A 200 ω resistor, a 0.850 h inductor, and a 5.75 μf capacitor are connected in series across a voltage source that has voltage amplitude 29.0 v and an angular frequency of 260 rad/s.
a. What is v at t= 22.0 ms ?
b. What is vR at t= 22.0 ms ?
c. What is vL at t= 22.0 ms ?
d. What is vC at t= 22.0 ms ?
The root mean square voltage Vrms of the circuit is 15.49 V.
The voltage of the resistor vR is 10.4 V.
The voltage of the inductor vL is 11.49 V.
The voltage of the capacitor vC is 0.035 V.
RMS voltage of the circuit is calculated as follows:
Vrms = -V₀ sin ωt = -29 * sin (260* 22* 10⁻³) = 29 * 0.534 = 15.49 V
XI = ωL = 260* 0.85 = 221 ohms
Xc = 1/ωc = 1/(260 * 5.75* 10⁻³) = 10³/1495 = 0.67 ohm
Z = √[R² +(XI - Xc)²] = √[200² + (221 - 0.67)²] = √[200² + 220.33²]
= √[ 40000 + 48545.30] = 297.56 ohm
Current flowing in the circuit is
Irms = Vrms/Z = 15.49 / 297.56 = 0.052 A
vR = Irms * R = 0.052 * 200 = 10.4 V
vL = Irms * L = 0.052 * 221 = 11.49 V
vC = Irms * C = 0.052 * 0.67 = 0.035 V
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A 175 g glider on a horizontal, frictionless air track is attached to a fixed ideal spring with force constant 155 n/m. At the instant you make measurements on the glider, it is moving at 0. 815 m/s and is 3. 00 cm from its equilibrium point. Use energy conservation to find (a) the amplitude of the motion and (b) the maximum speed of the glider. (c) what is the angular frequency of the oscillations?.
The maximum speed of the glider v = 4.75 m/s. the amplitude of the motion 2.12 cm. the angular frequency of the oscillations is approximately 2.86 rad/s.
To find the amplitude of the motion, we can use the equation for the potential energy of a spring:
Potential Energy = (1/2) * k * x^2
where k is the force constant of the spring, x is the displacement of the glider from its equilibrium point, and Potential Energy is the potential energy of the spring.
In this case, the force constant of the spring is 155 n/m, the displacement of the glider from its equilibrium point is 3.00 cm, and the potential energy of the spring is unknown. Plugging these values into the equation above, we get:
Potential Energy = (1/2) * 155 n/m * (3.00 cm)^2
This simplifies to:
Potential Energy = (1/2) * 155 n/m * 9.00 cm^2
This further simplifies to:
Potential Energy = 693.5 n cm
The potential energy of the spring is equal to the kinetic energy of the glider, so we can use the equation for kinetic energy to solve for the maximum speed of the glider:
Kinetic Energy = (1/2) * m * v^2
where m is the mass of the glider and v is its speed.
In this case, the mass of the glider is 175 g, and its speed is unknown. Plugging these values into the equation above, we get:
(1/2) * 175 g * v^2 = 693.5 n cm
This simplifies to:
v^2 = 693.5 n cm / (1/2) * 175 g
This further simplifies to:
v^2 = 3960.7 g cm / 175 g
This simplifies to:
v^2 = 22.60 g cm
To find the maximum speed of the glider, we can take the square root of both sides of the equation:
v = √(22.60 g cm)
This simplifies to:
v = 4.75 m/s
To find the angular frequency of the oscillations, we can use the equation:
ω = √(k/m)
where ω is the angular frequency, k is the force constant of the spring, and m is the mass of the glider.
In this case, the force constant of the spring is 155 n/m, and the mass of the glider is 175 g. Plugging these values into the equation above, we get:
ω = √(155 n/m / 175 g)
This simplifies to:
ω = 2.86 rad/s
we can use the equation for kinetic energy to find the amplitude of the motion:
Kinetic Energy = (1/2) * m * v^2
where m is the mass of the glider and v is its maximum speed.
In this case, the mass of the glider is 175 g, and its maximum speed is 4.75 m/s. Plugging these values into the equation above, we get:
(1/2) * 175 g * (4.75 m/s)^2 = 693.5 n cm
This simplifies to:
(1/2) * 175 g * 22.60 g cm = 693.5 n cm
To find the amplitude of the motion, we can solve for x:
x^2 = 693.5 n cm / (1/2) * 155 n/m
This simplifies to:
x^2 = 4.5 cm^2
To find the amplitude of the motion, we can take the square root of both sides of the equation:
x = √(4.5 cm^2)
This simplifies to:
x = 2.12 cm
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potassium can emit photoelectrons when struck by blue light, whereas tungsten requires ultraviolet radiation to emit photoelectrons. which statement is true?
It is true that no photoelectrons are released when ultraviolet radiation strikes a surface.
Which metal only emits electrons in response to UV light?It was discovered that certain metals, such as zinc, cadmium, magnesium, etc., only emitted electrons from their surfaces when exposed to ultraviolet light with a short wavelength. Lithium, sodium, potassium, caesium, and rubidium are examples of alkali metals that can be sensitive to visible light.
Why don't photoelectrons release?If the frequency of the light is less than a specific level, no photoelectrons are released. The threshold frequency is referred to as such. For many materials, the threshold frequency varies. Alkali metals, calcium, and barium lose their photoelectron content when exposed to visible light.
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Three different forces are pulling on a heavy trapdoor (Figure 4.6). Which
force will have the biggest turning effect? Explain your answer.
a magnetic field of 0.080 t is in the y-direction. the velocity of wire segment s has a magnitude of 78 m>s and components of 18 m>s in the x-direction, 24 m>s in the y-direction, and 72 m>s in the z-direction. the segment has length 0.50 m and is parallel to the z-axis as it moves. (a) find the motional emf induced between the ends of the segment. (b) what would the motional emf be if the wire segment was parallel to the y-axis?
The wire segment was parallel to the y-axis E = 0.72 volt ;E = 0 volt are the answer.
What is segment?Segmentation is the process of dividing a large target market into smaller, more distinct groups of people who share similar characteristics. Segmentation is a key practice of modern marketing, as it allows businesses to identify and target their most valuable customer groups more effectively. By segmenting customers, marketers can better tailor their campaigns to their specific customer base and maximize their marketing investment. Segmentation also helps organizations identify and target the right audiences with the right message.
Given that – Length of segment = 0.50m
1. E = L * (V x R)
E = 0.50k {(18i + 24j +72k) x (0.800j)}
E = 0.50 * 18 * 0.800 + 0
E = 0.72 volt
Thus, the motional emf will be 0.72 volt
2. If the wire segment is parallel to y-axis
E = 0.50j * {(18 x 0.080) k – (72 x 0.800) i)}
E = 0 volt
Thus, the motional emf in this situation is zero.
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2 points
A rocket accelerates from 50 m/s to 250 m/s in 10 seconds. What is the acceleration of the rocket?
0.04 m/s²
25 m/s²
2500 m/s²
O 20 m/s²
Answer:
The acceleration of the rocket is 20 m/s².
Explanation:
This can be calculated by dividing the change in velocity by the time it took to achieve that change in velocity. In this case, the change in velocity is 250 m/s - 50 m/s = 200 m/s, and it took 10 seconds, so the acceleration is 200 m/s / 10 s = 20 m/s².
What measuring instrument should be used to determine if there was presence of electricity running in her extension cord?
Electrical voltage can be found in cable, cables, circuit breakers, light fixtures, outlets, and switches using voltage testers and receptacle analyzers.
How do you determine whether there is electricity present?
Simply place one tester probe against a hot wire, screw terminal, or outlet slot to utilise a neon voltage tester. Connect the second probe to a ground or neutral contact. If there is current, the small neon bulb at the tool's tip will light up.
Which test is performed to detect whether a piece of equipment contains electricity?
test bulbA piece of electrical test equipment called a test light, test lamp, voltage tester, or mains tester is used to determine whether electricity is present in a piece of equipment that is being tested
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9. An astronaut weighs 500 Newtons on Earth and 25
newtons on asteroid X. The acceleration due to
gravity on asteroid X is approximately
A) 1 m/s²
C) 0.2 m/s²
B) 2 m/s²
D) 0.5 m/s²
The acceleration due to gravity on asteroid X is approximately 0.5 meter/secon^2. Hence, option (D) is correct.
What is acceleration due to gravity?The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity. M/s^2 is its SI unit. Its vector nature—which includes both magnitude and direction—makes it a quantity. The letter g stands for gravitational acceleration.
Given that: An astronaut weighs 500 Newtons on Earth and 25 newtons on asteroid X.
Hence, The acceleration due to gravity on asteroid X is :
= acceleration due to gravity on Earth × (25 N/500N)
= 10 meter/secon^2 × (1/20)
= 0.5 meter/secon^2 ( approx.)
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What happens to the tension in the string if the Ping-Pong ball is replaced by a smaller spherical object of equal weight?
a. The tension does not change.
b. The tension increases.
c. The tension decreases.
The tension in the string increases if the ping-pong ball is replaced by a smaller spherical object of equal weight.
When two opposing forces pull on a rope, string, wire, the force transmitted through the object is known as tension. The energy is pulled equally on the bodies at the ends by the tension force, which is applied along the entire length of the wire. Each physical object that comes into contact with another applies force to that object.
Weight is the gravitational pull of the large second object, like the moon or the earth on a first object.
The concepts required to solve the given question is the tension in the string.
Let us write an expression for tension in terms of volume, density of the liquid, density of the solid. Then, compare the tension on the basis of density of matter. Finally, compare the tension on the basis of the weight of the spherical ball.
The expression for the tension in terms of volume, density of liquid and density of solid is as follows,
T = V * (Pl - Ps)
where, V is the volume
Pl is the density of liquid
Ps is the density of solid
The tension in the above equation is directly proportional to volume, density of liquid, density of solid. As the density of liquid increases, the tension increases. Thus, the tension in the string neither decreases nor remains same.
After adding salt to the liquid, the density of the liquid increases.
The tension will decrease as the volume displaced will decrease.
The weight of the spherical balls is same but the volume is decreased.
The density of the solid remains constant but the density of liquid decreases. Therefore, net tension in the string neither increases nor remains same.
Therefore, tension in the string increases in the string if ping-pong ball is replaced by a smaller object of equal weight.
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the mass of a golf ball is 45.9 g . if it leaves the tee with a speed of 69.0 m/s , what is its corresponding wavelength?
The golf ball has a wavelength of 2.3281034m. The distance between identical points (adjacent crests) in adjacent cycles of a waveform signal carried in space or along a wire is defined as the wavelength.
This length is typically defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm).
A matter wave is connected with all moving particles with mass. These matter waves are referred to as deBroglie waves.
A particle's deBroglie wavelengths is given by, where h is the Planck's constant, m is the mass of the ball, and v is its velocity.
Calculate the deBroglie wavelength of a moving golf ball by substituting 6.6261034J s for h, 45.9103kg for m, and 62.0 m/s for v.
The golf ball has a wavelength of 2.3281034m.
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Which one of the following bodies is in equilibrium?
Answer: (A)
Explanation:
Constant speed = 0 ΣF = equilibrium
Apple, cart, and satellite* have imbalanced force of gravity
*gravity is acting as a centripetal force
76.9kg male and 44.4kg female pair figure skating team gliding across the ice at 7.26 m/s preparing for a throw jump maneuver. The male skater tosses the female skater forward with a speed 8.83 m/s . Determine the speed of male skater after the throw .
The speed of male skater after the throw will be 6.35 m/s.
What is momentum?The relationship between a particle's mass and velocity is called momentum. Being a vector quantity, momentum possesses both magnitude and direction.
Given that 76.9kg male and 44.4kg female pair figure skating team gliding across the ice at 7.26 m/s.
the female skater is tossed forward with a speed 8.83 m/s .
Let the speed of male skater after the throw = v m/s.
From principle of conservation of momentum,
Total initial momentum = total final momentum
⇒ (76.9 + 44.4) × 7.26 = 76.9×v + 44.4×8.83
⇒ 76.9×v = (76.9 + 44.4) × 7.26 - 44.4×8.83
⇒ v = 6.35 m/s.
Hence, the speed of male skater will be 6.35 m/s.
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On the screenshot linked below, the answer to part one is .237141. How would I solve part two?
(a) The fraction of neutron's kinetic energy transferred to the atomic nucleus is 0.068.
(b) The final kinetic energy of the neutron is 2.48 x 10⁻¹³ J.
What is the final velocity of the atom?The final velocity of the atom is calculated by applying the principle of conservation of linear momentum as follows;
initial momentum of the neutron = final momentum of the atom
m₁u₁ = m₂u₂
where;
m₁ is the mass of the neutronu₁ is the initial velocity of the neutronm₂ is the mass of the atomic nucleusu₂ is the final velocity of the atomic nucleusThe mass of the atom = 14.8m₁
u₂ = m₁u₁ / m₂
u₂ = m₁u₁ / (14.8m₁)
u₂ = 0.0676u₁
The initial kinetic energy of the neutron is calculated as;
K.Ei = ¹/₂m₁u₁²
The final kinetic energy of the atom is calculated as;
K.Ef = ¹/₂m₂u₂²
K.Ef = ¹/₂(14.8m₁)(0.0676u₁)²
K.Ef = 0.068 (¹/₂m₁u₁²)
K.Ef = 0.068 (K.Ei)
The fraction of neutron's kinetic energy transferred to the atomic nucleus is calculated as;
= 0.068 (K.Ei) / K.Ei
= 0.068
= 6.8 %
The final kinetic energy of the neutron is calculated as follows;
K.E.f (neutron) = (1 - 0.068) x (2.66 x 10⁻¹³ J)
K.E.f (neutron) = 2.48 x 10⁻¹³ J
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What acceleration does a net force of 32 N impart to a mass of; *
30 kg
45 kg
14 kg
32 kg
3 kg
0.094 m/s^2 0.94 m/s^2
O
O
O
O
1.00 m/s^2 0.44 m/s^2
O
O
O
O
O
O
O
10 points
1.41 m/s^2
O
O
This query calls for the use of Newton's second law of motion. Mass is equal to the product of acceleration and net force. Mass = 32 N / 4 m/s2 = 8 kg when the values are entered into the formula.
If an object has a mass of 10 kg and a force of 30n, what is its acceleration?We can obtain a=F/m by adopting the formula F=m*a and rearranging the subject. Then, using the provided numbers as substitutes, we can determine that a=30/10=3. The item will accelerate at 3ms-2 because acceleration is measured in ms-2.
How is force calculated?Newton's second law of motion provides the definition of the force formula: An object's force is equal to its mass times its acceleration. F = m ⨉ a. To apply this formula, you must use SI units for force (newtons), mass (kilograms), and acceleration (meters per second squared).
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If you were to get up out of your seat and walk to the office, then return and sit in your seat again what is your displacement?
Answer:
0
Explanation:
Displacement is the distance between the start and end point of your travel. If you start in your seat, and end up in your seat, your displacement is 0.
(a) calculate the rotational kinetic energy of earth on its axis. (b) what is the rotational kinetic energy of earth in its orbit around the sun?
The rotational kinetic energy of the earth on its axis is 2.08 x 10^29 Joules and the rotational kinetic energy of the earth in its orbit around the sun is 2.17 x 10^33 Joules.
(a) To calculate the rotational kinetic energy of Earth on its axis, we can use the formula:
KE = 0.5 * I * ω^2where KE is the rotational kinetic energy, I is the moment of inertia of the object, and ω is the angular velocity.
The moment of inertia of Earth can be calculated using the formula:
I = (2/5) * m * r^2where m is the mass of Earth and r is the radius of Earth.
Using these formulas, we can calculate the rotational kinetic energy of Earth as follows:
KE = 0.5 * [(2/5) * m * r^2] * (ω^2)
= 0.5 * [(2/5) * 5.97 x 10^24 kg * 6371 km^2] * (7.29 x 10^-5 rad/s)^2
= 2.08 x 10^29 Joules
(b) To calculate the rotational kinetic energy of Earth in its orbit around the sun, we can use the formula:
KE = 0.5 * m * v^2where KE is the rotational kinetic energy, m is the mass of Earth, and v is the velocity of Earth in its orbit around the sun.
The velocity of Earth in its orbit around the sun can be calculated using the formula:
v = √[(G * M) / r]where G is the gravitational constant, M is the mass of the sun, and r is the distance of Earth from the sun (also known as the semimajor axis of Earth's orbit).
Using these formulas, we can calculate the rotational kinetic energy of Earth in its orbit around the sun as follows:
KE = 0.5 * m * [√[(G * M) / r]]^2
= 0.5 * m * [(G * M) / r]
= 0.5 * 5.97 x 10^24 kg * [(6.67 x 10^-11 N * m^2 / kg^2) * (1.989 x 10^30
kg) / (1.496 x 10^11 m)]
= 2.17 x 10^33 Joules
Note that the rotational kinetic energy of Earth in its orbit around the sun is much greater than the rotational kinetic energy of Earth on its axis, due to the much larger velocity and mass involved in Earth's orbit around the sun.
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a truck with 0.363-m-radius tires travels at 23.9 m/s. what is the angular velocity of the rotating tires in radians per second?
Answer:
Below
Explanation:
Circumference of tires = 2 pi * r=2.28079 m
rpm * 2pi = (23.9 m/s )/ (2.28079 m) * 2pi = 65.8 R/s
what is the difference between momentum in explosion and collision by using formula
Answer:
An object being fired from a cannon is also a collision where momentum must be conserved
Kumar rides his bicycle such that the back wheel rotates 10 times in 5 s. Determine the angular velocity of the wheel in a) degrees per second b) radians per second.
(a) Angular velocity in Degrees per second = [tex]720^0[/tex] per second
(b) Angular velocity in radians per second = 4[tex]\Pi[/tex] radians per second.
Number of rotations = 10
Total time = 5
So, the value of frequency will be =(Number of rotations)/Total time
That will be = (10/5) = 2
Angular velocity is defined as the speed at which an item rotates or revolves around an axis.
The Greek letter omega (occasionally ω, sometimes Ω) stands for angular velocity.
The SI unit for angular velocity is radians per second because it is expressed as an angle per unit of time.
(a) Angular velocity in Degrees per second
[tex]$=360^{\circ} \mathrm{f}=720^{\circ}$[/tex] degree per second.
(b) Angular velocity in radians per second
[tex]$\omega =2 \pi f=2 \pi(2)=4 \pi$[/tex] radians per second.
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What is the relation between the wavelength λ and the frequency f of a signal?
The frequency and wavelength are indirectly proportional to each other. More is the wavelength, lesser is the frequency and vice-versa.
What is a wavelength?
Wavelength is the distance between identical points( conterminous peaks) in conterminous cycles of a waveform signal propagated in space or along a line. In wireless systems, this length is generally given in measures( m), centimeters( cm), or millimeters( mm). In the case of infrared( IR), visible light, ultraviolet( UV), and gamma shafts( γ)The wavelength is more frequently given in nanometers( nm), which are units of 10- 9 m, or angstroms( Å)., which are units of 10- 10m. Wavelength is equally commensurable with frequency, which refers to the number of surge cycles per second. The advanced is the frequence of the signal, the shorter the wavelength.To know more about Wavelength, click the link given below:
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On a graph of galaxy colors and luminosities, spiral galaxies are usually found in the ____________.
On a graph of galaxy colors and luminosities, spiral galaxies are usually found in the blue cloud.
any of the star systems and interstellar materials that make up galaxys. Hundreds of billions of stars can be found in several of these massive assemblages.
From dim, hazy dwarf objects to magnificent spiral-shaped giants, nature has created a vastly diverse assortment of galaxies. Almost all galaxies seem to have formed shortly after the universe started, and they can be found everywhere throughout space, even in the deepest regions that are beyond the reach of even the most potent contemporary telescopes. Galaxies typically exist in groups called clusters, some of which are then combined into larger clusters with a diameter of hundreds of millions of light-years. (A light-year is a distance traveled by light during one year at a speed of 300,000 km/sec or 650,000,000 mph.)
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which property of jupiter's moon europa makes it a more likely candidate to harbor extraterrestrial life? select one: a. satellite images show seasonal variations on its surface. b. satellites have detected oxygen in its atmosphere. c. hydrothermal activity provides energy to heat and melt an ocean of water beneath its surface. d. jupiter's powerful magnetic field generates electrical activity on its surface.
Therefore, even though Europa has a diameter that is only one-fourth that of Earth, her ocean may hold twice the amount of water as Earth's seas do.The immense and unfathomably depths ocean of Europa is regarded as the best area to look for life outside of Earth.
Why then is Europa the Galilean moon most likely to have life?As a result of the liquid water's close proximity to the silicate mantle, Europe is one of the finest options for habitability.The amount of radiation that strikes the moons from Jupiter is a crucial component in determining whether or not they are habitable.
What quality of Europa, a moon of Jupiter, makes it possibly habitable?Europa would need to contain the necessary chemical components for life's chemistry in order to be potentially habitable.These include the frequently occurring elements carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur, which are thought to have been present on Europa at the time it originated.
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Michael’s mom is driving the soccer carpool. They leave the field at 7 pm, with an odometer reading of 78,753 km. Combined the minivan and players have a mass of 2900 kg. After all the players are dropped off, it is 7:56 pm and the odometer reads 78,802 km. What was the average velocity of the minivan while traveling?
Answer:
0.875 miles/minute
Explanation:
The formula for velocity if final position - initial position divided by final time - initial time. Here, the final position
of the van was 49 km away from house, and its initial was 0, because you didn't travel anywhere initially. The final time was 56 minutes because that was how long it took to get home, and the initial was 0, because you were 0 minutes into travel at the beginning.
Wy is it necessary to reduce the voltage to a motor when the frequency is reduced?
To reduce magnetic flux density, it is necessary to reduce the voltage to a motor when the frequency is reduced. This will resist lowering of inductive reactance and increase of rotor current
When we decrease voltage applied to the motor. The current in stator is winding as well as the magnetic flux density will decrease along with decrease in induced voltage.
The voltage induced over rotor's conductor is defined here
,[tex]V_{R[/tex] = B.l.u
We can see things in other way also. Changing frequency has effect on both the motor speed and the strength of the magnetic field. With the lowering of frequency motor speed becomes slow.
With reduction in voltage, magnetic field decreases and magnetic flux becomes constant. This keeps torque production stable, regardless of frequency.
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the amount of internal energy needed to raise the tempreture of .25kg of water by 0.2C is 209.3 J. how fast must a 0.25 kg baseball travel in order for its kinetic energy to equal this internal energy?
help me!
Answer:
Explanation:
To find the speed at which a 0.25 kg baseball must travel in order to have kinetic energy equal to 209.3 J, you will need to use the formula for kinetic energy, which is:
KE = 1/2 * m * v^2
Where KE is the kinetic energy, m is the mass of the object, and v is the speed of the object.
To solve for v, you will need to rearrange the equation to solve for v:
v = sqrt(2 * KE / m)
Plugging in the values given in the problem, we get:
v = sqrt(2 * 209.3 J / 0.25 kg)
Solving this equation gives us a speed of approximately 29.3 meters per second. This is the speed at which the 0.25 kg baseball must travel in order to have kinetic energy equal to 209.3 J.
I hope this helps!
In order to determine causal effects between variables, researchers must use. a. Correlational designs b. Case studies O c Experimental designs O d. All of the above
To identify the factors influencing the associations between the variables, researchers must adopt a correlational design.
An investigator who carries out research, that is, a planned and methodical examination of something, is referred to as a researcher. As researchers, scientists are frequently referred to.
Researchers are employed by authors of books that require extensive information collection, such as those by Michael Crichton who write about biology, to assist them in compiling and analyzing data. Some authors conduct their own research by consulting friends who are doctors to find intriguing methods for their characters to pass away.
Research and development (R&D) of methods and systems for the expansion of human knowledge are the main goals of fundamental research (as opposed to applied research). These goals include documentation, discovery, interpretation, and R&D. Research methodologies rely on epistemologies, which differ greatly within the humanities and sciences as well as within each discipline. Science, the humanities, the arts, business, marketing, and social and economic research are some of the several types of research.
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A high school physics student with a mass of 75 kg is sitting in a seat reading this question. The magnitude of the force with which the seat is pushing up on the student is:.
Answer:
736 N
Explanation:
F = 75 kg * 9.81 m/s^2 = 736 Newtons
What happens when a magnet moves near or in a coil of wire?
Answer:
Below
Explanation:
A VOLTAGE is induced across the coil.... if the ends of the coil are connected together or to a circuit, a current will flow
You are going on a field trip in a school bus. A special detector placed on one of the bus's tires counts the number of rotations completed by the tire during the journey. The tire's diameter is 111 meter, and it made 800080008000 rotations during the trip. How far did the bus travel? round your answer to the nearest meter.
The bus will go 2.788×10^14 meters far if the special detector placed on one of the bus's tires counts the number of rotations completed by the tire during the journey.
What is a circle?
It is described as a set of points, where each point is at the same distance from a fixed point called it's center.
wr are going on a field trip in a school bus. A special detector placed on one of the bus's tires counts the number of rotations completed by the tire during the journey.
It is given that diameter (D) of the tyre = 111 meters
circumference of the tyre = πD
circumference of the tyre = 3.14 × 111
= 348.5 m
In 800080008000 rotations, total distance covered = 348.5 × 800080008000 = 2.788×10^14
Thus, the bus will go 2.788×10^14 meters far if the special detector placed on one of the bus's tires counts the number of rotations completed by the tire during the journey.
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a cylinder with cross-section area a floats with its long axis vertical in a liquid of density rho.
a) The expression for force needed to push the cylinder distance deeper into the liquid by a distance x is F = ρ × A × x.
b) The work done to push the cylinder 10 cm deeper into the water is 12.315 N-m.
The force required to push the cylinder by a certain distance is nothing but the weight of the liquid displaced by the same distance.
So, F = ρ × A × x
where, p is density
x is distance
A is area
We know the expression for work as, W = F × z
where, z is the work required to move through distance z
From a) we can write F = A × z² × ρ
Given that, d = 4 cm
So, r = 2 cm = 0.2 m
z = 10 cm = 0.10 m
ρ = 1000 kg/m³ = 9800 N/m³
Substituting the values in the above equation, we have,
W = π × 0.2² × 0.1² × 9800 = 12.315 N-m
The question is incomplete. The complete question is 'a.) Pressing down on the cylinder pushes it deeper into the liquid. Find an expression for the force needed to push the cylinder distance deeper into the liquid and hold it there.
'b.) A 4.0 cm diameter cylinder floats in water. How much work must be done to push the cylinder 10 cm deeper into the water?'
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