The point that the axis of rotation passes through in the pencil of length 15.0 cm and mass 10.0 g is point B.
The free body diagram of the pencil that rotates about an axis perpendicular to the plane of the figure is shown in the image attached below.
N = Normal force
mg = Weight
C = Center of mass point
f = Frictional force
The weight of the pencil acts in vertically downward direction at the center of mass of the pencil, that is, at point C. Since, the pencil touches the surface at point B, the force due to weight of the pencil produces a torque and makes the pencil rotate about point B.
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an mri technician moves his hand from a region of very low (almost negligible) magnetic field strength into an mri scanner’s 2.00 t field with his fingers pointing in the direction of the field. (a) find the average emf induced in his wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field. (b) what current is induced in the ring if its resistance is 0.0100 ω? (c) what average power is dissipated?
The average emf induced in his wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field is 3mV.
What is magnetic field?
The magnetic impact on moving electric charges, electric currents, and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it while the charge is travelling through a magnetic field.
Given:
[tex]- $B=2 T$[/tex] is the magnetic field strength
[tex]- $d=2.2 \mathrm{~cm}=0.022 \mathrm{~m}$[/tex] is the ring diameter
[tex]- $t=0.25 \mathrm{~s}$[/tex] is the time needed to move the ring
(a) The electromotive force (emf) can be calculated using Faraday's law as:
[tex]$$\epsilon=-\frac{d \phi}{d t}$$[/tex]
We can expand the magnetic flux term here:
[tex]$$\epsilon=-\frac{d}{d t}[B A]$$[/tex]
The magnetic field here is constant so it is the area that is changing:
[tex]$$\epsilon=-B\left(\frac{d A}{d t}\right)$$[/tex]
Since we have no actual functions and just the initial area exposed to the magnetic field (zero) and the final area (entire ring area), we can re-write this as:
[tex]$$\epsilon=-B\left(\frac{0-\pi r^2}{t}\right)$$[/tex]
We substitute and recall that the radius is half the diameter:
[tex]$$\epsilon=-(2 T)\left(\frac{0-\pi\left(\frac{0.022 \mathrm{~m}}{2}\right)^2}{0.25 \mathrm{~s}}\right)$$[/tex]
We thus get:
[tex]$$\epsilon=0.003 \mathrm{~V} \approx 3 \mathrm{mV}$$[/tex]
(b) Wedding rings are usually made of metals like gold or silver, which means they are conducting. This means that the resistance of a wedding ring should be low. So here if we use Ohm's law:
[tex]$\epsilon=I R$[/tex]
We can assume that the current is also small here since the emf is fairly small and the resistance is expected to be small. With a small current, the temperature of the wedding ring shouldn't change much.
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the clock on the big ben tower in london reads 12 noon. if you travel away from the clock at a very high speed and view it with a telescope, you would see group of answer choices run faster than a clock in your vehicle. run slower than a clock in your vehicle. be frozen at 12 noon.
"The clock on the big ben tower in London reads 12 noon. If you travel away from the clock at a very high speed and view it with a telescope, you would see it run slower than a clock in your vehicle" (Option A) This phenomenon is known as Time Dilation.
What is time dilation?
Time dilation is defined in physics and relativity as the difference in elapsed time as measured by two clocks. It is either owing to a difference in relative velocity or a difference in gravitational potential between their places.
When left undefined, "time dilation" generally refers to the impact of velocity.
Time dilation is the "slowing down" of a clock as determined by an observer in relative motion with regard to that clock under the theory of special relativity.
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[NOTE: THIS IS AN INCOMPLETE QUESTIO. THE COMPLETE QUESTION IS:
Suppose you look at the huge clock on the Big Ben Tower in London and it reads 12 noon. If you could travel away from the clock at the speed of light and view it with a telescope, it would:
a) run slower than usual
b) run faster than usual
c) be frozen at 12 noon]
a swimmer is floating on his back on the sea surface. if his density is 980 kg/m3 and he has a volume of 0.060 m3, what is the buoyant force that supports him in the sea water of density 1025 kg/m3?
The buoyant force that supports him in the sea water of density is 3931.613N.
On the water's surface, a swimmer is lying on his back. if his volume is 0.060 m, and his density is 980 kg/m³.
When an object floats, a force called buoyancy is responsible for this. It is specifically the external force that an object that is partially or completely submerged in water or any other fluid experiences. A body or object is said to be buoyant when it is placed in or submerged in a fluid.
We can also define buoyancy as the upward force applied by the fluid on a body or object in this way. The pressure on two sides of a body submerged in a static fluid causes the buoyancy phenomenon.
The Buoyant Force is measured in Newtons (N), which is also the unit of Force (F).
F=hpg
h=∛0.060
=0.3914m
F=0.3914 x 1025 x 9.8
F=3931.613N
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why did einstein introduce the cosmological constant into the equations of his general theory of relativity when describing the universe?
Because Einstein could neither see or accept the cosmos expanding or contracting, he added a component to his equations that prevented the universe from changing.
Why is there so much stuff in the cosmos?Even the existence of matter in the cosmos is unknown to us. The early cosmos should have created an equal amount of mass and positron, which would subsequently destroy one another, according to modern physics theories.
Do we already know the universe's secrets?Yet modern physicists will be the first to recognize they are not in possession of all the solutions. Dr. Daniel Whiteson, a physicist at the University of California and a co-author of the new book, claims that "there are fundamental facts about the world that we're ignorant of."
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Because Einstein could neither see or accept the cosmos expanding or contracting, he added a component to his equations that prevented the universe from changing.
Why is there so much stuff in the cosmos?Even the existence of matter in the cosmos is unknown to us. The early cosmos should have created an equal amount of mass and positron, which would subsequently destroy one another, according to modern physics theories.
Do we already know the universe's secrets?Yet modern physicists will be the first to recognize they are not in possession of all the solutions. Dr. Daniel Whiteson, a physicist at the University of California and a co-author of the new book, claims that "there are fundamental facts about the world that we're ignorant of."
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g what is the magnitude of the tension ta in rope a? a. 500 n b. 3200 n c. 370 n d. 130 n e. 100 n f. 400 n value: 10 if the axis of rotation is placed on rope a, then the torques of f
The torque of rope F = 500 N * 3 m * sin(30 degrees) = 800 Nm.
What is torque?
Torque seems to be the rotational equivalent of force in physics and mechanics. Depending on the area of study, it is also known as that of the moment, instant of force, rotational force, or turning effect. It illustrates how a force can cause a change in the body's rotational motion. In his famous adage, "Give me a lever as well as a place to stand, and I'll move the Earth," Archimedes, who studied the use of levers, is credited with developing the idea. A torque could be thought as a twist to the an object around a particular axis, similar to how a linear force is indeed a push or a pull.
The torque of rope F is equal to the product of the force (F) and the lever arm (r). The lever arm is equal to the length of the rope multiplied by the sine of the angle between the rope and the axis of rotation.
Therefore, the torque of rope F = F * r = F * (length of rope) * sin(angle between rope and axis of rotation).
For example, if F = 500 N, the length of the rope = 3 m, and the angle between the rope and the axis of rotation is 30 degrees, then the torque of rope F = 500 N * 3 m * sin(30 degrees) = 800 Nm.
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which component of an ideal vapor-compression refrigeration cycle is modeled as having internal reversibilities
The heat exchangers, evaporator and condenser, which are where the most irreversibilities are seen, are the most important parts of the VCR system.
Evaporator: What is it?The evaporator operates in opposition to the condenser; here, refrigerant liquid is transformed into gas while absorbing heat from compartment's air. The pressure of the liquid refrigerant has decreased by the time it reaches the evaporator, losing its heat content thus causing it to become significantly colder than the fan air circulating around it.
what are they Condenser and evaporator: what are they?Condenser coils discharge heat into outdoor air while evaporator coils absorb heat from indoor air. When heated refrigerant vapor cycles into the coil and condenses to liquid, it quickly releases the load of heat energy that has been collected from your home and compacted in it.
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two people hear a tornado siren, but one listener is 71.1 times farther away from the source of the sound than the other. what is the intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener? relative intensity:
-37.03 dB is the intensity level of the sound for the more distant listener relative to that for the nearer listener.
What is intensity level?
The intensity level of a sound, in decibels, is described as 10 times the logarithm to the base 10 of the ratio of the intensity of this sound to a reference intensity.
By using the inverse square law,
As one listener is 71.1 times farther away from the source of the sound than the other.
Then Increasing the distance by 71.1 times reduces the intensity by
(71.1)^2 = 5055.21
The intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener is:
= 10log(ratio of intensities)
= 10log(1/5055.21)
= 10log(0.00019782)
=10 × -3.7028
= -37.03 dB (The negative sign represents the sound is less intense for the farther listener)
So, the intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener is -37.03 dB.
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. how does the energy of photons change as they travel from the core to the surface of the sun? explain the methods of energy transfer that occur and why they change as the photons travel from the core.
As the photons travel from the center to the surface, their energy decreases; they cool to a temperature of about 6000 K, which is similar to the sunlight we observe.
Conduction is quite ineffective in this situation, but convection does contribute—it begins at the outer core. The outer core provides energy to the inner convection cells, which then interact with the outer convection cells.
However, radiation is the main cause. It takes a photon a long time to reach the surface because after it emits, hits something, and is excited by that something, the photon is then released once more in an arbitrary direction.
What does radiation signify from a physics perspective?
Radiation is the name for energy that comes from a source and travels through space at the speed of light.
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a railroad car of mass 2.00 3 104 kg moving at 3.00 m/s col- lides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 1.20 m/s. (a) what is the speed of the three coupled cars after the collision? (b) how much kinetic energy is lost in the collision?
The speed of the three couple car after the collision is 1.8 m/s and the total loss in kinetic energy of the system during the collision is 2.16 x 10⁴ J.
The mass M of the each railroad car is given to be 2 x 10³ kg and the speed U of the each railroad car is 3m/s. The speed V of the coupled car is given to be 1.20 m/s.
(a) According to the law Conservation of Linear Momentum, the linear momentum before and after the collision is always conserved.
So, we can write here,
MU + 2MV = (M+2M)V'
Where,
V' is the speed after collision.
U + 2V = 3V'
V' = (U+2V)/3
V' = (3+2.4)/3
V' = 1.8m/s.
(b) The loss in kinetic energy of the system can be calculated as,
∆K = final kinetic energy - initial kinetic energy
∆K = (1/2MU²+1/2×2MV²) - 1/2 × 3MV'²
Putting values,
∆K = (0.5×2.00×10⁴×(3.00)2+0.5×2(2.00×10⁴)(1.20)2)−0.5×3(2.00×10⁴)(1.8)2
∆K = 2.16 x 10⁴ J.
So, the loss in kinetic energy of the system after the collision is 2.16x10⁴ J.
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An object is thrown horizontally off a cliff with an initial velocity of 5. 0 m/s.
The vertical speed is 29.4 m/s.
What is vertical speed?
In aeronautics, the rate of climb is an aircraft's vertical speed, that is the positive or negative rate of altitude change with respect to time. In most ICAO member countries, even in otherwise metric countries, this is usually expressed in feet per minute; elsewhere, it is commonly expressed in meters per second.
The acceleration of gravity is 9.8 m/s². This simply means that when anything falls, its downward speed keeps increasing, and it falls 9.8 m/s faster every second than it fell 1 second earlier.
After 3 seconds of falling, the object is falling at (3 x 9.8 m/s) = 29.4 m/s faster than at the beginning of the 3 seconds. If it had no vertical speed at the beginning of the 3 seconds, then THAT's its speed after 3 seconds . . . . . 29.4 m/s downward.
As far as being thrown horizontally off the cliff . . . that has no effect on its vertical speed. Horizontally, it doesn't matter whether it rolls gently over the edge, or somebody throws it horizontally, or it gets shot horizontally out of a high power rifle. It hits the ground at the same time and at the same speed in every case.
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The following images show five planets in our solar system. Rank these planets from left to right based on their average surface (or cloud-top) temperature, from highest to lowest. (Not to scale.)
Highest -- Mercury, Earth, Mars, Jupiter, Neptune -- Lowest
Notice that, for these five planets, temperature correlates with distance from the Sun: the closer to the Sun, the hotter the planet. Remember, however, that this is not always the case, because a planet’s temperature also depends on its reflectivity and on the strength of its greenhouse effect (if any). For example, the greenhouse effect gives Venus a higher average temperature than Mercury, even though Venus is nearly twice as far from the Sun.
Highest to Lowest temperature:
Mercury
Earth
Mars
Jupiter
Neptune
What is average surface temperature?
Planetary surface temperatures range from over 400°C on Mercury and Venus to below -200°C on distant planets. The factors that determine temperature are the complex balance of heat received and lost.
For these five planets, temperature correlates with distance from the Sun. The closer to the sun, the hotter the earth. Note, however, that this is not always the case, as the planet's temperature also depends on its reflectance and the strength of the greenhouse effect (if present). For example, although Venus is almost twice as far from the Sun, the average temperature on Venus is higher than on Mercury due to the greenhouse effect.
Therefore, the temperature on each planet is according to the composition of that planet and the surrounding atmospheric gases.
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An electromagnetic wave of wavelength 435nm is traveling in vacuum in the − z-direction. The electric field has amplitude 2. 70×10−3v/m and is parallel to the x-axis.
The frequency of wave generated is [tex]6.9 * 10^{14} Hz[/tex].
The electromagnetic wave travels at the speed of light.
Speed of light (c) = [tex]3 * 10^{8} m/s[/tex]
Given wavelength is 435nm = [tex]435 * 10^{-9} m[/tex]
We can find the frequency(f) of the wave by using the relationship between f and c:
Frequency = speed of light/ wavelength
= [tex]3 * 10^{8} / 435 * 10^{-9}[/tex]
= [tex]6.9 * 10^{14} Hz[/tex]
So the frequency of wave generated is [tex]6.9 * 10^{14} Hz[/tex].
Complete question:
An electromagnetic wave of wavelength 435nm is traveling in vacuum in the − z-direction. The electric field has amplitude 2. 70×10−3v/m and is parallel to the x-axis. Find frequency of wave generated.
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A force of 10. Newtons toward the right is exerted on a wooden crate initially moving to the right on a horizontal wooden floor. The crate weighs 25 newtons. Calculate the magnitude of the force of friction between the crate and the floor.
The magnitude of the force of friction between the crate and the floor is calculated to be 5 N.
What is force of friction?Force generated by two surfaces that contact and slide against each other is referred to as frictional force.
Given: A force of 10 N towards right is exerted on a wooden crate initially moving to the right on horizontal wooden floor and weight of crate is 25 N
The magnitude of the force of friction between the crate and the floor is given as ;
F= μ* m * g
= 0.2 * 25
= 5N
The magnitude of the force of friction between the crate and the floor is 5 N.
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A moon orbits a planet in a nearly circular orbit of radius R, as shown in the figure.
Which of the following free-body diagrams could be used to analyze the forces exerted on the moon when it is at the position indicated in the figure?
The correct diagram is option F where GRAVITY arrow pointed to the right.
Explain how the moon orbits a planet ?A planet's gravitational influence on a moon is felt. The moon is dragged into a slightly extended shape because the near side of the moon experiences a stronger pull than the far side. We have ocean tides because the moon has a similar differential attraction on the Earth.
This specific instance of tidal locking was brought on by the gravitational pull of the Moon and Earth (called synchronous rotation).
The Earth takes 365 1/4 days, or one year, to complete one orbit of the Sun. The Moon revolves around the Earth as it revolves around the Sun. The orbit of the Moon lasts 27 1/2 days.
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if the objects are brought into thermal contact, is the temperature change of object 1 greater than, less than, or equal to the temperature change of object 2?
If the two objects are brought into thermal contact, object B gives up more heat and changes its temperature more than object A. The heat released by one object is absorbed by the other, and the temperature change of each is the same because the specific heats are the same.
What happens when objects at different temperatures come into contact ?When two objects with different temperatures come into contact with one another, energy moves from the hotter (higher temperature) object to the cooler (lower temperature) object until both objects reach the same temperature.
The thermal energy of the object increases as the average kinetic energy of its constituent particles rises. Therefore, as an object's temperature rises, so does its thermal energy.
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two of the three atoms in a molecule of water (h2o) are hydrogen. why are earth’s oceans not fusing hydrogen into helium, transforming our planet into a star?
The earth’s oceans is not fusing hydrogen into helium, transforming our planet into a star because Protons (hydrogen nuclei) carry positive electric charge and thus repel each other.
The earth as a planet?The third planet from the sun, Earth is the only place in the known universe confirmed to host life and has a radius of 3,959 miles, Earth is the fifth largest planet in our solar system, and it is the only one known for sure to have liquid water on its surface.
In order for two protons to come close enough to each other that the nuclear force that has short range can bind them, they must be moving at very high speeds.
This is only possible at temperatures in the solar core, but it is very hard to achieve these temperatures on Earth, thus the reason why fusion power has been so difficult to develop.
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if the power delivered were 59.32 kw, evaluate the outer surface temperature, in k, and the rate of entropy production, in kw/k, for the gearbox as the system, keeping input power, h, and a from example 2.4 the same.
In the case of the gearbox as the system, the outer surface temperature is 297 K, and the rate of entropy formation is 2.3*10-3kW.A surface's temperature is its ambient temperature.
More specifically, it can be talking about: Surface temperature, the temperature of the air at the earth's Surface temperature. A state of disorder, randomness, or uncertainty are frequently associated with the scientific notion of entropy, which is also a quantifiable physical attribute. Since work is produced by ordered molecular motion, entropy also serves as a proxy for a system's molecular disorder or unpredictability.
Q = ha(Ta-Tb) (Ta-Tb)
Q = (0.171)((1.0)(347k) (347k)
Q = 2.3*10^-3kW
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what is the distance on the screen from the center of the central maximum to the point where the intensity has fallen to i0/2?
Complete Question:
Two slits spaced 0.260 mm apart are placed 0.700 m from a screen and illuminated by coherent light with a wavelength of 660 nm. The intensity at the center of the central maximum ( = 0°) is [tex]I_{0}[/tex].
What is the distance on the screen from the center of the central maximum to the point where the intensity has fallen to [tex]I_{0}/2[/tex]
The distance on the screen from the center of the central maximum 0.44 mm where the intensity has fallen to [tex]I_{0}/2[/tex]
The two slits are separated by 0.260 mm.
The screen's distance from the slits is 0.700 meters.
The coherent light has a wavelength of 660 nm.
The value of the path difference will equal to [tex]\pi /2[/tex] because the intensity has decreased to [tex]I_{0}/2[/tex].
This path difference's above formula can be expressed as,
[tex]y_{n} = \frac{(2n-1)D\alpha }{2d}[/tex]
D is the distance of the screen to the slits.
[tex]\alpha[/tex] is the wavelength of the light
d is the distance between slits.
The intensity at the center of the central maximum is [tex]I_{0}[/tex]
Now,
[tex]y = \frac{(2*1)D}{d} *\frac{\alpha }{2\pi } *\frac{\pi }{2}[/tex]
Putting all the values in the formula, we get:
y = 0.44 m
Thus, the distance on the screen from the center of the central maximum 0.44 mm.
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Why do astronomers suspect that a supernova explosion occurred near the nebula that gave birth to the solar system?.
Astronomers suspect that a supernova explosion occurred near the nebula that gave birth to the solar system because it generated telltale patterns of unstable, short-lived radioactive isotopes.
Did a supernova cause the solar system to form?Our solar system may have formed when a cataclysmic supernova explosion's shockwave collided with a gas cloud.Samples of early meteorites still contain traces of the material ejected from the ancient blast.The supernova explosion that gave birth to our sun may have also contributed to the rotation of our solar system, enabling the construction of the planets, including Earth, according to scientists researching this process.The shock wave from a supernova may have had enough energy to crush the dust cloud before it, according to earlier research. And investigators have looked for signs of that explosion: Radioactive isotopes that are unstable and short-lived form distinctive patterns after supernovae.The identification of these anomalies' telltale signs in prehistoric rocks would support the theory that a supernova sparked the formation of the solar system.What Is a Supernova?The largest explosion that humans have ever witnessed is a supernova. Each blast is the extremely bright, super-powerful explosion of a star.Can learn more about supernova from https://brainly.com/question/24811835
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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 gravitational acceleration symbol is G. The standard value of the g is 9.8 m/s2 at sea level.
What respond with a square meter per second estimate?The magnitude of g, or Earth's gravitational acceleration, is 9.8 m/s2. The acceleration of a free falling object on Earth would be 9.8 meters per second, according to this. This acceleration is due to the Earth's gravitational pull.
Which of the following statements about the acceleration of Earth's gravitation is true?The acceleration that every thing experiences as it moves toward or away from the earth is due to gravity, and the average acceleration is the same for all objects. The object's mass has no bearing on i.
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What must an object be doing in order to have kinetic energy?
Answer:
An object must be in motion
Explanation:
In order for an object to have kinetic energey it must be moving. However, if it has potential energy, it hasn't started moving yet, but it has the potential to move.
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 2.20m/s to the right and an acceleration of 8.40m/s2 to the left. for related problem-solving tips and strategies, you may want to view a video tutor solution of velocity, acceleration, and energy in shm.
The object can move as farther as 0.2m.
Using the Sine Equation,
= x(t) = Asin(ωt)
=Here, t=0, x=0,
Given that,
Distance = x(t) = 0.60 = A sin(ωt)
Velocity = v(t) = 2.20 m/s = Aωcos(ωt)
Acceleration = a(t) = 8.40 m/s² = -Aω²sin(ωt)
Using wave equation,
= x(t) / a(t) = A sin(ωt) / -Aω²sin(ωt)
= ω² = 14 rad²/s²
= ω = 3.74 rad/s
The amplitude of the motion =
= x(t) / v(t) = A sin(ωt) / Aωcos(ωt)
= A = 0.2 m
Therefore, the amplitude of the motion is 0.2 m
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what is the maximum speed with which a 1200- kg car can round a turn of radius 87.0 m on a flat road if the coefficient of static friction between tires and road is 0.55?
The value of speed will be 21.67 m/s
It is given that,
Mass of the car = m=1200 kg
Radius of the round road = r=87.0 m,
Coefficient of static friction= 0.55
As we know,
The value of friction can be determined by using the relationship:
Friction = mCfg
Where, Cf = centripetal force, which can be calculated by relationship:
centripetal force = mv^2/r
As we know,
The point at which the speed is maximum
Then,
Ff = Fc
So, we can write it as:
[tex]mC_fg = \frac{mv^2}{r}\\v^2=\frac{rmC_fg}{m}\\v={\sqrt{C_fgr}[/tex]
So, the value of speed will be:
[tex]v = \sqrt{0.55 \times 9.81 \times 87)}\\v = 21.6658 \approx 21.67\: m/s[/tex]
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Help me please!!
Label the 3 forms of heat transfer. Conduction,
convection, or radiation.
Answer:
a. radiation
b. convention
c. conduction
Explanation:
a 12 kg runaway grocery cart runs into a spring, attached to a wall, with spring constant 290 n/m and compresses it by 80 cm . part a what was the speed of the cart just before it hit the spring? neglect any friction.
The initial speed of the cart is 1.3m/s.
The velocity of an object is the rate of change of its position with respect to a given time interval.
Given
Mass m of the cart = 12kg
Spring constant =290 N/m.
The compressed length of the spring = 10 cm.
The initial kinetic energy of the cart is given below.
K.E. = 1/2 m v2
v = initial velocity of the cart.
When the cart hits the spring, it is compressed by the cart. When the cart stops, due to the maximum compression, the kinetic energy of the cart will be zero. Hence its kinetic energy will be converted into elastic potential energy of the spring. This is given as,
U = 1/2 kx²
k = spring constant
x = compressed length of the spring.
This elastic potential energy of the spring will be equal to the initial kinetic energy of the cart.
U = 1/2 * 290*(0.80)² = 0.64.
U = 64J.
Elastic potential energy of the spring will be equal to the initial kinetic energy of the cart.
64 = (1/2) * 80 * v²
128 = 80 * v²
v² = 128/ 80
v² = 1.6
v = 1.26 ≅ 1.3
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The frequency which, under the sampling theorem, must be exceeded by the sampling frequency is called the Nyquist rate. Determine the Nyquist rate corresponding to each of the following signals:a) x(t) = 1 + cos(2,000πt) + sin(4,000πt)b) x(t)= sin(4000 π t) / π tc) x(t)= 2 [sin(4000 π t) / πt]2
Nyquist rate = 2*(maximum signal frequency)
Sampling rate must exceed Nyquist rate in order to be able to fully reconstruct the signal.
a) x(t) = 1 + cos (2000πt) + sin(4000πt)
Frequency for each term:-
Term 1 is DC -> w₁ = 0
Term 2 -> w₂ = 2000π
Term 3 -> w₃ = 4000π
Maximum signal frequency (wm) = 4000π
Another way of saying this is that X(jw) = 0 for |w| > 4000π
Acc to Sampling theorem ws > 2wm, ws>8000π
So, the Nyquist rate is 8000π
b) x(t) = sin(4000πt) / πt
Using Fourier Transport table, we have X(jw) = 1 for |w| < 4000π
.0 for |w| > 4000π
Therefore, maximum signal frequency (wm) = 4000π
Acc to the sampling theorem ws > 2wm, ws > 8000π
c) x(t) = {sin(4000πt) / πt}²
We can rewrite the above function as x(t) = x₁(t) x₁(t), where,
x₁(t) = sin(4000πt) / πt
Using the convolution property X(jw) = (1/2π)X₁(jw) * X₁(jw)
We know that convolving a signal with itself will double the maximum frequency therefore:
Therefore, maximum signal frequency (wm) = 8000π
Acc to the sampling theorem ws > 2wm, ws > 16000π
Therefore, the frequency to determine the Nyquist rate is 16000π.
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If the sun mysteriously gets twice as massive as it is right now, what effect will it have on its pull on mars?.
If the sun mysteriously gets twice as massive as it is right now, it's gravitational pull on Mars will be twice as much.
How are masses and gravitational pull of sun are related?The mass of the object also affects how strong the gravitational attraction is. The sun is very large and very powerful. It weighs somewhere between 2 times 10 raised to the 30th power kilos. More than 99 percent of the mass of the solar system is made up of the Sun. Because of its size, the Sun pulls the planets in with its strong gravity, which causes them to orbit it. Gravity is stronger for heavier objects. With distance, gravity also becomes weaker. Therefore, the gravitational pull of things increases with their proximity to one another. All of the mass on Earth contributes to gravity.To learn more about gravitational pull, refer:
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a 4.0-mm-diameter hole is below the surface of a 2.0-m-diameter tank of water. what is the rate, in mm/min, at which the water level will initially drop if the water is not replenished?
The rate that the water level would first decrease if it is not refilled is 1.06 mm/min.
Meaning of the water level:water volume (plural water levels) the height at which a water body is measured, particularly when done beyond a datum line. the height of the underground water table. the ship's waterline. a device that uses the water's surface on a trough or in vertical tubes connected by the a pipe to indicate level.
How exact is the level of the water?The accuracy of water levels is theoretically limited only by human vision. The length of the tube and the thickness of the liquid are two significant problems that can impair accuracy.
Briefing:h = height of the water level above the hole = 1 m
dh = diameter of hole = 4 mm = 0.004 m
Ah = Area of cross-section of hole = (0.25)\pi d^{2} (for hole)
dt = diameter of tank = 2 m
At = Area of cross-section of tank = (0.25)\pi d^{2} (for tank)
R = rate at which the water level drop
Rate at which the water level drop is given as
R=[Ah(\sqrt{2gh)]/At
R= [ (0.25)\pi d^{2}(\sqrt{2gh) ] /2^{2}
R=17.7*(10)^-6 m/s
R=0.0177mm/s
R=(0.0177)(60) mm/min.
R=1.06 mm/min.
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while looking at her image in a cosmetic mirror, dina motes that her face is highly magnified when she is close to the mirror, but as she backs away from the mirror, her image first becomes blurry, then disappears when she is about 30 cm from the mirror, and then inverts when she is beyond 30 cm. based on these observations, what can she conclude about the properties of the mirror?
R=60cm We determine that Dina's upright picture is produced as she steps back from the mirror, which is spherical with a concave f=30 cm. Thus, the mirror is spherical but concave and the image of the object is
What are some instances of concave?A form with an inward curvature is said to be concave. Concave shapes include those like the sideview window of a car, which curls inward. When a shape curves outward, it is said to be convex. One excellent example of a convex form is the outward-curving (American) football.
What form is concave?One that veers inward at a single point is said to have a concave shape. A polygon with a sharp inside angle or a curved form with an inwardly curving part can both fit the bill. When a line connects two points inside a shape and leaves the shape at an angle, the shape is said to be concave.
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50 g of sugar is dissolved in 500 g of water. What is the percent by mass of salt?
HINT: find the total mass of the solution first.
The percentage by mass of the salt, given it was dissolved in 500 g of water is 9.09%
How do I determine the percentage of the salt?we'll begin by obtaining the mass of the solution. This is shown below:
Mass of salt = 50 gramsMass of water = 500 gramsMass of solution =?Mass of solution = Mass of salt + Mass of water
Mass of solution = 50 + 500
Mass of solution = 550 grams
Finally, we shall determine the percentage of the salt. Details below:
Mass of salt = 50 gramsMass of solution = 550 gramsPercentage of salt =?Percentage = (mass of solute / mass of solution) × 100
Percentage of salt = (50 / 550) × 100
Percentage of salt = 9.09%
Thus, the percentage of the salt is 9.09%
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