Boyle's law states that the volume of a given quantity of gas sustained at a fixed temperature is inversely proportional to the measurement's measurement of pressure.
Describe Newton's law.The motion of an item is related to the forces operating on it by Newton's equations of motion. According to the first law, until a force strikes on an item, it will not alter its motion. According to the second law, an object's force is determined by multiplying its mass by its acceleration. According to the third law, when two objects interact, they exert equal-sized and opposite-direction pressures upon one another.
Bernoulli equation: what is it?Static pressure plus dynamic pressure equals total pressure is a simple way to express Bernoulli's equation. Each point Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own unique static pressure p and dynamic pressure q.
What is Gay-Lussac's Law and Charles' Law?Joseph-Louis Gay-Lussac investigated the expansion of gases as the temperature is increased. His data helped establishCharles' law, which says, in its modern form, that the volume of a gas is directly proportional to the absolute temperature.
Now we need to say which law is there which state that at a fixed temperature, pressure and volume of a gas are inversely proportional.
The law that states this is Boyle's law.
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if the moon were five times more distant from earth than it is now, how would the gravitational force that earth feels from the moon be different?
If the moon were five times more distant from earth than it is now, the gravitational force would decrease.
How are distance and gravitational forces related?Inversely related to the square of the distance between the two objects is the gravitational force, which is directly proportional to the masses of the two objects. In other words, as objects get heavier, their gravitational pull is stronger; however, as objects get farther apart, their pull is weaker.Gravity's pulling power weakens as a pair of objects are separated by more space.As one gets farther away from a planet, the gravitational field weakens. Distances measured from the Earth's centre have a clear inverse square relationship with the dilution of gravity that occurs as you move away from the planet's surface.For, masses [tex]{M_{1},M_{2}}[/tex] , the gravitational constant G, and the increasing distance R ,the gravitational force F is given by,[tex]F= G\frac{M_{1}M_{2}}{R^{2} }[/tex]
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a cylinder is filled with of gas and a piston is put into it. the initial pressure of the gas is measured to be . the piston is now pushed down, compressing the gas, until the gas has a final volume of . calculate the final pressure of the gas. be sure your answer has the correct number of significant digits.
The final pressure of the gas will be 26.8 kPa when has a final volume of 78.0L.
Boyle's law, also known as the Boyle-Mariotte law, is an experimental gas law that explains the connection between a confined gas's pressure and volume. The pressure of a gas is inversely related to its volume at constant temperature, as well as its number of moles, according to Boyle's law.
P ∝ 1/V
[tex]PV=k[/tex] or [tex]P_{1} V_{1} =P_{2} V_{2}[/tex]
[tex]P_{1}[/tex]= initial gas pressure is 209 kPa
[tex]P_{2}[/tex]= final pressure which is unknown.
[tex]V_{1[/tex]= 10.0 L, which is the gas's initial volume.
[tex]V_{2}[/tex]= 78.0 L, which is the gas's final volume.
We can now use this formula to obtain the final gas pressure by entering all the specified variables.
[tex](209kPa)(10.0L)=P_{2}(78.0L)\\P_{2}=26.8kPa[/tex]
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what do we see when white light passes through a cool cloud of gas? what do we see when white light passes through a cool cloud of gas? an emission line spectrum infrared light visible light thermal radiation an absorption line spectrum
When white light passes through a cool cloud of gas an absorption line spectrum is observed.
An absorption line spectrum is made up of frequencies of light transmitted with dark bands when electrons absorb energy in the ground state to reach higher energy states.
This type of spectrum is created when atoms absorb energy.No two types of atoms or molecules give the same patterns.
In other words, any particular gas can absorb or emit only certain wavelengths of light that are typical for that gas.
In contrast, absorption spectra are produced when white light passes through a cold, rarefied gas.
Since cloud of gases are cold and hence when white light passes through a cool cloud of gas an absorption line spectrum can be observed.
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You are watching an object that is moving in SHM. When the object is displaced 0.600 m to the right of its equilibrium position, it has a velocity of 2.20 m/s to the right and an acceleration of 8.40m/s2 to the left.
How much farther from this point will the object move before it stops momentarily and then starts to move back to the left?
The oscillating and regular motion of an object is known as the SHM. The object must move 0.532 meters from x(t) = 0.65 meters to x(t) = A = 1.182 meters.
It is a periodic and oscillating movement that moves in a rectilinear fashion.
Knowing that there will always be a restoring force (F) that tends to return the motion to its initial location when it moves an amount called an amplitude is important when thinking about simple harmonic motion.
There are some important factors to take into account with this motion,
The movement's position, X (m), in its initial, equilibrium, and other positions.
The speed is a (m/s2).
Speed, V (m/s)
The volume, A (m)
The periodicity, w (rad/s),
The distance that the object needs to move from x(t) = 0.65m to x(t) = A = 1.182m is 0.532m.
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The internal energy within a system associated with the motion of particles and that can be added to a substance is called.
Internal energy associated with systems and particles is thermal energy.
What is Internal energy?
A thermodynamic system's internal energy is the entire amount of energy it contains. The energy required to construct or prepare the system in its current internal condition comprises both internal kinetic energy and potential energy contributions.
The internal energy has been described as the energy that has been assessed by the molecules and bonds at the STP. Thermal energy has been the energy of particular molecules and the system comprising all the molecules have the summation of the thermal energy.
Thus, internal energy associated with systems and particles is thermal energy.
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a weather emergency siren is mounted on a tower, 105 m above the ground. on one hand, it would be a good idea to make the siren very loud so that it will warn as many people as possible. on the other hand, safety regulations prohibit the siren from exceeding an intensity level of 116 db for workers standing on the ground directly below the siren. assuming that the sound is uniformly emitted, what is the maximum power that the siren can put out? maximium power output: 4387.95 tools x10y w how far away from the base of the tower can a person be and still be able to hear the siren? neglect any absorption of sound energy by the air; although, in reality, such absorption would be significant at long distances. maximum audible distance:
The maximum power that the siren can put out is of 4.74 dB.
Given that,
The height of the tower above the ground is, h = 105 m
Sound intensity from the siren is, I = 116 dB
We know that, the maximum intensity of sound allowed is 11.6 B.
Then the intensity of sound in terms of W/m² can be found as follows,
log(I / I₀) = 11.6
I / I₀ = 10¹¹°⁶
I = 10¹¹°⁶ * I₀
⇒ 10¹¹°⁶ * 10⁻¹²
⇒ 10⁻⁰°⁴
At 105 m above the ground the intensity will be 105² times.
Then the intensity at source point = 10⁻⁰°⁴ * 105²
⇒ 0.398 * 105² = 4387.95 W/m²
The energy of sound from the source is given as,
4π* intensity= 4* 3.14* 4387.95 = 55112.65 W/m²
To convert into decibels:
log(55112.65/ 10⁻¹²) = log(55112.65+12) = 4.74 dB
Thus, we can conclude that the maximum power that the siren can put out is of 4.74 dB.
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it has been suggested that extraterrestrial civilizations (if they exist) might try to communicate by using electromagnetic waves having the same frequency as that given off by the spin flip of the electron in hydrogen, which is 1.43 ghz . to what wavelength should we tune our telescopes in order to search for such signals?
In order to search for the signal, we would need to tune our telescopes to a wavelength of 208.3 cm.
If an extraterrestrial civilization were to transmit a signal using the spin-flip of the electron in hydrogen, the frequency of the signal would be 1.43 GHz, now to determine the wavelength of the signal, we can use the formula (λ = c/f), where c is the speed of light and f is the frequency. The speed of light is 299,792,458 meters per second, so the wavelength of the signal would be 208.3 cm.
In order to search for the signal, we would need to tune our telescopes to a wavelength of 208.3 cm. This is because radio telescopes detect electromagnetic radiation in the radio frequency range, which is measured in wavelengths.
By tuning our telescopes to the wavelength of 208.3 cm, we will be able to detect any signals transmitted by an extraterrestrial civilization using the spin-flip of the electron in hydrogen.
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a solid disk with a mass of 2.00 kg and a radius of 3.00 m is spinning with an angular velocity of 4.00 rad/s. what is the angular momentum of the disk?
Angle of the disk's momentum. 0881 kg*m^2/s.
Given:- mass is 2.00 kg, radius is 3.00 m, velocity of 4.00 rad/s.
How would you define velocity in plain English?The most important metric for determining an object's position and rate of movement is its velocity. The distance that an object travels in a certain amount of time might be used to define it. The object's movement in a unit of time is referred to as velocity.
What are velocity and speed?In contrast to velocity, which describes the speed and direction of an object's movement, speed is the rate of movement along a path. Alternatively, velocity is a vector while speed is a scalar quantity.
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Nuclear decay occurs according to first-order kinetics. Argon-37 decays with a rate constant of 0. 0198 days–1. After 98. 3 days, a sample has a mass of 2. 14 g. What was the original mass of the sample?.
The original mass of the Argon-37 sample (N₀) was 14.98651g or approximately 15g. We Use the equation for first-order kinetics for determining the original mass of the given Argon-37 sample.
What is first order rate equation?If the rate of radioactive decay is first order, we can write r = k[N]1, where N is the quantity of radioisotope present at the time the rate is recorded, k is the isotope's first order rate constant, and r is the rate of decay as observed.
According to First-Order Rate Equation,
[tex]ln(\frac{N}{N_{0} } )=-kt[/tex]
Here,
N = The amount of radioisotope left after "t" time.
N₀= The initial amount of radioisotope,
k = Rate constant of the radioisotope.
t = Time
Given,
N = 2. 14 g.
N₀ = ?
k = 0. 0198
t = 98. 3 days
Now, substituting these values in the first order rate equation we get,
[tex]ln(\frac{N}{N_{0} } )=-kt\\ln(\frac{2.14}{N_{0} } )=-0.0198*98.3\\ln(\frac{2,14}{N_{0} } )=-1.94634\\\frac{2.14}{N_{0} } =e^{-1.94634} \\\frac{2.14}{N_{0} }=0.142795\\N_{0} = 14.98651g[/tex]
Hence, the original mass of the sample (N₀) was 14.98651 g or approximately 15 g.
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a 500 kg motorcycle accelerates from rest to 25 m/s over a time interval of 5.5 s. find the force exerted on the motorcycle by the road due to friction.
The force exerted on the motorcycle of mass 500 kg is 2272.72 N.
How to calculate for force?Force can be calculated by multiplying the mass of a body to its acceleration. The S.I Unit of force is Newton (N).
To calculate the force exerted on the motorcycle, we use the formula below.
Formula:
F = m(v-u)/t.......... Equation 1Where:
F = Force on the motorcyclem = Mass of the motorcyclev = Final velocity of the motorcycleu = Intial velocity of the motorcyclet = Time taken to change its velocity.From the question,
Given:
m = 500 kgv = 25 m/su = 0 m/st = 5.5 sSubstitute these values into equation 1
F = 500(25-0)/5.5F = 2272.72 NHence, the force acting on the motorcycle is 2272.72 N.
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If you drop the sand bag out of the cart right at the equibrium location, what effect will that have on the amplitude of your oscillation?.
At maximal displacement, the speed is zero, the kinetic energy is zero, and the only source of energy is the potential energy held in the spring. E = 1/2 kA² is the energy at the greatest distance.
What is meant by oscillation?The process of any variable or measure fluctuating repeatedly about its equilibrium value in time is known as oscillation. A periodic change in a substance's quality between discrete choices or around its central value is another way to describe oscillation.
Briefing:Here, A represents the oscillation's amplitude.
Dropping the sandbag won't change the system's overall energy since all of the energy is derived from the energy stored of spring.
Therefore, the amplitude won't be affected.
The square of oscillation's intensity determines the system's energy in an exact correlation. The energy in the system remains constant, hence the oscillation's amplitude does not vary.
Hint:
Utilize the energy at balance to ascertain whether the maximum speed for dropping the sandbag at the cart's maximal changes in any way.
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an undamped 1.21 kg1.21 kg horizontal spring oscillator has a spring constant of 26.1 n/m.26.1 n/m. while oscillating, it is found to have a speed of 2.31 m/s2.31 m/s as it passes through its equilibrium position. what is its amplitude ????a of oscillation?
The kinetic energy in the spring is equal to the mechanical work done by the spring
The kinetic energy in then spring is
E = 1 / 2 kA2
The mechanical work done by the spring is,
E= 1 / 2 mv2
Compare the above two equations to find the amplitude of oscillation:
1 / 1 kA2 = 1 / 2 mv2
A = v√ m/k
(3.58 m/s) √ 1.12 kg / 32.3 N/m
= 0.66m
The mechanical work done by the spring is,
E = 1/2 mv2
= 1 / 2 (1.12 kg) (3.58 m/s)2
= 7.17 J
Work modifications the quantity of mechanical and internal energy possessed by gadgets. Whole work is achieved on a machine or item, energy is introduced to it.
The character of work achieved can be categorised in three classes. they are +ve work, -ve work and zero work. The character of work relies upon on the perspective among pressure and displacement.
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a beam of light is incident from air on the surface of a liquid. if the angle of incidence is 30.0° and the angle of refraction is 22.0°, find the critical angle for the liquid when surrounded by air.
The critical angle for the liquid when surrounded by air is 48.75°.
What is critical angle?The critical angle is the maximum angle at which a light beam traversing a transparent media can collide with the surface of a second medium having a lower refractive index without being completely reflected within the first medium.
Given that:
Angle of incident: i = 30.0°.
Angle of refraction, r = 22.0°.
Hence, refractive index of the medium: n = sini/sinr
= sin 30.0°/sin22.0°
= 1.34.
Hence, the critical angle for the liquid when surrounded by air:
= sin⁻¹(1/n)
= sin⁻¹(1/1.33)
= 48.75°.
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A magnetic field near the floor points down and is decreasing. Looking down at the floor, which option best describes the direction of the non-Coulomb electric field A. Clockwise B. Counter Clockwise C. Into the page D. Out of the page E. There is no curly electric field
Answer: B: counter clockwise
Explanation: I learned about this in the 9th grade!
an object starts from rest and falls freely for 40 meters near the surface of planet p if the time of fall is 4 seconds what is the magnitue of the acceleration due to gravioty on planet p
The magnitude of the acceleration due to gravity on planet p is 5 meters per seconds squared.
What is the magnitude of the acceleration due to gravity on planet p?From the Second Equation of Motion;
s = ut + (1/2)gt²
Where v is final velocity, u is initial velocity, g is acceleration due to gravity and t is time elapsed.
Given the data in the question;
Initial velocity u = 0m/sHeight s = 40mElapsed time t = 4 sAcceleration due to gravity g = ?Plug the given data in the above formula and solve for g.
s = ut + (1/2)gt²
40m = (0 × 4s) + ( (1/2) × g × (4s)²
40m = (1/2) × g × 16s²
Multiply both sides by 2
2 × 40m = 2 × (1/2) × g × 16s²
80m = g × 16s²
g × 16s² = 80m
g = 80m / 16s²
g = 5m/s²
Therefore, the acceleration due to gravity is 5m/s².
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If log 3 4=1. 2619, evaluate log3 0. 25. Give your answer to four decimal places
PLEASEEEEEEEEEE HELPPPPPPPPPP I HAVE BEEN STUCK ON THIS SAME QUESTION FOR ABOUT 2 -4 HOURS NOW
If log 3 4 = 1. 2619, then the solution to the equation above, which evaluates log 3 0, 25, is -1. 2619.
What does evaluate mean example?When one assess something or someone, then take them into account in order to form an opinion on them, such as whether or not they are good or terrible. It's challenging to assess the state of the market. Synonyms: evaluate, rank, value, and decide More alternatives to analyze. to evaluate or determine the degree, significance, scope, or worth of something: Doctors assess the patient's health. He was only genuinely content while working alone since then he had complete control over the strategy and the dangers.
Briefing:Convert decimal to fraction:
log₃ 25/100
Reduce the fraction:
log₃ 1/4
Round the number:
=-1.2619
hence, its evaluate -1.2619 when If log 3 4=1. 2619.
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a heuristic device in which a solution to a problem is found by evaluating the difference between the current situation and the goal is the:
A heuristic device in which a solution to a problem is found by evaluating the difference between the current situation and the goal is the mean end analysis.
Heuristics are mental shortcuts that are frequently utilized to streamline issues and prevent cognitive overload. Heuristics, which enable people to arrive at rational conclusions or answers to complex situations rapidly, are a function of how the human brain evolved and is wired.
This designates a notion or idea that is employed more because it facilitates our thinking about the issue than because it is strongly supported by the data. A heuristic tool is Max Weber's ideal type. The three heuristics that attracted the most attention were representativeness, anchoring and adjustment, and availability.
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Imagine a ball that is pushed off a desk completely horizontal and falls 9.47 m down to the floor. If it landed 3.32 m away from the edge of the desk, how fast was it moving in the horizonal direction just before it hit the ground? Round to 1 decimal.
Itis going to the speed of obstinacy.
what is speed?speed is the fastest movement of something.
n the question time of flight of blocked ball time off flight of the ball that is represented by capital D This is the time of flight. It is given time of flight, height of time of flight, and hi of both ball, the same or equal, yet. We need to find out how fast production is. We need to find the projection that is represented by you. It was not possible to be on the time of projectile flight. The value of time of flight is equal to the number of years you have left in your life. We'll get equal to 11.1 until 9.81 upon two and two signed 27.4, because he dies at 27.4. Two is 118.31 little per second. obstinacy is the right answer. I think that is Mhm. Correct answer is obstinacy It is necessary to explain this questio.
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The expansion of the universe after its origin takes place by a phenomenon called.
The expansion of the universe after its origin takes place by a phenomenon called Big bang
What is Big bang theory ?As the universe widened, it cooled and matter began to form. Neutrons, protons, electrons, anti-electron, photons, and neutrinos were all present in the universe one second after the Big Bang. The Big Bang nucleosynthesis, which took place during the first three minutes of the universe, produced the light elements.
The big bang theory is the most commonly accepted explanation. Learn about the initial explosion and how the universe expanded from the size of an atom to include everything that exists today.
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An object has 23 Kg*m/s of momentum and a mass of 3 Kg. What is the objects velocity
Answer:
23 m/s
Explanation:
in the pictorial system, what indicates that an extinguisher is not suitable for a particular class of fire?
An extinguisher is not suitable for a certain class of fire if it has a red diagonal line through it on a black background.
With an illustration, define a symbol.Other concepts and beliefs can be conveyed using symbols. Words, music, gestures, ideas, or visual images could all be used to describe them. For example, on maps, rivers are commonly represented by blue lines, and a red rose is frequently associated with compassion and love. A typical symbol for "STOP" is a red octagon.
How do you recognize a symbol?When an image in a text seems to suggest something beyond its exact meaning, symbolism is present. Although authors don't always do this, it could be repeated or seem startling, as if the author is purposefully drawing attention to it.
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Two kindergartners are having a game of tug-of-war. The kid on the left has a mass of
27 kg and the kid on the right is 31 kg. As the game progresses, neither kid is going
anywhere. What is the momentum of the kid on the right?
The momentum of the kid on the right having a mass of 31 kilograms is 0 Kg.m/s
How do I determine the momentum?Momentum is defined as the product of mass and velocity. It is expressed mathematically as:
Momentum = mass × velocity
With the above formula, we can obtain the momentum of the kid on the right as follow:
Mass of kid on the right = 31 kilogramsVelocity of kid on the right = 0 m/sMomentum of kid on the right =?Momentum = mass × velocity
Momentum = 31 Kg × 0 m/s
Momentum = 0 Kg.m/s
Thus, the momentum of the kid on the right is 0 Kg.m/s
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hearing the siren of an approaching fire truck, you pull over to the side of the road and stop. as the truck approaches, you hear a tone of 470 hzhz ; as the truck recedes, you hear a tone of 420 hzhz . How much time will it take for the truck to get from your position to the fire 5.0km away, assuming it maintains a constant speed? Express your answer using two significant figures.
The time taken by the truck to get to the required position 5 km away from the fire is 261.55 s.
Tone at which the truck approaches at = 470 hz
Tone at which the truck recedes = 420 hz
Distance = 5.0 Km away
Speed = constant
Speed of sound = v
Speed of air = V
Frequency of sound = f
Frequency when truck approaches = f₁ =
= f₁ = [( V + v) / V ] X f
Frequency when the truck recedes = f₂ =
= f₂ = [( V - v) / V ] X f
Thus, equating both equations =
= f₁ / f₂ = (V + v) / (V - v)
= 470/420 = (340.278 + v) / (340.278 - v )
= [ 470 X 340.278 ] - 470v = [ 420 X 340.278 ] + 420v
= 159930.66 - 470v = 142916.76 + 420v
= 17013.9 = 890v
= v = 19.117 m/s
The time taken = t =
= s = ut + (1/2)at²
= 5 X 10³ = 0 + (19.117 X t)
= t = 261.55 s
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A red ball with a velocity of +3. 0 m/s collides head-on with a yellow ball of equal mass moving with a velocity of -2. 0 m/s. What is the velocity of the yellow ball after the collision?.
After collision velocity of yellow ball become 3 m/s.
What is collision velocity?
Collision is short-duration interaction between two bodies or more than two bodies simultaneously causing change in motion of bodies involved due to internal forces acted between them during this. Collisions involve forces (there is a change in velocity).
Velocity of red ball = 3 m/s
Velocity of yellow ball = -2m/s
Red ball and yellow ball both have same mass
So, after head on collision their velocity will be exchanged.
So after collision velocity of yellow ball become 3 m/s.
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the two ropes seen in (figure 1) are used to lower a 255 kg piano 6.10 m from a second-story window to the ground.
The work done have been calculated as : Wgravity = 15,250 joules, W rope1 = - 9667.158 joules and W rope2 = - 5584.94 joules
Given ; Force of gravity on piano = 2500 N
r = distance of the ground = 6.10 m
As the angles are mentioned in the diagram, thus we can write
Work done can be calculated by ;
Wgravity = 2500 N . 6.10m . cos 0 = 15,250 joules
W rope1 = 1830 N . 6.10 m . cos 150 = - 9667.158 joules
W rope2 = 1295 N . 6.10 m . cos 135 = - 5584.94 joules
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Answer:
W = 12500 J
T1 = -7920 J
T2 = - 4580 J
Explanation:
The angle between the force w and the displacement is 0 degrees, therefore:
[tex]W_{w} = wdcos(0) = (2500)(5)(1) =[/tex] 12500 J
The angle between the force T1 and the displacement is 90 + 60 = 150 degrees, therefore:
[tex]T_{1}= T_{1} dcos (150) = (1830)(5)(cos(150)) =[/tex] - 7920 J
The angle between the force T2 and the displacement is 90 + 45 = 135 degrees, therefore:
[tex]T_{2} = T_{2} dcos(135) = (1295)(5)(cos (135)) =[/tex] - 4580 J
a 12kg lantern is suspended frm the ceiling by two vertical wires. what is the tension in each wire?
Two vertical wires are used to hoist a 12 kilogram lantern from the ceiling; as a result, each wire is under 58.8 N of tension.
Why is it known as "wires"?The phrase "wire transfer" dates back to a time when banks used telegraph wires to transmit this type of financial transfer. A bank wire stored procedures on who should receive the funds, along with the user's bank account information and the amount they should receive.
Briefing:Well, we know from Newton that, if m is the mass of the lantern,
Fnet = ma
Additionally, it is clear that the two forces pulling on the candle are now the strain on the two wires and the gravitational force. Since the candle isn't moving, its speed is 0, which means that the final quantity of forces acting on it must likewise be zero.
The positive y-axis should point up, and also the negative y-axis should point below. Listing the forces reveals that
-mg + T1 + T2 = 0
The two wires' tensions are also equal because they are both straight and orbital angular momentum, or T1 = T2 = T. The preceding equation can be revised to say
-mg + 2T = 0, or
2T = mg.
Thus,
T = mg/2 = (12kg*9.8m/s2) / 2 = 58.8N
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In which type of transistor does current flow from the base to the emitter?
In an PNP transistor, the base controls the amount of current passing through it while allowing current flow from the base to the emitter.
The goal of the NPN transistor is to allow electrons to move from the emitter to the collector (so conventional current flows from collector to emitter).The base, which regulates the number of electrons the emitter "emits," receives electrons from the emitter.A PNP operates in a similar but reverse manner. The base still regulates the current flow, but it now goes from emitter to collector in the reverse direction.The emitter emits "holes" (a hypothetical absence of electrons), which are gathered by the collector, rather than electrons.PNP transistors, on the other hand, are made to allow current to flow from the collector to the emitter.To know more about transistors visit:
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A 80 g , 35-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 11 g ball of clay traveling horizontally at 2.3 m/s hits and sticks to the very bottom tip of the rod. To what maximum angle, measured from vertical, does the rod (with the attached ball of clay) rotate?
The maximum angle due to angular momentum measured from vertical, does the rod (with the attached ball of clay) rotate is 57°.
Given that,
Mass of the rod, [tex]\small M= 80\;g=0.08\; kg[/tex]
Mass of the clay ball, [tex]\small m=11\;g=0.011\;g[/tex]
Length of the rod, \small[tex]L=35\;cm=0.35\;m[/tex]
Initial speed of the ball, [tex]\small v_{i}=2.3\;m/s[/tex]
From law of conservation of angular momentum, Total initial angular momentum of the system = total final angular momentum of the system[tex]\small mv_{i}\frac{L}{2}=\frac{1}{2}(I_{rod}+I_{ball})\omega_{f}\small mv_{i}L=(I_{rod}+I_{ball})\frac{V_{f}}{(L/2)}[/tex].
[tex]\small mv_{i}L=\left (\frac{1}{12}ML^{2}+m\left (\frac{L}{2} \right )^{2} \right )\frac{V_{f}}{(L/2)}[/tex]
Now, From law of conservation of energy, Initial rotational kinetic energy = final potential energy:
[tex]\small \frac{1}{2}(I_{rod}+I_{ball})\left (\frac{V_{f}}{(L/2)} \right )^{2}=m(L/2)g(1-\cos\theta)[/tex]
[tex]\small \frac{1}{2}\left (\frac{1}{12}ML^{2}+m\left (\frac{L}{2} \right )^{2} \right )\left (\frac{V_{f}}{(L/2)} \right )^{2}=m(L/2)g(1-\cos\theta)[/tex]
[tex]\small \left (\frac{1}{12}M+m\left (\frac{1}{2} \right )^{2} \right )\left (\frac{V_{f}}{(1/2)} \right )^{2}=mLg(1-\cos\theta)[/tex]
[tex]\small \therefore \theta=\cos^{-1}\left (0.5496 \right )\small \boldsymbol{\therefore \theta=56.66^{o}}[/tex]
ROUNDING TO 2 SIGNIFICANT FIGURES
[tex]\small \boldsymbol{\therefore \theta=57^{o}}[/tex]
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If the expansion of the Universe is currently accelerating, can we conclude that the Universe will necessarily expand forever? Why?
If the expansion of the Universe is currently accelerating, can we conclude that the Universe will necessarily expand forever Since little is currently known about the source of the dark energy which is causing the present accelerated expansion of the Universe, it cannot be concluded that it will continue unchanged in the future? Thus, the Universe might, or might not expand forever.
According to the relativistic perspective, although the space around the Earth is contracting, its atoms are resisting this compression. This implies that the Earth's surface is moving higher at a constant rate. On Earth, falling would be the only option to avoid accelerating up. When you are at rest, you fall.
A falling apple, the moon orbiting the earth, and a car stopped at a stop sign are a few instances of acceleration. Through these illustrations, we can see that acceleration happens whenever a moving object changes its direction or speed, or both.
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a collection of logic gates for which the static power dissipation is zero, and the dynamic power dissipation is 10 mw is operating at 1 ghz with a 1.2-v supply. by what fraction could the power dissipation be reduced if operation at 1.0 v were possible? if the frequency of operation is reduced by the same factor as the supply voltage (i.e., 1.0/1.2), what additional power can be saved?
Additional Saving in power is 1.48mw.
What exactly is power dissipation?As a result of primary action, power dissipation is the process by which power is lost as heat. The process of power dissipation happens naturally. The power will be dissipated by each resistor in the circuit that has a voltage drop across it.
Since Pdyn = fc v²oo is proportional to v²oo reducing power supply
from 5v to 3v reduces the power dissipation by a factor of
(3.3)²/5² = 0.436
The power dissipation now become 0.436×10×10⁻³ = 436×10⁻³ = 4.36mw.
Since Pdyn is proportional to reducing f by the some factor as the supply voltage 3.3/5 = 0.66results in reducing the power dissipation
further by factor of 0.66
Additional Saving in power = (1.0.66) X(4.36 × 10⁻³ )
Additional Saving in power = 1.48mw.
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