The displacement in SHM is 2/3 of amplitude and the fraction of total kinetic energy is Ek = 5/9.
Let’s derive the equations needed from the first principle. The displacement for SHM with amplitude A and angular speed is:
s = A sin(ωt) ---- (1)
Differentiate the displacement to get the velocity:
v = s′ = A ωcos(ωt)
So for a mass m, the kinetic energy is:
Ek = 1/2 mv²
Ek = 1/2 m × (Aωcos(ωt) )² ---- (2)
At time t = 0 the displacement s = 0 and so all the energy is kinetic. Therefore the total energy is:
E (total) = 1/2m ×( Aωcos(0) )²
E (total) = 1/2m × (Aω)² ---- (3)
We can rephrase the kinetic energy in terms of the total energy by comparing (2) and (3):
Ek = E (total) cos²(ωt)
Using the identity cos² (x) + sin² (x) = 1, we can rewrite this equation as:
Ek = E total (1 − sin²) (ωt)) ---- (4)
Additionally, we are aware that potential energy U = E(total) Ek, so
U = E (total) − E (total) (1 − sin²(ωt) )
U = E (total) sin²(ωt) ---- (5)
Now in this question, we’re given that s = 2/3 A, so from our displacement formula (1) we have:
s = Asin (ωt) = 2/3 A
This is what we get for the kinetic energy when we insert it into equation (4):
Ek = E (total)(1 − (2/3)²)
Ek = 5/9 (E (total) )
Hence, the displacement in SHM is 2/3 of the amplitude, and the fraction of total kinetic energy is Ek = 5/9.
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The doctor lands his tardis on a planet whose radius is 1. 2x10^7m the acceleration due to gravity is 18m/s^2. What is the mass of the planet
The mass of planet is 3.886×10^25 kg. The radius of planet is 1. 2x10^7m.
What is a planet with half the mass's acceleration caused by gravity?Complete Resolution. If the acceleration caused by gravity on the surface of the earth is given by the formula g, then the acceleration caused by gravity on a planet with a mass half that of the earth and a radius equal to that of the earth is given by the formula g/2. Where G = 6.67 ×10^-11 N m2/kg2 (Newton's gravitational constant).
Is the explanation for the gravitational acceleration independent of mass?As a result, acceleration due to gravity (a) depends on the gravitational constant (G), the mass of the Earth (M), and the radius of the Earth (R), but not on the mass of the body (m).
Given:
Radius of planet (r) = 1. 2x10^7m
Acceleration due to gravity (g) = 18 m/s^2
The acceleration due to gravity at the surface of the planet is,
[tex]g=G\frac{M}{r^2}[/tex]
Where, G = Universal gravitational constant
[tex]G= 6.67*10^-11N.m^2/kg^2[/tex]
[tex]M=\frac{g*r^2}{G}[/tex]
[tex]M=\frac{18*(1.2*10^7)^2}{6.67*10^-11}[/tex]
M =3.886×10^25 kg
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Lenz's Law The magnetic flux through the loop shown in the accompanying figure varies with time according to4Pm milliwebers. What are the direction and magnitude of the current through the 5.00-Ω resistor at (a) t = 0 ; (b) =2.00e-31 sin( 120m), where Pm is '' ' ' t= 2.17×10-2 s, and (c) t=3.00 s? 5.0 Ω
At t = 0, the current through the 5.00-Ω resistor is 0 A. At t = 2.17×10-2 s, the current through the resistor is -2.2 A, flowing in the opposite direction to the arrow .
(a) At t = 0, the current through the resistor is 0 A.
(b) At t = 2.17×10-2 s, the current through the resistor is -2.2 A. The negative sign indicates that the current is flowing in the opposite direction to the arrow
(c) At t = 3.00 s, the current through the resistor is 0 A.
At t = 0, the current through the 5.00-Ω resistor is 0 A. At t = 2.17×10-2 s, the current through the resistor is -2.2 A, flowing in the opposite direction to the arrow.At t = 3.00 s, the current through the resistor is 0 A.
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if 15.0 g of water vapour at 135°C cools to 100°C, condenses to liquid water, and then cools to 90°, how much energy is released to the environment?
The heat that is evolved by the environment is 36.42 kJ.
What is the heat that is involved?We know that heat is a form of energy that can be known for the fact that it could lead to a change in the temperature of the object. We have to note that the energy that is released is a sum total of all the process that are involved here.
We know that;
H = (15 * 4.18 * (135 - 100)) + (15 * 2240) + (15 * 4.18 * (100 - 90))
H = 2194.5 + 33600 + 627
H = 36.42 kJ
The total heat that has been evolved would now be 36.42 kJ.
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An athlete runs 140 m across a level field at an angle of 45.0° north of east. What is the north component of this displacement?
Displacement is a vector quantity thus, having different directional component. The component of the given displacement to the north is 98.99 m.
What is displacement ?The displacement is the measure of how long and in which direction an object is moved from the starting position. Displacement is a vector quantity thus, characterized by a magnitude and direction.
In physics, displacement is the product of velocity and time. The vertical component of the displacement = d sin θ
horizontal component = d cos θ.
The component to the north for a displacement of 140m with the angle of 45° is = 140 × sin 45 = 98.99 m.
Therefore, the north component of the displacement is about 99 m.
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The 6 kg block is then released and accelerates to the right, toward the 5 kg block. The surface is rough and the coefficient of friction between each block and the surface is 0.3 . The two blocks collide, stick together, and move to the right. Remember that the spring is not attached to the 6 kg block. Find the speed of the 6 kg block just before it collides with the 5 kg
Assuming a 6 kg block is coupled to a spring with a 350 N/m spring constant, and that there is 0.5 m between the two blocks.
Solution:Use the formula
U=1/2kx2
U=1/23500.52
U=43.75 J
Utilizing the law of conservation of energy, KE = U - f.d, where f is the frictional force acting on
1/2 mv2 = 43.75 - mgd
1/2 ×6×v²= 43.75-0.3×6×9.8×0.5\s
v= √11.643
The spring constant is k, what is it?The "spring constant," denoted by the letter "k," is a figure that effectively indicates how "stiff" a spring is. A significant value of k indicates that more power is needed to extend it a given distance than would be necessary to stretch a less stiff spring the same distance.
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How much of the world's energy is hydroelectric?
According to the United Nations Environment Programme, hydropower accounted for 16.6% of global electricity generation in 2018.
This is equivalent to a total installed capacity of 706 GW, making it the second largest energy source after thermal sources.
Hydropower is a renewable energy source and is often seen as a more sustainable alternative to thermal sources, as it does not release any greenhouse gases into the atmosphere. Additionally, hydropower is a reliable source of energy, and can be used to meet peak energy demand.
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Two points, point 1 and point 2, are located inside a region with an electric field pointing to the left, as shown in the figure. 1 50% Part (a) If a proton is moved from point 1 to point 2, how will the potential energy of the charge-field system change? How will the potential change?
If protons move in the direction of the electric field, the electric potential would change, and it decreases, but if you move opposite the field, the potential energy increases.
If the field is directed from lower potential to higher then the direction is taken to be positive. If the field is directed from higher potential to lower potential then the direction is taken as negative. Potential energy can be converted to kinetic energy and vice versa.
Potential energy is the stored energy in any object or system by virtue of its position or arrangement of parts. However, it isn't affected by the environment outside of the object or system, such as air or height.
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a potential difference of 12 volts causes 2.0 x 10^ 20 electrons to pass a point in a wire in 1 minute calculate
1) the amount of the charge that passes the point in 1 minute ,given that the charge of each electron is 1.6 x10^-19
coulomb
2)electric current in the wire
3)resistance of the wire
Answer:
Q = N e total charge passing point
Q = 2.0E20 * 1.6E-19 coul = 32 coulombs
2) I = Q / t = 32 C / 60 s = .53 amps
3) R = V / i = 12 volts / .53 amps = 23 ohms
Describe the gestalt principles of proximity similarity continuity and closure
Gestalt principles refer to a set of laws in psychology that describe how people perceive visual information. The four principles you mentioned are:
Proximity: Objects that are close to each other are perceived as being related to each other.
Similarity: Objects that are similar in appearance are perceived as being related to each other.
Continuity: People tend to perceive lines and shapes as continuing in the same direction, even if they are interrupted.
Closure: People tend to perceive incomplete shapes as complete, such as seeing a full circle when presented with a set of dots arranged in a circular pattern.
Who is Gestalt?Gestalt theory reinforces the fact the whole of anything is greater than its parts. That is, the attributes of the whole are not deducible from analysis of the parts in isolation. The word Gestalt is utilized in modern German to imply the way a thing has been “placed,” or “put together.” There is no exact equivalent in English.
These principles help us understand how our brain organizes and interprets visual information, and are often used in design to create clear and effective visual layouts.
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At an outdoor phyie demontration, a delay of 0. 50 econd wa oberved between the time ound wave left a loudpeaker and the time thee ound wave reached a tudent through the air. If the air i at STP, how far wa the tudent from the peaker? (1) 1. 5 × 10-m (91. 7 × 102 m (3) 6. 6 × 10? m (4) 1. 5 × 108 m
1.7×10^2 m
The student was 1.7×10^2 m far from the speaker.
Is sound slower to travel in water?The distance that sound waves travel is mostly influenced by the temperature and pressure of the ocean, even though sound travels through water at a far faster rate than it does through air.
What sounds like a sound with a high amplitude?The change in pressure that a sound wave causes when it is measured at a particular location is related to the amplitude of the wave. If the amplitude grows, the sound is heard as louder, and if it drops, it is heard as quieter.
Does greater amplitude equate to greater speed?The pace at which a wave moves has nothing to do with its amplitude. Waves A and B move forward at the same speed. Only changes in the characteristics of the medium a wave travels through can change its speed.
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To calculate the distance between the loudspeaker and the student, we can use the speed of sound in air, which is approximately 340 meters per second (m/s) at standard temperature and pressure (STP).
How is this calculated?The formula to calculate distance is:
distance = speed x time
where distance is the distance between the loudspeaker and the student, speed is the speed of sound in air, and time is the delay that was observed between the time the sound wave left the loudspeaker and the time it reached the student.
distance = 340 m/s x 0.50 s
distance = 170 m
So, the distance between the loudspeaker and the student is 170 meters.
This answer corresponds to (2) 91.7 x 102m.
It's worth mentioning that sound speed can be affected by temperature, humidity, and atmospheric pressure which can cause slight variations from the standard 340 m/s at STP.
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How does dynamic stretching help an individual prepare for an activity brainly?
Dynamic stretching helps to prepare the body for an activity by increasing:
body temperatureimproving range of motionactivating the muscles and nervous system for the activity. also helps to reduce the risk of injury by improving the body's ability to move through a full range of motion.improving coordination and balance.What is dynamic stretching?Dynamic stretching is a form of stretching that involves active, controlled movements such as swinging, bouncing, and twisting. The goal of dynamic stretching is to improve range of motion and flexibility while preparing the body for physical activity.
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What is the sound intensity level of a sound with an intensity of 4.0×10−6 W/m2 ?
Express your answer in decibels.
Answer: 66.02dB
Explanation: We use the equation β=(10dB)㏒([tex]\frac{I}{I_0}[/tex])
[tex]I_{0}[/tex]= the threshold of hearing which is 1.0×[tex]10^{-12}[/tex]W/[tex]m^{2}[/tex]
Plug in our knowns β=(10dB)㏒([tex]\frac{4.0*10^{-6} }{1.0*10^{-12} }[/tex])=66.02dB
The Cessna Cardinal, a single-engine light plane, has a wing with an area of 16. 2 m^2, and an aspect ratio of 7. 31. Assume the span efficiency factor is 0. 62. A. If the airplane is flying at standard sea-level conditions with velocity of 251 km/h, what is the induced drag when the total weight is 9800N b. Calculate the induced drag when the
The Cessna Cardinal, a single-engine light plane, has a wing area of 16.2 m² and an aspect ratio of 7.31 with span efficiency factor of 0.62 then the induced drag when the total weight is 9800 N is 18.8 N.
Given that,
Wing area (A) = 16.2m²
Aspect ratio (r) = 7.31
Efficiency factor (e) = 0.62
Weight of plane (W) = 9800 N
Velocity of airplane (v) = 251 km/h = 251× 5/18 = 69.72 m/s
We know,
Dynamic pressure (p) = 1/2ρv²
where ρ is density of plane = 1.225
p = 1/2 × 1.225 × 69.72 × 69.72 = 2977.29 pa
Lift coefficient Cl = W/p × A = W/(1/2ρv²) A
where, A is the area of wing
Cl = 9800/2977.29 × 16.2 = 0.203
Induced drag coefficient (Cd) = Cl²/πer² = (0.203 × 0.203)/(π × 0.62 × 7.31 × 7.31) = 0.041/(104.08) = 0.39×10⁻³
Induced drag (d) = p × A × Cd = 2977.29 × 16.2 × 0.39 × 10⁻³ = 18.8 N.
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A car drives up a straight hill at a constant speed of 50 kilometers per hour. A truck drives over the crest of the hill at a constant speed of 50 miles per hour. What is the net force on the car and on the truck
As a result, the net pressures on the automobile and truck are zero.
what is pressure ?
If you tried to smash a bowling pin into the wall, nothing would happen except that people would stop lending you bowling pins. If you used the same force to hammer a nail, the nail would be far more likely to pierce the wall. This demonstrates that knowing the quantity of the force isn't always enough: you also need to know how that force is distributed over the impact surface. The nail condensed all of the power between the wall and the nail into a relatively tiny region on the pointed tip of the nail. However, because the area of the bowling pin that touched the wall was significantly bigger, the force was much less focused.
Newton's Second Law states that the net Force acting on an object is given by
MA Fnet = MA
The acceleration is given by the ratio of the change in velocity of an object and the time it takes to change velocity.
(Vf - Vi)/T = a
If the vehicles are driving at constant speeds, their velocity change is zero (0).
If the velocity change is zero, the acceleration is also zero (0).
As a result, Fnet = M(0) = 0.
As a result, the net pressures on the automobile and truck are zero.
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An electron of mass m and charge -e is moving through a uniform magnetic field B=(B2,0,0) in vacuum. (Figure 1)At the origin, it has velocity v = (vx, Vy, 0), where vx >0 and Vy > 0. A screen is mounted perpendicular to the x axis at a distance D from the origin. Throughout, you can assume that the effect of gravity is negligible. First, suppose B, = 0. Find the y coordinate y of the point at which the electron strikes the screen. Express your answer in terms of D and the velocity components V, and Vy. View Available Hint(s) Figure 1 of 1 Now suppose B > 0, and another electron is projected in the same manner. Which of the following is the most accurate qualitative description of the electron's motion once it enters the region of nonzero magnetic field? O The electron decelerates before coming to a halt and turning around while always moving along a straight line. O The electron's motion will be unaffected. (It will continue moving in a straight line with the same constant velocity.) O The electron moves in a circle in the xy plane. screen O The electron moves along a helical path about an axis parallel to the field lines with constant radius and constant velocity in the x direction.
C:The electron moves in a circle in the xy plane.
What is electron ?
Electron is a free and open-source framework created by GitHub that helps developers build cross-platform desktop applications with HTML, CSS, and JavaScript. Electron is based on Node.js and Chromium, making it a powerful tool for creating native applications with web technologies. Electron enables developers to build desktop applications that can run on Windows, Mac, and Linux, as well as Android and iOS devices.
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A medical defibrillator stores 950 J of energy in a 100uF capacitor.
What is the voltage across the capacitor?
If the capacitor discharges 350J of its stored energy in 3.1ms , what power is delivered during this time?
Power is given at p=1.13 *10^(-5) throughout this period.
An electrical component that can store and release electric energy is a power capacitor. The device comprises of one or more pairs of plates that are connected to two terminals and allow the stored energy to be released into a circuit as needed. The plates are separated from one another by an insulating material (the dielectric). By removing the reactive power from the supply line, a capacitor aids in the improvement of power factor.
This is accomplished through the capacitor's storage of magnetic reversal energy. Power is defined as energy multiplied by the frequency of an operation. (a) Computation needs switching from one voltage (V 1) to another voltage (V 2) before most likely returning to a starting voltage (like V 1).
Power = u/t
p = 350/(3.1*(1/1000))
p= 1.13 *10^(-5)
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a box of chocolate bars weighs 180N. Its base has an area of 0.09m2. what pressure does it exert on the ground
Answer:
2000
Explanation:
180/0.09
=2000
pressure=force/area
explain why many houses in hot areas like Mombasa should be painted white while those in colder places like timboroa should be painted with dark colours
Answer:
In places of hot climate, it is advised that the outer walls of house be painted white because white color does not absorb any heat radiation from the sun which keep inside cool even if there is hot climate outside the house.
which of the two stationary charges q1=2 c and q2=10 c will create stronger magnetic field?
Because the charges at rest are unable to produce a magnetic field, neither of the two stationary charges will do so.
There is no magnetic field created when a charge is stationary since there is no motion inside the charge. Thus, nothing except an electric field is created.
Charges that are at rest can also feel the electric force. Charges in motion can experience magnetic force. Therefore, the electric field must not be zero and the magnetic field may or may not be zero if a charged particle at rest experiences an electromagnetic force.
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3. The rougher the surface the ____________ the friction. (Greater or lesser) The _____________ the surface the lesser the friction produced. (Rougher or smoother) 4. Which would b
The rougher the surface the _Greater_ the friction. The _Smooth_ the surface the lesser the friction produced.
The rougher surface has Greater friction, as rough surfaces have more irregularities which lead to interlocking of the surface as a result it increases the friction between two surfaces.
Similarly, in the case of a Smooth surface, there are no irregularities so two surfaces could easily slit without any friction.
Friction is necessary for a number of places so that contact between two surfaces could be improved for walking we need friction and in so many places we try to reduce the friction so that we can save energy.
And we can reduce the friction by applying lubricates between the surfaces, and increase the friction we make the surface rougher.
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What is the SI unit of momentum?
Answer:
kgm/s(-1)
Explanation:
the units of momentum will be the product of the units of mass and velocity. Mass is measured in kg and velocity in ms-1, therefore, the SI unit of momentum will be kgm/s(-1).
a force of 15 N is used to push a box along the floor a distance of 3 meters. find the amount of work done
Answer:
The amount of work done is 45 J.
Explanation:
We know that the force applied is 15N. The amount of displacement experienced by the box is 3 metres along the floor.
Thus, F= 15N
D= 3 metres
The formula for calculating work done is W= F×D
Thus, W=15×3
W=45J
Thus, the amount of work done is 45J.
It has been suggested that rotating cylinders about 10 mi long and 5.0 mi in diameter be placed in space and used as colonies. What
The proposed size of 10 miles long and 5 miles in diameter for such a colony is quite large and would require significant technological advancements in terms of materials, and construction to be feasible.
What causes lift from a rotating cylinder?In general, a spinning cylinder produces lift when its top and bottom are subjected to higher pressure and quicker velocities, respectively. The lifting force, it was said, is pointed perpendicular to the cylinder velocity.
How do you calculate angular speed using radius and linear velocity?If r is an object's radius, v is its linear speed and is its angular velocity in radians per unit of time, then v = r. This formula connects these three values so that we can always determine the third if we know the first two.
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Which of the following is an example of erosion in action ?
Example of erosion: Wind carries small pieces of rock away from the side of a mountain.
Which of the following are examples of erosion?Erosion is the procedure by which the surface of the Earth gets worn down. Erosion can be created by natural elements such as erosion as wind and glacial ice. But everyone who has ever seen a picture of the Grand Canyon knows that nothing strikes the erosion slow steady movement of the water when it comes to commuting the Earth
Rain, rivers, floods, lakes, and the ocean convey away bits of soil and sand and slowly wash away the deposit. Rainfall produces four types of soil erosion: splash erosion, sheet erosion, rill erosion, and ravine erosion.
So we can conclude that Erosion is a ruinous force that wears away land features.
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Suppose two dinosaurs with masses of 80. 0 kg and 120. 0 kg sat on the middle and the far end, respectively, of a tree branch. The dinosaurs produced a net counterclockwise torque of 9,400N•m about the end of the branch that was attached to the tree. What was the length of the branch?
The dinosaurs produced a net counterclockwise torque of 9,400Nm about the end of the branch that was attached to the tree. The length of the branch is 4.7m.
τ = Σr × F = rmg
where g is the acceleration caused by gravity, m is the mass, and r is the distance.
Torque has a direct relationship with -
1.the object's mass, in m
2. The mass's separation, r, from the location where the torque is being calculated.
Therefore, the torque will change whether we increase or reduce them.
Therefore, increasing mass will result in an increase in torque, but since we must retain the same torque, we must reduce mass's distance from the location of the torque.
As a result, the mass should be moved closer to the location of the torque.
Total Mass = (80 + 120)kg
= 200kg
Torque = 9400N
τ = Σr × F = rmg
τ = 200 × r × 10
9400 = 200 × r × 10
r = 9400 / 2000
r = 4.7m
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According to Gordon Allport, which type of personality traits are the most dominant?
According to Gordon Allport, the type of personality traits that are the most dominant is the central trait or the basic trait.
What is trait?This refers to a distinctive quality or character of a person. For example curiosity, fair, and dark. etc.
Gordon Allport is a psychologist and personality theorist. He divided personality traits into three categories: cardinal, central, and secondary. According to Allport, the most dominant type of personality trait is the central trait, also called as the "basic trait."
These traits are fundamental to a person's character and shape their overall personalities, such as honesty, kindness, and intelligence. Cardinal traits, on the other hand, are rare and extremely influential traits that shape a person's entire life and behavior, such as religious devotion or political ideology. Secondary traits are less important and more specific, such as being punctual or having a sense of humor.
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(i) Object A has a charge of +2 µC, and object B has a charge of +6 µC. Which of the following statements is true about the electric forces on the objects? (a) F_{ AB }=-3 F_{ BA }F AB =−3F BA
(b) F_{ AB }=- F_{ BA }F AB =−F BA
(c) 3F_{ AB }=- F_{ BA }3F AB =−F BA
(d) F_{ AB }= 3 F_{ BA }F AB =3F BA
(e) F_{ AB }= F_{ BA }F AB =F BA
(f ) 3F_{ AB }= F_{ BA }3F AB =F BA
The electric force between objects A and B is F_{ AB }=- F_{ BA }.
What is charge ?
Charge is a fundamental property of matter that is related to electricity. It is an electrical property that allows matter to experience a force when placed in an electric field. Charge can be either positive or negative. Positive charge is the opposite of negative charge, and vice versa. Charge is measured in coulombs (C).
The electric force between two objects is determined by Coulomb’s Law, which states that the magnitude of the force is proportional to the product of the charges and inversely proportional to the square of the distance between the two objects. Therefore, the electric force between objects A and B is F_{ AB }=- F_{ BA }.
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Describe what you could do to make the magnetic disk rotate faster
You could do to make the magnetic disk rotate faster: regular usage of a disc defragmentation program.
What is magnetic disk?A magnetic disk is a storage device that writes, rewrites, and accesses data using the magnetization process. It has a magnetic layer that retains data as tracks, spots, and sectors.
You could do to make the magnetic disk rotate faster:
Plan regular usage of a disc defragmentation program.Try to keep at least 20% of your disc space free, if you can. Defragmentation is facilitated and fragmentation is reduced as a result. Utilize a program like Crystal DiskInfo to regularly check the condition of your drive.Learn more about magnetic disk here:
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The figure shows a graph of the output from an AC voltage source.
What is the maximum voltage Vmax of the source?
What is the average voltage Vavg of the source?
What is the root-mean-square voltage Vrms of the source?
From the graph,
Vmax = 3V
Vavg = 2*Vmax/π = 2*3/π = 1.91 V
Vrms = Vmax/√2 = 3/√2 = 2.121 V
Note: The graph that has been considered for theses calculation, is uploaded as an attachment along with the answer.
The sine wave can achieve a maximum value known as VMax for both negative and positive directions. It is VMax for a positive cycle and (-)VMax for a negative cycle.
The average of the instantaneous voltages selected at correctly spaced intervals during the half - cycles of an AC sinusoidal (or other periodic) waveform is the average voltage. The average value is a representation of the area beneath the AC wave form as a function of time.
A sinusoidal origin of electromotive force is described by its root-mean-square (rms) voltage (Vrms), denoted by Vmax/√2.
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Is there ever a case where one of the two charges in Coulomb's Law experiences a different force magnitude than the other charge? Why or why not?
Answer:
Yes, there is a case where one of the two charges in Coulomb's Law experiences a different force magnitude than the other charge. Coulomb's Law states that the electric force between two charged particles is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. If the magnitudes of the charges or the distance between them changes, the force experienced by one of the charges will also change. For example, if one of the charges is doubled in magnitude while the other charge and the distance between them remain the same, the force experienced by the charge with the increased magnitude will also double.