The gauge pressure that a pump must produce to pump the water from the bottom of Grand Canyon to Indian Gardens is about 627080 pascals and 6.17 atm.
What is the gauge pressure?The difference in elevation of the two points = 1370 - 730 = 640m
Density of water, `ρ` = 1000 kg/m³
g = 9.8 m/s²
The gauge pressure must a pump produce to pump water from the bottom of Grand Canyon (elevation 730 m) to Indian Gardens (elevation 1370 m).
Formula used: `P = ρgh`
where, `P` is pressure, `ρ` is density of water, `g` is acceleration due to gravity, `h` is height difference between the two points.
The gauge pressure that must a pump produce to pump water from the bottom of Grand Canyon to Indian Gardens is 627080 Pa and 6.17 atm.
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This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Pin A, which is attached to link AB, is constrained to move in the circular slot CD. At t=0, the pin starts from rest and moves so that its speed increases at a constant rate of 1.2 in/s2 D 3.5 in. А B Determine the magnitude of its total acceleration when t= 0. The magnitude of its total acceleration is in/s2
The magnitude of the total acceleration of the pin when t=0 is 1.2 in/s^2.
To explain further, the acceleration of the pin is the sum of two components: tangential acceleration and centripetal acceleration. The tangential acceleration is responsible for increasing the speed of the pin, and its magnitude is constant at 1.2 in/s^2.
The centripetal acceleration is due to the circular motion of the pin in the slot CD and is directed towards the center of the circle.
To find the magnitude of the total acceleration at t=0, we need to first find the magnitude of the tangential acceleration and the centripetal acceleration separately. We know that the tangential acceleration is 1.2 in/s^2, and we can use the formula for centripetal acceleration, a_c = v^2/r, where v is the velocity of the pin and r is the radius of the circle. At t=0, the velocity of the pin is zero, and the radius of the circle is 3.5 inches.
Therefore, the centripetal acceleration is also zero.
Since the centripetal acceleration is zero, the magnitude of the total acceleration is equal to the magnitude of the tangential acceleration, which is 1.2 in/s^2.
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what is the weight of a 225-kg space probe on the moon? the acceleration of gravity on the moon is 1.62 m/s2.
Answer:
The weight of the 225-kg space probe on the moon is 364.5 N (newtons).
Explanation:
To calculate the weight of the space probe on the moon, we can use the formula:
weight = mass x acceleration due to gravity
where mass is given as 225 kg and acceleration due to gravity on the moon is 1.62 m/s^2.
weight = 225 kg x 1.62 m/s^2
weight = 364.5 N
Therefore, the weight of the 225-kg space probe on the moon is 364.5 N (newtons).
Assume that a drop of mercury is an isolated sphere. What is the capacitance in picofarads of a drop that results when two drops each of radius R = 5.61 mm merge?
The formula C=4R, where is the permittivity of open space, may be used to determine the capacitance of a merged mercury drop, assuming it is an isolated sphere. The capacitance is around 1.68 pF with R = 5.61 mm.
The formula C=4R, where R is the drop's radius and is the permittivity of free space, may be used to determine the capacitance of a merged mercury drop. As the capacitance of an isolated sphere is exactly proportional to its radius, the capacitance produced by the merger of two drops with similar radii is equal to the total of the capacitances of the individual drops. Given that the radius of the combined drop in this instance is R = 5.61 mm, the capacitance can be estimated using the formula C = 4(8.85 x 10-12 F/m) (5.61 x 10-3 m)2, yielding a capacitance of around 1.68 pF.
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in addition to hundreds of smaller objects they have been discovering in the kuiper belt recently, astronomers were surprised to find
In addition to hundreds of smaller objects they have been discovering in the Kuiper Belt recently, astronomers were surprised to find dwarf planet Eris.
The first object that was bigger than Pluto was Eris. The initial estimate of Eris' size was 1,240 miles (2,000 kilometers) in diameter. It was later discovered to be a bit smaller, with a diameter of 1,163 miles (1,864 kilometers). Its moon, Dysnomia, was also discovered.Eris' orbit is far more eccentric than Pluto's, ranging from 38 to 97 astronomical units (AU) from the Sun.
Eris takes 557 Earth years to orbit the Sun. Despite the fact that Pluto's path also varies in shape, it is always closer to the Sun than Eris. Pluto and Eris were both discovered in the early 21st century, in 1930 and 2005, respectively. Because it was the largest known body in the Kuiper Belt, Pluto was formerly classified as the Solar System's ninth planet. Following the discovery of Eris and other trans-Neptunian objects, Pluto was reclassified as a dwarf planet.
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A small grinding wheel has a moment of inertia of 4. 0×10−5 kg⋅m2
k
g
⋅
m
2. What net torque must be applied to the wheel for its angular acceleration to be 150 rad/s2
r
a
d
/
s
2
?
A net torque of [tex]6.0×10^−3 N⋅m[/tex] is sufficient to produce the desired angular acceleration of [tex]150 rad/s^2[/tex].
The net torque required to produce an angular acceleration in a rotating object can be calculated using the formula: net torque = moment of inertia × angular acceleration In this case, the moment of inertia of the grinding wheel is given as 4.0×10^−5 kg⋅m^2 and the angular acceleration required is 150 rad/s^2.
Therefore, the net torque required can be calculated as: net torque = [tex](4.0×10^−5 kg⋅m^2) × (150 rad/s^2) = 6.0×10^−3 N⋅m[/tex]To explain this result, we need to understand the relationship between torque and angular acceleration. Torque is the rotational equivalent of force and it is defined as the product of force and the perpendicular distance between the line of action of the force and the axis of rotation.
When a torque is applied to a rotating object, it produces an angular acceleration in the object, which is a measure of how quickly the object's rotational speed changes.
The moment of inertia of an object is a measure of its resistance to changes in its rotational motion. It depends on the object's mass distribution and the distance of each element of mass from the axis of rotation. Objects with larger moments of inertia require more torque to produce a given angular acceleration than objects with smaller moments of inertia.
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Three identical conducting spheres are charged as follows. Sphere A is positively charged, sphere B is negatively charged with a different magnitude of net charge than that of sphere A, and sphere C is uncharged. Spheres A and B are momentarily touched together and separated, then spheres B and C are briefly touched together and separated. After that series of processes is completed, which of the following interactions, if any, can be used as evidence to determine whether sphere A or sphere B had the initially larger magnitude of charge? A Sphere C is repelled from sphere A. B Sphere C is repelled from sphere B. Sphere A is repelled from sphere B. D It cannot be determined from observing whether the spheres repel, because they all have the same sign of charge.
The answer is C. Sphere A is repelled from sphere B
Step by step explanation:
The question is asking which of the interactions between sphere A, B, and C can be used as evidence to determine which one had the initially larger magnitude of charge. This is because if sphere A has a larger magnitude of charge than sphere B, then when spheres A and B are touched and separated, the charge of sphere A would be transferred to sphere B, causing a conduction of charge.
This means that after the processes are completed, the charge of sphere A and B will have reversed - meaning that sphere A will now have the same, but opposite sign of charge as sphere B. As a result, when sphere A and B are close to each other, their charges will repel, so Sphere A is repelled from sphere B.
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What two planets are coming together?
The two planets that are coming together are Saturn and Jupiter. On December 21st, 2020, the two planets will be at their closest point, an event known as the Great Conjunction.
To observe the Great Conjunction, look in the direction of the southwest sky shortly after sunset. The two planets will appear to be close together and will look like one bright star. Make sure to look for them with binoculars or a telescope if you can, as you'll get a better view.The Great Conjunction occurs because Saturn and Jupiter have different orbital periods. Jupiter completes its orbit around the Sun every 11.86 Earth years, while Saturn takes 29.5 Earth years. This means that their orbits don't intersect and they don't come this close together very often. The next time the two planets will come this close together will be in 2080, so be sure to take advantage of this rare opportunity to witness this event in 2020.For more questions on Great Conjunction
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a particle's velocity is described by the function vx=kt2 , where vx is in m/s , t is in s , and k is a constant. the particle's position at t0=0s is x0 = -5.40 m . at t1 = 2.00 s , the particle is at x1 = 5.80 m .
A particle's velocity is described by the function vx=kt2 , where vx is in m/s , t is in s , and k is a constant. The particle's position at t0=0s is x0 = -5.40 m. At t1 = 2.00 s , the particle is at x1 = 5.80 m. The value of k is 2.80 m/s2.
The given equation describes the velocity of a particle in terms of a constant, k, and time, t. The velocity, vx, is given in m/s. The initial position of the particle at t0=0s is x0=-5.40 m, and at t1=2.00 s the particle is at x1=5.80 m. To find the value of the constant k, we can solve the equation for the change in velocity Δvx.
Δvx = vx1 – vx0 = k(t12 – t02)
Δvx = 5.80 – (-5.40) = 11.20 m/s
k = (11.20 m/s) / (2.002 s2) = 2.80 m/s2
Now that we have found the value of the constant k, we can use it to find the velocity of the particle at any time t. For example, at t2=4.00 s the velocity of the particle is vx2=11.20 m/s. This can be calculated using the equation vx2 = k(t22) = 2.80(4.002) = 11.20 m/s.
From the velocity equation, we can also calculate the position of the particle at any time t. The position of the particle at t2=4.00 s is x2= 11.20(4.00) = 44.80 m. We can also calculate the position of the particle at any other time t, by simply substituting in the corresponding value of t into the equation.
In conclusion, the equation vx = kt2 describes the velocity of a particle in terms of a constant, k, and time, t. Using this equation, we can calculate the velocity and position of the particle at any given time.
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Complete Question:
A particle’s velocity is described by the function vx = [tex]kt^2m/s[/tex], where k is a constant and t is in s. The particle’s position at [tex]t_0[/tex] = 0s is [tex]x_0[/tex] = -5.40 m. At [tex]t_1[/tex] = 2.00 s, the particle is at [tex]x_1[/tex] = 5.80 m. Determine the value of the constant k. Be sure to include the proper units
you live on an island in the pacific. an earthquake of magnitude 8.5 off the coast of japan, 8000 km away, generates a tsunami with a wavelength of 200 km. the average water depth between your island and japan is 4900 m. if a tsunami warning is issued for your island, how many hours will you have before the waves arrive?
If a tsunami warning is issued for the island, they will have approximately 11.7 hours before the waves arrive.
What is Magnitude?
Magnitude is a measure of the strength or intensity of a physical quantity or phenomenon, such as an earthquake or a sound wave. It is often expressed using a numerical scale, with higher values indicating greater strength or intensity. In the case of earthquakes, magnitude is typically measured using the Richter scale or the moment magnitude scale, which take into account the amplitude of seismic waves and the energy released by the earthquake.
To calculate the time it takes for a tsunami to travel from Japan to the island, we can use the following formula:
t = (2 * pi * d) / g * ln(1 + sqrt(h/d))
where t is the time it takes for the tsunami to travel, d is the average water depth, h is the wave height, and g is the acceleration due to gravity (9.8 m/s^2).
Magnitude of the earthquake: 8.5
Wavelength of the tsunami: 200 km = 200,000 m
Average water depth: 4,900 m
To calculate the wave height, we can use the following formula:
h = (M / 5) * (D / 10)^1/2
where M is the magnitude of the earthquake and D is the distance between the earthquake epicenter and the observation point (in this case, the island). Note that this formula is an approximation and may not be accurate for all cases.
Using the given values, we get:
D = 8,000 km = 8,000,000 m
h = (8.5 / 5) * ((8,000,000 / 10)^1/2) = 2,738.6 m
Substituting these values into the formula for t, we get:
t = (2 * pi * 4,900) / 9.8 * ln(1 + sqrt(2,738.6/4,900)) = 11.7 hours
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an arrow leaves a bow with a speed of 42 m/s. its velocity is reduced to 34 m/s by the time it hits its target. how much distance did the arrow travel over if it were in the air for 2.4 seconds?
The distance did the arrow travel over if it were in the air for 2.4 seconds is 100.8 meters.
What is the distance?An arrow leaves a bow with a speed of 42 m/s. Its velocity is reduced to 34 m/s by the time it hits its target. And the arrow traveled in the air for 2.4 seconds.
To find the distance traveled by the arrow, we can use the following formula:
S = v₀t + 1/2at²
where, S = distance traveled v₀ = initial velocity = 42 m/s, t = time taken = 2.4 s, a = acceleration = ? u = final velocity = 34 m/s.
As per the question, the arrow is traveling through the air, so the acceleration is due to gravity, which is equal to 9.8 m/s².So, a = 9.8 m/s². Now, we can substitute the given values in the above formula:
S = 42 m/s × 2.4 s + 1/2 × 9.8 m/s² × (2.4 s)²
S = 100.8 m.
The arrow traveled approximately 100.8 meters in the air.
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two blocks with masses 4m and 7m are on a collision course with the same initial speeds vi. the block with mass 4m is traveling to the left, and the 7m block is traveling to the right. they undergo a head-on elastic collision and each bounces back, retracing its original path. find the final speeds of the particles. (enter your answers in terms of
The final speeds of the particles expressed in terms of the initial velocity are |v1'| = |v1| = 27/8|vi| and |v2'| = |v2| = 27/14|vi|
The conservation of momentum can be applied. The total momentum of the system before the collision is:
P before = m1v1 + m2v2
where m1 and v1 are the mass and velocity of the 4m block and m2 and v2 are the mass and velocity of the 7m block. Since the two blocks have the same initial speed, the momentum before the collision is:
P before = (4m)(-vi) + (7m)(vi)
P before = 3mvi
After the collision, the two blocks bounce back, so their final velocities are:
v1' = -v1
v2' = -v2
where v1 and v2 are the velocities of the blocks after the collision. Using the conservation of momentum again, the total momentum of the system after the collision is:
Pafter = m1v1' + m2v2'
Pafter = -4mv1 - 7mv2
Pafter = -4m(-v1) - 7m(-v2)
Pafter = 4mv1 + 7mv2
Since the collision is elastic, the total kinetic energy of the system is conserved. Therefore, the kinetic energy before the collision is equal to the kinetic energy after the collision:
Kbefore = Kafter
where Kbefore is the kinetic energy of the system before the collision and Kafter is the kinetic energy of the system after the collision. The kinetic energy can be expressed as:
K = 1/2mv²
Therefore, the total kinetic energy of the system before the collision is:
Kbefore = 1/2(4m)(vi)² + 1/2(7m)(vi)²
Kbefore = 27/2m(vi)²
The total kinetic energy of the system after the collision is:
Kafter = 1/2(4m)(-v1)² + 1/2(7m)(-v2)²
Kafter = 1/2(4m)(v1)² + 1/2(7m)(v2)²
Using the conservation of kinetic energy, Kbefore = Kafter:
27/2m(vi)² = 1/2(4m)(v1)² + 1/2(7m)(v2)²
Simplifying, the final velocities can be expressed in terms of the initial velocity:
v1 = 27/8vi
v2 = 27/14vi
Therefore, the final speeds of the particles are: |v1'| = |v1| = 27/8|vi| and |v2'| = |v2| = 27/14|vi|
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Taking the following list on an item-by-item basis (i.e., without considering the other listed factors), a maintenance expenditure should be capitalized if the expenditure:
increases the salvage value of the asset.
extends the useful life of the asset.
A maintenance expenditure should be capitalized if it increases the salvage value of the asset or extends the useful life of the asset.
An expenditure is a payment made in return for a product or service. Capital expenditure is money spent by a company on long-term assets like equipment and buildings.
Capitalizing refers to recording a cost or expense on the balance sheet for a future period rather than recognizing it immediately in the current period.
Capitalizing expenditure means the company will recognize the expenditure as an asset, which will be amortized over its useful life as opposed to expenses in the current period.
Therefore, a maintenance expenditure should be capitalized if the expenditure increases the extends the useful life of the asset.
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Devon is running an experiment in which children are observed interacting with simple toys, and their behavior is coded based on different categories. Devon has two experimenters observing and coding the behavior. Devon computes a correlation coefficient to see if the two experimenters produce similar scores. Which of the following describes how Devon is attempting to verify his observational method?
In outer space will a liquid in a beaker exert a pressure on the bottom or on the sides of a beaker?
Answer:
Yo dude, if you had a beaker of liquid in outer space, it wouldn't push down on the bottom or the sides of the beaker like it would on Earth. In space, there's no gravity to make the liquid settle down, so it forms a round shape because of surface tension. So basically, the liquid would just float around in a ball inside the beaker. If you moved the beaker around, the liquid would just roll around with it like a bouncy ball.
consider two planets in space that gravitationally attract each other. if the masses of both planets are doubled, and the distance between them is also doubled, then the force between them is group of answer choices four times as much. half as much. twice as much. remains the same. one quarter.
If the masses of two planets in space that gravitationally attract each other are doubled and the distance between them is also doubled, then the force between them remains the same.
To determine the force between two planets, we use the formula:
F = Gm1m2/r^2
where F is the force of gravitational attraction between the two planets, G is the gravitational constant, m1 and m2 are the masses of the planets, and r is the distance between them.
If both masses are doubled and the distance between them is also doubled, the new force between them can be calculated as follows:
F' = G(2m1)(2m2)/(2r)^2
Simplifying this expression, we get:
F' = Gm1m2/r^2
which is the same as the original force between the planets.
Therefore, if the masses of two planets are doubled and the distance between them is also doubled, the force between them remains the same.
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A marble rolled down an inclined ramp with an acceleration of 0.500 m/s for 7.00 seconds will travel meters from the point where it was released, A. 12.3 B. 24.5 C. 1.80 D. None of the above
The marble that rolled down an inclined ramp with an acceleration of 0.500 m/s for 7.00 seconds will travel 12.3 meters from the point where it was released. Thus, the correct option is A.
What is the distance covered by marble?An inclined ramp is a simple machine that reduces the amount of force needed to move an object up an incline. The force that makes the marble move is gravity. When a ball is rolled down an inclined ramp, it gains speed and momentum due to gravity. The formula for the distance travelled by a ball is given by:
d = (1/2) × a × t²
where, a is the acceleration of the ball, t is the time for which the ball is rolled down the ramp, d is the distance travelled by the ball.
Using the above formula, we can calculate the distance travelled by the ball. So, substituting the given values in the formula:
d = (1/2) × 0.500 m/s² × (7.00 s)²
d = (1/2) × 0.500 m/s² × 49.00 s²
d = 12.3 meters
Therefore, the correct option is A.
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Galena's specific gravity is 7.5, that of quartz 2.65, and that of liquid mercury 13.6. Given equal-sized samples (volumes) of galena and quartz, which will feel heavier? Choose one: A. galena B. The same volume of water will feel heavier than both of them. C. They will feel about equal. D. quartz
Given equal-sized samples (volumes) of galena and quartz, the Galena sample will feel heavier because of its higher specific gravity. Thus, the correct option is A.
What is the Specific gravity of a substance?Specific gravity is the ratio of the density of a substance to the density of a standard substance in physics. It's typically applied to liquids and solids, but it may also be applied to gases. The most often utilized standard material for liquids and solids is water at 4°C. A substance's specific gravity is dimensionless and is often represented by the Greek symbol ρ.
Relative Density of the given substances:
Galena's specific gravity is 7.5, Quartz's specific gravity is 2.65, and Liquid mercury's specific gravity is 13.6. An object with a specific gravity greater than 1 sinks in water, while one with a specific gravity less than 1 floats in water. The specific gravity of water is 1.0. An object with a specific gravity greater than 1 sinks in water, while one with a specific gravity less than 1 floats in water.
We can conclude from the values above that liquid mercury is heavier than galena, which is in turn heavier than quartz. Therefore, since both quartz and galena are being measured with equal sizes or volumes, galena will feel heavier than quartz.
Therefore, the correct option is A.
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Imagine sitting on a merry-go-round and riding along as it spins. Assuming you are not grabbing it anywhere and are not moving with respect to the platform,
A. static friction (directed inwards) causes you to accelerate.
B. you are not accelerating because you aren't moving on the platform.
C. static friction (directed outwards) causes you to accelerate.
D. sliding friction makes you accelerate inwards.
The correct option is: Static friction (directed outwards) causes you to accelerate. (Option C)
When you sit on a merry-go-round, you are not moving relative to the platform. Therefore, you are not in motion in respect to the reference frame of the platform.
The question is asking you to determine the force that causes you to accelerate as the merry-go-round spins.
Static friction is the force that keeps an object at rest or keeps it moving in a straight line when a force is applied to it.
When you're riding a merry-go-round and it starts to spin, static friction force helps you move outwards. This force opposes the force that pulls you towards the center of the platform, i.e., centripetal force.
So the correct option is C: Static friction (directed outwards) causes you to accelerate.
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the maximum energy of photoelectrons from aluminium is 2.3 ev for radiation of 2000 a and 0.90 ev for radiation of 3130 a. use this data to calculate plancks constant and the work function of aluminium
The maximum energy of photoelectrons from aluminium is 2.3 eV for radiation of 2000 Å and 0.90 eV for radiation of 3130 Å.
To calculate Planck's constant and the work function of aluminium, we need to use the equation:
h = E2 - E1/ λ2 - λ1
Where h is Planck's constant, E1 and E2 are the maximum energy of photoelectrons for each wavelength, and λ1 and λ2 are the wavelengths.
Using the given data, we have:
h = (2.3 - 0.90) / (2000 - 3130)
Therefore, h = -1.4 eV / -930 Å, which simplifies to h = 0.0015 eVÅ.
The work function of aluminium is equal to the maximum energy of the photoelectrons for the longest wavelength, in this case, 0.90 eV. Therefore, the work function of aluminium is 0.90 eV.
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spherical capacitor contains a charge of 3.20nCwhen connected to a potential difference of250V. If its plates are separated by vacuum and theinner radius of the outer shell is 4.60cm.
A) Calculate the capacitance.
B) Calculate the radius of the inner sphere.
C) Calculate the electric field just outside the surface of theinner sphere.
A) The capacitance of the spherical capacitor is 1.45 pF (picofarads), B) The radius of the inner sphere is 3.60 cm. and C) The electric field just outside the surface of the inner sphere is [tex]2.36 * 10^6 V/m[/tex] (volts per meter).
To calculate the capacitance, we can use the formula C = Q/V, where Q is the charge and V is the potential difference. Plugging in the values, we get [tex]C = (3.20 * 10^{-9} C)/(250 V) = 1.28 * 10^{-11} F[/tex].
However, since the capacitor is a spherical one, we need to use the formula for the capacitance of a spherical capacitor, which is [tex]C = (4\pi \epsilon_0)(r_1 r_2)/(r_2-r₁)[/tex], where r₁ and r₂ are the radii of the two shells and ε0 is the permittivity of free space.
Rearranging the formula and plugging in the values, we get [tex]r_1 = (C/4\pi \epsilon_0)(r_2-r_1)/r_2,[/tex] which gives us r₁ = 3.60 cm.
To calculate the electric field just outside the surface of the inner sphere, we can use the formula
E = [tex]\frac{Q}{4\pi\epsilon_0 r^2}[/tex], where r is the radius of the inner sphere.
Plugging in the values, we get [tex]E = (3.20 * 10^{-9} C)/(4\pi\epsilon_0(0.0460 m)^2) = 2.36 * 10^6 V/m.[/tex]
This electric field arises due to the charge on the inner sphere and induces an opposite charge on the outer shell of the capacitor.
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Problem 1. In this problem, you need to determine the additive inverse1of each given vector in the appropriate vector space. (a)[ 23]inR 2. (b)−1+3x−8x 2inP 2. (c)[ 12−20]inM 2×2.
The additive inverse of each given vector in the appropriate vector space are
(a) The additive inverse of [2, 3] in [tex]R_2[/tex] is [-2, -3].
(b) The additive inverse of [tex]-1 + 3x - 8x^2[/tex] in P2 is [tex]1 - 3x + 8x^2[/tex].
(c) The additive inverse of [1, 2; - 2, 0] in [tex]M_{2\times2[/tex] is [-1, -2; 2, 0].
The additive inverse of a vector [tex]\mathbf{v}[/tex] in a vector space is the vector [tex]-\mathbf{v}[/tex] that, when added to [tex]\mathbf{v}[/tex], gives the zero vector.
(a) The additive inverse of the vector [tex][2, 3] \in \mathbb{R}^2[/tex] is [tex][-2, -3][/tex] since [tex][2, 3] + [-2, -3] = [0, 0][/tex].
(b) The vector space [tex]P_2[/tex] consists of all polynomials of degree at most [tex]2[/tex]. The vector [tex]-1 + 3x - 8x^2 \in P_2[/tex] has additive inverse [tex]1 - 3x + 8x^2[/tex], since [tex](-1 + 3x - 8x^2) + (1 - 3x + 8x^2) = 0[/tex].
(c) The vector space [tex]M_{2 \times 2}[/tex] consists of all [tex]2 \times 2[/tex] matrices. The matrix [tex][1, 2; -2, 0] \in M_{2 \times 2}[/tex] has additive inverse [tex]$[-1, -2; 2, 0]$[/tex], since [tex]\begin{bmatrix} 1 & 2 \ -2 & 0 \end{bmatrix} + \begin{bmatrix} -1 & -2 \ 2 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}[/tex].
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You are the process engineer at Corvallis Automobiles Inc., and you have received an order to turn a cylindrical bar on an engine lathe to the dimensions specified in Fig. 1. For this order you will use cylindrical bar stock that is 48-inches long and 4-inches in diameter. The 48-inch length bar will be chucked in the lathe and supported at the opposite end using a live center. You are planning to complete the operation in one pass using a cutting speed of 400 ft./min. and a feed of 0.010 in./rev. Determine the following: a) The required depth of cut (in inches) b) The material removal rate (in cubic inches per minute)
c) The time required to complete the cutting pass (in minutes)
a. the depth of cut is 0.625 inches.
b. the material removal rate is 0.003125 cubic inches per minute.
c. the time required to complete the cutting pass is 20 minutes.
How do we calculate?a) The required depth of cut can be determined by :
DOC = (4 in - 2.75 in)/2 = 0.625 in
Therefore, the depth of cut is 0.625 inches.
b) The material removal rate can be found by applying:
MRR = DOC x Width of cut x Feed rate
assuming we are using a standard carbide insert tool with a width of cut of 0.5 inches.
MRR = 0.625 in x 0.5 in x 0.010 in/rev = 0.003125 cubic inches per minute
c) The time required to complete the cutting pass is determined by:
Time = Length of cut / (Cutting speed x Width of cut x Feed rate)
Time = 48 in / (400 ft/min x (0.5 in) x (0.010 in/rev) x (1/12 ft/in)) = 20 minutes
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why do nuclear reactors have three separate water loops instead of just a single one that runs from the water source, through the reactor, then back to the cooling tower?
Nuclear reactors have three separate water loops instead of just a single one that runs from the water source, through the reactor, then back to the cooling tower because the water running through the reactor is highly radioactive.
What are nuclear reactors?A nuclear reactor is a device that controls and maintains a sustained nuclear chain reaction for the purpose of generating heat or power, as well as the materials that make up a nuclear reactor.
The water running through the reactor is highly radioactive, which means that it cannot be released into the atmosphere or allowed to come into touch with humans or the environment. As a result, nuclear reactors are designed with three separate water loops.
The first loop circulates ordinary water that passes through the reactor and generates heat. The second loop, which is a separate circuit, brings this water to a steam turbine. The third loop, which is also a closed circuit, recovers the cooling water after it has passed through the turbine and transports it back to the reactor's inlet.In summary, nuclear reactors have three separate water loops instead of a single one that runs from the water source, through the reactor, and back to the cooling tower because the water running through the reactor is highly radioactive.
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A car has an intial velocity of 50 km hr after 5 h, its final velocity is 70 km hr. solve for the car acceleration
Answer:
4 km/hr^2
Explanation:
We can use the formula for acceleration:
a = (v_f - v_i) / t
where:
a = acceleration
v_f = final velocity
v_i = initial velocity
t = time taken
Substituting the given values, we get:
a = (70 km/hr - 50 km/hr) / 5 hr
a = 20 km/hr / 5 hr
a = 4 km/hr^2
The colors on an oil slick are caused by reflection and (explain why)
a. Diffraction
b. Interference
c. Refraction
d. Polarization
e. Ionization
"The colours on an oil slick are caused by reflection and interference." Correct option is B.
Different bands of the oil slick create different colours as the oil film progressively thins from the centre to the edges.
Interference is what gives an oil slick drifting on water or a soap bubble in the sun their vibrant colours. The colours that interact most positively are the ones that are most vibrant. Thin film interference is the name given to the phenomenon because it occurs when light reflected from various thin film surfaces interferes with one another.
The most crucial interfering principle is the superposition principle.
This hair colour procedure primarily uses jewel tones and rainbow colours, including burgundy, royal blue, deep purple, green, and deep red. Alternating the colours that give your hair an oil spill appearance is the best method to make your skin tone and hair look good together. Best choice is B.
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three forces applied to a trunk that moves leftward by 3.010 m over a frictionless floor. The force magnitudes are F1 = 5.86 N, F2 = 9.180 N, and F3 = 3.850 N, and the indicated angle is θ = 67.8°. During the displacement, what is the net work done on the trunk by the three forces? (Note that there are other forces acting on the block, but we only care about the net work done by these three forces.) And by how much does the kinetic energy of the trunk increase (enter a positive value) or decrease (negative value)?
The kinetic energy of the trunk increases by ½ mvf² = ½ m(10.65 m/s)²= 71.44 J during the displacement.
Net work = ΔK
W = Fd cosθ
W1 = F1d cosθ = (5.86 N)(3.010 m) cos(67.8°) = 6.99 J
W2 = F2d cosθ = (9.180 N)(3.010 m) cos(67.8°) = 10.97 J
W3 = F3d cosθ = (3.850 N)(3.010 m) cos(67.8°) = 4.58 J
Net work = W1 + W2 + W3 = 6.99 J + 10.97 J + 4.58 J = 22.54 J
Therefore, the net work done on the trunk by the three forces is 22.54 J.
ΔK = ½ mvf² - ½ mvi²
Since the trunk moves a distance of 3.010 m and is initially at rest, we can use the equation:
vf² = 2ad
where a is the acceleration of the trunk, which is given by:
a = ΣF / m
where ΣF is the net force on the trunk, which we can find using:
ΣF = F1 + F2 + F3
ΣF = (5.86 N + 9.180 N + 3.850 N) = 18.89 N
Therefore, the acceleration of the trunk is:
a = ΣF / m = 18.89 N / m
Since the trunk moves leftward, the acceleration is also leftward, so we can use a negative value for a.
Substituting the values for a and d, we get:
vf² = -2(-18.89 N / m)(3.010 m) = 113.51 (m/s)²
Taking the square root, we get:
vf = 10.65 m/s
Therefore, the change in kinetic energy of the trunk is:
ΔK = ½ mvf² - ½ mvi² = ½ m(10.65 m/s)²- 0 = ½ mvf²
Kinetic energy is a type of energy that an object possesses by virtue of its motion. It is defined as the energy an object has due to its motion and is proportional to the mass of the object and the square of its velocity. The formula for kinetic energy is KE = 1/2mv^2, where m is the mass of the object and v is its velocity.
Kinetic energy is a scalar quantity and has units of joules in the International System of Units (SI). It is a fundamental concept in physics and is used to describe many physical phenomena, including the motion of particles, the behavior of gases, and the motion of waves. In many cases, kinetic energy can be transformed into other forms of energy. For example, when a ball is thrown upwards, its kinetic energy is gradually converted into gravitational potential energy as it moves higher and higher.
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When two metal spheres are connected by a metal wire?
The charge is shared equally between the two spheres because metals are good conductors of electricity.
When two metal spheres are connected by a metal wire, the charge is distributed equally between the two spheres. This occurs because metals are good conductors of electricity, which allows electrons to flow freely between them.
The electrons will move from one sphere to the other, redistributing the charge until their charges are equal. This is because of the principle of electric charge distribution, which states that a conductor will always redistribute electric charge until it reaches equilibrium.
The process of connecting two metal spheres with a wire and allowing the electrons to flow between them is an example of electrical conduction.
This is a fundamental process in electrical circuits and is the basis for many important technologies, including electronics, power generation, and transmission.
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a researcher is studying the distribution of auxin in roots and stems exposed to sunlight. he notices that more auxin collects in the sides of stems and roots that are not exposed to light. why?
The researcher's observation that more auxin collects in the sides of stems and roots that are not exposed to light is likely due to the phenomenon of phototropism.
In the process of phototropism, light influences the direction and rate of growth of plant cells. In particular, light induces the cells on one side of a stem or root to create less auxin than the cells on the shaded side. Less auxin is produced on the lighted side and more auxin is produced on the shaded side as a result. The hormone auxin is essential for controlling the growth and development of plants. Auxin generally promotes cell growth and elongation at greater concentrations while inhibiting cell elongation at lower concentrations. Since the cells on the lighted side of the stem or root will contain less auxin when there is light.
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When current flows through a conductor, it develops a magnetic field of concentric circles expanding ? and outward from the conductor. a. circularly b. parallel c. perpendicular d. wavy
When a current travels through a conductor in a circular motion, a magnetic field with growing concentric circles is created.
What happens when current flows through a conductor?Electromagnetism is established when an electrical current flows through a simple conductor, such as a length of wire or cable.
What magnetic field is created when current travels through a conductor?As magnetic fields produced by moving charges are proportional to the current, a conductor carrying current creates a magnetic field around it. Generally speaking, the sub-atomic particles in the conductor, such as the moving electrons in the atomic orbitals, are responsible for this magnetic field.
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When a ball bounces against a wall there will be large change in velocity in short period of time. This means the ____ is large, hence the net ___ must be proportionately large as well.
A change in velocity in short period of time means the acceleration is large, hence the net force must be proportionately large as well.
What is a force?A force is a physical quantity that induces a body to undergo an alteration in speed, direction of motion, or shape. A force can be classified as a push or a pull. When forces are equal, the forces are balanced and the object is not moving. Otherwise, if the forces are not equal, making it unbalanced will not give the object any movement.
The force that induces the change in the speed or direction of an object is referred to as a net force. The net force is equal to the product of the mass of the object and its acceleration. Newton (N) is the unit of measurement for force.
When a ball bounces against a wall, there will be a large change in velocity in a short period of time. This means the acceleration is large, hence the net force must be proportionately large as well.
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