Tension must the string be placed is 86.75 N.
What is Tension?
In physics, tension is defined as the pulling force that is transmitted axially by a string, rope, chain, or similar object, or by each end of a rod, truss member, or other comparable three-dimensional object. Tension can also be defined as the action-reaction pair of forces acting at each end of the aforementioned elements.
f = 440 Hz
l = 32 cm = 0.32 m
m = 0.35 g = 0.35 x 10^-3 kg
μ = m / l = 0.35 x 10^-3 / 0.32 = 1.094 x 10^-3 kg/m
The formula for the fundamental frequency is given by
[tex]f=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}$$[/tex]
Where, T be the tension
[tex]$$\begin{aligned}& 440=\frac{1}{2 \times 0.32} \sqrt{\frac{T}{1.094 \times 10^{-3}}} \\& 281.6=\sqrt{\frac{T}{1.094 \times 10^{-3}}}\end{aligned}$$[/tex]
T = 86.75 N
Thus, the tension in the string is 86.75 N.
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one end of a string is attached to a ball, with the other end held by a student such that the ball is swung in a horizontal circular path of radius r at a constant tangential speed. at a later time, the tension force exerted on the ball remains constant, but the length of the string is decreased to r4. what is the new tangential speed of the ball?
According to the given statement Half the original speed is the new tangential speed of the ball.
Why is it called tangential speed?Any item moving along the circular path has a linear component to its speed called tangential velocity. An object's velocity is always pointed tangentially when it travels in a circle at a distance rr from the center. Tangential velocity is the name given to this.
Is tangential speed a constant quantity?Although the tangential velocity vector's direction changes as the item spins, the tangential speed remains constant. Note that along the circular motion's radius vector, the centripital speed is constantly moving inward. Two vectors combine to form circular motion as one of their components. The first is when anything moves forward (the tangential velocity).
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A gas is taken through the cyclic process described in the figure. (The x axis is marked in increments of 2.5 m3.;) P (kPa) V (m3) (a) Find the net energy transferred to the system by heat during one complete cycle. (b) If the cycle is reversed-that is, the process follows the path ACBA-what is the net energy input per cycle by heat?
The correct solutions are -
(a) The net energy transferred to the system by heat during one complete cycle is 15 kJ
(b) The net energy input per cycle by heat is -15 kJ
The net energy transferred to the system is equal to work done. The work done will be calculated by the calculating the area enclosed in the figure.
The area = 1/2 × (8 - 2) × 5
Performing multiplication and division on Right Hand Side of the equation
Work done = 1/2 × 6 × 5
Work done = 3 × 5
Work done = 15 kJ
On reversing the cycle, the net energy input per cycle be heat will be -15kJ.
Hence, work done is 15 kj and net energy input is -15kJ.
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The complete question is attached in the figure.
hree uniform spheres fig. p13.45. (a) what are the mag- nitude and direction of the force on a 0.0150 kg particle placed at p? (b) if the spheres are in deep outer space and a 0.0150
a) the magnitude of the force on particle is 9.7 x 10⁻¹² N and direction is 45° counter clockwise.
b) if spheres are in outer space of 0.0150, then velocity will be 3 x 10⁻⁵ km/s
We know
Force = G (m₁m₂/d²)
(a) F(net) = F₁ + F₂ + F₃
G (mm(p)/d²) + G (mm(p)/d²) + 2G (mm(p)/2d²)
|F(net)| = G[ mm(p) / d² ](√2 + 1)
= [6.67 x 10⁻¹¹ x 1 x (0.015) / (0.5)² ] (√2 + 1) = 9.7 x 10⁻¹² N
The magnitude of the force is 9.7 x 10⁻¹² N.
Direction 45° counter clockwise
(b) Initial velocity U(p) = √2Gm(2+√2/d - 2/150)
= √2 x 6.67 x 10⁻¹¹(2 + √2 / 0.5 - 2/150)
= 3 x 10⁻⁵ m/s
Therefore, the velocity at which it moves is 3 x 10⁻⁵ km/s.
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Please hurry
Part A: A force of 8 N is exerted on a box with a mass of 2 kg. What is the acceleration of the
box?
Part B:If the box accelerates from rest to a velocity of 4 m/s, what is the impulse?
hope this helps solve your question
An old version of stellar evolution, popular at the beginning of the twentieth century, maintained that stars begin their lives as large, cool spheres of gas, like the giant stars on the H-R diagram. They then contract and heat up under the pull of their own gravity to become hot, bright blue O stars. For the remainder of their lives they lose energy, becoming dimmer and redder with age. As they slowly move down the main sequence, they eventually end up as cool, dim red M stars. Explain how observations of stellar clusters, plotted on the H-R diagram, contradict this idea.
Every star goes through distinct evolutionary stages that are determined by its internal structure and method of energy production depending on its initial mass. The temperature and luminosity of the star change with each of these stages, and as the star develops, it can be seen moving to various locations on the HR diagram.
One of the most crucial tools for studying stellar evolution is the HR diagram, also known as the Hertzsprung-Russell diagram (HR diagram). It was independently created by Ejnar Hertzsprung and Henry Norris Russell in the early 1900s and plots either the colour of stars (or spectral type) against their absolute magnitude or the temperature of stars against their luminosity.
The HR diagram is dominated by the main sequence, which extends from the upper left (hot, luminous stars) to the bottom right (cool, faint stars). In their cores, stars spend about 90% of their lives converting hydrogen to helium.
In the area above the main sequence, red giant and supergiant stars of luminosity classes I through III can be found. The Stefan-Boltzmann law states that because of their low surface temperatures and high luminosities, they also have large radii. Once a star's core has run out of hydrogen fuel and has begun to burn helium and other heavier elements, it enters this stage of evolution.
Low-mass stars reach their final evolutionary stage as white dwarf stars (luminosity class D).
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an astronomer has calculated the radius of a black hole to be 51.0 au by observing its period of variability in brightness. what period, in hours, did she observe?
The astronomer will take 0.086 hours to observe the radius of the black hole.
A black hole is a place in space where gravity pulls so hard that even light cannot escape.
The astronomer has calculated the radius of a black hole to be 51.0 au by observing its period of variability in brightness.
'au' is the abbreviation for astronomical unit which is a unit of length used to measure the distance from Earth to sun.
1 au = 93 million kilometers
Also the radius is calculated on the variability in brightness, i.e. speed of light can be considered
Speed of light = 3 * [tex]10^{8}[/tex] m/s
So according to the formula of speed, time can be calculated as
time = distance / speed
time = 93 * [tex]10^{9}[/tex] / 3 * [tex]10^{8}[/tex]
time = 310 seconds
1 second = 0.0002 hour
310 seconds = 0.086 hour
The astronomer observed for 0.086 hours.
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an automobile sounds its horn while passing an observer at 25.5 m/s. the actual horn frequency is 405 hz. assume the speed of sound is 345 m/s. find its frequency heard by the observer while the car is approaching.
The frequency heard by the observer while the car is approacing 437.3 Hz.
What is doppler effect?
A wave's frequency changes in response to an observer moving in respect to the wave source, which is known as the Doppler effect or Doppler shift. The change in pitch that happens as an automobile approaches and drives away from a spectator while sounding its horn is a common way to demonstrate doppler shift.
By using Doppler's Formula:
fo = v+vo/v+vs x fs
where,
fo = observer frequency of sound
v= speed of sound waves
vo= observer velocity
vs= source velocity
fs= actual frequency of sound waves
It is given that,
fs= 405Hz
vs= 25.5 m/s
v= 345 m/s
fo= 0 m/s
Observer to source = Positive
Source to observer = Negative
fo = v+vo/v+vs x fs
fo = 345/ 345 - 25.5× 405
fo = 437.3 Hz
Hence, The frequency heard by the observer is 437.3 Hz.
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The frequency heard by the observer while the car is approacing 437.3 Hz.
What is doppler effect?
A wave's frequency changes in response to an observer moving in respect to the wave source, which is known as the Doppler effect or Doppler shift. The change in pitch that happens as an automobile approaches and drives away from a spectator while sounding its horn is a common way to demonstrate doppler shift.
By using Doppler's Formula:
fo = v+vo/v+vs x fs
where,
fo = observer frequency of sound
v= speed of sound waves
vo= observer velocity
vs= source velocity
fs= actual frequency of sound waves
It is given that,
fs= 405Hz
vs= 25.5 m/s
v= 345 m/s
fo= 0 m/s
Observer to source = Positive
Source to observer = Negative
fo = v+vo/v+vs x fs
fo = 345/ 345 - 25.5× 405
fo = 437.3 Hz
Hence, The frequency heard by the observer is 437.3 Hz.
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Calculate the total mass of the protons and electrons in 19 9f. Use 1. 007825 amu as the mass of 11h (mass of a proton and an electron).
We can conclude that total mass of protons and electrons in is 9.07043 u.
What is Atomic mass ?
Atomic mass means the sum of total number of protons and neutrons present in an atom.
When an atom is neutral then number of protons equal the number of electrons.
Mass of a proton equals to 1.007276 u, mass of neutron equals to 1.008664 u.
For example, in a atom there are total 9 protons and number of neutrons is 19 - 9 = 10.
Since, it is a neutral atom so number of electrons will also be 9.
So, total mass will be calculated as follows.
Total mass = 9 (mass of electron + mass of proton)
= 9 (1.007825 u)
= 9.07043 u
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what do asteroids and comets have in common? question 7 options: most are unchanged since their formation in the solar nebula. they have similar orbital radii. they have nothing in common with each other. they have a similar range of orbital inclinations.
The majority of comets and asteroids have not changed much since they were formed in the nebula.
What components make up comets?
The principal components of comets, which resemble dirty snowballs, are ice and freezing carbon dioxide, as well as some sand and biological molecules that were left over from Planetary System's origin. They function as "time capsules," revealing to us the circumstances of our Known Universe 4,5 billion years ago.
Which comet made the largest impact on Earth?
The nucleus of this comet has a diameter of 119 kilometers, according to recent measurements made the with Hubble Space Telescope. making it by far the largest comet ever discovered. Only 5 kilometers broad, the asteroid collision that triggered the last extinction event on Earth about 65 million years ago.
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the amount of heat necessary to change 1 kg of a liquid into a gas at the same temperature is called the
Latent heat of vaporisation is required for liquidation of bag per 1 kilogram.
What is latent heat of vapourisation?The amount of thermal energy produced when a gas condenses into a liquid or the amount needed for a liquid to evaporate into a gas is known as the latent heat of vaporization.
The enthalpy of vaporization is another name for the latent heat of vaporization. Steam burns are extremely harmful because of the high latent heat of vaporization that water has.
The energy required to change the state of 1 kg of a substance without affecting its temperature is known as the specific latent heat of that substance.
We can tell that the substance is being measured per unit mass due to the distinction from latent heat. Additionally, specific latent heat is a dense feature of matter because it is measured per unit mass.
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if the distance between two charges is tripled, what will happen to the force between the charges? (3 points)
The force exerted between two electric charges is inversely proportional to their squared distance, according to Coulomb's Law. The force will therefore weaken by a factor of 9 if the distance is tripled.
How does Coulomb's law work?Describe Coulomb's Law. Coulomb's law states that the force of attraction or repulsion between positively colliding bodies is inversely proportional to the square of the length between them and directly proportional towards the product of their charges.
What three elements combine to form Coulomb's law?A non-contact attraction that works over a specified distance is called charged object interaction. Distance, charge, and distance. Every electrical connection requires force, which highlights how important these three elements are.
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lc circuit, part h 0 points possible (ungraded) what is the current in the circuit when the magnetic energy stored in the coil is exactly equal to the electric energy stored in the capacitor?
The magnetic field that is created around the inductor is where this energy is actually kept. Again, think about the circuit we created with two coils wound on base of one another.
, what is an energy?Energy is characterized as having the "ability to accomplish effort, which is the capacity to apply a force sufficient to move an object." Despite this unclear definition, the concept is actually quite straightforward: energy is merely the force that moves objects. Potential and kinetic energy are the two different categories.
What makes energy crucial?Because it is a fundamental human requirement, energy is crucial to our daily activities. Not only do we utilize energy to heat the buildings we have built, but we also use it to cool them. In order to get out of bed, walk down the street, or even lift your finge, you need energy.
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why can you assume that the Mechanical energy is equal to the Initial gravitational energy
The Mechanical energy is equal to the Initial gravitational energy as mechanical energy is stored in the object as gravitational potential energy.
What is law of conservation of energy?
Energy cannot be created or destroyed, according to the rule of conservation of energy. However, it is capable of change from one form to another.
An isolated system's total energy is constant regardless of the types of energy present. The law of energy conservation is adhered to by all energy forms. The law of conservation of energy essentially says that:
The total energy of the system is conserved in a closed system, also known as an isolated system.
Therefore, in a closed system like the universe, if energy is lost in one area, energy must be gained in a different area of the system by an equal amount. There is no known instance of the conservation of energy being broken, despite the fact that it cannot be proven.
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two cups are filled to the same level with water. one of the two cups has plastic balls floating in it. if the density of the plastic balls is less than that of ice, which of the two cups weighs more?
Two cups are filled to the same level with water. one of the two cups has plastic balls floating in it. if the density of the plastic balls is less than that of ice, the two cups will; tend to weighs the same.
What is density?The mass contained in a given volume determines a material's density. Due to their tight structure and stronger intermolecular force than that of liquids and gases, solids often have denser molecules than liquids. However, compared to ice, which is a solid form of water, liquid water has a higher density.
Therefore, two cups have the same weight since the weight of the plastic ball is precisely equal to the weight of the displaced water, according to Archimedes' Principle sue to the fact that the Buoyant force need to be equal the weight of the ball.
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this wire has a 221 ma current moving to the right. ignoring any external fields, such as the earth, what is the magnetic force on a proton that is 5.8 millimeters from the wire and moving 5800 m/s?
The magnetic force on a proton that is 5.8 millimeters from the wire and moving 5800 m/s will be ( 7.15×10 ^−24)i^
Define magnetic field.
An electric charge, an electric current, and magnetic materials are all affected magnetically by a magnetic field, which is a vector field. A force perpendicular to the magnetic field and its own velocity acts on a moving charge in a magnetic field.
Assume the particle is at a distance d in the +y direction and the current is flowing in the +x direction (away from the wire). Afterward, the magnetic field at a proton's position with charge q is
B =(μ0 i/2πd) ^k
Thus,
F=qv × B
=qv ×(μ0 i/2πd) ^k
In this situation,
v =v(− j)
where v is the speed and is a positive value and q>0. Thus,
F =q(-j) ×(μ0 i/2πd) ^k
= − 4(π×10 ^−7 T.m/A)(0.221A)(1.60×10 ^−19)(5800m/s)i^/ {2π(5.8m)}
=( 7.15×10 ^−24)i^.
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if a roller coaster has a min speed of 12,/s, what does the radius of curvature need to be at the top of a loop to ensure that passengers stay safely in the ride
The radius of the curvature will be 1.49 m. Because to balance the passengers safely, acceleration due to gravity (mg) should be equally balanced by centripetal force (Fc).
What is Centripetal force?
The force applied to an item in curved motion that is pointed toward the axis of rotation or the centre of curvature is known as a centripetal force.
[tex]F = \frac{Mv^{2}}{r}[/tex]
What is acceleration?
It is a vector quantity that can be described as the speed at which an object changes its speed. When an object's velocity changes, it is said to be accelerating.
What are the calculations?
[tex]F_{c} = m a_{c} \\mg = ma_{c} \\g = a_{c} \\9.8 m/s = a_{c} \\V = 12 m/s (given)\\a_{c} = \frac{V^{2} }{r} * r\\V = \sqrt{a_{c} r } \\12 m/s = \sqrt{9.8* r} \\\frac{12}{9.8} ^{2} = r\\\\1.49 m = r[/tex]
Hence, the radius of the curvature will be 1.49 m.
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a vehicle with will take longer to stop. a. worn brakes b. under-inflated tires c. worn tires d. all of the above
The vehicle with take longer to stop is worn brakes , under-inflated tires and worn tires
Which braking system do you usually use to slow down your vehicle while driving?Controlled braking is a hard braking technique that applies just the right amount of pressure to slow your car without throwing it off balance. This lets you keep both your front and back wheels effectively traction. With the cover brake technique, the change from accelerating to braking is smooth.
The master cylinder's hydraulic pressure squeezes the brake pads on either side of the rotor cylinder acting on a caliper, which is located slightly outside the rotor and holds the brake pads. Friction between the pads and the rotor causes the car to slow down and halt.
The secret to doing this is to apply normal braking until the vehicle slows to about walking speed, at which point you should lift the brake pedal slightly to reduce the force of the brakes.
The complete question is : What are four factors that affect breaking?
a vehicle with will take longer to stop. a. worn brakes b. under-inflated tires c. worn tires d. all of the above
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______require high temperatures and pressures to react with other elements.
Inert gases require high temperatures and pressures to react with other elements.
What are inert gases?A gas is considered to be inert if, under a specific set of circumstances, no chemical reactions occur. The noble gases, formerly known as the inert gases, frequently do not react with a wide variety of substances as argon and neon (at normal conditions).
Because they contain a fully filled valence shell and an electronic configuration of ns²np⁶, inert gases do not react with other chemicals.
As a result, they are referred to as noble gases and are in the periodic table's group 18.
But under high temperatures and pressures Inert gases react with other elements.
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a uniform block of granite in the shape of a book has face dimensions of 18 cm and 13 cm and a thickness of 1.2 cm. the density (mass per unit volume) of granite is 2.64 g/cm3. the block rotates around an axis that is perpendicular to its face and half way between its center and a corner. its angular momentum about that axis is 0.104 kg · m2/s. what is its rotational kinetic energy about that axis?
The rotational kinetic energy is 0.62 J.
How do you find rotational kinetic energy?The rotational kinetic energy, also known as "rotational mass," is the moment of inertia, or "rotational mass," of a rotating rigid body or system of particles, and is given by the formula K=12I2 K = 1 2 I 2.The definition of rotational energy, sometimes referred to as angular kinetic energy, is as follows: It is the portion of an object's total kinetic energy that results from rotation. The rotational inertia and the square of the angular velocity have a direct relationship with rotational kinetic energy.Moment of inertia, I = 8.04 times 1037 kg m2, and angular velocity, omega = 7.29 times 10-5 rad per second. As a result, the rotational kinetic energy is 2.13 x 1029 J.Step 1: Given Data
l = 20 cm = 0.2 m
w = 15 cm = 0.15 m
t = 1.2 cm = 0.012 m
ῤ = 2.64 g / [tex]cm^{3}[/tex] = 2.64 x [tex]10^{-3}[/tex] x [tex]10^{6}[/tex] kg / [tex]m^{3}[/tex]
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if a diesel cycle and an otto cycle work at the same compression ratio, the ideal cycle with the lowest thermal efficiency is:
When a diesel cycle and Otto cycle work at the same compression ratio, the ideal cycle with the lowest thermal efficiency is Otto cycle because the area shown in the P-V graph for the same ratio is more than diesel cycle.
What is compression ratio?In an engine cylinder the ratio of maximum and minimum volume of the combustion chamber and cylinder is termed as compression ratio.
Hence, When a diesel cycle and Otto cycle work at the same compression ratio, the ideal cycle with the lowest thermal efficiency is Otto cycle because the area shown in the P-V graph for the same ratio is more than diesel cycle.
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what evidence suggests that the protogalactic cloud that formed the milky way resulted from several collisions among smaller clouds?
The fact that the age and heavy element content of halo stars vary but do not appear to be correlated with the stars' distance from the galactic center indicates that the protogalactic cloud that gave rise to the Milky Way was the product of multiple collisions between smaller clouds .
How is it an indicating element?It makes plausible to think that the protogalactic cloud that gave birth to our Galaxy was nearly spherical given that the oldest stars, those in the halo and in globular clusters, are spread in a sphere of galaxy.Since the oldest stars in the halo are between 12 and 13 billion years old, we infer that the Galaxy first formed about that time.Other proof that galaxies in general started forming a bit more than 13 billion years ago can be found in the chapter on The Big Bang.The protogalactic cloud eventually condensed and created a thin revolving disk, much like in the case of star formation. Stars born before the cloud disintegrated did not take part in the disintegration, but have continued to orbit in the halo to the present day.Gas in the thin disk was broken up by gravitational forces into clouds or clumps with masses akin to star clusters. Later, these distinct clouds broke up even further to create stars.Due to the fact that the oldest stars in the disk are almost as old as the youngest stars in the halo, the collapse must have occurred quickly from an astronomical perspective, possibly taking only a few hundred million years.What are halo stars?The galaxy's outermost points, or halo stars, are simply regions where the imperium cannot spread since the astronomical's light does not shine. Several xenos races that the imperium has never encountered essentially make up its population.
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explain the difference between the if then block and the if then else block: how does each work? how do we know which to use?
If you want to tell a block of code to run only if a certain condition is true, use the if statement. If the same condition is false, use else to declare that a different block of code should be run.
The most fundamental control flow expression is the if-then clause. It instructs your software to run a specific chunk of code only when a specific test returns true. For instance, the Bicycle class might only permit the brakes to slow the bicycle down after it is moving.
When a "if" clause evaluates to false, an alternative path of execution is provided by the if-then-else statement. If the brakes are applied while the bicycle is not moving, you might use an if-then-else clause in the apply Brakes method to do some action.
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What's the temperature 32 degrees Fahrenheit in degrees Celsius?
A)
20°C
B)
0°C
C)
–10°C
D)
10°C
Answer:B) 0
Explanation:
an astronaut on mars (mass 6.42×1023kg , radius 3.39×106m ) launches a probe straight upward from the surface at 3.00×103m/s . what is the maximum height above the surface that the probe reaches? neglect air resistance and the gravitational pull of the two small moons of mars.
Answer:
H = 1 200 km
Explanation:
Given:
M = 6.42·10²³ kg
R = 3.39·10⁶ m
V₀ = 3.00·10³ m/s
______________
H - ?
Acceleration of free fall on Mars:
g = G·M / R²
g = 6.67·10⁻¹¹·6.42·10²³/ (3.39·10⁶)² ≈ 3.73 m/s²
The maximum height above the surface that the probe reaches:
H = V₀² / (2·g)
H = (3.00·10³)² / (2·3.73) ≈ 1 200 000 m = 1 200 km
A runner accelerates toward the finish line. Identify the action force in the example.
The runner's feet pressing against the ground serves as the example's action force.
Describe a force.A push or pull of an item or physical body may be described as a force. This change in motion, known as acceleration, often arises from the interaction of the object or physical body with another.
Newton's Second Law of Motion states that a physical body's acceleration and mass have a significant impact on the force acting on it.
An example of an action force in this situation is the pressure put on the ground by the runner's feet as they sprint faster toward the finish line.
The runner's feet pressing against the ground serves as the example's action force.
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Shear Force and Bending Moment diagrams for Simply Supported Beams subjected to different types of loading
(i) Simply Supported Beam subjected to concentrated load at mid span
(ii) Simply supported beam subjected to a concentrated load placed eccentrically on the span
(iii) Simply supported beam subjected to more than one concentrated load
(iv)Simply supported beam subjected to uniformly distributed load of w per unit run over the whole span
(v)Simply supported beam subjected to a uniformly distributed load over some part of the span
(vi)simply supported beam subjected to two couples.
The following are the diagrams:
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(i) Simply Supported Beam subjected to concentrated load at mid span
(ii) Simply supported beam subjected to a concentrated load placed eccentrically on the span
(iii) Simply supported beam subjected to more than one concentrated load
(iv)Simply supported beam subjected to uniformly distributed load of w per unit run over the whole span
(v)Simply supported beam subjected to a uniformly distributed load over some part of the span
(vi)simply supported beam subjected to two couples.
These all are explained through the given diagrams:
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Oil is spilled from an oil rig in the Gulf of Mexico andspreads in a circle with the circumference changing at a rate of 40m/sec. How fast is the area of the spill increasing when thecircumference of the circle is 100Ï€ meters?
The area of the spill increasing when the circumference of the circle is 100π meters at a rate of 2000 sq. m/sec.
What is circumference ?The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.
The curve length around any closed figure is more often referred to as the perimeter. The term "circumference" can also refer to the circle's actual location, which corresponds to a disk's edge.
Given parameters:
circumference changing at a rate = 2π dr = 40m/sec.
the circumference of the circle is = 2πr = 100π meters
Hence, the rate of area of the spill increasing = 2πrdr
= 100π meters × 40m/sec/2π
= 2000 sq. m/sec.
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consider an electron for which n 4, 3, and m 3. calculate the numerical value of (a) the orbital angular momentum and (b) the z component of the orbital angular momentum.
The L operates on [tex]\psi_3^3[/tex] eigenvalue will be equal to [tex]\sqrt{12}.[/tex]
z component of angular momentum is operates on [tex]\psi_3^3[/tex] gives [tex]L_z=3[/tex]
As per the data given in the question,
Quantum numbers of Electron n=4, l=3, and m=3.
Here, we need to find
(a) orbital angular momentum L and
(b) z component of orbital angular momentum [tex]\left(L_z\right)[/tex].
(a)
If orbital angular momentum (L) operates on spherical harmonic wave function of electron it gives an eigenvalue.
Then, we can write it as:
[tex]L^2 \psi_l^m=l(l+1) \hbar^2 \psi_l^m \\\\L \psi_l^m=\sqrt{l(l+1)} \hbar \psi_l^m[/tex]
Where, l is orbital quantum number and [tex]\hbar[/tex] is the reduced plank's constant.
We have l=3 and m=3
So,
[tex]& L \psi_3^3=\sqrt{3(3+1)} \hbar \psi_3^3 \\& L \psi_3^3=\sqrt{3(4)} \hbar \psi_3^3 \\& L \psi_3^3=\sqrt{12} \hbar \psi_3^3 \\& L=\sqrt{12} \hbar[/tex]
Therefore, the L operates on [tex]\psi_3^3[/tex] eigenvalue will be equal to [tex]\sqrt{12}.[/tex]
(b)
If z component of orbital angular momentum is operates on [tex]\psi_1^m[/tex], it give eigenvalue as follows,
[tex]L_z \psi_l^m=m_z \hbar \psi_1^m[/tex]
Here, [tex]m_z[/tex] is the magnetic quantum number.
[tex]L_z \psi_3^3=3 \hbar \psi_3^3 \\L_z=3 \hbar[/tex]
Therefore, if z component of angular momentum is operates on [tex]\psi_3^3[/tex] gives [tex]L_z=3[/tex]
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The numerical value of the orbital angular momentum is 1.8265719672742281e-34 J s, and the numerical value of the z component of the orbital angular momentum is 1.5818577255e-34 J s
The orbital angular momentum of an electron is given by the formula:
L = √l(l + 1) (h/2π)
where l is the orbital quantum number.
In this case, l = 3, so the orbital angular momentum is:
L = √3(3 + 1) (h/2π) = √12 (h/2π) = 1.8265719672742281e-34 J s
The z component of the orbital angular momentum is given by the formula:
Lz = m(h/2π)
where m is the magnetic quantum number.
In this case, m = 3, so the z component of the orbital angular momentum is:
Lz = 3(h/2π) = 1.5818577255e-34 J s
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35 grams of salt is dissolved in 500 grams of total solution. What is the percent by mass of salt?
The percentage by mass of the salt in the solution is 7%
How do I determine the percentage of the salt?Percentage composition can be obtained by using the following formula:
Percentage = (mass of solute / mass of solution) × 100
Now, we shall determine the percentage of the salt as illustrated below:
Mass of salt = 35 gramsMass of solution = 500 gramsPercentage of salt =?Percentage = (mass of solute / mass of solution) × 100
Percentage of salt = (35 grams / 500 grams) × 100
Percentage of salt = 7%
Thus, we can conclude that the percentage of the salt is 7%
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when a particular metal is illuminated with photons, one electron is observed for each absorbed photon. what effect would decreasing the wavelength and number of photons have on the electrons leaving the surface?
The numbers of electrons leaving the surface would decrease if number of photons and wavelength will be decreased.
Since, number of electrons ejects out from the surface which is expose to photons attack is totally dependent on the amount of photons striking that open area in per unit time.
When count of photons would decrease, in that case count of those photons which have frequency greater than the threshold frequency will be lesser and due to that count of electrons will also decrease.
Similarly, photons which are able to eject the electrons from the surface have certain wavelength which is greater than threshold wavelength. In that case count of photons which are able to eject out the electrons will also decrease.
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