an astronomer has calculated the radius of a black hole to be 51.0 au by observing its period of variability in brightness. what period, in hours, did she observe?

The minimum diameter at section (1) in the pipe below to avoid cavitation at the location is 16.6 cm.

Look at the picture

According to Bernoulli's equation in sections (1) and (2)

p₁ + 0.5 ρv₁² = p₂ + 0.5 ρv₂²

1.5 × 10⁵ + (0.5 × 1,000 × 14²) = 1.01 × 10⁵ + (0.5 × 1,000 × v₂²)

1.5 × 10⁵ - 1.01 × 10⁵ + 98,000 = 500 × v₂²

49,000 + 98,000 = 500 × v₂²

147,000 = 500 × v₂²

v₂² = 147,000 ÷ 500

v₂² = 294

[tex]v_2 = \sqrt{294}[/tex]

v₂ = 17.15 m/s

According to the continuity equation for fluids

A₁ v₁ = A₂ v₂

[tex]\frac{1}{4} D_1^2 v_1 = \frac{1}{4} D_2^2 v_2[/tex]

D₁² v₁ = D₂² v₂

D₁² × 14 = 15² × 17.15

D₁² = 3,858.75 ÷ 14

D₁² = 275.625

[tex]D_1 = \sqrt{275.625}[/tex]

D₁ = 16.6 cm

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a) Kinetic energy of ball is 450J.

A 1kg ball is thrown into the air with an initial velocity of 30m/s. Newtonian physics says the kinetic energy that the ball have is:

( [tex]\frac{1}{2} )[/tex] ×1 kg×[tex](30 \frac{m}{s}) ^{2}[/tex]= 450 J.

In physics, what is kinetic energy?

The energy a thing has as a result of motion is known as kinetic energy. A force must be applied to a thing in order to accelerate it. We must put forth effort in order to apply a force. After the job is finished, energy is transferred to the thing, which then moves at a new, constant speed.

b) Potential energy of ball is 450J

The whole amount of energy will be in the form of potential energy since the ball's kinetic energy will be equal to zero. As a result, when the ball reaches the peak of its climb, its potential energy will be 450 J.

c) 45m high into the air ball travel.

KE at start = GPE at the peak

450 = mgh

450 = (1)(g)(h)

450= (1)(10)(h)

45=h

Therefore, the ball will reach up to a height of 45m.

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The potential energy stored in the 1 μF capacitor is 4.5 x 10^-18 J.

What is potential energy?

Potential energy is the form of stored energy that depends on the interactions of various system elements. A spring's potential energy rises when it is crushed or stretched.

The energy stored in the 1.0 μF capacitor is 9.0*10^-5J

Data given;

c₁ = 1.0 μF

c₂ = 0.50 μF

V = 100 v

Calculation for Capacitor:

as given the capacitors are in series, the total capacitance is;

C = 1/c1 + 1/c2

C = 3 μF

The capacitance in the capacitor is 3 μF.

The charge of a capacitor is given as:

[tex]q = cV[/tex]

[tex]q = (3.0 \times 10^{-6}) 100[/tex]

[tex]q = 3 \times 10^{-4}[/tex] C

Calculation of Potential Energy:

The energy stored in the capacitor can be calculate as:

U = (1/2)q²c

Here, U = potential energy, q = charge, C = capacitor.

We can now proceed to use this formula and solve for the potential energy stored in the 1.0mF capacitor.

[tex]U = \frac{1}{2} (10^{-6})(3\times 10^{-6})^2[/tex]

[tex]U = 4.5 \times 10^{-18}[/tex]

From the calculations above, we can conclude that the potential energy stored in the 1mF capacitor is 4.5 x 10^-18 J.

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Newton's second law of motion gives the following definition of the force formula: "Force exerted by an object equals mass times that object's acceleration." F = m ⨉ a.

To apply this formula, you must use SI units for force (newtons), mass (kilograms), and acceleration (meters per second squared). Every automobile, truck, boat, helicopter, plane, and even spacecraft, Lift, Weight, Thrust, and Drag Newton's first law states that your body, like all mass, tries to remain in its current location. Your body attempts to stay where it was, which is on the left, if the car turns to the right. If an object is travelling and its mass is m, its rate of slowing down is v, and the time it takes is t, then.

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Answer:

TRUE

Explanation:

The wire has a diameter of  1.596 × (10) -5 m.

L = 4.0 m is the length of the wire.

The battery's emf is 1.5 volts.

I = 4 mA = 0.004 A is the wire's current.

The wire's resistance can be calculated using;

R = V / I

R = 1.5 / 0.004

R = 375 ohms

The wire's resistance in terms of resistivity is determined by;

R = pL / A

A = pL / R

Where;

The wire's area A is

Gold has a resistivity of (2.44 x 10)-8 ohm.

A = (2.44 x 10)-8 × 4 /375

A = 2.603 × (10) -10 m²

A = πd² / A

πd²  = 4A

d = √4A / π

d = √4/ (2.602 × (10) -10 / π

d = 1.596 × (10) -5 m.

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The momentum after the collision is 25500 kg⋅m/s. Each object's momentum may change, but the overall momentum must not change.

In Newtonian mechanics, momentum is calculated as the sum of an object's mass and velocity. It has a magnitude and a direction, making it a vector quantity.

The rate of change of a body's momentum is equal to the net force exerted on it, according to Newton's second law of motion. Regardless of the frame of reference, momentum is a conserved quantity in any inertial frame, which means that if an enclosed system is not subject to outside influences, its total linear momentum remains constant.

The formula for calculating momentum is expressed as

momentum = mass x velocity

According to the law of conservation of momentum, initial momentum = final momentum

The formula for initial momentum is

m1u1 + m2u2

where

m1 = mass of first car

u1 = initial velocity of first car

m2 = mass of second car

u2 = initial velocity of second car

From the information given,

m1 = 900

u1 = 0 because it is at rest

m2 =  1700

u2 = 15.0 m/s

Initial momentum = 900 x 0 +  1700 x 15.0 = 25500

Momentum after the collision is 25500 kg⋅m/s

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Yes. If the smaller force is farther from the fulcrum than the larger mass.

A body that does not deform or alter shape is idealized as a hard body. Formally, it is described as a group of particles with the feature that their distance from one another does not change as the body moves.

When an engine exerts itself, torque, which is a twisting force, speaks to the rotational force of the engine and quantifies how much of that twisting force is accessible. Everyday activities like turning a doorknob, opening a drink bottle, using a wrench, or peddling a bicycle all involve torque.

The definition of force in physics is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.

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The shape of the worldline of an object when it is plotted on the vertical axis will be a vertical line to point.

When an object is at rest, it will not change its coordinates when it moves. At this time, it will be fixed on the horizontal axis and move on the vertical axis. So, the shape of the object will be a straight vertical line.

The concept explained is the theory of relativity, which was proposed by Albert Einstein. It's a theory of gravity that mentions that the force of gravity occurs from the curvature of space and time. The worldline of an object is the time or way that an object spends in space.

This theory mainly explains how an object behaves in space and an object with a higher mass takes a lot of time.

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The center of mass of an irregularly shaped object 10 m long that is placed with each end on a scale from the left is 5.57 m

Let the object length be L.

L = 10 m

Let the distance from center of mass to the right end be x. The irregular shaped object exerts an upward force on both left and right side.

Fl = 74 N

Fr = 93 N

Since the object is at rest,

τ = 0

Fr * x - Fl ( L - x ) = 0

93 x = 74 ( 10 - x )

93 x = 740 - 74 x

167 x = 740

x = 4.43 m

Distance from left end = L - x

d = 10 - 4.43

d = 5.57 m

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The bright interference fringes seen on the screen 5.00 m from the double slits is 34.7 mm apart.

yn = n λ D / d

yn+1 = ( n + 1 ) λ D / d

λ = Wavelength

D = Distance of fringe from slit

d = Distance between slits

Δy = yn+1 - yn

λ = 694 nm = 694 * 10⁻⁹ m

D = 5 m

d = 0.1 mm = 0.1 * 10⁻³ m

Δy = [ ( n + 1 ) λ D / d ] - n λ D / d

Δy = ( n + 1 - n ) λ D / d

Δy = 694 * 10⁻⁹ * 5 / 0.1 * 10⁻³

Δy = 3470 * 10⁻⁵

Δy = 34.7 * 10⁻³ m

Δy = 34.7 mm

The interference pattern's central fringe is caused by the constructive interference of light from two slits travelling the same distance to the screen and is bright and destructive if it is dark. The central fringe is known as the zero-order fringe

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Answer: In order for an object to move at a constant speed or to accelerate or decelerate, the applied (horizontal) force and the frictional force must be unequal.

Explanation: How does the frictional force compare to the applied force?

Frictional force serves to keep the crate in place by acting in the opposite direction as the applied force. The term for this rubbing force is static friction. If you push harder, the frictional force will rise until it achieves its maximum value as a result of the increased applied force.

Do we have even or uneven friction?

Friction was the driving force that kept the bucket in place. It absorbed the tiny force applied to the bucket and offset it. a move

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The reflected rays of light don't produce visible colored interference fringes in a window pane because the glass structure of a window pane prevents the interference patterns to be observed.

A window pane is the glass that acts as a window in a building. While usually a window pane is only composed of a single piece of glass, sometimes two or more glass sheets are used with some space between each.

When it strikes a window pane, some rays will be reflected back and forth between the glass surfaces. Theoretically, it should produce some visible colored interference fringes. However, the glass structures in window panes do not have the ability to produce these visible fringes. They do produce the effect, but they are negated by the effect of other sections of the glass.

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If the solar cells are 15% efficient, the electrical power that the calculator is receiving is 0.10962mW.

It is a photovoltaic cell, an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon.

So, the solar cells on your calculator will trap solar energy and convert it into electrical energy to give power your calculator's liquid display.

How to calculate the electrical power that the calculator will receive?

P = 120W

r = 2.8m

A = 3cm² = 3 * 10^-4 m²

Intensity = 15/100 * P/4*π*r^2

= 0.15 * 120 / 0.5 * 4π * 2.8²

I = 0.3654 W/m^2 (rounded)

Received power = I * A

= 0.3654 * 3 * 10^-4

= 1.0962 * 10^-4 W

= 0.10962 mW

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The heating coil of a water heater has a resistance of 20 ω and operates at 210 v.  It takes 5 hrs to raise the it take to raise the temperature of 200 kg of water from 15oc to 80oc.

What is resistance?

Obstruction is a proportion of the resistance to flow stream in an electrical circuit. Opposition is estimated in ohms, represented by the Greek letter omega (Ω). Ohms are named after Georg Simon Ohm (1784-1854), a German physicist who concentrated on the connection between voltage, current and opposition. In any case, obstruction and conductance are broad as opposed to mass properties, implying that they additionally rely upon the size and state of an item. Channels permit the free progression of power. Yet, in materials, for example, semiconductors and covers, the power encounters a specific power that goes against the free progression of electrons.

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According to the query, the centrifuge's constant angular acceleration is -305.14 rad/s².

Micro centrifuges and tabletop centrifuges are the two main types of centrifuges. Both of these are to use for sample extraction by rotating the specimens in a contained receptacle at such a high speed. Their sample capacities and rotor types differ, though.

The number of rotation is n = 3650 rev/min

Therefore n = 60.83 rev/sec

ω initial = 2πn

             = 382.012 rad/s

ω final = 0

∅ = 2πn

  = 2*3.14*54

  = 339.12 rad

ω final² = ω initial² + 2a∅

a = (ω final² - ω initial²)/2∅

a = (0 - 382.012²)/2(339.12)

a = -305.14 rad/s²

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Latent heat per molecule of H2O expressed in joules is 124976.7 J/mol.

Latent heat is the amount of heat energy required to change the state of a substance without changing its temperature. To calculate the latent heat per molecule of H2O, we need to use the following equation:

Latent heat per molecule = (Latent heat / Mass of 1 molecule of H2O)

The mass of one molecule of H2O is approximately 18 x 10-3 kg.

Therefore, the latent heat per molecule of H2O is:

Latent heat per molecule = (2256 kJ / 18 x 10-3 kg) = 125333.33 kJ/mol

This is equivalent to 125333.33 kJ/mol = 124976.7 J/mol

In terms of electron volts, this is equivalent to 124976.7 J/mol = 7.2 x 1020 eV.

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The sign of heat exchange is positive.

Work Done on the gas is zero.

The sign of change in thermal energy is also positive.

Since the chamber container is closed, So, Volume of the container is fixed.

dV = 0

Since Work Done by the system is dW = PdV = 0

Work Done by the gas and Work done by the gas is zero.

We use First Law of Thermodynamics, we have :

dQ = dU +dW

dQ = dU + PdV

dQ = dU = [tex]C_{v} dT[/tex]

Also thermal energy ∝ T

In the given situation, The temperature is rising, dT > 0

So, we can conclude that dQ > 0, dU > 0 and [tex]dE_{thermal} > 0[/tex]

The sign of heat exchange is positive.

Work Done on the gas is zero.

The sign of change in thermal energy is also positive.

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The car will slow down. If the rock is big enough and moving fast enough, the kinetic energy from the rock will transfer to the car. And because of that, the car will slow down (and the windshield will most likely shatter)

An object is put through work (energy) when it is lifted off the ground. You might think of it as the force operating on an object to try to get it back to its lowest potential energy (the "ground state") when you do so.

The object obtains potential energy equal to the force needed to raise it (roughly) when you do so. Water towers and dams are frequent examples of structures that humans have used to harvest gravitational potential energy.

Every facet of modern life, including using your phone or turning on your hose, depends on your ability to harness potential energy (we do it more with fuels rather than gravity nowaday though if you think about it, gravity is why we have oil inthefirstplace).

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Answer: Speed and velocity both involve distance traveled over time, but velocity also includes direction

Explanation: speed is the time rate at which the object travels & velocity is the time rate at which the object travels also but includes direction too.  

The fraction of the mass needed to halt expansion is known to exist in the form of visible mass in the universe is 1 percent

Baryons, a general term for subatomic particles including protons, neutrons, and electrons, make up visible matter, also known as baryonic matter. What dark matter is constituted of is a topic of conjecture among scientists.

A mysterious, invisible substance called dark matter (25%) and a force that defies gravity called dark energy appear to make up the rest of the universe.

It is estimated that dark energy is responsible for 73% of the universe's total mass and energy. Dark matter makes up another 23% of the universe, leaving only 4% of it to be made up of ordinary matter like stars, planets, and people.

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We may determine the height of the branch using the pendulum's expression of time period. The swinging tyre can be compared to the pendulum's swinging bob. Here, the pendulum's length will match the height of the branch.

So let h be. From the formula for the pendulum's duration, let T denote the time period of the tire's swing.

T = 2π√l/g where l is length of pendulum

l = h so

T = 2π√h/g

h = T^2g/4π^2

Calculating the tyre swing time allows us to determine the height of the branch.

A stop watch can be used to estimate the length of the tyre swing. Time period is the length of time it will take the tyre to go from one extreme to the other before returning.

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A skater is rotating with her arms stretched out away from her body. As she pulls her arms in towards her body, her angular velocity increases.

If she pulls her arms in towards her body, moment of inertia reduces. And her angular momentum is conserved.

According to the law of conservation of angular momentum, we can say that, in the absence of external torque, the angular momentum of a system of particles does not change.

So, as she reduces her moment of inertia, her angular velocity increases. This results in the increase of her spinning speed.

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In this case the angle made by fringes is 0.5291

Explain in detail.

Tan θ = 15.7 x 10-3 / 1.7

         = 0.5291

The condition of Interference is

d sin θ 0.5291 = (1) 633NM

d = (1)633nm / sin 0.5291

   = 68.54 x 10-6 m

    = 69.54 um

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The duration of the impact, given that the head has a mass of 4.12 Kg is 0.005 s

We'll begin by obtaing the impulse. This can be obtained as follow:

Impulse = m(v + u)

Impulse = 4.12 × (0 + 2.09)

Impulse = 4.12 × 2.09

Impulse = 8.61 Ns

Finally, we can obtain the duration of the impact. This can be obtained as follow:

Impulse = force × time

8.61 = 1770 × t

Divide both sides by 1770

t = 8.61 / 1770

t = 0.005 s

Thus, we can conclude that the duration is 0.005 s

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It continues to move in a new angle or direction as it slows down.

When a light ray travels from a rarer medium to a denser medium, it bends toward the normal to the boundary between the two media due to refraction.

Refraction is the bending of light beams when they pass through a medium with a variable speed. When a light ray travels from a rarer medium to a denser medium, it bends toward the normal to the boundary between the two media due to refraction. The indices of refraction of the two mediums affect how much bending occurs. As a result, when an airborne light beam encounters a denser material, it bends in the direction of normal.

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The angle of the first-order maximum (constructive interference) for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm is 10.47 degrees.

The angle of the first-order maximum can be calculated using the formula,

θ = mλ/d

Where θ is the angle

m is the order of the maximum

λ is the wavelength

d is the slit separation.

Plugging in the given values, we get:

θ = 1 * 450 nm / 0.0500 mm

θ = 9000 nm/mm

Converting to degrees, we get:

θ = 9000 nm/mm * (1 rad/1000 nm) * (180°/π rad)

θ = 10.47 degrees

Therefore, the angle of the first-order maximum (constructive interference) for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm is 10.47 degrees.

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The total time that the ball with spend in the air is 2.04 Seconds.

As per the data given in the above question.

It is given that the initial velocity of football is 22 meters per second.

And vertical velocity is 10 meters per second.

Also the ball reaches its maximum height within 1. 02 seconds.

We have to find the Time of flight.

As we know that the time of flight i.e ball travel in air is just double the maximum-height time.

Total time of ball in air is equal to double the maximum-height time.

[tex]=2 \times 1.02\\=2.04 \:Seconds[/tex]

The ball will be in the air for a total of 2.04 seconds.

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Yes, in comparing two unequal forces on a rigid body, it is  possible to have the larger force produce less torque than the smaller force.

                            [tex]\tau = Fd[/tex]

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