The most practical application of sonar is measuring the distance between objects in the ocean.
option A.
What is sonar?
Sonar is a technique that uses sound propagation to navigate, measure distances, communicate with or detect objects on or under the surface of the water, such as other vessels.
So basically, sonar is applied under water to measure the distance of objects such minerals, vessels , etc.
Thus, we can conclude that the most practical application of sonar is found under water, for measuring the distance between objects in the ocean.
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A ball is thrown with a initial upward velocity of 15m/s. What is the velocity after 1.5seconds?
The velocity after 1.5seconds is 0.3 m/s.
What is velocity?The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
Initial upward velocity: u = 15 m/s.
Time interval: t = 1.5 second.
Acceleration due to gravity acting downward is = 9.78 m/s².
Let the final velocity is v.
Therefore,
v = u -gt
= (15 - 9.8 × 1.5) m/s
= 0.3 m/s.
So, the velocity after 1.5seconds is 0.3 m/s.
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What is simple harmonic oscillation? Select all that apply.1. Simple harmonic oscillation occurs for objects whose motion can be defined by a sine or cosine curve. x(t)=x_0\cos(\omega t)x(t)=x 0 cos(ωt), for example2. Simple harmonic oscillation occurs for objects which experience a position (xx) dependent force (FF) of the form F=-CxF=−Cx, where C is some positive constant.3. Simple harmonic oscillation occurs when an object regularly returns to an equilibrium position.4. Simple harmonic oscillation only occurs for a mas-on-a-spring system.
a) [tex]x(t)=x_0\cos(\omega t)x(t)=x 0\ cos(\omega t),[/tex] for example
b) Simple harmonic oscillation occurs for objects which experience a position (xx) dependent force (FF) of the form F=-CxF=−Cx, where C is some positive constant.
What is Simple harmonic oscillation?Simple harmonic oscillation is a type of oscillatory motion in which an object oscillates back and forth around an equilibrium position. It is a special type of periodic motion in which the restoring force is always proportional to the displacement of the object from its equilibrium position, and acts in the direction opposite to that of the displacement. This type of motion is usually modeled by a mass-spring system.
a) Simple harmonic oscillation occurs for objects whose motion can be defined by a sine or cosine curve. x(t)=x_0\cos(\omega t)x(t)=x 0 cos(ωt), for example
b) Simple harmonic oscillation occurs for objects which experience a position (xx) dependent force (FF) of the form F=-CxF=−Cx, where C is some positive constant.
c) Simple harmonic oscillation occurs when an object regularly returns to an equilibrium position.
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two speakers play a 500 hz sound in phase. the speakers are arranged to face each other a what is the minimum distance you can move speaker a to achieve constructive interference along the x-axis? give a positive answer regardless of direction, in m.d are 6 m apart. how many points of constructive interference are there between the speakers?
As n is not an integer, so there will be no constructive interference between the speakers, if speaker A is moved by minimum distance.
What is interference?Interference is a phenomenon in which two waves combine by adding displacement together at every single point in space and time and to form a resultant wave of greater, lower, or same amplitude.
Wavelength of a 500 Hz sound wave is the speed of sound (about 343 m/s) divided by the frequency of the sound, which is 343/500 m = 0.686 m. Therefore, minimum distance you can move speaker A to achieve constructive interference along x-axis is 0.686/2 m = 0.343 m.
Given, distance between the speakers is 6m. Constructive interference will occur when path difference between two waves is equal to integer multiple of the wavelength. To achieve constructive interference, distance between the speakers + the distance moved by speaker A should be equal to n*wavelength where n is integer.
So, 6 + 0.343 = n* 0.686
n = (6+0.343)/0.686 = 8.8
As n is not an integer, so there will be no constructive interference between the speakers, if speaker A is moved by minimum distance.
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approximately when does the full moon rise? select one: a. near sunrise b. near sunset c. near noon d. near midnight
approximately when does the full moon rise d. near midnight
When the full moon rises, where is the Sun?At Full Moon, the Moon is 180 degrees distant from the Sun and 12 hours behind it. As a result, the Moon rises as the Sun sets; it is high in the south around midnight and sets in the morning, at daybreak.
As a result, the moon advances eastward by around 12 degrees every day with regard to the sun (13 minus 1). This implies that the moon rises later and later each day, occasionally in the morning, occasionally in the afternoon, and occasionally at night.
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How much work is done when a 100 Ib rock is lifted to a height of 3 ft? Work= . ft . lb
When a 100 lb rock is raised to a height of 3 feet, it takes 397.5 Joules to complete the work. It is a scalar quantity and is measured in units of energy such as Joules (J) or Foot-pounds (ft-lb).
When a force moves an object in the force's direction, work has been done. The formula: can be used to determine the amount of work completed.
work = force x distance x cos(theta)
where force is measured in newtons (N), distance is measured in meters (m) and theta is the angle between the force and the direction of motion.
In this case, the force required to lift the rock is equal to the weight of the rock, which can be calculated using the equation:
force = mass x gravity
where mass is measured in kilograms (kg) and gravity is 9.8 m/s^2.
To find the amount of work done, we need to convert the weight of the rock from pounds to kilograms, convert the height from feet to meters, and use the formula for work:
mass = 100 lb / 2.2 kg/lb = 45.45 kg
distance = 3 ft x 0.3048 m/ft = 0.9144 m
work = force x distance x cos(theta) = 45.45 kg x 9.8 m/s^2 x 0.9144 m = 397.5 J
So the amount of work done is 397.5 Joules.
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a diver measures an ambient absolute pressure of 0.686 atm while diving in the ocean. what is the divers depth in feet?
2.250656 feet which are around 68.6 cm is the depth of the ocean at the place where the diver measured an absolute pressure is 0.686 atm.
As we know the pressure on the depth is directly proportional to that of depth in the meter as 1 atm has a meter of the column of water below which results in 1 atm of pressure.
And as given the pressure was 0.686 atm which shows the column below is just 0.686 mt or 68.6 cm. And to convert cm to feet we need to divide it by 30.48. So in this case
68.6/ 30.48 => 2.250656
So length in feet will be 2.250656 feet. We can say 2.25 feet after the round-off.
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beneath the surface of which moon of saturn is there evidence for the existence of a subsurface ocean of liquid water?
Saturn's moons has evidence for the existence of a subsurface ocean of liquid water known as Enceladus
Enceladus is a living moon with a vast ocean of liquid salty water beneath its crust. Furthermore, jets of icy particles from that ocean, laced with a brew of water and simple organic chemicals, erupt from this fascinating ocean world on a continuous basis.
Saturn, like Jupiter, has no surface but an atmosphere that contains traces of water vapor. Furthermore, Saturn's spectacular rings are mostly composed of water ice. Titan, Saturn's largest moon, has a surface made up of water ice and other hydrocarbon-based ices.
Cassini discovered water constantly spewing out of jets around Saturn's moon Enceladus' south polar region, leading scientists to conclude that its subsurface ocean contains all of the ingredients for life - liquid water, heat, and food (methane).
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You are riding a bike with a bag in the front basket. A friend
on the sidewalk watches you ride by, heading south.
Which statement best describes how the bag's motion is
relative to the frame of reference - you and your friend?
O You observe the bag at rest, but your friend
observes it moving south.
You and your friend both observe the bag
moving to the south.
Your friend observes the bag accelerating
north, while you see it standing still.
O You and your friend observe the bag's velocity
decreasing.
Acceleration refers to an object's change in direction or speed or Velocity.
What is Acceleration?Forces have an impact on how things move. They have the power to initiate motion, as well as to stop, slow down, or alter the course of an item already in motion. We can contend that forces induce changes in velocity since they alter an object's velocity, which is the change in speed or direction.Remember that acceleration is a change in velocity. If the velocity is positive, a position is said to be increasing with time, and if the velocity is negative, a position is said to be decreasing with time.If the distance remains constant during that time, the velocity will remain zero. hence, the Acceleration Objects are said to be accelerating if they are altering their speed or direction.Forces affect how an object moves. They have the power to start anything moving, stop it mid-motion, slow it down, or change its course. Considering that forces alter an object's velocity, which is the change in speed or direction, we can claim that forces induce changes in velocity.As a result, when the object's velocity and acceleration are multiplied, the result is positive, the object moves faster, and when the result is negative, the object moves slower.To learn more about acceleration from the given link
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what is the relationship between the amount of energy required to remove thermal energy from a system, and the amount of thermal energy removed?
The amount of energy required to remove thermal energy is always greater or equal to the thermal energy removed, as per Second Law of Thermodynamics.
The Second Law of Thermodynamics is a fundamental principle of thermodynamics that states that the amount of energy required to remove a given amount of thermal energy from a system is greater than or equal to the amount of thermal energy removed.
This is also known as the Carnot's theorem and it is expressed mathematically as ΔQ < TΔS, where ΔQ is the heat absorbed or rejected, T is the temperature, and ΔS is the change in entropy. This means that it is impossible to completely convert heat into work, and some energy will always be lost as waste heat. This is why it is not possible to have a perpetual motion machine of the second kind.
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during a nascar race a car goes 76 m/s around a curved section of track that has a radius of 240 m. what is the car's acceleration?
The acceleration of the car is 24.07 m/s², if the velocity of the car is 76 m/s on a curve section of radius 240 m.
The speed of the car, v = 76 m/s
The radius of the curve, R = 240 m
On a curve there is a chance of overturning of the vehicle due to the lateral sloping of the curve(called super-elevation). This overturning force is balanced by the centrifugal force. Which is equal to, F = Mv²/R.
Where M is the mass of the vehicle and v, and R velocity and radius of the curve respectively.
So the acceleration would be, a = v²/R
a = 76²/240
a = 24.07 m/s²
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when the object of mass m2 has descended a distance h, the potential energy of the system has decreased by
When the object of mass m2 has descended a distance h, the potential energy of the system has decreased by mg x h
The potential energy of the system has decreased by m2 x g x h.
Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases. If a steel ball is raised above the ground as opposed to falling to the ground, it has more potential energy.
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a point charge of 8.47 x 10-6 c and a mass of 5.49 x 10-6 kg is initially at rest within a constant electric field with a magnitude of 914 n/c. what is the magnitude of the acceleration of the point charge assuming that only the electric field force acts on it?
The magnitude of the acceleration of the point charge assuming that only the electric field force acts on it is 1.54×[tex]10^{7}[/tex].
The magnitude of the acceleration of the point charge can be calculated using the equation a = F/m, where F is the electric field force and m is the mass of the point charge. The electric field force is equal to the charge of the point charge times the magnitude of the electric field, or
F = (8.47 ×[tex]10^{-6}[/tex] C) x (914 N/C).
Therefore, the magnitude of the acceleration can be calculated as
a = (8.47×[tex]10^{-6}[/tex]C x 914 N/C)/(5.49 ×[tex]10^{-6}[/tex] kg) = 1.54 ×[tex]10^{7}[/tex] m/s2.
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a ball is tossed vertically upward with an initial speed of 25.5 m/s. how long does it take before the ball is back on the ground?
The ball will take 5.2 seconds to return back to its original position on the ground, if its initial speed is 25.5 m/sec.
The initial sped of the ball, u = 25.5 m/sec
Acceleration due to gravity of the earth, g = 9.81 m/s²
Let the time taken by the ball to reach highest point, = t
We know the final velocity of the ball after reaching the highest point is zero(0).
By the first equation of motion,
v = u + at
0 = 25.5 + (-9.81) × t
t = 25.5/9.81
t = 2.6 seconds
So the total time taken would be 2t = 2 × 2.6 = 5.2 seconds.
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Please someone help this is urgent!!!
The total amount of matter in an object is known as its mass. The weight of an object is the gravitational pull it feels as it falls.
What does mass mean in forces?A substance's mass is its total amount of matter. The gravitational force an object experiences as it falls is known as its weight. Because of gravity, the object accelerates. All falling objects on Earth experience some upward air resistance force, which prevents them from ever falling completely freely.
The quantity of material in an object is measured by its mass, which is inversely proportional to the quantity and type of atoms it contains. Unless material is added to or taken away from a body, mass does not change with changes in position, motion, or shape. The kilogram serves as the unit of mass in the SI system (kg).
Therefore, the correct answer is option A) the amount of matter in something.
The complete question is:
What does the word mass mean?
A) the amount of matter in something
B) the speed an object falls
C) how high a person can jump
D) how far an object can be thrown
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A) What happens when new evidence is found that contradicts part of a theory?(1 point)
The theory is discarded for a new one.
New pieces are added to the original ideas.
It gets ignored to maintain the original idea.
Science reevaluates the validity of the theory.
Science reevaluates the validity of the theory when new evidence is found that contradicts part of a theory.
When new evidence is found that contradicts part of a theory, scientists reevaluate the theory to see if it needs to be modified or if a new theory should be proposed. Scientists will look at the new evidence and try to reconcile it with the existing theory by adjusting or refining their understanding of the theory. If the new evidence cannot be reconciled with the existing theory, scientists may propose a new theory or modify the existing theory to better explain the new evidence. This process is an essential part of the scientific method and allows for theories to be continually refined and improved over time.
when new evidence is found that contradicts part of a theory, scientists engage in a process of critical evaluation and testing of the theory. This process can involve a variety of different steps and can lead to different outcomes depending on the nature of the new evidence and the existing theory.
One outcome could be that the new evidence is found to be inaccurate or unreliable, in which case the theory remains unchanged. Another outcome could be that the new evidence is found to be credible and significant, and so the theory is modified to account for the new information. This process of modifying a theory in light of new evidence is known as "theory modification" or "theoretical revision" and it is an important aspect of scientific inquiry.
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Why is the gravitational
force that a friend
exerts on you less than
the gravitational force
exerted on you by
Earth?
As compared to Earth, humans have relatively low masses, which results in a very small and negligible gravitational force.
What does gravity mean?
The force of gravity, often known as gravitation, affects every material object in the universe. The force of gravity tends to draw any two objects or particles with nonzero mass toward one another. From subatomic particles to galaxy clusters, gravity affects things of all sizes.
The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them, according to Newton's universal law of gravitation.
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a negative charge moves in a direction opposite to that of an electric field. what happens to the energy associated with the charge? a negative charge moves in a direction opposite to that of an electric field. what happens to the energy associated with the charge? the electric potential energy of the charge increases, and the kinetic energy decreases. both the electric potential energy and the kinetic energy of the charge increase. both the electric potential energy and the kinetic energy of the charge decrease. the electric potential energy of the charge decreases, and the kinetic energy increases.
The electric potential energy of the charge decreases, and the kinetic energy increases.
What is Electric potential?Electric potential, the amount of work needed to move a unit charge from a reference point to a specific point against an electric field. Typically, the reference point is Earth, although any point beyond the influence of the electric field charge can be used.
What is Kinetic energy?In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.
What is potentially Energy ?Potential energy, stored energy that depends upon the relative position of various parts of a system. A spring has more potential energy when it is compressed or stretched. A steel ball has more potential energy raised above the ground than it has after falling to Earth.
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Two gases—neon and air—are compressed in a closed system from P1 to P2 using a polytropic process with n = 1. 5. _____ requires lesser work to be compressed. The gas constants for neon and air are R = 0. 4119 and 0. 287 kJ/kg·K, respectively
In a closed system, two gases—neon and air—are compressed via a polytropic process with n = 1.5 from P1 to P2. Neon gas requires lesser work to be compressed.
In a polytropic process with n = 1.5, the equation that relates the initial pressure, P1, the final pressure, P2, and the specific heat ratio, n, is:
P1 x V1^n = P2 x V2^n
where V1 and V2 are the initial and final specific volumes of the gas, respectively.
Since the work done to compress a gas is given by the equation:
work = n x R x T x (V2^(1-n) - V1^(1-n))
We can find the work done to compress the two gases neon and air by substituting the values of the gas constant and the specific heat ratio into the equation:
Work to compress neon = 1.5 * 0.4119 kJ/kg·K * (V2^(1-1.5) - V1^(1-1.5))
Work to compress air = 1.5 * 0.287 kJ/kg·K * (V2^(1-1.5) - V1^(1-1.5))
Since the gas constant for neon is greater than the gas constant for air, it requires less work to compress neon than air. Therefore neon requires lesser work to be compressed.
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write the formula of velocity ratio
object a has a charge q on it, object b has a charge q on it, and object c has a charge 2q on it. these charges are arranged, one each at the vertices of an equilateral triangle. which charge has the greatest magnitude electic force on it?
Different from the forces operating on objects A and B, object C is subject to a force that is twice as great. Therefore, the electric force exerted on object C by its charge is of the highest magnitude.
F AB = (kqq)/r2, where k is the Coulomb's constant, q is the charge on object A, and r is the separation between object A and B, determines the electric force acting on object A.
F AC is calculated using the formula (kq2q)/r2, where r is the distance between item A and C, q is the charge on object A, and 2q is the charge on object C.
F BC = (kq2q)/r2, where k is the Coulomb's constant, q is the charge on object B, 2q is the charge on object C, and r is the separation between objects B and C, determines the electric force acting on object B.
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A student designs a gravity experiment. She will time how long it takes different objects to fall from her school’s roof to the ground. She will use three objects: a 2-foot-long board, a toy car, and a paper bag. What is wrong with her experiment’s design?(1 point)
The experiment’s design is not fair because the three objects do not have equal length to ensure they fall the same height.
What is a fair experiment?
A fair experiment or testis an investigation where one variable (the independent variable) is changed and all other conditions (controlled variables) are kept the same.
To fairly determine the time taken for different object to fall to the ground, the length of the objects should be the same, this ensures that the dependent variable is kept constant.
2-foot-long board is not the same length as a toy car, and a paper bag, so the experiment is not fair.
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recent significant breakthrough in space exploration
Recent significant breakthrough in the space exploration field is that webb telescope reveals the invisible universe.
With the help of various international space agencies, NASA notched steps forward in scientific endeavors. After decades of working, the James Webb Space Telescope finally began observing the universe in July. The world’s most powerful space telescope has turned its eyes on stars, planets, and galaxies by infrared light, which is invisible to the human eye.
The telescope has explored the unseen aspects of the universe and previously hidden figures, including the most distant galaxies ever observed. Webb has also shared new way of looking on some of astronomy’s favorite cosmic phenomenon and captured them in a new light, such as the Pillars of Creation.
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Select the correct answer from each drop-down menu.
Ellen is a prosecuting attorney. She ensures that only two parties have touched the physical evidence in her case. Who are these two parties?
Ellen ensures that only the
who initially collected the evidence, and the
✓ who
analyzed the evidence, are the only two people that touched the physical evidence, as indicated by their signatures on the seals of the
evidence bag and chain of custody document.
The selection of the correct word is as follows:
Ellen ensures that only the crime scene investigator initially collected the evidence, and the forensic technicians analyzed the evidence, are the only two people that touched the physical evidence, as indicated by their signatures on the seals of the evidence bag and chain of custody document.What is the role of forensic technicians?The role of forensic technicians is to visit crime scenes and gather, identify, classify, and analyze physical evidence related to criminal investigations. As a Forensic Science Technician, you will have required to perform tests on weapons or substances in order to determine their significance to the investigation.
They generally analyze crime scenes to determine what evidence should be collected and how. Along with this, they also take photographs of the crime scene and evidence and make sketches of the crime scene.
While the role of the crime scene investigator is to gather forensic evidence from crime scenes that will ultimately lead to the detection and prosecution of criminals. You'll process crime scenes using specialist techniques to visualize, capture and recover evidence.
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When seat and steering wheel are adjusted properly, the driver should be at least _HOW_MANY_ inches from the steering wheel?
The driver must be least "10 inches" away as from steering wheel when seated properly.
Explain some safety guidelines of driving?It is essential to become familiar with the local traffic laws when travelling to or relocating to a new nation.
No matter how you plan to use a vehicle, adhering to the traffic laws will ensure your safety.
Having stated that, here are some guidelines for driving: On left side of the vehicle is always where the steering wheel is located.Drive just on right side of the roadway at all times. The same-direction lanes of traffic are divided by white lines.opposing-direction traffic is divided by yellow lines.To pass other vehicles moving in the opposite way, use the left lane.Watch out for cyclists. They frequently share the highway with automobiles and are required to abide by standard traffic regulations.The driver must be least "10 inches" away as from steering wheel when seated properly.To know more about the safety guidelines of driving, here
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how far from the center of the earth would the net gravitational force of the earth and the moon on an object be zero?
At 346306 km from the center of the earth would the net gravitational force of the earth and the moon on an object be zero.
Let the mass of the earth and the mass of the moon be m1 and m2 respectively. The distance between the earth and the moon be D.
The formula for the gravitational force between two objects having masses m1 and m2 saperated by a distance D is given by the formula:
F = Gm1m2/r^2
The distance between the earth and the moon is also known:
D=384400km
Let at distance x from the earth the gravitational force between the earth and the sun is zero.
∴ Gm1/x^2=Gm2/(D-x)^2
⇒ (D-x)^2 /x^2 = m2/m1
Substituting the values we get of m1,m2 and D we get:
x=346306 km
Therefore, at 346306 km from the center of the earth would the net gravitational force of the earth and the moon on an object be zero.
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How much power is used if a force of 180N is used to push a box a distance if 60m in 20s
Answer:
Answer is in attached photo.
Explanation:
SolutionSolution is in attached photo, do take note there are 2 separate formulas to be used in this questions:
1) Work Done = Force x Distance
2) Power = [tex]\frac{Work \ Done}{Time}[/tex]
a smart phone charger delivers charge to the phone, in the form of electrons, at a rate of -0.75 c/s .how many electrons are delivered to the phone during 23 min of charging?
No. of electrons are delivered to the phone during 23 min of charging
6.46875 x 10^21
Charge is q = ne
where , e = - 1.6 x 10^-19
n = no.of electrons
The rate of accumulation of the electrons is ,q/t = Q
Q x t = -0.75 / 23 min = q
For time t = 23 min
1min = 60 sec
so time in sec, t = 23 x 60 = 1380 sec
therefore , Q x t = -0.75 x 1380
= -1035 c
No. of electrons = n = q/e
= -1035 / -1.6 x 10^-19
= 6.46875 x 10^21 electrons
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(c16p12) suppose that the attraction between the moon and the earth were due to coulomb forces rather than gravitational force. what would be the magnitude of the charge required if equal but opposite charges resided on both earth and moon? mass of earth
The magnitude of the charge required if equal but opposite charges resided on both earth and moon is 1.037 × 10²⁰ Coulombs.
The magnitude of the charge required would be very large. Coulomb's law states that the force between two charges is given by
F = (k × q1 × q2) / r²
where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.
To balance the gravitational force between the Earth and the Moon, we would need to set the Coulomb force equal to the gravitational force:
F_gravity = (G × m1 × m2) / r²
where G is the gravitational constant, m1 is the mass of the first object, m2 is the mass of the second object, and r is the distance between the objects.
By equating the two forces and solving for q1 and q2, we can find the magnitude of the charges required:
q1 × q2 = (m1 × m2 * G) / (k × r²)
q1 = q2 = √( (m1 × m2 × G) / (k × r²))
where mass of earth is 5.98 × 10²⁴ kg, mass of moon is 7.35 × 10²² kg, distance between earth and moon = 3.84 × 10⁸ m, and the Coulombs constant is 8.9875517873681764 × 10⁹ N×m²/C²
q1 = q2 = √( (5.98 × 10²⁴ kg × 7.35 × 10²² kg × 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²) / (8.9875517873681764 × 10⁹ N×m²/C² × (3.84 × 10⁸ m)²)) = 1.037 × 10²⁰ Coulombs
Both the charges on Earth and Moon would be of 1.037 × 10²⁰ Coulombs
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Your question seems incomplete, but I assume the full question is:
"Suppose that the attraction between the moon and the earth was due to Coulomb forces rather than the gravitational force. What would be the magnitude of the charge required if equal but opposite charges resided on both earth and moon? Mass of earth = 5.98 × 10²⁴ kg; mass of moon = 7.35 × 10²² kg; earth-moon distance = 3.84 × 10⁸ m."
A highway curves to the left with radius of
curvature of 38 m and is banked at 24° so
that cars can take this curve at higher speeds.
Consider a car of mass 1283 kg whose tires
have a static friction coefficient 0.66 against
the pavement.
With a static friction coefficient of 0.66 against the pavement at 29.131 m/s.
Explanation:
Describe the free body diagram. There are three forces at work: weight force mg drawing the object downward, normal force N pushing perpendicular to the road, and friction force N pushing the object downward similarly to the road.
force total acting in a centripetal direction:
F = ma N sin + N cos = m v2/r N (sin + cos) = m v2/r.
Combined forces acting vertically:
F = ma N (cos sin ) = mg N = mg / (cos sin ), where:
G (sin + cos) = v2 / r v2 = gr (sin + cos) / (cos sin) is the replacement for the equation: mg (sin + cos) / (cos sin)
Values to be entered:
v² = (9.8 m/s²) (39 m) (sin 30° + 0.72 cos 30°) / (cos 30° − 0.72 sin 30°)
v = 29.131 m/s
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a meter stick lies along the optical axis of a convex mirror of focal length 40 cm, with its nearer end 60 cm from the mirror surface. how long is the image of the meter stick?
The image of the meter stick is 8 cm long which is found by the mirror's formula.
Given:
Focal length of the convex mirror = f = -40 cm
Length of the stick =1m = 100 cm
Distance of the nearer/front end = s1 = 60 cm
Distance of the far/back end = s2 = 60 + 100 = 160 m
By finding out the image positions of the nearer end and the far end. We can find out the length of the image a meter stick.
Mirror formula,
1/s + 1/s' = 1/f
Using mirror formula we find expression for s',
s' = sf/(s-f)
To find the image position of front end of the stick facing towards the convex mirror
s'1 = (60 x- 40) / (60-(-40))
s'1 = -24 cm
Similarly, the image position of back end of the stick
s'2 = -32 cm
The length of the image is given by
s'1 - s'2 = -24 -(-32)
= 8 cm
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