Answer:
0.615j would be the answer to your question.
Two charges each 2 x 10-7 C but opposite in sign forms a system. These charges are located at
points A (0,0, -10) cm and B(0,0, +10) cm respectively. What is the total charge and electric dipole
moment of the system?
Answer:
i) Total charge of the
system
= 2 x 10 -7 + (-2 x 10 -7)
= zero P
(ii)
P =q x 2i
P= 2 x 10-7 x 20 x 10-2
P = 4 x 10-8 cm
Direction of Dipole moment – Along negative z-axis.
Explanation:
A roller skater kept her balance and traveled in a perfect straight line. Her motion slowed down as she cruised along the street. Which of the following statements describes the forces on the skater?
The net force was not 0 on the skater during her motion.
The net force was 0, which is why the skater moved in a straight line.
The forces were unbalanced due to the skater's inertia.
The forces were balanced due to the action-reaction pair required to cruise.
Answer: (A)The net force was not 0 on the skater during her motion.
Explanation:
The net force was not 0 on the skater during her motion. The roller skated slowed down, which indicates that there is another force acting on her roller skates.
The correct statement is "The net force was 0, which is why the skater moved in a straight line." The correct answer is B.
What is Newton's First Law of Motion?Newton's First Law of Motion, states that an object at rest or in motion will remain at rest or in motion with a constant velocity in a straight line unless acted upon by an external force. In this case, the skater is traveling at a constant velocity, which means that the net force acting on her must be zero.
Option A is incorrect because if the net force was not zero, then the skater would not have moved in a straight line. She would have accelerated or changed direction, as per Newton's Second Law of Motion.
Option C is also incorrect because the skater's inertia does not have any effect on the forces acting on her. Inertia is a property of matter that resists changes in motion, but it does not cause any forces to be unbalanced.
Option D is incorrect because the action-reaction pair of forces cancel each other out and do not affect the skater's motion. The action-reaction pair only affects the interaction between two objects, but it does not affect the motion of a single object.
Therefore, The correct option is B i.e. The net force was 0, which is why the skater moved in a straight line.
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Food can be eaten in or form
Answer:
from - from the mouth .............
Car A and car B set off from the same point to travel the same journey. Car A sets off three minutes before car B. If car A travels at 60 km/h and car B travels at 70 km/h, how many kilometres from the starting point will the two cars draw level?
Answer:
Let's start by calculating how much of a head start Car A has in distance before Car B starts.
In 3 minutes, Car A will have travelled:
d = r * t = (60 km/h) * (3/60) h = 3 km
So when Car B starts, Car A is 3 km ahead.
Now let's consider the time it takes for both cars to meet. Let's call the time it takes for both cars to meet t.
During that time, Car A will travel at a speed of 60 km/h, and Car B will travel at a speed of 70 km/h.
The distance that Car A will travel during that time is:
dA = 60 km/h * t
The distance that Car B will travel during that time is:
dB = 70 km/h * t
The total distance between the two cars when they meet is:
d = dA + dB
We want to find the value of t that makes dA + dB = 3 km (the distance that Car A is ahead of Car B when Car B starts).
Substituting the expressions for dA and dB, we get:
60 km/h * t + 70 km/h * t = 3 km
Simplifying, we get:
130 km/h * t = 3 km
t = 3 km / 130 km/h
t = 0.0231 h
Now we can calculate the distance that both cars will have travelled when they meet:
dA = 60 km/h * 0.0231 h = 1.38 km
dB = 70 km/h * 0.0231 h = 1.61 km
d = dA + dB = 1.38 km + 1.61 km = 2.99 km
Therefore, the two cars will draw level after travelling approximately 2.99 km from the starting point.
1. What is the maximum possible number of components of a vector can have
Answer:
The maximum possible number of components a vector can have is infinite
Explanation:
In mathematics, a vector is a mathematical object that has both magnitude and direction, and it can have any number of components, as long as it makes mathematical sense.
For example, a vector in two-dimensional space has two components (x and y), while a vector in three-dimensional space has three components (x, y, and z). However, vectors can also exist in higher-dimensional spaces, such as four-dimensional space or n-dimensional space, and in those cases, they can have more components.
It is worth noting that in practice, vectors with an extremely large number of components may not be useful or computationally feasible to work with. However, from a theoretical standpoint, vectors can have as many components as needed to describe a given situation.
Ariyana is studying sound waves and radio waves for a presentation in class. Which of the following questions would be appropriate to ask for this investigation?
The study of sound generation, regulation, transmission, reception, and effects is known as acoustics. The word comes from the Greek word akoustos, which means "heard."
Why might astronomers use radio waves to study celestial objects? How do radio waves help us understand the cosmos?The advantage of radio astronomy is that it does not interfere with observations due to sunshine, clouds, or rain. Since radio waves travel farther than optical waves, they are constructed differently from visible light telescopes.
What kind of telescopes receive radio waves from celestial objects?They release some energy in the form of radio waves, which have extremely long wavelengths. Radio telescopes are tools used to pick up radio waves from celestial objects.
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Name Label the Parts of the Waves in the Diagram Below. a. b. C. d. e.
The parts of the wave are;
A - CrestB - AmplitudeC - TroughD - WavelengthWhat are the parts of the wave in a wave diagram?A typical wave diagram shows the various parts of a wave. The following are the key parts of a wave:
Crest: The highest point or peak of the wave.
Trough: The lowest point or valley of the wave.
Amplitude: The maximum displacement of the wave from its rest position, which is usually measured from the crest or trough to the equilibrium or rest position.
Wavelength: The distance between two successive crests or two successive troughs of a wave.
Frequency: The number of waves passing through a particular point per unit time, typically measured in hertz (Hz).
Period: The time taken for one complete wave to pass through a particular point, typically measured in seconds.
Velocity: The speed at which the wave propagates, which is usually measured in meters per second.
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Abody of mass 12kg at rest on smooth surface is affected by a force 48 n what is the acceleration of the body?
Answer:
Acceleration of the body will be 4 m/s²Explanation :
We have ,
Force = 48 NMass = 12 kgAcceleration = ?According to Newton's second law of motion,
F = mawhere F is force, m is mass and a is acceleration.
On putting the values in above formula we will get :
=> 48 = 12 × a
=> a = 48/12
=> a = 4 m/s²Therefore,
The acceleration of the body will be 4 m/s²An airplane A flies north with velocity 300 km/h relative to the ground; Another airplane Bhave a velocity of 200 km/h toward a direction 60° west of north. Find the velocity of A relative to B.
Velocity of airplane A relative to B is 200 km/h east and 126.8 km/h north-west.
What is velocity?Rate and direction of an object's movement is known as velocity.
Let velocity of airplane A with respect to the ground be "vA" and velocity of airplane B with respect to the ground be "vB". Velocity of A relative to B, denoted as vAB, is calculated:
vBx = vB cos(60°) = 200 km/h x cos(60°) = 100 km/h
vBy = vB sin(60°) = 200 km/h x sin(60°) = 173.2 km/h
Direction of vBy is north-west.
Velocity of A with respect to the ground is given as 300 km/h north.
vAB = vA - vB
vABx = vAx - vBx = 300 km/h - 100 km/h = 200 km/h
vABy = vAy - vBy = 300 km/h - 173.2 km/h = 126.8 km/h
So, the velocity of airplane A relative to B is 200 km/h east and 126.8 km/h north-west.
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5. The mechanical advantage of a jaw when it is used as a second-class lever is 1.4.
a. If the input force is 100 newtons, what is the output force?
b. How does the input lever arm compare to the output lever arm when the jaw is used as a
second-class lever? Draw a diagram to illustrate your answer.
Answer: a. It would be 140 N
I don’t know, I just got it right
WILL GIVE BRAINLIEST PLS HELP
Design a repeatable experiment using various seismograph stations around the
globe to verify the hypothesis that the Earth has a liquid outer core and a solid
inner core. Describe how you would set up the experiment, what equipment would
be needed, and what information you would gather. What evidence would prove
that the outer core is liquid? What evidence would prove that the inner core is not
liquid? How would you use repeatability to show whether the hypothesis is valid or
not?
Answer:
Explanation:
To verify the hypothesis that the Earth has a liquid outer core and a solid inner core, we can use seismographs to study seismic waves that pass through the Earth's interior. The experiment can be set up as follows:
1. Select multiple seismograph stations around the globe to record seismic waves.
2. Choose a location for an earthquake to occur. The earthquake should be large enough to generate seismic waves that travel through the Earth's interior and be located far away from the selected seismograph stations.
3. Record the seismic waves generated by the earthquake at the various seismograph stations.
4. Analyze the seismic waves to determine how they interact with the Earth's interior. Specifically, we will study how the seismic waves pass through the Earth's outer and inner core.
5. Repeat the experiment using earthquakes of different magnitudes and at different locations, and record the resulting seismic waves.
Equipment needed for the experiment include seismographs, computers for data analysis, and earthquake monitoring systems. Seismographs can be installed in various locations around the globe to record the seismic waves generated by the earthquake. Data from these seismographs can be collected and analyzed using computer software to determine how the seismic waves interact with the Earth's interior.
Evidence that proves the outer core is liquid includes the observation of seismic waves that cannot travel through the liquid outer core, resulting in a shadow zone on the opposite side of the Earth from the earthquake. This shadow zone indicates that the seismic waves are refracted or absorbed by the liquid outer core. In contrast, evidence that proves the inner core is not liquid includes the observation of seismic waves that are reflected and refracted by the inner core boundary. This is due to the fact that the inner core is solid and has a different density and composition than the outer core.
To use repeatability to show whether the hypothesis is valid or not, we can repeat the experiment using earthquakes of different magnitudes and at different locations, and record the resulting seismic waves. If the results from multiple experiments are consistent with the hypothesis, then we can have greater confidence that the hypothesis is valid. If the results from multiple experiments are inconsistent, then we would need to investigate further to determine the cause of the inconsistency and revise the hypothesis accordingly.
Place the following descriptions, formulas, and terms in the correct category for Newton's Laws.
For every action, there is an equal and opposite reaction. Action-reaction pairs
Explain in detail about the following categories of the newtons laws ?
Category 1: Newton's First Law
An object at rest stays at rest and an object in motion stays in motion with a constant velocity, unless acted upon by an unbalanced force.
ΣF = 0 (the sum of all forces acting on an object is zero)
Law of Inertia
Category 2: Newton's Second Law
F = m*a (the force applied on an object is equal to the mass of the object multiplied by its acceleration)
Force
Mass
Acceleration
Category 3: Newton's Third Law
For every action, there is an equal and opposite reaction.
Action-reaction pairs
Reaction force
Action force
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A 7.00 g bullet moving horizontally at 200 m s-1 strikes and passes through a 150 g wooden block which is on a smooth horizontal surface. Just after the impact the block gained a velocity of 180 cm s-1. Calculate the speed of the bullet after it passed through the block.
The speed of the bullet after it passed through the block is 198.138 m/s. We can make use of the conservation of momentum principle, which asserts that if no outside forces are acting on a system, its overall momentum will remain constant.
In physics, what is a momentum?Mass in motion is quantified by momentum, which is the measure of how much mass is moving. It typically has the sign p.
Before the collision, the bullet has a momentum given by:
p1 = mv1
where m = mass of the bullet and v1 = velocity.
After the collision, the bullet and the wooden block move together with a common velocity v2. The momentum of the combined system is,
p2 = (m + M) v2
where M = mass of the wooden block.
Since there are no external forces acting on the system, we can equate the initial and final momenta:
p1 = p2
mv1 = (m + M) v2
Solving for v2:
v2 = (mv1) / (m + M)
Substituting the given values:
m = 7.00 g = 0.00700 kg
v1 = 200 m/s
M = 150 g = 0.150 kg
v2 = (0.00700 kg x 200 m/s) / (0.00700 kg + 0.150 kg)
v2 = 1.862 m/s
Since the wooden block gained a velocity of 180 cm/s (1.8 m/s) after the impact, the velocity of the bullet after passing through the block is:
v3 = v1 - v2
v3 = 200 m/s - 1.862 m/s
v3 = 198.138 m/s
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How might form and function of a structure influence
each other?
Answer:
Explanation:
Form must follow function, otherwise the design of a structure is a failure. For example, the function (purpose) of a bridge is to provide a means of crossing an obstacle, such as a body of water, a valley, another road, etc. The form of the bridge must serve the purpose of providing safe and reliable passage of pedestrians, vehicles, trains, etc. A most basic form of a bridge is a beam design: simple, efficient, cost-effective, functional. If budget and public sentiment allow, additions to the design can be incorporated to make the bridge more aesthetically pleasing, but such additions do not add to the basic function.
The wave in the liquid travels towards the surface at an angle. Fig 9.2 shows the centres of the compressions of the sound wave in liquid. Some compressions shown have reached the liquid-air boundary. The parts of these compressions in the air are not shown on Fig 9.2 These waves are also reflected at the boundary. Draw on the diagram the reflected wavefronts.
The image of the reflected sound wavefronts traveling through a liquid is found in the attachment.
What are reflected sound wavefronts?Reflected sound wavefronts refer to the waves of sound that are bounced back or reflected off of a surface such as a wall, ceiling, or floor.
When a sound wave travels through the air and encounters a surface, some of the sound energy is absorbed by the surface, while some of it is reflected back into the air.
These reflected sound waves can interfere with the original sound waves, leading to complex patterns of sound intensity and phase.
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A 6.00v storage battery is connected to
three resistors 6.00, 11.0, and 20.0 respectively
According to the question the equivalent resistance is 37.0 Ω.
What is equivalent resistance?Equivalent resistance is the resistance of a circuit when its individual resistors are replaced with a single resistor that has the same overall effect on the circuit. It is a measure of resistance that is used to simplify calculations of electrical circuits. Equivalent resistance is calculated by taking the sum of the inverse of the individual resistances and then inverting the sum to find the equivalent resistance. This is useful for analyzing complex circuits as it allows for easier calculations.
The equivalent resistance of the three resistors joined in series is equal to the sum of the individual resistances.
Therefore, the equivalent resistance is 6.00 Ω + 11.0 Ω + 20.0 Ω = 37.0 Ω.
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It takes 80 pounds of force to
stretch a particular spring 2
inches. How much work is done
in stretching it from its relaxed
state a total of 4 inches?
[?] inch - pounds
The United States consumes about 2.5 ✕ 1019 J of energy in all forms in a year. How many years could we run the United States on the energy released by a 1023 J solar flare?
Answer:
Explanation:
To find out how many years the United States could run on the energy released by a 10²³ J solar flare, we need to divide the energy of the solar flare by the energy consumed by the United States in one year:
Number of years = Energy of solar flare / Energy consumed by the United States per year
Number of years = 10²³ J / 2.5 x 10¹⁹ J/year
Number of years = 4 x 10³ years
Therefore, the United States could run for approximately 4,000 years on the energy released by a 10²³ J solar flare.
when a58g tennis ball is served.it accelerate from rest to aspeed of 45m/s.the impact with the racket gives the ball acontant acceleration over adistance of44cm.what is the magnitude of the net force acting on the ball?
Answer: We first calculate the acceleration on the ball using:
2as = v² - u²; u = 0 because ball is initially at rest
a = (36)²/(2 x 0.35)
a = 1850 m/s²
F = ma
F = 0.058 x 1850
= 107.3 Newtons
Explanation:
16. The density difference between warm, moist air and cold air causes the moist
air to rise. This is key to forming
A. lightning.
B. clouds.
C. stars.
D. snow.
Warm, moist air rises because of the difference in densities between warm, moist air and cold air, which is essential for the formation of clouds.
The moisture in the air condenses into minute water droplets or ice crystals when warm, wet air rises and cools. Clouds are made up of these suspended ice crystals and water droplets.
By reflecting sunlight back into space and storing heat, clouds play a significant part in the Earth's climate system, influencing temperature and weather patterns.
Although lightning is frequently connected to clouds, moist air does not directly cause lightning to occur. Electric charge builds up in the atmosphere, typically during thunderstorms, which leads to lightning.
Snow is created by the freezing of water vapor in the atmosphere, just as stars are created by the gravitational collapse of gas and dust clouds in space.
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After rubbing two balloons against a sweater, each are held 0.75 meters apart. One balloon has a charge of 2.6 E−6 C. The other balloon has a charge of 2.2 E−7 C. Calculate the electrical force between them.
Remember to identify all data (givens and unknowns), list equations used, show all your work, and include units and the proper number of significant digits to receive full credit.
Answer:
Given:
Distance between the balloons (r) = 0.75 m
Charge on balloon 1 (q1) = 2.6 E−6 C
Charge on balloon 2 (q2) = 2.2 E−7 C
Electric constant (k) = 8.99 × 10^9 N·m^2/C^2
Unknown:
Electrical force (F) between the two balloons
The equation for the electrical force between two point charges is:
F = k * (q1*q2)/r^2
Substituting the given values, we get:
F = (8.99 × 10^9 N·m^2/C^2) * ((2.6 E−6 C) * (2.2 E−7 C))/(0.75 m)^2
F = 4.16 × 10^-6 N
Therefore, the electrical force between the two balloons is 4.16 × 10^-6 N.
Explanation:
Answer:
The electrical force between two balloons is 67.5N.
Explanation:
There are two charged balloons, let's say a and b.
The charge on the balloon a = C
The charge on the balloon b = C
Both balloons are 1 cm apart; it means that the distance r between the balloon a and the balloon b is 0.01 m (since 1 cm = 0.01 m).
We need to find the electrical force between them. By using the Coulomb's law, the magnitude of the electrical force between both the balloon is given as follows:
---------------
Hence, the electrical force between two balloons is 67.5N (three significant figures).
A turntable must spin at 33.3 rev/min (3.49 rad/s) to play an old fashion vinyl record . How much torque must the motor deliver if the turntable is to reach its angular speed in 2.20 revolutions starting from rest ? The turntable is an uniform disk of diameter 30.5 cm and mass 0.240kg
Answer……. N-m
0.002355 N-m torque must the motor deliver if the turntable is to reach its angular speed in 2.20 revolutions starting from rest
What is torque and how is it related to rotational motion?Torque is a measure of the twisting force that causes rotational motion. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation at which the force is applied.
Given:
Angular speed, ω = 3.49 rad/s
Number of revolutions, N = 2.20 rev
Diameter of disk, D = 30.5 cm = 0.305 m
Mass of disk, m = 0.240 kg
The moment of inertia of a uniform disk about its center is (1/2) * m * r^2, where r is the radius of the disk. Here, r = D/2 = 0.1525 m.
Moment of inertia, I = (1/2) * m * r^2 = (1/2) * 0.240 kg * (0.1525 m)^2 = 0.002198 J-s^2/rad
The torque required to bring the disk to its angular speed can be found using the formula:
τ = I * α
where α is the angular acceleration of the disk. Since the disk starts from rest, we have:
α = ω^2 / (2 * π * N)
where π is the constant pi. Substituting the given values, we get:
α = (3.49 rad/s)^2 / (2 * π * 2.20 rev) = 1.071 rad/s^2
Therefore, the torque required is:
τ = I * α = 0.002198 J-s^2/rad * 1.071 rad/s^2 = 0.002355 N-m
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Waves in a lake are 6.0 m apart and pass a person on a raft every 2.0 s.
What is the speed of the waves?
Answer:
The speed of wave is 3m/s
wich the following hasta the most momentum?
A)50 g bullet moving at 200m/s
B)50kg boy running at 8 m/s
C)1000 kg automobile moving at 4m/s
D1,000,000 kg Cruise ship docked in a harbor
Answer for A) momentum = 10 N/s B) momentum = 400 N/s C) momentum = 4000 N/s D) momentum = 0 N/s. Hence, the option C has the most momentum.
To determine which of the given options has the most momentum, we need to calculate the momentum of each object using the formula:
momentum = mass x velocity
A) 50 g bullet moving at 200 m/s:
mass = 50 g = 0.05 kg
velocity = 200 m/s
momentum = 0.05 kg x 200 m/s = 10 N/s
B) 50 kg boy running at 8 m/s:
mass = 50 kg
velocity = 8 m/s
momentum = 50 kg x 8 m/s = 400 N/s
C) 1000 kg automobile moving at 4 m/s:
mass = 1000 kg
velocity = 4 m/s
momentum = 1000 kg x 4 m/s = 4000 N/s
D) 1,000,000 kg Cruise ship docked in a harbor:
mass = 1,000,000 kg
velocity = 0 m/s (since the ship is docked)
momentum = 1,000,000 kg x 0 m/s = 0 N/s
Therefore, option C, the 1000 kg automobile moving at 4 m/s, has the most momentum with a value of 4000 N s. This is because momentum is directly proportional to both mass and velocity. The greater the mass and velocity of an object, the greater its momentum will be.
Option A, the 50 g bullet moving at 200 m/s, has a smaller momentum compared to the others due to its low mass despite having a high velocity.
Option B, the 50 kg boy running at 8 m/s, has a higher momentum than the bullet but lower than the automobile because of its higher mass but lower velocity.
Lastly, option D, the 1,000,000 kg Cruise ship docked in a harbor, has zero momentum since it is not moving (velocity is zero).
The momentum of an object is an important concept in physics that describes the quantity of motion possessed by it. It is determined by the product of mass and velocity, and the object with the highest mass and velocity has the greatest momentum.
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A A Camot engine works between the se and the sink with efficiency 40% How much perature of the sink be lowered keeping the source parature constant so that its efficiency increases by 10%?
To increase the efficiency of the engine by 10%, the temperature of the cold sink needs to be lowered by 0.25 times the difference between the hot source and cold sink temperatures.
What is the new temperature of the sink?The efficiency of a Carnot engine is given by:
efficiency = (T_source - T_sink) / T_source
where;
T_source is the temperature of the hot source and T_sink is the temperature of the cold sink.If the efficiency of the engine increases by 10%, we can write:
new efficiency = 1.1 x old efficiency
Substituting the expression for efficiency of a Carnot engine, we get:
(T_source - new T_sink) / T_source = 1.1 x (T_source - T_sink) / T_source
Simplifying this equation, we get:
new T_sink = T_sink - 0.1 x (T_source - T_sink) / 0.4
new T_sink = T_sink - 0.25 x (T_source - T_sink)
new T_sink = 0.75 x T_sink + 0.25 x T_source
Therefore, the new temperature of the cold sink is given by 0.75 times the original temperature of the cold sink plus 0.25 times the temperature of the hot source.
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A caterpillar crawls 15 centimeters east along a leaf, turns around, and crawls 8.3 centimeters west. What is the caterpillar's total displacement in centimeters?
Answer: 6.7 CENTIMETERS
Explanation: 15 EAST AND 8.3 WAST
NET DISPLACEMENT 15-8.3= 6.7
2)A three-phase four-pole winding of the double-layer type is to be installed on a 48-slot stator. The pitch of the stator windings is 5/6, and there are 10 turns per coil in the windings. All coils in each phase are connected in series, and the three phases are connected in . The flux per pole in the machine is 0.054 Wb,and the speed of rotation of the magnetic field is 1800 r/min. (a) What is the pitch factor of this winding? (b) What is the distribution factor of this winding? (c) What is the frequency of the voltage produced in this winding? (d) What are the resulting phase and terminal voltages of this stator?
(a) The pitch factor of a three-phase winding is given by Kp = cos(π/6m), where m is the number of slots per pole per phase. Here, m = 48 slots/(4 poles x 3 phases) = 4 slots/pole/phase. Therefore, Kp = cos(π/6 x 4) = cos(π/2) = 0.
(b) The distribution factor of a double-layer winding is given by Kd = sin(π/2p), where p is the number of poles. Here, p = 4, so Kd = sin(π/8) = 0.3827.
(c) The frequency of the voltage produced in the stator winding is given by f = (P/2) × (N/60), where P is the number of poles and N is the speed of rotation in rpm. Here, P = 4 and N = 1800 rpm, so f = (4/2) × (1800/60) = 60 Hz.
(d) The resulting phase voltage of this stator can be calculated using the formula Vφ = 4.44 × f × Φ × Z × K, where Φ is the flux per pole, Z is the total number of conductors in series per phase, and K is the product of the pitch factor and the distribution factor. For this winding, Z = 10 turns/coil x 2 coils/slot x 48 slots/3 phases = 160 conductors/phase, and K = 0 x 0.3827 = 0.
Therefore, Vφ = 4.44 × 60 × 0.054 × 160 × 0 = 0 V.
Since this is a three-phase winding, the resulting terminal voltage will be the line-to-line voltage, which is √3 times the phase voltage. Therefore, the resulting terminal voltage of this stator is 3 × Vφ = 3 × 0 = 0 V.
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Please calculate the frequency of the waves in Hz
Answer: 7,6 hz
Explanation:
50/23.4=x+5.5x 18= The equation so its basically 7,6 x 18 to get ur answer in HZ. So yeah thanks and hope this helped !!!!
A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 23.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 3.67 m/s2 for a distance of 50.0 m to the edge of the cliff, which is 35.0 m above the ocean.
(a) Find the car's position relative to the base of the cliff when the car lands in the ocean.
Incorrect: Your answer is incorrect.
m
(b) Find the length of time the car is in the air.
Incorrect: Your answer is incorrect.
s
Answer:
a) the car lands in the ocean 85.1 meters away from the base of the cliff.
b) the length of time the car is in the air is 2.50 seconds.
Explanation:
Let's start with part (a) of the problem.
First, we need to find the car's velocity at the bottom of the incline using the kinematic equation:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity (which is 0 m/s), a is the acceleration (which is 3.67 m/s^2), and s is the distance traveled down the incline (which is 50.0 m).
Plugging in these values, we get:
v^2 = 0^2 + 2(3.67 m/s^2)(50.0 m)
v^2 = 367 m^2/s^2
v = 19.1 m/s (rounded to one decimal place)
Next, we can use the vertical motion equations to find the time it takes for the car to fall from the cliff to the ocean. We'll use the equation:
h = ut + (1/2)at^2
where h is the height of the cliff (35.0 m), u is the initial vertical velocity (which is 0 m/s), a is the acceleration due to gravity (-9.81 m/s^2), and we're solving for t.
Plugging in these values, we get:
35.0 m = 0 m/s * t + (1/2)(-9.81 m/s^2)t^2
19.9 = t^2
t = 4.46 s (rounded to two decimal places)
Therefore, the car is in the air for 4.46 seconds.
Finally, to find the car's position relative to the base of the cliff when it lands in the ocean, we can use the horizontal motion equation:
s = ut + (1/2)at^2
where s is the horizontal distance the car travels (which is what we're solving for), u is the horizontal velocity (which is the same as the velocity at the bottom of the incline, 19.1 m/s), a is the horizontal acceleration (which is 0 m/s^2), and t is the time the car is in the air (which is 4.46 s).
Plugging in these values, we get:
s = 19.1 m/s * 4.46 s + (1/2)(0 m/s^2)(4.46 s)^2
s = 85.1 m (rounded to one decimal place)
Therefore, the car lands in the ocean 85.1 meters away from the base of the cliff.
[Use g = 10 m/s2]
A spring whose constant is 200 N/m can be stretched up to 0.2 meters.
(a) Draw a graph of Force vs. Stretch for this spring, where stretch ranges from zero to the maximum stretch. Be sure to put an appropriate scale on the graph. [HINT: The y-axis does not go from 0 to 200!!!]
(b) If the spring is set vertically and a mass of 0.8 kg hangs from it, what is the stretch of the spring? Mark this point on the graph.
(c) If the spring is stretched from zero to 0.06 meters, what is the potential energy stored in the spring?
(d) How much work must be done to stretch the spring from 0.1 meters to 0.16 meters? Show what this quantity represents on the graph.
Explanation:
(a) The graph of Force vs. Stretch for the given spring can be represented by a straight line passing through the origin with a slope equal to the spring constant. The equation of the line is:
Force = Spring constant × Stretch
F = kx
where k = 200 N/m and x is the stretch of the spring in meters. The graph is shown below:
Force vs. Stretch graph for a spring with k = 200 N/m
(b) When a mass of 0.8 kg hangs from the spring, it experiences a force due to gravity equal to:
F = m × g = 0.8 kg × 10 m/s² = 8 N
Since the spring is in equilibrium, the force exerted by the spring must be equal and opposite to the force due to gravity. Therefore, the stretch of the spring is given by:
F = kx
x = F/k = 8 N / 200 N/m = 0.04 m
The point corresponding to this stretch is marked on the graph as shown below:
Force vs. Stretch graph with a point for a hanging mass of 0.8 kg
(c) The potential energy stored in the spring when it is stretched from zero to 0.06 meters can be calculated using the formula:
U = (1/2) k x²
U = (1/2) × 200 N/m × (0.06 m)² = 0.36 J
(d) The work done to stretch the spring from 0.1 meters to 0.16 meters can be calculated by finding the area under the Force vs. Stretch graph between these two stretches. This represents the change in potential energy of the spring due to the stretching. The work done is given by:
W = ΔU = U₂ - U₁
where U₁ and U₂ are the potential energies of the spring at stretches of 0.1 m and 0.16 m, respectively.
Using the formula for potential energy, we have:
U₁ = (1/2) k x₁² = (1/2) × 200 N/m × (0.1 m)² = 1 J
U₂ = (1/2) k x₂² = (1/2) × 200 N/m × (0.16 m)² = 2.56 J
Therefore, the work done is:
W = ΔU = U₂ - U₁ = 2.56 J - 1 J = 1.56 J
The area under the graph representing this work is shown below:
Force vs. Stretch graph with shaded area representing work done