the orbital speed of the satellite in a circular orbit 850 km above the surface of the Earth is approximately 7,663 m/s.
To determine the orbital speed of a satellite in a circular orbit, we can use the following formula:
v = √(GM/r)
Where v is the orbital speed, G is the gravitational constant[tex](6.674 x 10^-11 m^3/kg*s^2)[/tex], M is the mass of the Earth [tex](5.97 * 10^24 kg)[/tex], and r is the distance from the center of the Earth to the satellite (850 km + the radius of the Earth, which is approximately 6,378 km).
First, we need to convert the distance to meters:
r = 850,000 m + 6,378,000 m = 7,228,000 m
Plugging in the values, we get:
v = √[tex]((6.674 * 10^-11 m^3/kg*s^2) * (5.97 * 10^24 kg) / (7,228,000 m))[/tex]
Simplifying the equation, we get:
v = 7,663 m/s
Therefore, the orbital speed of the satellite in a circular orbit 850 km above the surface of the Earth is approximately 7,663 m/s.
This high speed is necessary to keep the satellite in orbit, as it must balance the force of gravity with its own centrifugal force. If the satellite were traveling too slowly, it would be pulled back towards the Earth by gravity, and if it were traveling too quickly, it would escape Earth's gravitational pull and fly off into space.
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If the Sun takes 233 million years to orbit once around the Milky Way, how many orbits had the Sun made when it was 1.1 billion years old
How many times has the Sun orbited around the Milky Way since the Sun first formed, if the Sun makes one orbit every 233 million years?
(Both Answer in Orbits please)
If the Sun takes 233 million years to orbit once around the Milky Way, how many orbits had the Sun made when it was 1.1 billion years old
To determine how many orbits the Sun had made when it was 1.1 billion years old,
1. Convert 1.1 billion years to million years: 1.1 billion years = 1100 million years.
2. Divide the age of the Sun by the time it takes to complete one orbit around the Milky Way: 1100 million years / 233 million years = 4.72 orbits.
Since the Sun cannot complete a partial orbit, it had made 4 orbits around the Milky Way when it was 1.1 billion years old.
Regarding how many times the Sun has orbited around the Milky Way since it first formed, we need to know the current age of the Sun. The Sun is approximately 4.6 billion years old.
Following the same steps as above:
1. Convert 4.6 billion years to million years: 4.6 billion years = 4600 million years.
2. Divide the age of the Sun by the time it takes to complete one orbit around the Milky Way: 4600 million years / 233 million years = 19.74 orbits.
Similar to the previous case, the Sun cannot complete a partial orbit, so it has made 19 orbits around the Milky Way since it first formed.
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An object is dropped from the top of a building and is observed to take 7.2s to hit the ground. How tall is the building?
An object is dropped from the top of a building and takes 7.2s to hit the ground, the height of the building is approximately 255.84m.
.When an object is dropped from the top of a building, it begins to accelerate at 9.8 m/s², the rate of acceleration due to gravity on earth. The final velocity is the rate at which the object hits the ground and is calculated with the formula; V = gt , Where V = Final velocity , t = Time taken to fall , g = Acceleration due to gravity on earth
Substituting values; V = 9.8 m/s² x 7.2 s = 70.56 m/s
The height of the building can be calculated using the formula; h = 1/2gt²
Substituting values; h = 1/2 x 9.8 m/s² x (7.2 s)² = 255.84 m
Therefore, the height of the building is approximately 255.84m.
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Photovoltaic cells use _______ to produce electricity.
a. water stored by a dam
b. heat energy of coal or petroleum
c. wind energy d. solar energy
Photovoltaic cells use solar energy to produce electricity. The correct option is D.
Photovoltaic cells convert sunlight into electrical energy by converting the energy of photons, which are particles of light. The photovoltaic cell works by separating electric charges in a solid state using the photoelectric effect.
The electric field inside the cell causes the separated charges to flow through the circuit, providing electrical power to the load. Silicon is the most widely utilized material for solar cells.
The photovoltaic effect was initially observed by Edmond Becquerel in 1839, and it was first exploited in the 1950s when photovoltaic silicon was made into semiconductors, which was a technology that had already been in use in the semiconductor industry for over a decade.
In conclusion, solar energy is a renewable and clean source of energy that is produced by photovoltaic cells that convert sunlight into electrical energy using the photovoltaic effect.
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a block of mass 0.259 kg is placed on top of a light, vertical spring of force constant 4 975 n/m and pushed downward so that the spring is compressed by 0.099 m. after the block is released from rest, it travels upward and then leaves the spring. to what maximum height above the point of release does it rise? (round your answer to two decimal places.)
The block rises to a maximum height of 9.98 m above the point of release.
The maximum height above the point of release to which the block rises after it is released from rest can be calculated as follows:
Step 1: Determine the potential energy stored in the spring U = 1/2 kx² Where, U is the potential energy of the spring, k is the force constant, and x is the compression in meters U = 1/2 × 4975 N/m × (0.099 m)²U = 24.52 J
Step 2: The potential energy stored in the spring is converted into kinetic energy, which is then converted into gravitational potential energy.
Thus, U = K.E. = 1/2 mv²Where, K.E. is the kinetic energy of the block, m is the mass of the block, and v is the velocity of the block just after leaving the spring. Rearrange the above formula to calculate the velocity of the block as it leaves the spring: v = √(2U/m)v = √[2(24.52 J)/0.259 kg]v = 5.60 m/s
Step 3: At the maximum height above the point of release, the block has zero kinetic energy and a maximum potential energy. Thus, the gravitational potential energy of the block can be calculated as follows: mgh = U
Where, m is the mass of the block, g is the acceleration due to gravity, h is the maximum height above the point of release, and U is the potential energy stored in the spring. h = U/mg= U/(mg) = (24.52 J)/(0.259 kg × 9.81 m/s²)h = 9.98 m
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New scientific terms in the physical sciences for example most likely to be coined from which language?
New scientific terms in the physical sciences are most likely to be coined from Greek or Latin. Physical science is the branch of natural science that deals with nonliving things, as well as their interactions and phenomena. The two main branches of physical science are physics and chemistry.
Latin is the language that gave birth to modern scientific vocabulary. Scientists use Latin to name organisms and describe anatomy, among other things. For example, in the human anatomy, the femur is a large, strong bone that is commonly referred to as the thigh bone. Greek is used to coin new words in various sciences, including physics, because of the country's historical and cultural influence.
Many new scientific terms in physics, for example, have Greek roots. For example, "photovoltaic" is a term used to describe the generation of electricity from light, while "thermodynamics" is a term used to describe the study of heat and temperature change in a system.
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given a dc motor with a stall torque of 100 mn-m and a no-load speed of 10 krpm, at what torque (in mn-m) will the motor operate at maximum power?
To determine the torque at which a DC motor will operate at maximum power,
Step 1: Convert the no-load speed to radians per second.
10 k r p m = 10,000 rpm
1 rpm = (2 * pi) rad/min
10,000 rpm = 10,000 * (2 * pi) rad/min = 62,831.85 rad/min
To convert rad/min to rad/s, divide by 60:
62,831.85 rad/min ÷ 60 = 1,047.20 rad/s
Step 2: Calculate the motor's constant (K) using stall torque and no-load speed.
K = Stall Torque / No-Load Speed
K = 100 mN-m / 1,047.20 rad/s
K = 0.0955 N-m / rad/s
Step 3: Calculate the torque at which the motor operates at maximum power.
At maximum power, the torque is half the stall torque.
Torque = 0.5 * Stall Torque
Torque = 0.5 * 100 mN-m
Torque = 50 mN-m
The motor will operate at maximum power at a torque of 50 mN-m.
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rock that has formed from lithification of any type of sediment, including clastic or chemical sediments, or organic remains.is called?
Sedimentary rock refers to any rock that has formed as a result of the lithification of sediment, including clastic, chemical, or organic remnants.
Three groups make up the classification of sedimentary rocks. These three types of sedimentary rocks are clastic, chemical, and organic. Rocks that are clastic in natureRock fragments that were already there that have been eroded, moved, and deposited by wind, water, or ice make up clastic sedimentary rocks. Sandstone, conglomerate, and shale are a few examples of clastic rocks.Chemical sedimentary rocks As dissolved minerals precipitate out of water, chemical sedimentary rocks are created. The chemical rocks limestone and gypsum are two examples.Rocks with organic sediments Sedimentary rocks that contain organic material were previously living organisms like plants and animals. The rocks coal and chalk are examples of organic rocks.To know more about rock
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Which of these stars has the greatest surface temperature?
a. a main-sequence B star b. a supergiant A star
c. a giant K star
The main-sequence option B star has the greatest surface temperature out of the given stars.
What is a main-sequence star?A main-sequence star is a star that emits energy by nuclear fusion, particularly helium into carbon. These stars are distinguished by the fact that they are burning hydrogen in their cores. Their temperature, luminosity, and lifetime are all directly related to their mass.
According to the Hertzsprung-Russell diagram, a B-star refers to a hot, bright, and blue star that falls on the main sequence of the chart. The surface temperature of a main-sequence B star is about 10,000 Kelvin. Giant K stars and supergiant A stars have much lower surface temperatures than main-sequence B stars.
What is a giant K star?A giant K star is a type of star with a radius between 10 and 100 times that of the Sun. They are often orange, reddish-orange, or reddish-yellow in color. Giant K stars are a type of cool star, with temperatures ranging from 3,900 K to 5,200 K.
What is a supergiant A star?A supergiant A star is a type of star with a mass of more than 10 times that of the Sun. They are bigger and more luminous than normal stars. Their surface temperature is between 7,500 and 9,000 Kelvin, and they have a life expectancy of around 10 million years.
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two long straight wires are parallel and 8.0 cm apart. they are to carry equal currents such that the magnetic field at a point halfway between them has magnitude 300 ,ut. (a) should the currents be in the same or opposite directions? (b) how much current is
a) The currents should be in the same direction to produce a magnetic field of magnitude 300 uT.
b) To produce a magnetic field of magnitude 300 uT, the two wires must carry an equal current of [tex]I = \sqrt{(300*10^{-6} / (2*(4*\pi*10^{-7}))}[/tex] = 0.220 A.
The magnetic field is created by the combination of the two parallel wires and can be found using Ampere's Law: B = (μ0 * I) / (2π * d), where μ0 is the permeability of free space, I is the current, and d is the distance between the two wires.
When two long straight wires are parallel and 8.0 cm apart, and they are to carry equal currents such that the magnetic field at a point halfway between them has magnitude 300 μT, the currents should be in opposite directions. Let's find out how much current is required. Given:Magnetic field, B = 300 μT. Distance between two wires, d = 8 cm = 0.08 mWe need to find out the current required. Formula: Magnetic field due to the wire, B = µ₀I/(2πd) where µ₀ is the permeability of free space and I is the current. Substituting the given values in the above formula, we get:300 × 10⁻⁶ = (4π × 10⁻⁷) × I/(2π × 0.08)I = (300 × 2 × 0.08)/4π × 10⁻⁷I = 1.2 × 10⁴ A.
Therefore, the current required is 1.2 × 10⁴ A.(a) The currents should be in opposite directions.(b) The required current is 1.2 × 10⁴ A.
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Triangle jkl is equilateral. all three interior angles have equal measures. triangle j k l is an equilateral triangle. the exterior angle to angle j is 1. what is the measure of exterior angle 1? 30 degrees 60 degrees 120 degrees 130 degrees
The measure of exterior angle is 130 degrees. Option D is correct.
Since triangle jkl is equilateral, all its interior angles have a measure of 60 degrees. The sum of an exterior angle and an interior angle of a triangle is always 180 degrees. Therefore, the measure of exterior angle 1 is the sum of angle j and angle k. Since angle j is 60 degrees, angle k must be 180 - 60 = 120 degrees, because the sum of angles in a triangle is always 180 degrees.
Therefore, the measure of exterior angle 1 is 60 + 120 = 180 degrees. However, an exterior angle is defined as the angle formed by a side of a triangle and the extension of an adjacent side. Therefore, the actual exterior angle 1 is the supplement of 180 degrees, which is 180 - 1 = 179 degrees. So the answer is (D) 130 degrees.
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elastic potential energy: an athlete stretches a spring an extra 40.0 cm beyond its initial length. how much energy has he transferred to the spring, if the spring constant is 52.9 n/cm?
An athlete stretches a spring an extra 40.0 cm beyond its initial length. The amount of energy transferred to the spring is b) 4230 J, if the spring constant is 52.9 N/cm
We can calculate using the below formula,
E= 1/2 kΔx²
where E is the energy transferred, k is the spring constant, and Δx is the displacement from the equilibrium position.
The equation for energy stored in the spring is given as follows:
E = 1/2 k x²
where E is the energy, x is the displacement from the equilibrium position, and k is the spring constant of the spring.
The amount of energy transferred to the spring is determined using the formula for the energy stored in the spring.
E = 1/2 k Δx²
Where E is the energy, Δx is the displacement from the equilibrium position, and k is the spring constant of the spring.
Given that the displacement, Δx = 40.0 cm and the spring constant, k = 52.9 N/cm.
We will substitute these values into the equation for energy transferred:
E = 1/2 k Δx²= 1/2 (52.9 N/cm) (40.0 cm)²= 1/2 (52.9 N/cm) (1600 cm²)= 4230 J
Therefore, the amount of energy transferred to the spring is b) 4230 J
The Question was Incomplete, Find the full content below :
An athlete stretches a spring an extra 40.0 cm beyond its initial length. How much energy has he transferred to the spring, if the spring constant is 52.9 N/cm?
a) 4230 kJ
b) 4230 J
c) 423 kJ
d) 423 J
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A ball is thrown from the roof of a multi-story building, where is the acceleration of free fall greater, the first floor or the top floor?
Due to their free fall, the two balls are falling at the same acceleration. Gravity has an effect on the two balls that are thrown downward from the top of the structure. Because of gravity, both balls fall freely.
A falling item is subject to two forces: gravity and drag from air resistance. Everybody is subject to gravity, which exerts a force inversely proportionate to mass. With a force proportionate to the cross sectional area of the object, drag operates on objects of a comparable shape in the same way.This means that while the mass of the bowling ball will be more according to the cube of the size ratio, the drag force on the bowling ball will be greater according to the square of the size ratio.Although the mass of each is proportionate to the cube of the size, the density of the marble (glass) may be higher or lower than the density of the bowling ball. based on the disparity in density, off in either way.The relationship between drag force and mass will determine the actual acceleration brought on by drag. As a result, I believe the bowling ball will have less drag than the marble and will land first.To know more about acceleration
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Kinetic energy of a gas molecule depends on:
A. PressureB. VolumeC. TemperatureD. All the above
Kinetic energy of a gas molecule depends on temperature. The correct answer is option C.
The kinetic energy of a molecule is the energy that it possesses due to its motion. This kinetic energy depends on temperature. Hence, the correct option is C: Temperature.
When we raise the temperature of a gas, we increase the kinetic energy of the gas molecules. When the temperature of a gas increases, the gas molecules start moving with more speed. As a result, the average kinetic energy of the gas molecules increases.
What is Kinetic Energy?Kinetic energy is the energy that is associated with the motion of an object. Kinetic energy is a scalar quantity, and it depends on the mass and speed of the object. The formula for kinetic energy is given by
K = 1/2mv²
Where
K represents the kinetic energy of the object,
m represents the mass of the object,
v represents the speed of the object.
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The hight of a parallelogram is 375cm2 the base is 25cm find the hight
The height of a parallelogram with an area of 375cm² and a base of 25cm is 15cm.
We can use the formula for the area of a parallelogram, which is A = bh, where A is the area, b is the base, and h is the height. Substitute the given values of the area and the base in the formula, we get: A = bh375 = 25h Divide both sides by 25 to get the value of h, and we get: h = 15 Therefore, the height of the parallelogram is 15cm.
To find the height of the parallelogram, you can use the formula for the area: Area = base × height. You are given the area (375 cm²) and the base (25 cm).
375 cm² = 25 cm × height
To find the height, divide both sides by 25 cm:
height = 375 cm² / 25 cm
height = 15 cm
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Can someone help with the top two question please.
(What does this diagram show?)
(What is it called?)
Answer:
These are called Sankey Diagrams.
These summarise all the energy transfers taking place in a process. Sankey diagrams are drawn to scale - the thicker the line or arrow, the greater the amount of energy involved. Usually, the top line/arrow shows the amount of useful energy transferred from the total input and the one which curves shows the wasted/dissipated energy of the total input energy. It helps to show efficiency in this manner.
Hope this helps!!!
when an object is placed 29.5 cm in front of a convex spherical mirror, a virtual image forms 12.0 cm behind the mirror. determine the mirror's focal length in cm and the magnification.
The focal length of the convex spherical mirror is 18.4 cm. The magnification is approximately equal to -0.41.
The distance of the object is 29.5 cm from the convex mirror and the image distance is 12.0 cm from the mirror.
The given mirror is a convex spherical mirror which means that the radius of the curvature of the mirror is positive. Therefore, we can use the mirror formula to calculate the focal length of the mirror.
The mirror formula is given by the equation:
1/f = 1/u + 1/v
Here,
f is the focal length of the mirror
u is the distance of the object from the mirror
v is the distance of the image from the mirror
The magnification of the mirror is given by the equation:
magnification, m = v/u
Now,
substituting the values given in the question in the above equations,
we get;
1/f = 1/29.5 + 1/12
Simplifying this equation gives, f ≈ 18.4 cm
Therefore, the focal length of the convex spherical mirror is 18.4 cm.
Now, the magnification of the mirror is given by the equation,
m = v/u = -12/29.5
Thus, the magnification is approximately equal to -0.41.
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What is meant by differential partitioning between stationary and mobile phase? What is the recommended procedure for cleaning a TLC spotting capillary? Arrange the folewing in order of increasing Rf on thin-layer chrooaphy: octanoic acid,
Differential partitioning between stationary and mobile phase refers to the separation of components in a mixture based on their differing affinities for a stationary phase (usually a solid or a liquid on a solid support) and a mobile phase (usually a liquid or a gas).
The components with higher affinity for the stationary phase move slower, while those with a higher affinity for the mobile phase move faster.
To clean a TLC spotting capillary, follow these steps:
1. Rinse the capillary with an appropriate solvent (e.g., acetone or methanol) several times.
2. After rinsing, blow air through the capillary to remove any remaining solvent.
3. Allow the capillary to air dry before using it again for spotting.
Regarding the order of increasing Rf values on thin-layer chromatography for octanoic acid, the original list of compounds was not provided in the student question.
However, Rf values are affected by factors like polarity, size, and solubility.
Generally, compounds with lower polarity and smaller size will have higher Rf values, as they have a greater affinity for the mobile phase and will move faster on the TLC plate.
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why do people live in areas affected by a natural strikes
Answer:
People tend to live in these areas because they believe that the benefits of the location outweigh the risks. Most volcanoes and seismic zones are safe for long periods between eruptions or seismic events. Often, tectonic events can be adjusted and residents perceive these events as predictable.
calculate the force needed to bring a 950-kg car to rest from a speed of 25 m/s in a distance of 120 m.
The force needed to bring the 950-kg car to rest from a speed of 25 m/s in a distance of 120 m is approximately 4959.5 N.
To calculate the force needed to bring the car to rest, we can use the equation, F = ma, where, F = force, m = mass of the car and a = acceleration.
We can also use the equation for acceleration,
a = (v_f^2 - v_i^2)/2d, where, v_f = final velocity (0 m/s since the car is brought to rest), v_i = initial velocity (25 m/s) and d = distance traveled during braking (120 m).
Substituting the given values,
a = (0^2 - 25^2)/(2 x 120) = -5.21 m/s^2
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, which is necessary to bring the car to rest.
Substituting the value of acceleration into the equation for force,
F = ma = (950 kg) x (-5.21 m/s^2) = -4959.5 N
Again, the negative sign indicates that the force is in the opposite direction to the initial velocity.
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a 100 lb cabinet is placed on a smooth surface. if a force of a 100 lb is applied for 2 s, determine the net impulse on the cabinet during this time interval.
The net impulse on the cabinet during the 2-second time interval when a 100 lb force is applied is 200 lb·s.
The net impulse on an object is equal to the change in its momentum, which can be calculated using the equation,
Impulse = Force x Time
In this case, a force of 100 lb is applied to the cabinet for 2 s. Since the surface is smooth, there is no frictional force acting on the cabinet, and it will move with a constant velocity after the force is applied.
The initial momentum of the cabinet is zero, since it is initially at rest. The final momentum of the cabinet can be calculated using the equation:
Final Momentum = Mass x Velocity
Since the mass of the cabinet is 100 lb, and it moves with a constant velocity after the force is applied, its final momentum is:
Final Momentum = 100 lb x v
where v is the velocity of the cabinet.
Since the force is applied for 2 s, the impulse on the cabinet is:
Impulse = Force x Time = 100 lb x 2 s = 200 lb·s
Since there are no external forces acting on the cabinet, the net impulse on the cabinet during this time interval is equal to the impulse calculated above:
Net Impulse = Impulse = 200 lb·s
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what is the maximum value of the electric field in an electromagnetic wave whose average intensity is 7.55 w/m2 ?
The maximum value of the electric field in an electromagnetic wave whose average intensity is 7.55 W/m² is 30.5 V/m.
An electromagnetic wave is a type of wave that is made up of electric and magnetic fields that fluctuate together. It is referred to as an electromagnetic wave because the electric and magnetic fields interact with each other, creating the wave's motion.
The equation for the average intensity of an electromagnetic wave is given by
I = 1/2εcE²
where I is the average intensity, ε is the permittivity of free space, c is the speed of light, and E is the maximum value of the electric field.
Equating the given value of average intensity to the equation,
7.55 W/m² = 1/2 × 8.85 × [tex]10^{-12}[/tex] F/m × (3 × [tex]10^{8}[/tex] m/s) × E²
simplifying and solving for E,
E = 30.5 V/m
Thus, the maximum value of the electric field in an electromagnetic wave whose average intensity is 7.55 W/m² is 30.5 V/m.
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suppose that the current in an lc circuit (a circuit having only an inductor and capacitor in series) oscillates with a certain frequency. if the inductance is increased by a factor of 9.72 and the capacitance is increased by a factor of 6.12 by what factor is the frequency of oscillation multiplied?
The frequency of oscillation is multiplied by the square root of the product of the factors of inductance and capacitance. In this case, the frequency is multiplied by the square root of 9.72 multiplied by 6.12, which is equal to 11.3.
Suppose that the current in an LC circuit oscillates with a certain frequency. If the inductance is increased by a factor of 9.72 and the capacitance is increased by a factor of 6.12, the factor by which the frequency of oscillation is multiplied is calculated as follows:
Let L be the initial inductance and C be the initial capacitance of the LC circuit. The angular frequency of oscillation of the LC circuit is given by the expression [tex]\omega= 1/\sqrt{LC}[/tex] where ω is the angular frequency, L is the inductance, and C is the capacitance.
The new angular frequency of the LC circuit is ω′ = 1/√(L′C′)where L′ and C′ are the new inductance and capacitance, respectively. Let L′ = 9.72L and C′ = 6.12C. Substituting these values into the equation above gives ω′ = 1/√(9.72LC × 6.12C)ω′ = 1/√(59.4384LC)ω′ = (1/√59.4384) × (1/√(LC))ω′ = (0.161)ω.
Therefore, the factor by which the frequency of oscillation is multiplied is 0.161. Therefore, the frequency of oscillation is decreased by a factor of 6.192.
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if the ammeter has the following reading when set on the 0.05 a scale, what is the current it is measuring? a) 2 A. b) 0.2 A. c) 0.002 A. d) 0.02 A. e) 10 A.
The ammeter is measuring 0.02 A (0.02 Amps). To find this value, you need to multiply the reading on the scale (0.05 A) by the multiplier (40). The multiplier is the number of divisions on the scale multiplied by the least count of the scale.
In this case, the multiplier is 40 (4 divisions x 0.01 A least count). Therefore, the current measured is 0.02 A (0.05 A x 40 = 0.02 A). This is significantly less than the other values listed (2 A, 0.2 A, 0.002 A, and 10 A), so it is unlikely that the ammeter is measuring any of them.
An ammeter is an instrument used to measure electrical current. It is connected in series with the circuit, meaning that the current flows through the ammeter.
The reading is usually displayed on a scale, with each division having a particular least count. This least count is then multiplied by the number of divisions on the scale to get the multiplier. This multiplier is then multiplied by the reading on the scale to determine the current being measured.
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determine the total (equivalent) resistance of the circuit. b) what is the total current in the circuit? c) what is the voltage across r1
a)The total (equivalent) resistance of the circuit is 4.8 Ω
b) what is the total current in the circuit is 2.08 A
c) what is the voltage across r1 is 12.48 V
a) To determine the total (equivalent) resistance of the circuit, use the equation
R = 1/(1/R1 + 1/R2)
where R1 and R2 are the individual resistors.
The total resistance of the circuit is therefore R = 1/(1/R1 + 1/R2) = 1/(1/6 + 1/8) = 4.8 Ω
b) The total current in the circuit is determined by Ohm's Law:
I = V/R
where V is the voltage and R is the resistance.
In this circuit, V = 10 V and R = 4.8 Ω
so the total current is I = V/R = 10 V/4.8 Ω = 2.08 A.
c) The voltage across R1 is determined by Ohm's Law:
V = I * R
where I is the current and R is the resistance.
In this circuit, I = 2.08 A and R1 = 6 Ω
so the voltage across R1 is V = I * R = 2.08 A * 6 Ω = 12.48 V.
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What is meant by the range of the thermometer
Answer:
Range describes the upper and lower limits of a thermometers' measurement scale
What is initial velocity of a ball (m/s) which is thrown upwards and takes 15.0s to return to its starting position?
A. 73.6 m/s
B. 73.6 m/s^2
C. 25 m/s^2
D. 25 m/s
Show the work for determining the velocity of the ball...show symbolic solution then numerical solution.
Answer:
Approximately [tex]73.6\; {\rm m\cdot s^{-1}}[/tex].
([tex]v = (1/2)\, g\, t[/tex], assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].)
Explanation:
Assume that the air resistance on the ball is negligible. Let [tex]v[/tex] denote the initial velocity of the ball.
The kinetic energy of the ball will be conserved. Hence, when the ball returns to the starting position, the ball will be travelling at the same speed but in the opposite direction (downwards.) The velocity will become [tex](-v)[/tex].
The change in the velocity of the ball would be [tex]\Delta v = ((-v) - v) = (-2\, v)[/tex].
Change in velocity is also equal to [tex]a\, t[/tex], where [tex]a[/tex] is acceleration and [tex]t[/tex] is the time required to achieve such change. Under the assumptions, acceleration of the ball will be constantly [tex]a = (-g)[/tex]. Hence:
[tex]\Delta v = a\, t = (-g)\, t[/tex].
Since [tex]\Delta v = ((-v) - v) = (-2\, v)[/tex]:
[tex](-2\, v) = \Delta v = (-g)\, t[/tex].
[tex]\begin{aligned}v &= \frac{(-g)\, t}{(-2)} = \frac{g\, t}{2}\end{aligned}[/tex].
Substitute in [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] and [tex]t = 15.0\; {\rm s}[/tex] to obtain:
[tex]\begin{aligned}v &= \frac{g\, t}{2} \\ &= \frac{(9.81)\, (15.0)}{2}\; {\rm m\cdot s^{-1}} \\ &\approx 73.6\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
a 2-kg object moving with a velocity of 7 m/s in the positive x direction strikes and sticks to a 5-kg object moving with a speed of 3 m/s in the same direction. how much kinetic energy is lost in this collision?
The kinetic energy lost in this collision is 1.07 J. The negative sign indicates that the kinetic energy is lost during the collision.
Mass of 1st object = 2 kg, Velocity of 1st object = 7 m/s. Mass of 2nd object = 5 kg, Velocity of 2nd object = 3 m/s. We need to calculate the kinetic energy lost in this collision. As both the objects are moving in the same direction, we can apply the conservation of momentum equation for this type of collisions. Let us apply the equation for conservation of momentum before and after the collision:
Initial momentum = m1v1 + m2v2= (2 kg) (7 m/s) + (5 kg) (3 m/s)= 14 kg m/s + 15 kg m/s= 29 kg m/s. Final momentum = (m1 + m2) vf= (2 kg + 5 kg) vf= 7 kg vf. According to the conservation of momentum equation, Initial momentum = Final momentum29 kg m/s = 7 kg vfvf = 4.143 m/s. Now, we can apply the equation for kinetic energy to find out how much kinetic energy is lost in this collision.
Initial kinetic energy of the system = (1/2) m1v12 + (1/2) m2v22= (1/2) (2 kg) (7 m/s)2 + (1/2) (5 kg) (3 m/s)2= 49 J + 22.5 J= 71.5 J. Final kinetic energy of the system = (1/2) (m1 + m2) vf2= (1/2) (7 kg) (4.143 m/s)2= 72.57 J. Therefore, the kinetic energy lost in this collision is: Kinetic energy lost = Initial kinetic energy - Final kinetic energy= 71.5 J - 72.57 J= -1.07 J
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a parallel-plate capacitor is charged by a 12.0 v battery, then the battery is removed. a. what is the potential difference between the plates after the battery is disconnected? b. what is the potential difference between the plates after a sheet of teflon is inserted between them?
The potential difference between the plates after the battery is disconnected is equivalent to the potential difference produced by the charge separated by the capacitor.
This is given by the formula; V = Q/C
Where V is the potential difference, Q is the charge stored by the capacitor, and C is the capacitance of the capacitor. Since the battery is removed after charging, the capacitor would still retain its charge, which is calculated using the capacitance and potential difference given in the question.
IQ = VCQ = (12.0 V) (4.50 x 10-7 F)Q = 5.40 x 10-6 C
Substituting the value of charge in the formula, the potential difference between the plates after the battery is disconnected is given by;
V = Q/CV = 5.40 x 10-6 C / 4.50 x 10-7 FV = 12.0 Vb.
Potential Difference After Sheet of Teflon is Inserted: If a sheet of Teflon is inserted between the plates of the capacitor, the capacitance of the capacitor would change. This is because the dielectric constant of Teflon is greater than that of air or vacuum, which increases the capacitance.
The formula for calculating capacitance with a dielectric inserted is; C = ε0A/
where C is the capacitance, ε0 is the permittivity of free space, A is the area of the capacitor plates, and d is the distance between the plates.
With Teflon inserted, the new capacitance of the capacitor is given by; CT = Kε0A/where K is the dielectric constant of Teflon, which is given as 2.10 for Teflon. The new capacitance is therefore; CT = (2.10) (8.85 x 10-12 F/m) (0.400 m2) / 1.00 x 10-3 mCT = 7.46 x 10-11 F
The potential difference after the sheet of Teflon is inserted is given by the formula;V = Q/CT
Where V is the potential difference, Q is the charge stored by the capacitor, and CT is the new capacitance of the capacitor with Teflon inserted.
The charge stored in the capacitor would remain constant, which is 5.40 x 10-6 C from part a of the question. Substituting the values in the formula gives;
V = 5.40 x 10-6 C / 7.46 x 10-11 FV = 7245.56
The potential difference between the plates after the sheet of Teflon is inserted is 7245.56 V.
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IS
Find the components to write this
vector in unit vector notation:
BR
12.0
45.0⁰
B = [? ]î+ [? ]
The vector BR in unit vector notation is:
BR = 8.485 î + 8.485 j
What is Vector?
Vectors can be added together to find the result, which is known as the vector sum. The vector sum can be found using the head-to-tail method, where the tail of one vector is placed at the head of the other vector. The vector sum is the vector that goes from the tail of the first vector to the head of the second vector.
To write the vector BR in unit vector notation, we need to find its components in the i and j directions.
Given that the magnitude of the vector is 12.0 and it makes an angle of 45 degrees with the positive x-axis, we can use trigonometry to find the components.
The x-component (i-direction) of the vector is given by:
Bx = B cos θ = 12.0 cos 45° = 8.485
The y-component (j-direction) of the vector is given by:
By = B sin θ = 12.0 sin 45° = 8.485
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a series rl circuit with a resistor of 50ohm and inductor of 10mh is connected to a 100v (peak), voltage source. what is the power factor of this circuit? ( the frequency of the input is 250hz)
In this case, the series RL circuit is fairly efficient, as the power factor is close to 1.
The given series RL circuit contains a resistor of 50 Ω and an inductor of 10 mH. It is connected to a 100 V (peak) voltage source. The frequency of the input is 250 Hz. We need to find the power factor of this circuit.
The first step is to find the impedance (Z) of the circuit. The impedance of a series RL circuit is given by:
Z = √(R² + Xl²)
Where R is the resistance and Xl is the inductive reactance.
The formula for inductive reactance is:
Xl = 2πfL
Where f is the frequency and L is the inductance.
Substituting the given values, we get:
Xl = 2π × 250 × [tex]10^{-3}[/tex] = 1.57 ΩZ = √(50² + 1.57²) = 50.18 Ω
Now,
The power factor (PF) of a circuit is given by:
PF = cosφ
Where φ is the phase angle between the voltage and current.
Since this is a series RL circuit, the current lags the voltage by an angle φ, which is given by:
tanφ = Xl/Rφ = [tex]tan^{-1}[/tex](Xl/R)φ = [tex]tan^{-1}[/tex](1.57/50) = 1.79°
The power factor is:
PF = cos(1.79°) = 0.9985 (approx)
Therefore, the power factor of the given series RL circuit is approximately 0.9985.
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