Do you think Kepler will be able to detect Earth-sized planets in transit?

Answers

Answer 1

Answer: Less than 1% of the stars that Kepler will be looking at are closer than 600 light years. Stars farther than 3,000 light years are too faint for Kepler to observe the transits needed to detect Earth-size planets.

Explanation:


Related Questions

You want to average 90 km/h on a car trip. You cover the first half of the distance at an
average speed of 48 km/h.
a) What average speed must you have for the second half of the trip to meet your goal?
b) Is this reasonable? Note that the velocities are based on half the distance, not half the
time.

Answers

(a) The average speed must you have for the second half of the trip to meet your goal is 8 km/h.

(b) The value obtained (8 km/h) is not reasonable for the second half of the distance since the first half is 48km/h.

What is average velocity?

Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs.

average velocity = total distance / total time

v = (d)/(0.5d/v₁ + 0.5d/v₂)

where;

v is the average velocityv₁ is the average velocity during the first halfv₂ is the average velocity during the second half

90 km/h = (d) / (0.5d/48 + 0.5d/v₂)

90(0.5d/48 + 0.5d/v₂) = d

0.9375d + 0.5d/v₂ = d

d(0.9375 + 0.5/v₂) = d

0.9375 + 0.5/v₂ = 1

0.5/v₂ = 0.0625

v₂ = 0.5/0.0625

v₂ = 8 km/h

Thus, the average speed must you have for the second half of the trip to meet your goal is 8 km/h.

The value obtained (8 km/h) is not reasonable for the second half of the distance since the first half is 48km/h.

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4.2 Determine the reactions of the loads L and R. ↓ 5m
↓ 7 kN 6m 3 kN 4m R (8)​

Answers

The reaction of load L is 0 (no horizontal force), and the reaction of load R is 10 kN (vertical upward force).

How to find reaction?

To determine the reactions of the loads L and R, consider the equilibrium of the forces acting on the structure.

First, analyze the vertical equilibrium. The sum of the vertical forces must be zero:

ΣFy = R − 7 kN − 3 kN

ΣFy = 0

This gives:

R = 10kN

Next, analyze the horizontal equilibrium. The sum of the horizontal forces must be zero:

ΣFx = L

ΣFx = 0

This indicates that there is no horizontal force acting on the structure.

Therefore, the reaction of load L is zero (no horizontal force), and the reaction of load R is 10 kN (vertical upward force).

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what is the difference between total distance covered vs. total displacement of the rube goldberg

Answers

Answer:

The deer traveled 1300m + 500m + 300m, for a total distance. The exact same motion, distance and displacement have significantly different values. It tells you the rate at which an object's displacement, or position, changes.

Total distance covered is amount of distance cover during the course whereas total displacement is difference between initial and final position.

What is distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

What is displacement?

The term "displacement" refers to a shift in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial location to the ending place. For instance, if an object shifts from location A to position B, its position changes. Displacement is the term used to describe this shift in an object's position.

Hence total distance covered and  total displacement are different.  Total distance covered is amount of distance cover during the course whereas total displacement is difference between initial and final position.

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why aeroplanes cannot travel in space

Answers

Answer:

- They need oxygen to burn fuel

- Aerodynamics

- Extreme temperatures

- Radiation

- Pressure issues

Explanation:

A airplane is a heavier-than-air aircraft kept aloft by the upward thrust exerted by the passing air on its fixed wings and driven by propellers, jet propulsion, etc.

Aeroplanes cannot travel in space for several reasons:

They need oxygen to burn fuel - Aeroplane engines rely on the oxygen in the atmosphere to burn fuel and generate thrust. In space, there is no atmosphere so there is no oxygen for the engines to work.

Aerodynamics - Aeroplane wings generate lift by interacting with the air. In space, there is no air so wings would be unable to generate any lift. Aeroplanes rely on aerodynamics to fly which does not work in space.

Extreme temperatures - In space, temperatures can range from -150 degrees Celsius to 150 degrees Celsius. Aeroplanes are designed to operate within a much narrower temperature range. The extreme cold and heat of space could damage aeroplane components.

Radiation - In space, there are high levels of radiation from the Sun and cosmic rays. Aeroplane bodies are not designed to shield against this type of radiation and it could damage electronics and affect aeroplane systems.

Pressure issues - Aeroplanes are designed to withstand air pressures at altitudes up to around 12 kilometers. In low-Earth orbit and beyond, the air pressure is essentially zero. This extreme change in pressure could cause structural damage to the aeroplane.

In summary, while aeroplanes are designed to fly through the Earth's atmosphere, they lack the key features needed to operate in the extreme environment of outer space like spaceships. Aeroplanes require things like oxygen, aerodynamics and being able to withstand changes in pressure - all of which do not exist or work the same way in space.

Explanation:

The wing is pushed up by the air under it. Large planes can only fly as high as about 7.5 miles. The air is too thin above that height. It would not hold the plane up.

What are the phenomena that physics is applied in?

Answers

Answer:

Physics is applied every where? For example if you talking with you friends, that mean the sound that you produce oscillate through your friends' ear so he/ she can respond to you.

Explanation:

Physics is the fundamental unit about understanding the world around us.

There are several phenomena in our day-to-day life from the formation of the rainbow to the free falling of objects under the influence of gravity physics is applied almost everywhere.

What is science?

Science is the methodical, empirically-based pursuit and application of knowledge and understanding of the natural and social worlds.

Physics is a useful tool for seeing the real world, which is far larger than we can imagine. In every conceivable way, it describes the environment we live in. Almost all human activities, including walking, eating, and listening to music, require physics. Everywhere we look, there is physics.

In daily life, we encounter a number of events, such as the rainbow's emergence and items falling freely as a result of gravity. Nearly everywhere uses physics.

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A sea If the determine 103,000 N Im² divor. density 35M 10301 H=10M total ko no ros belos Surface of the Sea be Sea water is 1.03g/cm²³3 and g=10Nig take atmospheric Pressure to be 103000.calculate total pressure


Answers

A sea or an ocean's water is known as seawater or salt water. Oceans around the world have an average salinity of 3.5% (35 g/L, 35 ppt, 600 mM).

What is the density of the sea?Fresh water has a density of 1 g/cm3 at 4 oC (see section 5.1), but adding salts and other dissolved substances raises the density of surface seawater to between 1.02 and 1.03 g/cm3. Seawater's density can be raised by lowering its temperature, raising its salinity, or raising the pressure.Oceans are frequently referred to as "seas" by people. Geographers define a sea as an area of the water that is entirely or partially contained by land.Density can be defined as a substance's weight in relation to its volume. A gramme per millilitre is about how dense water is, however this might vary depending on temperature or the things that are dissolved in it.

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'State the appropriate serving size for a 3 to
5-year-old child for each of the following foods:
a. milk
b. dry cereal
c. fruit
d. vegetable
e. bread
2. Where can a program director locate information about state licensing requirements that address nutrition and food services for young children?
3. Name four sensory qualities that contribute to food's appeal.
4. What are two advantages of using fresh fruits and vegetables in season?
5. List two strategies the menu planner can use to control food costs.

Answers

Based on my own known, the right  serving size for a 3 to 5-year-old child  are:

a. milk - A single cup

b. dry cereal - 1/2 cup

c. fruit - 1/2 cup

d. vegetable - 2 leafty

e. bread - 1 slice of bread.

What is the serving size?

A program director can find state licensing requirements for nutrition and food services for young children on their state's education or health department website.

The four sensations that contribute to food appeal are appearance, aroma, taste, and texture. Using fresh seasonal produce is cheaper and more flavorful. To control food costs, menu planners can use less expensive ingredients and reduce waste.

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Some free market economist think that people would lack motivation without monetary incentives .

Answers

It is possible to study the connection between motivation, rewards, and production from a variety of angles, including those of economics, psychology, and physics.

Do incentives exist in a free market system?

Because producers are motivated to satisfy consumer demand, free markets offer a larger variety of commodities than any other system. What is created is under the control of the consumer.

What drawbacks exist in a free market economy?

In theory, free markets work best because supply and demand are efficiently distributed by an invisible hand. Yet, in practise, open markets are prone to manipulation, false information, and imbalances of power and knowledge, which also contribute to wealth disparity.

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what is the pressure of a tank of uniform cross sectional area 4.0m2 when the tank is filled with water a depth of 6m when given that 1 atm=1.013 x 10^5pa density of water=1000kgm-3 g=9.8m/s2​

Answers

The pressure of a tank of uniform cross-sectional area 4.0m2 when the tank is filled with water at a depth of 6m is 58800 Pa.

Pressure calculation

To find the pressure in the tank, we can use the formula for pressure:

Pressure = density x gravity x height

Density of water (ρ) = 1000 kg/m³

Acceleration due to gravity (g) = 9.8 m/s²

Height (h) = 6 m

Thus:

Pressure = 1000 kg/m³ x 9.8 m/s² x 6 m

Pressure = 58800 kg/(m·s²)

Since the unit of pressure is Pascal (Pa), which is equivalent to kg/(m·s²), the pressure in the tank is:

Pressure = 58800 Pa

Therefore, the pressure in the tank when it is filled with water to a depth of 6 m is 58800 Pascal.

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A spring of length 9.7 meters stretches to 9.8 meters when a 0.4 kg mass is hung vertically from one end. What is the spring constant?

Answers

Given,

The initial length of the spring, l=9.7 m

The length of the spring after stretching, L=9.8 m

The mass, m=0.4 kg

The magnitude of the restoring force of the spring due to the stretching from the mass will be equal to the force applied by the mass, which is nothing but the weight of the mass.

Thus,

\(\begin{gathered} mg=k\Delta x \\ =k(L-l) \end{gathered}\)

Where g is the acceleration due to gravity, k is the spring constant, and Δx is the stretch in the length of the spring.

On substituting the known values,

\(\begin{gathered} k=\frac{mg}{(L-l)_{}} \\ =\frac{0.4\times9.8}{9.8-9.7} \\ =\frac{3.92}{0.1} \\ =39.2\text{ N/m} \end{gathered}\)

Thus the spring constant is 39.2 m

An engine has an output energy of 2,400 J in 10 seconds. What is its average power in watts?

Answers

Answer:

P = 240 W

Explanation:

By definition, the average power is the rate of change of Energy (in Joules) regarding time (in seconds), as follows:

       \(P = \frac{\Delta E}{\Delta t} (1)\)

Replacing in (1) by the givens of ΔE = 2, 400 J and Δt = 10 sec, we can find the average power in Watts as follows:

       \(P = \frac{\Delta E}{\Delta t} =\frac{2,400J}{10s} = 240 W (2)\)

define parking orbit?​

Answers

A parking orbit is a temporary orbit used during the launch of a spacecraft. A launch vehicle boosts into the parking orbit, then coasts for a while, then fires again to enter the final desired trajectory.

Answer:

An orbit of a spacecraft from which the spacecraft or another vehicle may be launched on a new trajectory.

If a second light bulb was added to a circuit, what would you expect to happen to the current and potential difference?

Answers

Answer:

Explanation:

Ohm's law can be expressed as;

                    V = IR.

For the given question, two cases would be considered.

1. If the circuit is a series circuit.

For a series circuit, the potential difference across each bulb in the circuit varies. The current has the same value at any point in the circuit.

When the second bulb is added, less current would flow through the bulbs. The current reduces, same as the potential difference across each bulb. Thus the brightness of the first bulb decreases because the current is shared between the two bulbs.

2. If the circuit is a parallel circuit.

In a parallel circuit, the potential difference across its ends is the same. But the current is shared between the bulbs. The potential difference is the same, while the current varies. Therefore, the second light bulb would produce light without affecting the brightness of the first light bulb in the circuit.

The audio power of the human voice is concentrated at about 300 Hz. Antennas of the appropriate size for this frequency are impracticably large, so that to send voice by radio the voice signal must be used to modulate a higher (carrier) frequency for which the natural antenna size is smaller. a. What is the length of an antenna one-half wavelength long for sending radio at 300 Hz

Answers

Answer:

the length of an antenna one-half wavelength long for sending radio at 300 Hz is 500 km

Explanation:

Given the data in the question;

we know that wave length is;

λ = c/f

c is the speed of voice ( 3 × 10⁸  m/s )

frequency f = 300 Hz

so we substitute

λ = 3 × 10⁸ / 300

λ = 1000000 m

we know that; 1 km = 1000 m

so

λ = 1000000 m / 1000

λ = 1000 km

hence, an antenna one-half wavelength will be;

λ /2

=  1000 km / 2

= 500 km

Therefore, the length of an antenna one-half wavelength long for sending radio at 300 Hz is 500 km

the space Hubble Telescope is orbiting earth at a constant speed of 20m/s.The distance between it and planet earth is 100m.The radius of planet earth is 300km. How long will it take for the Space Hubble Telescope to make a complete rotation?​

Answers

It will take the Hubble Telescope 94,247 seconds or 26.18 hours to complete one full rotation around the Earth.

Rotation time of the Space Hub Telescope

The Hubble Telescope is in a circular orbit around the Earth at a constant speed of 20 m/s. The distance between the telescope and the center of the Earth is:

300 km + 100 m = 300,100 m.

Orbital period T of the Hubble Telescope = T = 2πr / v

where

r is the radius of the orbit v is the orbital speed.

In this case, r = 300,100 m and v = 20 m/s, so:

T = 2π(300,100 m) / (20 m/s) = 94247 seconds

Thus, it will take the Hubble Telescope approximately 94,247 seconds, or about 26.18 hours, to complete one full rotation around the Earth.

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Look at the attached photo:

Look at the attached photo:

Answers

Answer:

C) Mass of the ball

Explanation:

Independent variable is the variable the researcher changes.

Since Martin is testing the mass of the ball, he'll be using different balls and that is the only thing he changes.

The distance traveled by the ball is the dependent variable since it depends on the mass of the ball.

The height and length of the ramp are the constant variables since that's the only ones that remain the same throughout this experiment.

A 1.0 kg block is pushed 3.0 m at a constant velocity up a vertical wall by a constant force applied at an angle of 26.0 ◦ with the horizontal, as shown in the figure. The acceleration of gravity is 9.81 m/s 2 . If the coefficient of kinetic friction between the block and the wall is 0.40, find a) the work done by the force on the block. Answer in units of J.

Answers

Explanation:

a) 8.2 J

The work done by the force on the block is equal to the force multiplied by the distance moved in the direction of the force. Since the force is applied at an angle of 26.0° with the horizontal, only a component of the force is acting in the direction of motion. The component of the force in the direction of motion is equal to the magnitude of the force multiplied by the cosine of the angle between the force and the direction of motion. Therefore, the work done by the force on the block is equal to:

Work = Force x Distance x cos(26.0°)

= (1.0 kg)(9.81 m/s2)(3.0 m) x cos(26.0°)

= 8.2 J

I’n a miracle of modern physics a 20.0-kg frictionless…

In a miracle of modern physics a 20.0-kg frictionless

Answers

The acceleration of the lawn mower is  1.25 m/s².

The velocity of the lawn mower at the given time is 6.25 m/s.

What is the acceleration of the lawn mower?

The acceleration of the lawn mower is calculated by applying Newton's second law of motion as shown below.

Fx = ma

where;

Fx is the horizontal component of the forcem is the mass of the lawn mowera is the acceleration of the lawn mower

F cosθ = ma

where;

θ is the inclination of the force.

a = ( F cosθ ) / m

a = ( 50 N  x  cos60 ) / 20 kg

a = 1.25 m/s²

The velocity of the lawn mower at the given time is calculated as;

v = at

v = 1.25 m/s²  x 5 s

v = 6.25 m/s

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In a miracle of modern physics a 20.0-kg frictionless

a 0.250 kg ball is pressed against a vertical spring that has a spring constant of 75.0 n/m and is compressed 25 cm from its equilibrium position. the other end of the spring is firmly attached to the table. when the ball is released from rest it moves straight up.

Answers

As a result, the ball will reach a maximum height of 0.826 m above the release point.

What is equilibrium position?

In the absence of force, the item would naturally rest in the equilibrium position. The biggest deviation from equilibrium is referred to as the amplitude X. The units for amplitude and displacement are the same, but the kind of oscillation affects them.

Here,

When the ball is released from rest, it will start moving straight up due to the potential energy stored in the compressed spring. The ball's initial velocity can be calculated using the equation of motion:

v_initial = sqrt(2 * k * x / m)

where k is the spring constant, x is the compression distance, and m is the mass of the ball.

v_initial = sqrt(2 * 75 N/m * 0.25 m / 0.250 kg) = 6.13 m/s

The maximum height that the ball reaches can be calculated using the conservation of energy:

h = v_initial^2 / (2 * g)

where g is the acceleration due to gravity.

h = (6.13 m/s)^2 / (2 * 9.8 m/s^2) = 0.826 m

So the ball will reach a maximum height of 0.826 m above the point of release.

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A 5.3-cm -thick layer of oil (n=1.46) is sandwiched between a 1.5-cm -thick sheet of glass and a 2.3-cm -thick sheet of polystyrene plastic (n=1.59). How long (in ns ) does it take light incident perpendicular to the glass to pass through this 9.1- cm -thick sandwich?

Answers

Time taken to incident light perpendicular to glass to pass through this 9.1 cm thick sandwich is 0.399 ns.

How long it took to calculate:

Being aware of

Layer thickness / light speed equals the amount of time required.

Also,

V is equal to the product of the sound speed and the refractive index.

Now

T1 = 0.05*1.46/3*10^8 = 2.43*10^-10 s

t2 = 0.01*1.5/3*10^8 = 5*10^-11 s

t3 = 0.02*1.59/3*10^8 = 1.06*10^-10 s

So,

Total time is equal to 2.43*10-10, 5*10-11, and 1.06*10-10 s, or 0.399*10-9 s.

= 0.399 ns

Light Speed:

When a light beam passes through a certain media, its speed in that medium may be determined using the light speed in vacuum and the medium's refractive index. With the use of the medium's light speed, the value of the amount of time needed to travel a particular distance can be determined.

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a car is moving 5.82 m/s when it accelerates at 2.35 m/s2 for 3.25, what is its final velocity

Answers

The final velocity of the car can be calculated using the formula: final velocity = initial velocity + acceleration * time. Plugging in the values you provided, we get: final velocity = 5.82 m/s + 2.35 m/s² * 3.25 s = 13.44 m/s.

d. Two point charges, q1 = +25 nC and q2 = -75 nC, are separated by a distance of 3.0 cm. Find the magnitude and direction of; i. the electric force q1 exerts on q2 [5] ii. the force that q2 exerts on q1 [4] (take k = 9.0 x 109 N.m2 /C2 )

Answers

Answer:

a) F₂₁ = 0.02 N, attracting.

b) F₁₂ = 0.02 N, attracting.

Explanation:

a)

The magnitude of the force that q₁ exerts on q₂ (F₂₁) is given by Coulomb's Law, as follows:

      \(F_{21} = k * \frac{q_{1} *q_{2}}{r_{12}^{2} } = 9e9 N.m2/C2 * \frac{(25e-9C)*(75e-9C)}{(0.03m)^{2}} = 0.02 N (1)\)

Since q₁ and q₂ have opposite signs, the force between them will be always attractive, i.e., from q₂ towards q₁, along the line that joins both charges.

b)

The magnitude of the force on q₁ due to q₂ can be obtained applying Newton's 3rd Law, or using (1), because all parameters are the same, so F₁₂ (in  magnitude) = F₂₁ = 0.02 NAs we have already said, it must be opposite to the one found in a) so it must go from q₁ towards q₂, it is an attracting force also.

A parallel circuit has four branch currents: 120 mA, 380 mA, 250 mA, and 2.1 A. How much current is supplied by the source?

Answers

A parallel circuit is an electrical circuit with more than one current path and all circuit components are connected between the same two sets of electrically common points. The current supplied by the source in a parallel circuit is equal to the sum of all branch currents in the circuit.

The sum of the branch currents in a parallel circuit can be calculated by adding up the values of the individual branch currents. In this case, we have four branch currents: 120 mA, 380 mA, 250 mA, and 2.1 A. Thus, the sum of the branch currents is:120 mA + 380 mA + 250 mA + 2.1 A= 2.85 ATherefore, the current supplied by the source in this parallel circuit is 2.85 A. This is because, in a parallel circuit, the current from the source is split between the different branches of the circuit. Each branch will have a different current, but the sum of all the branch currents will always equal the current supplied by the source

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what you think is between the particles that make up a substance

Answers

Answer:

There is always space (vacuum) between particles. The particles are small objects that exist in (sometimes vast) empty space. In gas particles there's a lot more space between the particles; the particles fly around in vacuum, bumping into each other.

You apply a very small force, say 0.001 newtons, to a very large truck, with a mass of 2000 kilograms. What can you say for sure about what will happen to the truck?
The truck will accelerate (move from rest to motion) as long as that tiny force is larger than any force of friction that opposes it.

The truck will not move because small forces cannot move large objects.

The truck will accelerate (move from rest to motion) as long as the small applied force is large enough to overcome the inertia of the truck.

An extremely small force can never accelerate such a large truck. The truck will not move under any circumstance.

Answers

Answer:

it will stay still. unless its in space.

Explanation:

Lightning occurs when there is a flow of electric charge (principally electrons) between the ground and a thundercloud. The maximum rate of charge flow in a lightning bolt is about 20,000 C/s this lasts for 100 μs or less.1. How much charge flows between the ground and the cloud in this time? (Q= ? C)2. How many electrons flow during this time? (n_e = ?)

Answers

Answer:

a

 The  charge is  \(Q =  2.0*10^8 \  C\)

b

The number of electrons  \(N  =  1.25 *10^{27} \  electrons\)

Explanation:

From the question we are told that

    The  maximum rate of charge flow is  \(\frac{dq}{dt} = I =  20000 \  C/s\)

Here  I means current

    The time interval is \(t=100 \mu s  = 100*10^{-6}\)

Generally the amount of charge is mathematically represented as

        \(Q =  \frac{I}{t}\)

=>      \(Q =  \frac{20000}{ 100*10^{-6}}\)

=>    \(Q =  2.0*10^8 \  C\)

The number of electrons that flow during that time is evaluated as

    \(N  =  \frac{Q}{e}\)

Here e is the charge on a single electron with value \(e=  1.60*10^{-19} \  C\)

So

         \(N  =  \frac{2.0*10^8}{ 1.60*10^{-19}}\)

         \(N  =  1.25 *10^{27} \  electrons\)

Jupiter’s moon Callisto orbits the planet at a distance of 1.88 X 10^6 km in about 16.7 days. If one year is 365 days, and if 1 AU is 1.5 X 10^8 km, calculate the mass of Jupiter in solar mass units.
(We have been using Kepler's 3rd law)

Answers

The mass of Jupiter in solar mass units with the help of Kepler's Third Law is found to be 0.000935 Solar mass Unit.

According to the Kepler's Third law, "the squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits".

Mathematically, p² = a³M

where, p= years

           a= AU

           M= Solar Masses

In the given question,

p= 16.7 days = 0.0457 years

a= 1.88 x 10⁶ km = 0.0125 AU

M= a³/p²=(0.0125 AU)³/(0.0457)²

M= 0.000935 Solar mass Unit

M= 1.87 x 10²⁷ kg

Hence, the mass of Jupiter in solar mass units is found to be 0.000935 Solar mass Unit.

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An electric iron is Mark 120 volts and 500 Watts to units consumed by it in using it for 24 hours will be

Answers

An electric iron is marked 120 volts and 500 Watts. The units consumed by it in using it for 24 hours can be calculated using the formula:Power (in watts) = Voltage (in volts) x Current (in amperes)P = V x I

Using the above formula, we can find the current drawn by the electric iron as follows:I = P/VI = 500/120I = 4.17 ATherefore, the power consumed by the electric iron in 24 hours is:P = VI x tP = 120 x 4.17 x 24P = 120 x 100.08P = 12010.56 watt-hoursTo convert watt-hours to kilowatt-hours, we divide by 1000: Energy consumed = 12010.56 / 1000Energy consumed = 12.01 kWhHence, the units consumed by the electric iron in 24 hours is 12.01 kilowatt-hours.

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Image shows question, please help

Image shows question, please help

Answers

Jonathan needs to maintain a separation of 0.543 mm between the plates to get the desired charge, and a dielectric constant of 92.6 to achieve a separation of 5 mm with a dielectric.

(a) Using the equation Q = CV, where Q is the charge, C is the capacitance, and V is the voltage, we can solve for the capacitance: C = Q/V =\((8.15 x 10^-9 C) / (50 V) = 1.63 x 10^-10 F.\)

Then, using the formula for capacitance of parallel plate capacitors: C = ε0A/d, where ε0 is the permittivity of free space, A is the area of the plates, and d is the separation distance, we can solve for the separation distance: d =\(_{3}OA/C = (8.85 x 10^-12 F/m) x (0.01 m^2) / (1.63 x 10^-10 F) = 0.543 mm.\)

(b) To find the dielectric constant, we can use the formula for capacitance of a parallel plate capacitor with a dielectric: C = εrε0A/d, where εr is the relative permittivity or dielectric constant of the material. Solving for εr, we get: εr = Cd / ε0A = \((1.63 x 10^-10 F)\) x (0.005 m) / \((8.85 x 10^-12 F/m)\) x \((0.01 m^2)\) = 92.6.

Therefore, Jonathan should use a dielectric with a relative permittivity of 92.6 to achieve a separation of 5 mm.

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Explosives are used to blow a rock apart. The explosion blows the rock into three fragments. Two fragments go off at a 102 degree angle to each other--a 5.8 kg piece at 28.9 m/s and a 4.9 kg piece at 30.4 m/s. Calculate the speed of the third piece, if it has a mass of 3.6 kg. 55.49 m/s

Answers

The speed of the third fragment is 68.4 m/s.

Resultant momentum of the two fragments

The resultant momentum of the two fragments at the given angle is calculated as follows;

\(P_3^2 = P_1^2 + P_2 - 2P_1P_2 cos(102)\\\\P_3^2 = (5.8 \times 28.9)^2 + (4.9 \times 30.4)^2 \ - \ 2(5.8\times 28.9)(4.9 \times 30.4)\times cos(102)\\\\P_3^2 = 50285.55 \ + \ 10382.55\\\\P_3^2 = 60668.1\\\\P_3 = \sqrt{60668.1} \\\\P_3 = 246.31 \ kgm/s\)

Speed of the third fragment

The speed of the third fragment is calculated as follows;

P = mv

\(v = \frac{P}{m} \\\\v = \frac{246.31}{3.6} \\\\v = 68.4 \ m/s\)

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