass of gear C = 3.6 kg.

Radius of gear C = 100 mm to m = 0.1 m.

How can I calculate the time needed?

We would need to figure out the moment of inertia for gears A and C in order to compute the time needed for this system to come to rest.

Mathematically, the following formula can be used to determine the moment of inertia for a gear:

I = mr²

Where:

m is the mass.

r is the radius.

We have, For gear A:

I = mr²

I = 0.675 × 0.04²

I = 0.675 × 0.0016

I = 1.08 × 10⁻³ kg·m².

We have, For gear C:

I = mr²

I = 3.6 × 0.1²

I = 3.6 × 0.01

I = 0.036 kg·m².

The initial angular velocity of gear C would therefore be converted as follows from rotations per minute (rpm) to radians per second (rad/s):

ωc₁ = 2000 × 2π/60

ωc₁ = 4000π/60

ωc₁ = 209.44 rad/s.

Also, the initial angular velocity of gears A and B is given by:

ωA₁ = ωB₁ = rc/rA × (ωc₁)

ωA₁ = ωB₁ = 0.15/0.06 × (209.44)

ωA₁ = ωB₁ = 2.5 × (209.44)

ωA₁ = ωB₁ = 523.60 rad/s.

Taking the moment about A, we have:

I_A·ωA₁ + rA∫F_{AC}dt - M(f)_A·t = 0

On Substituting the given parameters into the formula, we have;

(1.08 × 10⁻³)·(523.60) + 0.06∫F_{AC}dt - 0.15t = 0

0.15t - 0.06∫F_{AC}dt = 0.56549   ----->equation 1.

Similarly, the moment about B is given by:

0.15t - 0.06∫F_{BC}dt = 0.56549    ------>equation 2.

Note: Let x = ∫F_{BC}dt + ∫F_{AC}dt

Adding eqn. 1 & eqn. 2, we have:

0.3t - 0.06x = (0.56549) × 2

0.3t - 0.06x = 1.13098  ------>equation 3.

Taking the moment about A, we have:

Ic·ωc₁ - rC∫F_{AC}dt - rC∫F_{BC}dt - Mc(f)_A·t = 0

0.036(209.44) - 0.3t - 0.15(∫F_{BC}dt + ∫F_{AC}dt) = 0

0.3t + 0.15x = 7.5398    ------->equation 4.

Solving eqn. 3 and eqn. 4 simultaneously, we have:

x = 30.5 Ns.

Time, t = 9.87 seconds.

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While a car is running, the alternator provides current to the battery and recharges it. Reduction  reaction occurs at the anode of a lead-storage battery during this process .

The Lead-acid battery or lead-storage battery is one of the oldest types of rechargeable batteries.

Lead-storage batteries can be classified as secondary batteries. The chemical reactions that occur in secondary cells are reversible. The chemical process of extracting current from a secondary battery (forward reaction) is called discharging. The method of regenerating active material is called charging.

While recharging, the automobile battery functions like an electrolytic cell. The energy required to drive the recharging comes from an external source, such as an engine of a car. While charging reduction takes place at anode and while discharging oxidation takes place at anode.

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