The pressure reading of the pitot tube is 12.0 mm hg at a speed of at 830 km/h will be 187.45 mm of Hg.
It is given that,
The pressure reading of the pitot tube =12 mm of Hg
[tex]$\mathbf{p}_1=12 \mathrm{~mm}$[/tex] of Hg
Velocity at this height [tex]$\mathrm{v}_1=210 \mathrm{~km} / \mathrm{h}$[/tex]
Pressure reading at height [tex]$\mathrm{h}_2=$[/tex]
Velocity at this height [tex]$\mathrm{v}_2=830 \mathrm{~km} / \mathrm{hr}$[/tex]
Now applying the concept of the Bernoulli principle
[tex]$$\mathrm{p}_1+\frac{1}{2} \rho \mathrm{v}_1^2+\rho \mathrm{gh}_1=\mathrm{p}_2+\frac{1}{2} \rho \mathrm{v}_2^2+\rho \mathrm{gh}_2$$[/tex]
From the above equation it is clear that
[tex]$$\begin{aligned}\Delta \mathrm{p}_1^2 & =\frac{1}{2} \rho \mathrm{v}_1^2 \\\Delta \mathrm{p}_2 & =\frac{1}{2} \rho \mathrm{v}_2^2 \\\frac{\Delta \mathrm{p}_2}{\Delta \mathrm{p}_1} & =\frac{\frac{1}{2} \rho \mathrm{v}_2^2}{\frac{1}{2} \mu \mathrm{v}_1^2} \\\frac{\mathrm{p}_2}{\mathrm{p}_1} & =\frac{\mathrm{v}_2^2}{\mathrm{v}_1^2}\end{aligned}$$[/tex]
Hence, the value of the Pressure is given in terms of mm of Hg will be:
[tex]$$\begin{aligned}& \frac{\mathrm{h}_2}{\mathrm{~h}_1}=\frac{\mathrm{v}_2^2}{\mathrm{v}_1^2} \\& \mathrm{~h}_2=\mathrm{h}_1\left(\frac{\mathrm{v}_2^2}{\mathrm{v}_1^2}\right) \\& \mathrm{h}_2=\frac{12(830)^2}{210^2}=187.45 \mathrm{~mm} \text { of } \mathrm{hg}\end{aligned}$$[/tex]
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although we know less about dark matter in elliptical galaxies than we do in spiral galaxies, what does current evidence suggest?
Elliptical galaxies probably contain about the same proportion of their mass in the form of dark matter as do spiral galaxies.
How do we know elliptical galaxies have dark matter?Strong evidence suggests that dark matter, whose specific form is unknown but which exerts gravitational attraction, makes up the majority of the Universe's mass. All galaxies, in particular, are thought to be encased in enormous haloes of dark matter. The detection of unexpectedly low random stellar velocities in the periphery of typical elliptical galaxies, which had been interpreted as pointing to a paucity of dark matter, has recently called into question this theory. Here, we demonstrate that galaxy formation in dark-matter haloes is indeed compatible with the low velocities. We discover that the star orbits in the outer regions of the resulting ellipticals are extremely elongated using numerical simulations of disk-galaxy mergers.To learn more about galaxies, refer to
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on a bicycle, two sprocket wheels are connected by a chain that moves with a constant translational speed as shown. the moving chain makes the sprocket wheels rotate. if the front sprocket has a diameter that is twice as large as the diameter of the rear sprocket, how do their angular velocities compare?
Answer: Angular velocity of the front sprocket is half of the rear sprocket's angular velocity
Reason:
Angular velocity is the time rate at which an object rotates, or revolves, about an axis, or at which the angular displacement between two bodies changes.
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Determine the energy of the least energetic photon that can be absorbed by these atoms when initially in their ground state.
The energy of the least energetic photon that can be absorbed by these atoms when initially in their ground state is numerically equal to energy of the electron at that orbit.
What are energy levels of electron in an atom?In chemistry and atomic physics, an electron shell—also known as a fundamental energy level—is the orbit of one or more electrons around the atomic nucleus. The shell that is closest to the nucleus is the "1 shell," often referred to as the "K shell."
The shells that are farther and farther away from the nucleus are the "2 shell," also known as the "L shell," "3 shell," also known as the "M shell," and so on. Either the main quantum numbers (n = 1, 2, 3, 4) or the X-ray notation letters are used to designate the shells (K, L, M, N...).
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a sailor strikes the side of his ship just below the surface of the sea. he hears the echo of the wave reflected from the ocean floor directly below 2.8 s later. how deep is the ocean at this point?
Answer:
Approximately [tex]2.1 \times 10^{3}\; {\rm m}[/tex] ([tex]2.1\; {\rm km}[/tex]) assuming that the speed of sound in the water is [tex]1482\; {\rm m\cdot s^{-1}}[/tex] ([tex]20\; ^{\circ}{\rm C}[/tex].)
Explanation:
Multiply speed [tex]v[/tex] by time [tex]t[/tex] to find the distance [tex]s[/tex] travelled.
The sound wave in this question has travelled a distance of at least:
[tex]\begin{aligned}s &= v\, t\\ &= (1482\; {\rm m\cdot s^{-1}})\, (2.8\; {\rm s}})\\ &\approx 4.15\times 10^{3}\; {\rm m}\end{aligned}[/tex].
Note that this distance is for a round trip- from the ship to the ocean floor and back. The depth of the ocean at this location will be one-half the distance of a round trip:
[tex]\begin{aligned} \frac{4.15\times 10^{3}\; {\rm m}}{2} \approx 2.1\times 10^{3}\; {\rm m} = 2.1\; {\rm km}\end{aligned}[/tex].
a solid cylinder rolls down an incline at 30^{\circ}30 ∘ from rest. part ashort answer correct 1 / 1 points what is its acceleration? number 3.26 unit m/s^2 1 of 5 attempts part bshort answer 0 / 1 points how far does it go in 3.0 s?
The solid cylinder travels 28.56 m in 3.0 s.
What is cylinder?
One of the most fundamental of curvilinear geometric shapes, a cylinder has traditionally become a three-dimensional solid. It is regarded as a prism with such a circle just like its base in basic geometry. In many contemporary branches of mathematics and topology, a cylinder can also be defined as just an infinitely curvilinear surface. There is some ambiguity in terminology because of the change in the fundamental meaning between "solid" and "surface" (as in "ball" and "sphere"). By making the distinction between solid cylinders as well as cylindrical surfaces, the two concepts can be separated. The unadorned term "cylinder" in the literature could be used to describe either of these or an even more specialised item, the right circular cylinder.
The distance the solid cylinder travels in 3.0 s can be calculated using the equation d = at^2,
where a is the acceleration and t is the time. In this case, a = 3.26 m/s^2 and t = 3.0 s.
Plugging these values into the equation, we get d = 3.26 * (3.0)^2 = 28.56 m.
Therefore, the solid cylinder travels 28.56 m in 3.0 s.
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A 30-cm-diameter, 1.4 kg solid turntable rotates on a 1.4-cm-diameter, 450 g shaft at a constant 33 rpm. When you hit the stop switch, a brake pad presses against the shaft and brings the turntable to a halt in 12 seconds. Part A How much friction force does the brake pad apply to the shaft?
The friction force the brake pad applies to the shaft f = 0.34 N.
Solution:
∝ = Rf sin∅
(-3.05 x 10⁻³) = (9 x 10⁻³) f sin(-90°)
f = 0.34N
As the two surfaces slide over each other small ridges are pressed against each other. Friction creates a force on a surface that opposes its motion. Friction can be reduced by applying lubricant. Friction is a type of contact force. It exists between tangent faces.
Friction is the force the resistance to movement when one object rubs against another. Friction occurs when two objects rub against each other. Friction works against the motion and works in the opposite direction. The amount of friction depends on the materials that make up the two surfaces.
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after stealing your sister's easy-bake oven (which uses a 100 watt light bulb to cook cupcakes and stuff), you place a glass of water inside. ignoring the glass (and assuming all of the light is used to heat the water), how long would it take to raise the temperature of 0.6 kg of water by 60 k? express your answer in minutes.
Answer: To raise the temperature of 0.6 kg of water by 60k 4200jkg-¹c-¹
Reason:
Using the formula Pt = (4.2 × L × T ) ÷ 3600 you can calculate the time it takes to heat a specific quantity of water from one temperature to another temperature.
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suppose reflected white light is used to observe a thin, transparent coating on glass as the coating material is gradually deposited by evaporation in a vacuum. describe some color changes that might occur during the process of building up the thickness of the coating.
A band of colors would form in the film due to the interference of waves reflected from its opposite surface.
What is interference ?In physics, interference refers to the combined result of two or more wave travelling along intersecting or converging trajectories. The outcome is the result of multiplying the individual wave amplitudes at each location where numerous waves have an impact.
According to the given definition
we got to know ;
A band of colors would form in the film due to the interference of waves reflected from its opposite surface.
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suppose that you wanted to reduce the resonant frequency of a mass and spring harmonic motion system, what could you do?
To reduce the resonant frequency of a mass, I would b)increase the mass .So, correct option is b.
A thunderous recurrence is the normal vibrating recurrence of an item and indicated as 'f' with an addendum zero (f 0). At the point when an item is in balance with acting powers and could continue to vibrate for quite a while under wonderful circumstances, this peculiarity is reverberation.
We know very well that resonant frequency of simple harmonic motion system is given by 2π√k/m where k is spring constant and m is the mass of the body,
Now, we can see that frequency is inversely proportional to mass and directly proportional to spring constant.
Now, on increasing the spring constant we can see that resonant frequency will also rise.
On increasing the mass of the body resonant frequency will decrease since resonant frequency is inversly proportional to mass.
Increasing the damping will not effect the resonant frequency since frequency does not depend on the material of the body.
Hence, option b is correct.
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(Complete question) is:
Suppose that you wanted to reduce the resonant frequency of a mass and spring harmonic motion system, what could you do?
a)increase the spring constant
b)increase the mass
c)decrease the spring constant
d)increase the damping.
What is the horizontal distance of the center of gravity of the person-ladder system from the point where the ladder touches the ground?.
A projectile's range is the horizontal distance it has traveled.
x = V * t x = V * t can be used to calculate horizontal distance.The formula y = - g * t2 / 2 describes vertical distance from the ground, where g is the acceleration of gravity and h is an elevation.
What does horizontal distance look like?An illustration of a horizontal distance is the space between a building and the observer, while an illustration of a vertical distance is the height of the building.
Are horizontal range and distance equivalent?The range is the horizontal distance from the launch position to the landing place.An angled-launch projectile's range is influenced by its launch speed and angle .
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The cable lifting an elevator is wrapped around a 1.2-m-diameter cylinder that is turned by the elevator's motor. The elevator is moving upward at a speed of 2.5m/s . It then slows to a stop, while the cylinder turns one complete revolution.
How long does it take for the elevator to stop?
Express your answer to two significant figures and include the appropriate units.
It will take 2.8 s for the elevator to stop when it is moving with a speed of 2.5m/s
1)The cable will travel a linear distance equal to the distance covered by the elevator because it is constantly taut and neither slipping nor stretching.
2) Since the cylinder makes one full rotation, the cable's length is equal to the cylinder's circumference.
3) As a result, you must determine the cylinder's circumference, which is determined using the formula C = 2[tex]\pi[/tex] radius.
The radius is half the diameter: 1.2 m / 2 = 0.6 m
Hence, C = 2π × 0.6m = 3.8m
⇒ Distance run by the elevator = 3.8m
4) Now, assuming that the elevator decelerated uniformly from its starting speed of 2.7 m/s to a complete halt (Vf = 0), you use the related formulas:
i) [tex](V_{f})^{2}[/tex]= [tex](V_{o})^{2}[/tex] - 2ad ⇒ 2ad = [tex](V_{o})^{2}[/tex]- [tex](V_{f})^{2}[/tex] ⇒ a = [tex](V_{0})^{2}-(V_{f})^{2}[/tex]/ (2d)
a = [2.7 m/s]² / (2×3.8m) = 0.96 m/s²
ii) [tex]V_{f}[/tex] = [tex]V_{0}[/tex]- at ⇒ t = [2.7 m/s] / (0.96 m/s²) = 2.8 s
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what minimum amount of force (famin) must i apply through the rope to keep the box from sliding down the hill?
The minimum amount of force (famin) required to keep the box from sliding down the hill depends on several factors, such as the angle of the hill, the size and weight of the box, and the type of surface the box is sitting on.
What is force?
A force is indeed an influence that really can alter an object's motion according to physics. A force may cause an object to mass to accelerate when it changes its velocity, such as when it moves away from rest. An intuitive way to describe force is as a push or even a pull. A force is a vector quantity because it has both direction and magnitude. It is calculated using the newton SI unit (N). Force is denoted by the letter F. (formerly P). The net force acting on an object seems to be equal to the speed that its momentum changes over time, according to Newton's second law in its original formulation.
Generally, the more inclined the hill, the more force you will need to apply. If the box is light and the surface is slippery, you may need to apply more force to keep it from sliding. The best way to determine the exact amount of force necessary is to experiment and adjust the amount of force as needed.
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1. consider these three patterns of water waves: a b c a. describe the similarities and differences of the three patterns of water waves. b. experiment to make similar patterns, then explain how you can use the simulation to make each. 2. experiment to make waves of different interference patterns with water, sound, and light. explain how you created an interference pattern with two sources, and ways that you changed the pattern. include a few captured images from the simulation to demonstrate.
The motion of the water atoms in a wave is orbital. When the depth exceeds 50% of the wave's wavelength, the wave is said to be in deep water.
Are longer wavelengths common in all water waves?Wavelengths vary wildly between different types of waves. Surf waves in the ocean have a wavelength of 30–50 m, but tsunamis have significantly longer wavelengths (about 100km). Humans can hear sounds with wavelengths between 70 mm and 70 m, depending on the pitch of the sound.
Which three wavelengths are these?The medium (such as air, water, or a vacuum) through which a wave travels determines its wavelength. The periodic electrical signals in a conductor, sound waves, light waves, and water waves are all examples of waves.
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you are driving down the highway when one of your tires suddenly blows out. you should choose an answer: a. pump your brakes rapidly, and steer your vehicle to control any skids.b. avoid using your brakes. slow down gradually and concentrate on steering.c. immediately apply medium pressure to the brake pedal and bring your vehicle to a stop.
choose the correct statement regarding a double slit experiment. if the light wavelength becomes shorter, then the interference fringes move closer together. if the light wavelength becomes longer, then the interference fringes move closer together. if the slit distance is increased, then the interference fringes move further apart. if the slit distance is decreased, then the interference fringes move closer together. if the light wavelength becomes shorter, then the interference fringes move further apart
The correct statement regarding the double-slit test is a process wherein you possibly can display the wave nature of light.
Via feeding mild of the appropriate wavelength through a couple of slits with separation distances corresponding to the light wavelength, then interference styles will occur with various intensities that reduce as one measure in addition to the slits. If the slit together with the light supply is moved in the direction of the double slits, the brilliant fringes produced are brighter because the depth of the light passing through the double slit is more.
As the wave passes through each slit, it basically splits into two new waves, every spreading out from one of the slits. these two waves then intrude on each other. At some factors, in which a top meets a trough, they will cancel each different out. The smaller the wavelength is to the slits the nearer the fringes could be. were W=wavelength, D=distance from the slit to the display a=distance among the slits and x is the space between the slits. So x=WD/a in order for the wavelength to decrease so does the perimeter spacing.
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4. what happens to the orbital period as the star-planet distance increases? why do you think there is a relationship?
The orbital period would increase if Moto moved further away from the star because its orbital speed would decrease and it would have a larger orbit to traverse.
The orbital period is directly related to the average distance between the planet and the sun. This law means that the orbital velocity of a planet decreases with increasing distance from the Sun. For example, Mercury's orbital velocity is much faster than Pluto's.
The square of a planet's period is directly proportional to the cube of its orbital radius. This is because the closer a planet is to the Sun the faster it rotates to resist gravity. The squared ratio of the periods of any two planets is equal to the cubed ratio of their average distances from the Sun.
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what do asteroids and comets have in common? question 7 options: they have similar densities. most are unchanged since their formation in the solar nebula. they have nothing in common with each other. they have a similar range of orbital inclinations. they have similar orbital radii.
Most are unchanged since their formation in the solar nebula are common in asteroids and comets.
The asteroid belt, a region of the solar system between Mars and Jupiter, is where asteroids are most frequently found. The first asteroids were not found until the beginning of the nineteenth century; they are too small to be seen without a telescope.
A number (corresponding to the order of discovery) and occasionally a name are assigned to asteroids. At first, goddesses from Greek and Roman mythology were used to name asteroids. Astronomers turned to the names of colleagues (and other notable people) they wished to honor after exhausting these and other female names (including, later, those of spouses, friends, flowers, cities, and others). For instance, Morrison, Fraknoi, and Sidneywolff are the names of asteroids 2410, 4859, and 68448 respectively.
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what is the acceleration due to gravity at the surface of this planet? express your answer in meters per second squared.
The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity.
It's SI unit is m/s^{2}. It is of vector nature which includes both magnitude and direction makes it a quantity. The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/s^{2}.
Acceleration due to gravity, acceleration of gravity or gravity acceleration may refer to:
Gravitational acceleration, the acceleration caused by the gravitational attraction of massive bodies in generalGravity of Earth, the acceleration caused by the combination of gravitational attraction and centrifugal force of the EarthStandard gravity, or g, the standard value of gravitational acceleration at sea level on EarthTo learn more visit:
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if material a has twice the specific heat of material b, compare the relative amount of heat required to raise the temperature of an equal amount of each by 1.0 degrees c.
if material a has twice the specific heat of material b then, If the specific heat is twice, it will need twice as much heat to raise it by 1 degree Celsius.
Specific heat is represented by the letter C and varies depending on the substance and phase. The amount of heat required to raise the temperature of 1 kg of mass by 1°C is known as the specific heat. The substance's characteristic is the specific heat c.
Heat capacity C is expressed mathematically as C=mc, where m is mass and c is specific heat. Keep in mind that heat capacity and specific heat are identical but independent of mass. As a result, the heat capacity of two objects constructed of the same material but of different masses will vary. This is so because while specific heat is a property of every object constructed of the same material, heat capacity is a property of an object.
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a block of mass 0.428 kg0.428 kg is hung from a vertical spring and allowed to reach equilibrium at rest. as a result, the spring is stretched by 0.626 m.0.626 m. find the spring constant. n/mn/m the block is then pulled down an additional 0.365 m0.365 m and released from rest. assuming no damping, what is its period of oscillation? ss how high above the point of release does the block reach as it oscillates?
The maximum height above the point of release that the block reaches as it oscillates is 0.0385 m and the spring constant is 6.63 N/m.
What is single harmonic motion?Simple harmonic motion (SHM) is a type of periodic motion or oscillation motion that is a repetitive motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement from an equilibrium position
Equation:a) The force exerted by the spring (F) is given by Hooke's law as:
F = -kx
where, k is the spring constant.
At equilibrium, the weight of the block is balanced by the force of the spring, so we have:
mg = kx
where, g is the acceleration due to gravity.
Substituting the given values, we get:
k = mg/x = 0.428 kg * 9.81 m/s² / 0.626 m = 6.63 N/m
b) The period of oscillation of the block (T) is given by:
T = 2π√(m/k)
Substituting the given values, we get:
T = 2π√(0.428 kg / 6.63 N/m) = 0.668 s
c) The maximum height above the point of release (h) can be found using the conservation of energy principle. At the point of release, the block has a potential energy of mgy and no kinetic energy. At the maximum height, the block has a kinetic energy of (1/2)mv² and no potential energy. Therefore, we have:
mgy = (1/2)mv²
Solving for h, we get:
h = y - v²/2g
where, v is the velocity of the block at the point of release.
The velocity of the block can be found using the conservation of mechanical energy principle as:
(1/2)k(y + x)² = (1/2)mv²
Substituting the given values, we get:
v = √[(k/m)(y + x)²] = √[(6.63 N/m / 0.428 kg)(0.365 m + 0.626 m)²] = 0.772 m/s
Substituting v into the equation for h, we get:
h = 0.365 m - (0.772 m/s)² / (2 * 9.81 m/s²) = 0.0385 m
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A 1750-kg car travels at 23 m/s when it crashes into the rear end of a 1500-kg car traveling at 20 m/s in the same direction on nearly frictionless ice. The two cars become stuck together and slide on the ice. How fast do the two cars move together immediately after the collision?
*use units*
Answer:
21.6 m/s
Explanation:
To solve this problem, we can use the principle of conservation of momentum. This principle states that the total momentum of a system remains constant unless an external force acts on it. In this case, the only external force acting on the system is the collision force between the two cars, which causes the cars to stick together and move as a single unit.
The initial momentum of the first car is 1750 kg * 23 m/s = 40250 kgm/s. The initial momentum of the second car is 1500 kg * 20 m/s = 30000 kgm/s. The total initial momentum of the system is 40250 kgm/s + 30000 kgm/s = 70250 kg*m/s.
After the collision, the two cars move together as a single unit, so the total mass of the system is 1750 kg + 1500 kg = 3250 kg. Since the total momentum of the system remains constant, the final velocity of the combined cars must be 70250 kg*m/s / 3250 kg = 21.6 m/s.
In summary, the two cars move together at a velocity of 21.6 m/s immediately after the collision.
A 50-gram block of copper is placed so it touches a 5-gram block of copper. The small block has been heated to 84 C and the large block has been cooled to 0 C. What will happen when these blocks are placed so that they touch each other?
When the two blocks touch each other, both blocks will have the same temperature and it will be closer to 0 degrees Celsius than 84 degrees Celsius.
option A is the correct answer.
What is the final temperature of the blocks?
The final temperature of the blocks or the equilibrium temperature of the blocks when they touch each other is determined by applying the principle of conservation of energy as follows;
Heat lost by the smaller block = Heat gained by the bigger block
m₁c(T₁ -T) = m₂c(T - T₂)
where;
T is the equilibrium temperature of the blocksc is the specific heat capacity of the copper blocksm₁ is the mass of the smaller blockm₂ is the mass of the bigger blocksm₁(T₁ -T) = m₂(T - T₂)
5 x (84 - T) = 50(T - 0)
420 - 5T = 50T
420 = 55T
T = 420/55
T = 7.64⁰C
Thus, we can conclude that both blocks will have the same temperature which will be closer to 0 degrees Celsius than 84 degrees Celsius.
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the a string on a violin has a fundamental frequency of 440 hz. the length of the vibrating portion is 30.8 cm and has a mass of 0.343 g. under what tension must the string be placed?
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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what is the force constant, in newtons per meter, needed to produce a period of 0.45 s for a 0.011-kg mass on the spring?
The force constant is 2.145 N/m.
What is spring constant?The spring constant is the force required to stretch or compress a spring divided by the distance traveled by the spring. It is used to determine whether a spring is stable or unstable.K is the proportionality constant, also known as the 'spring constant.' Hooke's law (F = -kx) specifies stiffness and strength via the k variable. The greater the value of k, the greater the force required to stretch an object to a given length.Using the relation;
T = 2π√m/k
T = time period = 0.45 s
m = mass of object in kilograms = 0.011kg
k = spring constant
To find k based on the formula,
k = 4 × (3.142)^2 × 0.011 / (0.45 )^2
k = 2.145 N/m
Therefore the force constant is 2.145 N/m.
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does the pair of equilibria produced by a saddle-node bifurcation have to consist of one that is stable and one that is unstable?
This bifurcation is called a saddle-node bifurcation. In it, a pair of hyperbolic equilibria, one stable and one unstable, coalesce at the bifurcation point, annihilate each other and disappear.
What is a bifurcation equilibria?The mathematical study of changes in a family of curves' qualitative or topological structure, such as the integral curves of a family of vector fields or the solutions to a family of differential equations, is known as bifurcation theory. A bifurcation happens when a tiny, gradual change in a system's parameter values (the bifurcation parameters) results in an abrupt, "qualitative," or topological change in the system's behavior. This term is most frequently used to refer to the mathematical study of dynamical systems. Both continuous systems (represented by ordinary, delay, or partial differential equations) and discrete systems can experience bifurcations (described by maps).To learn more about bifurcation equilibria, refer to
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a massless frame in the shape of a square with 2-m sides has a 1-kg ball at each corner. what is the moment of inertia of the four balls about an axis through the corner marked o and perpendicular to the plane of the paper?
The "sum of the product of mass" of each particle with the "square of its distance from the axis of rotation" is the formula for the moment of inertia.
The term "moment of inertia" refers to the quantity that describes how a body resists angular acceleration and is calculated by multiplying each particle's mass by its square of distance from the rotational axis. The sum of the moments of inertia about any two mutually perpendicular axes lying in the plane and passing through the given axis determines the moment of inertia (MI) of a plane area about that axis.
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Mrs. Byers is swinging a mass on a string above her head with a radius of 7 m. If she decreases the radius by a factor of 7, by what factor does the centripetal acceleration change?
Answer:
Explanation:
Given:
V₁ = V₂ = V
R₁ = 7 m
n = 7
R₂ = R₁ / n = 7 / 7 = 1 m
____________
aₙ₂ / aₙ₁ - ?
aₙ₁ = V₁² / R₁ = V² / 7
aₙ₂ = V₂² / R₂ = V² / 1 = V²
aₙ₂ / aₙ₁- = V² / (V²/7) = 7
Centripetal acceleration increased by 7 times
a household washing machine connected to a household 223 volt source draws 1 amp of current. what is the power (in watt) being supplied to the washing machine? use exact numbers; do not estimate.
The power supplied to the household washing machine connected to the 223 V source is 223 W.
Current = I = 1 A
Voltage = V = 223 V
We have to calculate power supplied to the household washing machine,
Power = P =
= Power = Voltage X Current
= P = V X I
= P = 223 X 1
= P = 223 Watt
Power is the amount of energy transferred or converted per unit time.
Thus, the power supplied to the washing machine by the source of 223 V which draws 1 A of current is 223 W.
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an object that is 4.00 cm tall is placed 18.0 cm in front of a concave mirror having a focal length of 20.0 cm. what is the location of its image in relation to the mirror and what are its characteristics?
The location of its image in rel-ation to the mirror is -2.5 m
Given that, an object placed 45.0 cm from a concave mirror having the focal length of 15.0 cm and height of image is 5.0 cm.
We have to find the image distance (v) from the mirror and height of the image (h).
From above data we have, focal length (f) of concave mirror is -15 cm, object distance (u) is -45 cm and height of image (h) is 5 cm.
Now, Using Mirror Formula
1/f = 1/v + 1/u
Where f is focal length, v is image distance from the mirror and u is object distance from the mirror (concave).
The known values in the above formula to find the value of 'v' i.e. image distance from the mirror.
1/(-15) = 1/v + 1/(-45)
-1/15 = 1/v1 - /45
-1/15 + 1/45 = 1/v
(-3+1)/45 = 1/v
-2/45 = 1/v
-45/2 = v
-22.5 = v
Therefore, the image distance from the concave mirror is -22.5 cm.
Now,
m = -v/u = h/h•
Replace the values,
-(-22.5)/(-45) = h/5
-0.5 = h/5
-2.5 = h
Hence, the location of its image in rel-ation to the mirror is -2.5 m
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Two cars start at the same point and drive in a straight line for 5 km. At the end of the drive their distances are the same but their displacements are different. Explain.
5 km North and 5 km South are the same distance but different displacement.
What is displacement?
The term "displacement" refers to a shift in an object's location. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial location to the ending place. For instance, if an object shifts from location A to position B, its position changes.
A 'displacement' always consists of a magnitude and a direction. The two cars you just described have displacements with the same magnitude ... 5 km. But if they didn't both drive in the same direction, then their displacements are different.
Remember:
-- 10 m/s² up and 10 m/s² down are different accelerations
-- 30 mph East and 30 mph West are the same speed but different velocity.
-- 5 km North and 5 km South are the same distance but different displacement.
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