Answer:
Approximately [tex]3.43\; {\rm m\cdot s^{-2}}[/tex], assuming that air resistance is negligible in both occasions, and that [tex]g_{\text{earth}} = 9.81\; {\rm m\cdot s^{-2}}[/tex] near the surface of the Earth.
Explanation:
Let [tex]x[/tex] denote the displacement of the marker. Let [tex]a[/tex] denote the acceleration of the marker. Let [tex]t[/tex] denote the time it takes for the marker to reach the ground.
Under the assumptions, acceleration of the marker would be constant, and the SUVAT equations would apply. Rearrange the SUVAT equation [tex]x = (1/2)\, a\, t^{2}[/tex] to find acceleration [tex]a[/tex]:
[tex]\begin{aligned}a &= \frac{2\, x}{t^{2}}\end{aligned}[/tex].
Let [tex]a_{\text{Mars}}[/tex] and [tex]t_{\text{Mars}}[/tex] denote the acceleration and time taken on Mars. Similarly, let [tex]a_{\text{Earth}}[/tex] and [tex]t_{\text{Earth}}[/tex] denote the acceleration and time taken on Earth. It is implied that the Marker travelled the same distance (same displacement, [tex]x[/tex]) both on Earth and on Mars.
Using the SUVAT equation from above:
[tex]\begin{aligned}a_{\text{Mars}} &= \frac{2\, x}{{t_{\text{Mars}}}^{2}}\end{aligned}[/tex].
[tex]\begin{aligned}a_{\text{Earth}} &= \frac{2\, x}{{t_{\text{Earth}}}^{2}}\end{aligned}[/tex].
[tex]\begin{aligned}\frac{a_{\text{Mars}}}{a_{\text{Earth}}} &= \frac{\displaystyle \frac{2\, x}{{{t_{\text{Mars}}}^{2}}}}{\displaystyle \frac{2\, x}{{{t_{\text{Earth}}}^{2}}}} \end{aligned}[/tex].
[tex]\begin{aligned}\frac{a_{\text{Mars}}}{a_{\text{Earth}}} &= \left(\frac{{t_{\text{Earth}}}}{{t_{\text{Mars}}}}\right)^{2}\end{aligned}[/tex].
[tex]\begin{aligned}a_{\text{Mars}} &= \left(\frac{{t_{\text{Earth}}}}{{t_{\text{Mars}}}}\right)^{2}\, a_{\text{Earth}} \\ &= \left(\frac{1.3\; {\rm s}}{2.2\; {\rm s}}\right)^{2}\, (9.81\; {\rm m\cdot s^{-2}}) \\ &\approx 3.43\; {\rm m\cdot s^{-2}}\end{aligned}[/tex].
two train cars of identical mass (m=10.0kg) collide and move off as shown. the left car was initially traveling at 2.0m/s right and the right car was initially traveling at a velocity of 3.0 m/s left. after the collision, the left car was traveling at a velocity og 2.5m/s to the left
Explanation:
m1u1+m2u2=m1v1+m2v2
10×2 + 10×-3 = 10×-2.5 + 10v2
20-30=-25+10v2
-10+25=10v2
15=10v2
v2=1.5m/s to the right
The two cars stick together and move off with a final velocity of 2.5 m/s to the left indicating that there is a loss of kinetic energy, and the collision is inelastic.
In an inelastic collision, two or more objects collide and stick together after the collision, resulting in a loss of kinetic energy. In such collisions, the objects involved deform or undergo some other form of internal interaction that dissipates energy. As a result, the total kinetic energy of the system decreases.
Momentum is still conserved, meaning that the total momentum of the system before the collision is equal to the total momentum after the collision.
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Your question is incomplete, most probably the full question is this:
Two train cars of identical mass (m=10.0kg) collide and move off as shown. the left car was initially traveling at 2.0m/s right and the right car was initially traveling at a velocity of 3.0 m/s left. after the collision, the left car was traveling at a velocity of 2.5m/s to the left. What type of collision is depicted here?
Are the magnitude and direction of a − b same as that B − A?.
No, its not. The direction of a vector is not the same as the direction of its negative. So, the direction of a - b is opposite to the direction of b - a.
Vector magnitude and directionThe magnitude of a vector is a scalar value and is independent of the direction of the vector. The direction of a vector is typically represented by a unit vector, which has a magnitude of 1.
The magnitude of a vector can be described as the length or the size of the vector. It is a scalar quantity and is independent of the direction of the vector. The magnitude can be calculated using the formula: |a| = √(a.x² + a.y² + a.z²) where a.x, a.y, and a.z are the x, y, and z components of the vector.
The direction of a vector can be described as the direction in which the vector is pointing. It is typically represented by a unit vector, which has a magnitude of 1. The direction of a vector can be calculated by normalizing the vector, which involves dividing the vector by its magnitude.
In the case of a - b and b - a, the magnitude of both vectors is the same, as the difference in position between two points is the same regardless of the order of the points. However, the direction of a - b is opposite to the direction of b - a, because the direction of the vector is the direction from the starting point to the ending point, and the starting and ending points are different between the two vectors.
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What is the smallest unit of power Mcq?.
The electron volt (eV) is the smallest unit of energy used in atomic and nuclear physics.
What is energy?In physics, energy is the quantitative property that is transferred to a body or a physical system and is visible in the form of heat and light. The law of conservation of energy states that energy can be converted in form but cannot be created or destroyed. Energy is defined by scientists as the ability to perform work. People have learned how to convert energy from one form to another and then use it to do work, which makes modern civilization possible. Energy is the ability to perform work. It can take the form of a potential, kinetic, thermal, electrical, chemical, nuclear, or other energy.
Here,
In atomic and nuclear physics, the electron volt (eV) is the smallest unit of energy.
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7. What kind of force acts on a ladybug inside a can that is
whirled in a circular path?
Neglecting gravity, just one force—directed toward the circular motion's center—is applied to the whirling can. This force is centripetal.
What happens to a body when whirled in a circular path?Because displacement is always perpendicular to applied force when a body is rotating in a circle, there is no work done. Additionally, the centripetal force acts along the circle's radius and at a right angle to the body's motion when a body moves in a circular route.The insect forces the can outward. A ladybird at the bottom of a rotating tin can feels centrifugal force pressing it against the can's bottom.When an object travels around a circle, its direction and speed change at each point. Centripetal force is the force responsible for this velocity or acceleration. Circular motion causes an object to constantly change.To learn more about force refer to:
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A 60 kg person runs with a velocity of 4 m/s and jumps onto a 5 kg skateboard and rolls away. What is the final velocity of the person on the skateboard?
(round your answer to the nearest tenth)
Answer: Final velocity is [tex]3.8 m/s[/tex]
Explanation:
We are given mass and velocity, or mass in motion, known in physics as "momentum".
The formula for momentum is [tex]p=mv[/tex] (mass*velocity)
First, calculate the momentum of the person running:
[tex]p=60kg*4m/s[/tex]
[tex]p=240(kg*m/s)[/tex]
When the person jumps on the skateboard, the mass changes and now we're solving for the velocity. Use the same formula above to solve.
[tex]240=(60+4)*v[/tex] can be rewritten as [tex]v=\frac{240kg*m/s}{(60+4)kg}[/tex] or [tex]v=\frac{p}{m}[/tex]
Solve and the kg cancels out and you're left with a final velocity of [tex]3.75 m/s[/tex] or [tex]3.8m/s[/tex] rounded to nearest tenth.
What is the unit and dimensional formula of torque?.
Force times distance, or T²L²M, is the dimension of torque. The official SI literature advises that use the unit newton-metre (Nm) and never the joule, despite the fact that these fundamental dimensions are identical to those used for energy or work. The appropriate abbreviation for the newton metre is Nm.
Which are the two torque equations?The formula for torque is T = F × r × sinθ. Torque is, in other words, the cross product of the shortest path (the distance between the pivot point and the point at which forces are applied) as well as the force vector, where 'a' is the angle of r and F.
How can I figure out torque?Between the pivot and the location where the force is delivered, measure the distance, r. Calculate the angle between the vector connecting the force's application point and the pivot point and the vector of the applied force. You may calculate the torque by multiplying r by F plus sin.
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What is the weight of a 10 kg object gravity 9. 8 m/s s?.
The weight of a 10 kg object gravity 9. 8 m/s² is 98 N.
What is weight?The gravitational force that pulls objects towards the centre of the Earth is known as weight. The subsequent force that a mass is drawn to Earth has something to do with gravity. So unlike gravitational force, which occurs between any two masses, this only occurs between Earth and a mass.
When two objects are in close proximity to one another, their gravitational pull is determined by their respective masses and the inverse square of their respective distances. The forces between larger objects are stronger, and the attraction between smaller objects is weaker as they are further apart. A single weight equation developed by Newton can capture the relationship.
We know that force
F = ma
F = force
m = mass of an object
a = acceleration
Here,
a = g = 9.8 m/s²
m = 10 kg
Then
Force, F = 10 × 9.8
= 98 N
Thus, the weight of a 10 kg object gravity 9. 8 m/s² is 98 N.
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In what time period did hydroelectric power usage?.
The period did hydroelectric power usage in the Late 19th/Early 20th century.
Hydroelectric power has been used for thousands of years in various forms. The ancient Greeks and Romans used water wheels to grind grain and perform other tasks. The first recorded use of hydroelectric power for industrial purposes was in 1878 when a water turbine was used to generate electricity at the Cragside estate in Northumberland, England. The first hydroelectric power station was built in 1881 by the inventor of the water turbine, James B. Francis, in Lowell, Massachusetts, USA.
However, it was not until the late 19th and early 20th centuries that hydroelectric power began to be widely used for industrial and commercial purposes. The growth of the hydroelectric power industry was driven by the increasing demand for electricity for lighting, heating, and power for industry. The use of hydroelectric power expanded rapidly in the early 20th century, particularly in Europe and North America, and it continues to be an essential source of electricity worldwide.
So, the period when hydroelectric power usage started to be widely used for industrial and commercial purposes was in the late 19th and early 20th century.
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How do pressure and temperature change inside Earth as depth increases? A. Pressure and temperature decrease. B. Pressure increases; temperature decreases. C. Pressure decreases; temperature increases. D. Pressure and temperature increase.
The pressure inside the Earth increases as depth increases; The temperature drops. Here option B is the correct answer.
As depth increases, the weight of the overlying rock and soil increases, causing an increase in pressure. Additionally, the temperature inside the Earth increases with depth due to the heat generated by the radioactive decay of elements in the Earth's crust.
However, the rate of temperature increase with depth is not as steep as the rate of pressure increase, so the temperature will decrease as the depth increases.
The geothermal gradient is the pace at which Earth's temperature increases with depth. It suggests that the Earth's surface is receiving heat from the planet's heated center. For every kilometer of depth, the temperature rises by around 25°C on average.
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How will the electrostatic force be changed if the distance between two electric charges is tripled?.
The force between two charged objects is inversely proportional to the square of their distance, according to Coulomb's Law. As a result, the force will weaken by a factor of 9 if the distance is tripled.
When the distance is tripled, what happens to the electrostatic force?Additionally, the electrostatic force decreases by a factor of nine when the separation distance is tripled, or increased by a factor of 3.
When there is a doubled distance between two charges, what will happen to the electrostatic force?As the distance between the two charges increases by a factor of four, so does the magnitude of the force. As a result, the attraction or repulsion decreases to one-fourth of its original value if the distance between the two charges is doubled.
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Which three activities consume the most fuel in modern societies?
a. Cooking, air conditioning, transportation
b. Construction, lighting, entertainment
c. Manufacturing, transportation, entertainment
d. Heating, transportation, electricity generation
The correct option is : (d) Heating, transportation and electricity generation.
Energy is one of the major inputs for the economic development of the country. Any sustainable energy source that comes from the natural environment is a renewable energy source. Renewable energy is inexhaustible and a clean alternative to fossil fuelsRenewable energy is energy that is produced from natural processes and continuously replenished. A few examples of renewable energy are sunlight, water, wind, tides, geothermal heat, and biomass. The energy that is provided by renewable energy resources is used in 5 important areas such as air and water cooling/heating, electricity generation, the rural sector, and transportation.The existence of renewable energy resources is spread over a wide geographical area in comparison to the conventional energy resources which are often concentrated in a limited number of countries like the oil and gas are mostly concentrated in the Middle East countries. The use of renewable energy resources in energy generation is resulting in less pollution and has a significant effect on economic benefits and energy security.To know more about renewable energy visit:
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The figure below shows the emission spectra for helium (He24) and uranium (U92238). A neutral helium atom has just two electrons, while a neutral uranium atom has 92. Briefly explain why the emission spectrum for uranium has so many more lines than the helium spectrum.
The emission spectrum for uranium has many more lines than the helium spectrum due to the increased number of energy levels and transitions possible in a neutral uranium atom as compared to a neutral helium atom.
What is the emission spectrum about?In order to understand why the emission spectrum for uranium has many more lines than the helium spectrum, it's important to understand how emission spectra work. When an atom is excited, for example by heating, electrons in the atom absorb energy and move to higher energy levels or orbitals.
The emission spectrum for helium has only a few lines because it has only two electrons. These electrons occupy only a few energy levels and can only make transitions between these levels, which results in a few emission lines.
However, in the case of uranium, it has 92 electrons which occupy many energy levels. As a result, there are many possible transitions between energy levels, and thus many lines in the emission spectrum. The more electrons an atom has, the more complex its emission spectrum will be.
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What are the 3 types of ballistics?.
Three types of ballistics are- Internal Ballistics, Transitional Ballistics and External Ballistics.
Internal ballistics, also known as initial ballistics, is concerned with what happens in the two milliseconds between the firing of the pin or striker and the exit of the bullet through the muzzle end of the barrel. The first phase involves the analysis of projection propulsion and flight.
The mediator between two regimes is involved in transitional ballistics ( internal and external). Intermediate ballistics is a process that begins shortly after a bullet has been fired.
External ballistics is concerned with the trajectory of the bullet after it has exited the barrel. The second phase investigates the situation when the bullet is about to strike the target and exit the projectile. It examines the trajectory of a projectile.
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What is Coulomb's law and its SI unit?.
What is the T formula in physics?.
Time (T) in physics : Divide is required, as shown by the T's top, and multiplication is required, as shown by the T's vertical line. distance ÷ speed = time.
Like how a meter is one foot and a second one second, so too. The relationship between speed, distance, and time is described using the formula speed distance time. Speed is calculated as distance divided by time.
You can also calculate the time by dividing the distance traveled by the speed. The third input can be calculated if you know two of the inputs. Drawing a T helps to visualize the T-Method, which is crucial for demonstrating the link between Total, Part, and Rate.
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What are Newton's 1st 2nd 3rd and 4th laws of motion?.
Newton's 1st, 2nd, 3rd, and 4th laws are 1) Law of inertia 2) Force's law 3) action-reaction relationship and 4) Newton's law of gravitation.
Newton's 1st law also known as the law of inertia. A balling rolling on the ground stops after some time due to the opposite force of friction working between the ball and the ground.
Newton's 2nd law of force states that the rate of change of momentum of an object is equal to the force applied by the object. When a bullet is fired from a gun change in the momentum of the bullet generate the force that cause the bullet to be fired and to generate the recoil velocity in the gun.
Newton's 3rd law states the action-reaction relationship. When a rocket is launched from the earth, it applies a force on the ground that generate the enough reaction force that causes the rocket to generate orbital velocity.
Newton's 4th law of gravitation states that every object attracts every other object in the universe with a force, called gravitational force. This force is directly proportional to the product of the masses of both the object and inversely proportional to the square of the distance between them. Mathematically it is described as:
F = GmM/R²
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Define the relationship between the ECG and the pulse wave. Explain why the timing of the QRS complex in the ECG and the maximum height of the pulse do not coincide
The ECG (electrocardiogram) records electrical activity within the heart, while the pulse wave records the physical pressure of the heart’s contractions.
The timing of the QRS complex in the ECG and the maximum height of the pulse do not coincide because the electrical impulse from the heart arrives at the body's surface before the physical pressure of the heart's contraction is felt.
The electrical impulse reaches the surface of the body faster than the physical pressure, causing a discrepancy between the two signals. In addition, the electrical impulse is usually larger than the physical pressure, which results in the QRS complex in the ECG having a higher peak than the pulse wave.
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What is the dot product of 2i 4j 5k and 3i 2j k?.
The dot product of 2i+4j+5k and 3i+2j+k is 19.
The total of the products of the matching components makes up the dot product, or inner product, of two vectors. It is equivalently equal to their product times the cosine of the angle between them. The square of a vector's magnitude is the dot product of a vector with itself.
A two-vector or bivector tensor is the type. It is a linear functional that transforms two-forms into real numbers while simultaneously being the dual of a two-form. The tensor product of two vectors yields a two-vector. In light of this, two vectors may only be said to be collinear if they are on the same line or parallel to one another in the same or opposite direction.
The first vector is: 2i+4j+5k
The second vector is: 3i+2j+k
The dot product of the two vectors:
= 2(3) +4(2) + 5(1)
= 6+8+5
=19
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Correct Question:
What is the dot product of 2i+4j+5k and 3i+2j+k ?
The magnitude of the electrostatic force between two point charges is F. If the distance between the charges is doubled, the electrostatic force between the charges will becomeanswer choicesF/44FF/22F
F/4F is the correct answer because the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between the charges.
This means that if the distance is doubled, the inverse of the square of the distance will increase four times, thus reducing the force by a factor of one-fourth. So, if the distance is doubled, the electrostatic force between the charges will become F/4F.
This can be expressed mathematically as F1/d2 = F2/d22, where F1 is the original force and d1 is the original distance and F2 is the new force and d2 is the new distance. Thus, if d2 is doubled, the new force will be F/4F.
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How can we find the direction of vector?.
To find the direction of the vector v⃗ = (x, y) , use the formula θ = arctan(y/x) , where θ is the smallest angle the vector forms with the horizontal axis, and x and y are the components of the resultant vector
Vector definitionA vector is a quantity that has both magnitude and direction and is described by a set of directed line segments. Examples of vector quantities are distance, velocity, acceleration, momentum, impulse, and so on.
Geometrically, a vector is described by a directed line segment, where the arrow indicates the direction of the vector, while the length of the line represents the magnitude or value of the vector. Vectors can be denoted by lowercase letters with an arrow above them or bold lowercase letters (a, b, c, and so on).
Vector PropertiesAfter knowing the definition of a vector, here are some vector properties that you need to know, namely:
1. Can be moved provided that the value/magnitude and direction do not change.
2. Can be summed up.
3. Deductible.
4. Can be deciphered.
5. Can be multiplied.
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the tension force in a cable can be resolved into a horizontal component and a vertical component.
the tension of the cable is 2000N
the cable makes an angle of 20 degrees with the horizontal.
draw a vector diagram to determine the magnitude of the two components of the tension force in the cable.
The two components of the force are;
Vertical component = 684 N
Horizontal component = 1879 N
How do we resolve the tension force?We have to note that the tension force that is know to act along a string. We have to note that the tension force just like all the other forces that we have must have direction. The direction of the force can also be resolved into the vertical and the horizontal components of the force.
Now we know that;
Vertical components of the force = 2000 N sin 20 = 684 N
Horizontal component of the force = 2000 N cos 20 = 1879 N
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What is the relationship between the formula weight of a substance and its molar mass?.
The formula weight of a substance is the sum of the atomic weights of all the atoms in the molecular formula of the substance, while the molar mass of a substance is the mass of one mole of that substance.
The formula weight and molar mass of a substance are related in that the molar mass of a substance is equal to the formula weight of the substance divided by the Avogadro constant (6.022x10^23). Thus, the molar mass of a substance is numerically equal to the formula weight but expressed in grams per mole instead of atomic mass units.
This is because the Avogadro constant is a conversion factor that is used to convert the formula weight of a substance to the molar mass of the substance.
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What is the formula of rate of change of momentum Class 9?.
We can then conclude that the force exerted equals the change in the rate of momentum. Momentum is well-known to be equal to mass times velocity.
Velocity or speed: which is greater?The direction & speed of a moving vehicle moving along a path are specified by velocity as opposed to speed. Speed is therefore a vector rather than a scalar.
the velocity formula's availability.According to the equation v = s/t, velocity (v) is a dimensionless quantity that quantifies displacement (notice shift in location, s) through shifts in time (t).
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Is gravitational field strength always 9. 8 N kg?.
The gravitational field strength of the Earth is 9.8 N/kg. Accordingly, an item will experience 9.8 N of force for every kg of mass. The weight of an object is smaller where the gravitational field is weaker.
The Moon, for instance, has a gravitational field that is 1.6 N/kg strong. This indicates that an object will encounter 1.6 N of force for every kg of mass. An astronaut will therefore be lighter on the Moon than they are on Earth.
One of the most significant forces in the universe is gravity. Weight is the force that an object with mass experiences when it is in a gravitational field.
Gravitational weight is not usually immediately apparent. The International Space Station astronauts look to be weightless. They still have weight, though, because they are still in orbit around the Earth and are subject to its gravitational field. Because they and the space station are always descending toward Earth, they appear to be weightless.
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What is the difference between g and g Class 9?.
arthur benjamin says that the current top of the pyramid of mathematics curriculum is
Arthur Benjamin says that the current top of the pyramid of mathematics curriculum is calculus.
Calculus is the subject that the mathematics curriculum builds up to, according to Arthur Benjamin, who made this statement in a well-known TED talk. The pyramid's incorrect summit is that one. Statistics should be the proper pinnacle that every high school graduate knows.
American mathematician Arthur T. Benjamin, who was born on March 19, 1961, specialises in combinatorics. He is the Smallwood Family Professor of Mathematics at Harvey Mudd College, where he has taught mathematics since 1989.
He is well renowned for his aptitude for mental math and for his live audience "Mathemagic" presentations. In newspaper and magazine stories, TED Talks, and the Colbert Report, his mathematical prowess has been praised.
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What are the formulas to calculate weight and mass?.
Answer:
[tex]w=mg[/tex] and [tex]m=\frac{w}{g}[/tex]
Explanation:
its formulas how can someone explain such simple stuff...
the service disconnecting switch for an installation consisting of a limited load on a single branch circuit shall have a rating of not less than ? .
The service disconnecting switch for an installation consisting of a limited load on a single branch circuit shall have a rating of not less than 15A.
The service disconnecting switch for an installation consisting of a limited load on a single branch circuit shall have a rating of not less than the ampacity of the branch circuit. The ampacity is the maximum amount of electrical current a conductor or circuit can safely carry without overheating. This rating ensures that the service disconnecting switch can handle the electrical load of the branch circuit without overheating or becoming damaged.
The National Electric Code (NEC) and local codes specify the ampacity of the conductors and the service disconnecting switch to be used for different types of electrical loads, such as residential, commercial or industrial. The ampacity of the conductors and the service disconnecting switch should be selected based on the anticipated load and the conditions of use, including the ambient temperature, the number of conductors in a raceway and the type of insulation.
It's worth noting that if the load is a non-continuous load the switch should be rated for the non-continuous load and if the load is a continuous load the switch should be rated for the continuous load. In both cases the switch should be able to handle the maximum load.
It's important to follow the NEC and local codes when selecting the ampacity of the service disconnecting switch to ensure that the electrical installation is safe and reliable.
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What is the volume flow rate of blood that moves at 0.20 m/s through an artery with a diameter of 1.0 × 10–2 m?
Volume flow rate is the product of blood speed artery with a diameter and cross-sectional area: (0.20m/s)(pi/4) (1x10^-2m)^2 = 5 (pi) x 10^-6 m^3/s.
Meaning of diametera straight line passing through the center of a spherical form or item and ending at one of its edges: Radius is divided by two to get the diameter. A six-foot radius surrounds the pond.
Circumference and diameter are what?The distance a circle travels in one full "lap" is called its circumference, and the distance a circle travels in one half is called its diameter. Consider the diameter as the inside of the circle, and the circumference as the exterior measurement.
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helpppp plss
Object A has a momentum of +20 kg m/s, and object B has a momentum of -6 kg m/s. The two objects collide. After the collision, object A has a momentum of -4 kg m/s. What is the momentum of object B after the collision?
The final momentum of the object B is obtained as 18 Kg m/s.
What is the momentum?We have to note that the momentum of the object would be the product of the mass and the velocity of of the object. The direction of the momentum is the direction of the velocity of the object.
Then we have that;
Momentum after collision = Momentum before collision and this would imply that;
20 + (-6) = (-4) + X
X = momentum of object B
X = 14 + 4
X = 18 Kg m/s
Hence, we have used the principle of the conservation of the linear momentum here.
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