The resultant force will be f/2. This means that the resultant force is half of the original repulsive force between the two charged particles.
What is Coulomb's law?According to B, the electrical force between two charged objects is inversely proportional to the square of the separation distance between the two objects and directly proportional to the product of the charges on the objects.
Mathematical expression of Coulomb's law:
[tex]F=\frac{kQ_{1}Q_{2} }{d^{2} }[/tex]
Here,
F = Electrical force
Q1 = Charge on the first object (in Coulombs)
Q2 = Charge on the second object (in Coulombs)
d = Distance between the two objects (in meters)
k = A proportionality constant (Coulomb's law constant)
According to the problem given, the force would double if one of the charges were doubled. The force would be four times lower if the distance were doubled. These two variations working together would result in a two-fold reduction in force thus resulting into f/2.
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a 25.0-mh inductor, a 2.00-μf capacitor, and a certain resistor are connected in series across an ac voltage source at 1000 hz. if the impedance of this circuit is 200 ω, what is the resistance of the resistor?
Resistor 184Ω has a resistance of.
Explanation of voltageThe "pressure" that drives electricity is known as voltage. Higher voltages cause more electricity to flow to an electronic equipment. The voltage is measured in units called volts (V), and it is symbolized by this unit.
What exactly are voltage and current?The difference in electric potential between two places is what is referred to as voltage, in other words. Simple electric charge flow rate is known as current. The current, put simply, is the rate at which electrical charge moves across a circuit at a specific location. Volts is the voltage measurement unit used in the SI (V).
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A rocket launched vertically rises with a constant speed for 60 s to a height of 10000 m. If the mass of the rocket is 1000 kg (and assume mass is constant), what is the power of the engine? (use g
The power of the rocket has a mass of 1000 kg is 16,33,333.33 Watt
The mass of the rocket = 1000 kg
The rocket travels at a constant speed for 60 s
The displacement of the rocket = 10000 m
The formula to find the power of the rocket engine is
P = F x v
where F is the force and
v is the velocity
Thus P = (m x g x d)/t
where m is the mass of the rocket
g is the acceleration due to gravity
d is the displacement
t is the time taken
Let us substitute the known values in the above equation, we get
P = ( 1000 x 9.8 x 10000 ) / 60
= 98000000 / 60
= 1633333.33
Therefore, the power of the rocket is 16,33,333.33 W
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monochromatic light of wavelength 694 nm is incident on two parallel slits. what is the distance y to the first maximum on a screen beyond the slits? answer in units of m.
The distance to the first maximum on a screen beyond the slits is 0.009512 m.
It is given that,
The wavelength of the monochromatic light = 694 nm
It is given that, monochromatic light is incident on two parallel slits.
We have to determine the value of the distance y to the first maximum on a screen beyond the slits
As we know,
The distance to the first maxima is given as,
[tex]\mathrm{y} & =\frac{\lambda \mathrm{D}}{\mathrm{d}} \\[/tex], y = distance to first maxima.
λ= wavelength of light
d = distance between slits
D = distance between slits and screen
From above given equation,
The value of distance y to the first maxima will be:
[tex]& =\frac{694 \times 10^{-9} \times 3.18}{0.232 \times 10^{-3}} \\\\ =0.009512 \mathrm{~m}[/tex]
Hence the distance to the first maxima is 0.009512 m
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The missing diagram is attached:
The measure of an object's mass and velocity is called __________. A. Gravityb. Accelerationc. Inertiad. Momentum.
the answer is momentum.
a nuclear reactor has a rated capacity of 1 gw and produces 7.9 billion kwh/year. it is fueled using fuel rods that contain 2.5% 235u by mass. the accompanying electric generator is 98% efficient, the thermal cycle of the plant is 33% efficient and 90% of the thermal energy released during fissioning is transferred to the working fluid. a) what is the capacity factor of the power plant? b) what is the rate of u-235 consumption in g/s in order to deliver the average output? c) what is the total mass of fuel rods consumed each year? d) based on the amount of energy released in fission reactions, what is the reduction in mass of fuel each year?
The reduction in mass of fuel each year $0.0075/kW-hr 0.75 cents/kW-hr.
What is electrical energy?
1 GW plant operating at full load produces 1,000,000 kW and an annual electrical energy generation of
1,000,000 . 365 . 24 = 8.76 × 109 kW-hr
With a heat rate of 7.9 Billion Btu/kW-hr, this requires a heat addition rate of
1000000 . 7900000000 = 7.9 X 1014
fueled using fuel rods that contain 2.5% U-235 by mass means
2.5% = 250 ( Fuel carried about 100 tons )
the plant needs = 2.5 X 24 / 100 = 0.6 unit trains per day
If fuel costs $30 per ton, the annual cost of fuel will be
30 X 250 X 24 X 365 = $65,700,000
The cost of fuel alone per kW-hr, based on 100% annual plant capacity, will be
65,700,000/(1000,000 X 365 X 24) = $0.0075/kW-hr 0.75 cents/kW-hr
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. A rock is thrown vertically upwards at 67 km/h. Find the height at which the rock is
going 23 km/h [down]. (DON'T FORGET UNITS CONVERSION)
The height at which the rock is going 23 km/h downwards be 15.59 m.
What is law of conservation of energy?Energy cannot be created or destroyed, according to the rule of conservation of energy. However, it is capable of change from one form to another. An isolated system's total energy is constant regardless of the types of energy present. The law of energy conservation is adhered to by all energy forms.
The law of conservation of energy essentially says that: The total energy of the system is conserved in a closed system, also known as an isolated system.
Given that: A rock is thrown vertically upwards at 67 km/h = 18.6111 m/s.
We have to find its height, when downwards velocity is 23 km/h = 6.389 m/s.
Let the mass of the rock be m and using law of conservation of energy:
1/2 m (18.6111)² = mgh + 1/2m(6.389)²
⇒ h = (18.611² - 6.389²)/(2×9.8) m = 15.59 m.
Hence, the height at which the rock is going 23 km/h downwards be 15.59 m.
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if the earth were of uniform density, what would be the value of g inside the earth at half its radius? (the value of g at the surface of earth is 9.8 m/s2 .)
The value of g inside the earth at half its radius would be 4.9 m/s2. This is calculated by halving the surface gravitational acceleration (9.8 m/s2) due to the inverse square law of gravity.
What is gravity?
Gravity is indeed a fundamental interaction in physics that causes all objects with mass or energy to attract one another. The electromagnetic force, the weak interaction, and the strong interaction are all significantly stronger than gravity, which is by far the weakest of a four fundamental interactions. As a result, it doesn't have any appreciable impact on subatomic particle level phenomena. However, at the macroscopic level, gravity is the most important interaction between objects and governs the motion of planets, celestial objects, galaxies, and even light.
The Moon's gravity causes sublunar tides inside the oceans, just as it does on Earth where gravity gives more weight to physical objects.
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A student set up a test tube containing sodium bicarbonate and topped it with a volumeter, but forgot to add the Elodea plant! Which of the statements below gives the result that the student would be likely to observe?
A. The level of liquid in the volumeter would rise due to diffusion.
B. The level of liquid in the volumeter would remain constant since gas is being produced and used at the same rate.
C. The level of the liquid in the volumeter would remain constant since gas is neither being produced nor being used.
D. The level of liquid in the volumeter would fall since there is less mass in the test tube.
E. The level of liquid in the volumeter would fall since atmospheric pressure is greater than the pressure within the test tube.
The result that the student would be likely to observe when A student set up a test tube containing sodium bicarbonate and topped it with a volumeter, but forgot to add the Elodea plant is he level of the liquid in the volumeter would remain constant since gas is neither being produced nor being used. the correct answer is c.
A volumetric meter can be described as any instrument used to measure the volume of solids, liquids, or gases.
Sodium bicarbonate dissolves in water to form carbonic acid and sodium hydroxide. This carbonic acid is further broken down into water and carbon dioxide.
The carbon dioxide produced can be used by Elodea plants for photosynthesis, a process that uses carbon dioxide to produce oxygen and energy.
However, in this case he did not add the Elodea plant, so no sodium bicarbonate was consumed or produced, and the volumetric level remained constant.
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Two trains emit 516-Hz whistles. One train is stationary. The conductor on the stationary train hears a 3.5-Hz beat frequency when the other train approaches. What is the speed of the moving train? b = beat f'_b = 3.5 Hz f = 516 Hz
The speed of the moving train is 2.31 m/s
What is called speed?
Speed is described as. the rate at which an object's position changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it only has a direction and no magnitude.
Speed is calculated as follows: speed = distance/time. Knowing the units for distance and time is necessary to calculate the units for speed.
According to the given information:
[tex]f=\frac{v}{s} *f_{0}[/tex]
s = speed in air,
v is the speed of the train,
f₀ is the frequency of the siren,
f₀ = 516 Hzs = 340.29 m/s
f = 3.5 Hz
v = (3.5 / 516) × 340.29 = 2.31 m/s.
So, the speed of the moving train is 2.31 m/s
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while cruising at 190 knots, you wish to establish a climb at 160 knots. when entering the climb (full panel), it would be proper to make the initial pitch change by increasing back elevator pressure until the group of answer choices airspeed indication reaches 160 knots. attitude indicator, airspeed, and vertical speed indicate a climb. attitude indicator shows the approximate pitch attitude appropriate for the 160-knot climb.
The correct answer is option D.
The attitude indicator shows the approximate pitch attitude for the 160-knot climb.
What is Weather station model?
Weather station model is basically the weather forecaster which tells about the weather conditions such speed of the wind, temperature of the weather, atmospheric pressure, sea levels change and the change in the weather since three years.
Therefore, knots established, can change the pressure until the attitude indicator shows the approximate pitch attitude appropriate for the 160-knot climb.
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When you view a distant rainbow, you view from each single water drop that contributes to the bow.
Answer:
Yes the light travelling gets refracted through the tiny water droplets suspended in the air.
Explanation:
There are 2 types of rainbow which includes - Primary and secondary rainbow.
A primary rainbow is a coloured bow or arc that appears on a “screen” of water drops when light from a bright light source (the Sun or Moon) falls upon them. A thick “screen” of raindrops will produce more vivid colours than a thin curtain of fewer drops.
A secondary rainbow is appears outside of a primary rainbow and develops when light entering a raindrop undergoes two internal reflections instead of just one.
Therefore whatever we see comes from each single water drop due to refraction.
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A proton and an electron are placed in an electric field. Which undergoes the lesser acceleration?.
Among proton and an electron which are placed in an electric field a proton will undergo lesser acceleration.
Why proton undergoes lesser acceleration?According to Newton's 2nd law ;
F[tex]net[/tex] = ma
m is the object's mass
a is its acceleration
F[tex]net[/tex] is the net force acting on it.
∴The electric force on a charged object is given by
F[tex]e[/tex] = Eq
Where,
F[tex]e[/tex] is the electric force
E is the electric field at the point where the object is
q is the object's charge.
Here, we assume that if the only force acting on the proton and electron is the electric force due to the electric field, that for both particles,
F[tex]net[/tex] = F[tex]e[/tex]
F[tex]e[/tex] = Eq
Eq = ma
a = Eq/m
We'll also suppose that the proton and electron are both subject to the same electric field. The charge of the proton and electron is the same (1.6 10⁻¹⁹ C). Their masses determine how differently they accelerate.
∴mass of proton = 1.67×10⁻²⁷kg
∴mass of electron = 9.11×10⁻³¹kg
Since an object's acceleration is inversely proportional to its mass, the electron will accelerate more slowly than the electron.
What is acceleration?The rate at which velocity varies with respect to time is referred to as acceleration. Since acceleration has both a magnitude and a direction, it is a vector quantity. Additionally, it is the first derivative of velocity with respect to time or the second derivative of position with respect to time.Can learn more about acceleration from https://brainly.com/question/12240608
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a long straight conductor has a circular cross section of radius r and carries a current i. inside the conductor, there is a cylindrical hole of radius a whose axis is parallel to the axis of the conductor and at a distance b from it.
When current is straight, it means the current is passing through a straight conductor, the magnetic field produced due to current through a straight conductor is in the form of concentric circle and are in a plane perpendicular to the plane of linear conductor. It means the magnetic field is circular.
What is straight line conductor?a straight conductor is a wire having magnetic field lines centre on it.
When a current in a circular loop is?Electric current in a circular loop creates a magnetic field which is more concentrated in the center of the loop than outside the loop. Stacking multiple loops concentrates the field even more into what is called a solenoid.
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As a result of the experiment scientists did with mexican tetras, it seems likely that their first hypothesis about blindness in the tetras is right. Explain how the result of the experiment supports their first hypothesis.
The first hypothesis put out by the researchers holds that the fish's blindness indirectly confers some form of evolutionary advantage.
Why can't the Mexican tetra see?
The loss of eyes is largely caused by cellular deterioration in the eye lens, according to experiments . Theoretically, the emergence of these eyeless fish was caused by this process in combination with natural selection over many generations.
Regressive evolution can be shown in cave fishes. This kind of evolution involves the loss of a property within a species. That characteristic is vision in cave fishes.
In conclusion, a finding supporting the theory that "blindness affords the fish some evolutionary advantage, although not directly" may be a greater fitness in fish relatives.
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what can the radial velocity method determine about an exoplanet that the transit detection method cannot?
A transiting exoplanet in relation to the star that it is orbiting. The photometric approach can figure out a planet's radius whereas the radial velocity technique can tell you how much mass a planet has.
How can you find extrasolar planets using the radial velocity method?Utilizing the Doppler changes in the wavelength of the planet's star, the radial velocity approach finds extrasolar planets. A star would show a bluish change as it approached the earth. The radial velocity technique detects the redshift of the spectrum of a star that is travelling away from Earth.
Why is it that low mass stars benefit from the radial velocity method?Because of the fact that planets' gravitational pull on low mass stars is stronger and also because these stars often spin slower rate.
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The radial velocity method can determine the mass of an exoplanet, while the transit detection method cannot.
The radial velocity method, also known as the Doppler spectroscopy method, measures the slight shifts in the wavelength of light emitted by a star due to the gravitational tug of an orbiting exoplanet. This method allows scientists to determine the mass of the exoplanet. When an exoplanet orbits its host star, it induces a small wobble in the star's motion. By measuring these periodic changes in the star's radial velocity (motion along the line of sight), scientists can infer the mass of the exoplanet.
On the other hand, the transit detection method involves observing the periodic dimming of a star's brightness as an exoplanet passes in front of it, blocking a fraction of the star's light. This method provides information about the exoplanet's size, orbital period, and distance from its host star. However, it cannot directly determine the exoplanet's mass.
By combining the radial velocity method with the transit detection method, scientists can gather more comprehensive information about exoplanets. The combination of these two techniques enables the determination of an exoplanet's density, which provides insights into its composition and potential characteristics such as whether it is rocky or gaseous.
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was newton a realist or anti-realist?
Answer: Newton was a realist
Explanation: Newton held a realist reading of scientific theory as based upon inference from facts and observation, and his gravitational theory (or NGT) as deduced from observed phenomena and Kepler's laws.
After glycolysis, the potential energy of glucose is now in the potential energy of.
After glycolysis, the potential energy of glucose is now in the potential energy of two pyruvate molecules.
How does glycolysis works?The eleven steps of glycolysis are used to obtain energy from glucose molecules.The process of glucose metabolism begins here.Both aerobic and anaerobic circumstances can cause it.Pyruvic acid joins the citric acid cycle in aerobic conditions. It passes through an oxidative phosphorylation process, which produces ATP.Pyruvic acid changes into lactic acid in anaerobic conditions, producing a net of two ATP molecules.Two ATP molecules are used by one glucose molecule, while four ATP, two NADH, and two pyruvates are also produced. The citric acid cycle or other reactions use this pyruvate molecule as a precursor.What is glycolysis?When glucose (a 6-carbon molecule) is broken down into two molecules of pyruvate (a 3-carbon molecule) under aerobic conditions or into lactate under anaerobic conditions, a tiny quantity of energy is also produced.
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the heaviest flying bird is the trumpeter swan which weighs in at 38 pounds. what is its weight in newtons
The heaviest flying bird is the trumpeter swan which weighs in at 38 pounds than its weight in newtons is = 169.1N
Given:
Flying bird Trumpeter swan weighs in pound = 38 pound
We have that each pound has 4.45 newtons
⇒ 38 × 4.45 = 169.1
What's the distinction between pounds and newtons?
Pound force is defined as the gravitational pull of one avoirdupois pound of mass on the surface of the earth. 1 lbf is equivalent to 4.4482216152605 Newton [N], the corresponding metric unit.
Is a pound of mass or force?
The fact that the Imperial (or U.S. Customary) system of measuring uses the same unit, the pound, to measure both mass and force, is one of the biggest sources of misunderstanding in this system. We refer to one sort of pound as the pound-mass (lbm) and the other as the pound-force to distinguish between the two (lbf).
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a train is moving at a speed of 65 mph. the ticket collector is walking 2 mph toward the front of the train. how fast, in mph is the ticket collector moving from the point of view of an observer on the side of the tracks?
The ticket collector's speed is the sum of the train's speed (65 mph) and their walking speed (2 mph).
What is speed?
The speed of an object, also known as v in kinematics, is a scalar quantity that refers to the size of the change in that object's position over time or the size of the change in that object's position per unit of time. An object's average speed over a period of time is calculated by dividing its distance travelled by length of the interval This same instantaneous speed is indeed the maximum possible speed as the interval's duration gets closer to zero. Velocity and speed are different concepts. Distance divided by the time is the dimension of speed.
From the point of view of an observer on the side of the tracks, the ticket collector is moving at a speed of 67 mph (65 mph + 2 mph). This is because the observer is stationary relative to the ground, and the ticket collector is moving relative to the ground. Therefore, the ticket collector's speed is the sum of the train's speed (65 mph) and their walking speed (2 mph).
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how much force in newtons is required to accelerate a 5 kg bowling ball at 2 m/s2?(1 point) responses 2.5 n 2.5 n 7 n 7 n 10 n 10 n 3 n
To accelerate a 5 kilogram bowling ball at 2 m/s2, 10N of force is needed.
How do you determine force?Newton's second principle of motion provides the definition of the force formula: An object's force is equal to its mass times its acceleration. F = m ⨉ a. To use this method, you must use SI units for force (newtons), mass (kilograms), and acceleration (meters per second squared).
What two categories of forces exist?Contact forces and function at a distance forces are the two different types of forces. Your daily use of force is evident. Basically, push and pull are forces. You exert force on an item when you push against it or pull against it.
Briefing:
To calculate F = ma,
multiply 5 kg by 2 m/s2.
which gives you 10N.
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a car speeds up from 3 m/s to 23 m/s. if the car has a mass of 749 kg,what is the change in the car’s momentum?
Answer:
f
Explanation:
a runner moving at a speed of 8.8 m/s rounds a bend with a radius of 25 m. what is the centripetal acceleration of the runner, and what agent exerts force on the runner?
The force on the runner is equal to the mass of the runner multiplied by the acceleration due to gravity, which is the force of gravity acting on the runner.
What is centripetal force?
A force that causes a body to follow a curved path is known as a centripetal force. It always moves in a direction that is the opposite of the body's motion and in the direction of the instantaneous centre of curvature of the path. It is "a force through which bodies are attracted or impelled, or in any other way tend, toward that point in relation to a centre," according to Isaac Newton. Gravity is the centripetal force that drives astronomical orbits according to Newtonian mechanics. A common illustration of centripetal force is when a body moves uniformly fast in a circular motion. The centripetal force is applied towards the center of the circle path both along the radius and at sharp angles to the motion. Dutch physicist Christiaan Huygens developed the mathematical description in 1659.
The centripetal acceleration of the runner can be calculated using the formula a = v²/r, where a is the centripetal acceleration, v is the speed of the runner, and r is the radius of the bend.
Therefore, the centripetal acceleration of the runner is:
a = (8.8 m/s)²/25 m
= 4.6 m/s²
The agent that exerts force on the runner is gravity, which acts downwards on the runner and produces the centripetal force needed to accelerate the runner around the bend. This can be demonstrated mathematically using the equation F = ma, where F is the force, m is the mass of the runner, and a is the centripetal acceleration.
F = m*(v²/r)
= m*4.6 m/s²
= m*g
Therefore, the force on the runner is equal to the mass of the runner multiplied by the acceleration due to gravity, which is the force of gravity acting on the runner.
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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. group of answer choices 2273 n 1800 n 1500 n 2500 n
The force exerted on the motorcycle by the road due to friction is 2273n.
Solution:
m = 500 kg
v = 25 m/s
u = 0 m/s
t = 5.5 s
F = 500(25-0)/5.5
F = 2272.72 N
Friction offsets the weight to keep the motorcycle moving on the loop at a constant speed. Both weights and normals point down towards the center of the loop. The net force is the centripetal force. Dry friction always opposes sliding between surfaces and can react or act on bodies in motion. This motorcycle creates dry friction between the tires and the road surface.
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how does the image distance (the distance from the lens to the focused image) change with the object distance (the distance from psy to the lens?)
The image distance (the distance from the lens to the focused image) change with the object distance (the distance from object to the lens) due to the lens formula.
Lens formula is defined as the relationship between object distance (u), image-distance (v) and the focal length (f). Following is the mathematical representation of lens formula:
Lens Formula : 1/f = 1/v - 1/u
Where f = focal length
v = image distance
u = object distance
The lens is a transparent material which is bound by two surfaces. It has a principal axis, principal focus, centre of curvature of lens, aperture and optical centre.The images obtained from these lenses can be either a real image or a virtual image.To know more about lens visit:
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t is 165 cm from your eyes to your toes. you are standing 200 cm in front of a tall mirror. how far is it from your eyes to the image of your toes?
The calculated total distance from the eyes to the toes is given by 432.7 cm.
Given:
Distance, x = 200 cm
Horizontal distance, h = 165 cm
We can use the idea of virtual images created by mirrors to calculate the distance between your eyes and the image of your toes in the mirror.
When you stare at a mirror, light rays from your eyes reflect off of it and give the impression that they are coming from behind the mirror. The virtual reflection created by the mirror appears to be at the same height as you are in front of it.
The horizontal distance is:
d = 2x
d = 2 × 200
d = 400 cm
The total distance from eyes to toes is:
D = √(d² + h²)
D = √(400² + 165²)
D = 432.7 cm
Hence, the calculated distance from the eyes to the toes is given by 432.7 cm.
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adisk of mass 2 kg and radius o.26 m hangs in the xy plane froma horizontal low-friction axle. the axle is o.07 m from the center of the disk. what is the frequency f of small-angle oscillations of the disk?
The frequency f of small-angle oscillations of the disk is:
f= 0.955Hz.
T = 2(π)²([tex]I_{s}[/tex] / mgh)
Given:
m = 2kg
r = 0.26m
h = 0.07m
[tex]I_{s}[/tex] = [tex]I_{c}[/tex] + md²
[tex]I_{c}[/tex] = [tex]\frac{mr^{2} }{2}[/tex] ( disk moment of Inertia)
d = h = 0.07
T = 2(π)²( [tex]\frac{mr^{2} }{2}[/tex] + [tex]\frac{m\frac{h^{2} }{2} }{mgh}[/tex] )
T = 2(π)² ( [tex]\frac{( r^{2} + 2h^{2} )}{2g}[/tex] )
T = 1.047s
f = [tex]\frac{1}{T}[/tex]
f = 0.955Hz
period
T = 1.047s
What is the definition of a frequency simple?
Frequency is the number of waves that pass a specific area in a defined amount of time. As a result, the frequency is 2 per second if a wave travels through in half a second.
What other names does frequency go by?
Cycles per second or temporal frequency are other terms for frequency. Frequency is often represented by the Greek letter ν or the Latin letter f. (nu).
Which five types of frequency are there?
Frequency Distribution Types
frequency distribution for groups.
Frequency distribution without grouping.
frequency distribution that is cumulative.
Frequency distribution relative.
distribution of the relative cumulative frequency.
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what theoretical device would generate the maximum possible amount of work from a given amount of heat?
Answer:
An ideal "Carnot" engine
E = (Q2 - Q1) / Q2 or 1 - Q1 / Q2
Q1 (heat wasted) would have to be zero for 100% efficiency
a diode laser emits at a wavelength of 987 nm. (a) in what portion of the electromagnetic spectrum is this radiation found? (b) all of its output energy is absorbed in a detector that measures a total energy of 0.52 j over a period of 32 s. how many photons per second are being emitted by the laser?
Answer: A
Explanation:
I took the test
a thin hubcap is modeled by the part of the sphere that lies above the plane , and is made of a material of constant density . what is the moment of inertia of when it is rotated around the -axis?
The moment of inertia of when it is rotated around the -axis [tex]\frac{10\pi }{3}[/tex].
Solution:
= [tex](\sqrt{2\pi _{d6} } ) (\sqrt{3} \frac{r^{3} dr}{4-r^{2} }[/tex]
= [tex]2\pi *\frac{5}{3}[/tex]
= [tex]\frac{10\pi }{3}[/tex]
Consider a line that passes through the center of the ring and is perpendicular to the plane of the ring. Let R be the radius of the ring and M be its mass. All elements are at the same distance from the axis of rotation. The moment of inertia formula is the sum of the mass products of each particle multiplied by the square of the distance from the axis of rotation.
Moments of inertia oppose the rotational motion, so they are called moments of inertia rather than moments of force. A moment of inertia is defined with respect to a particular axis of rotation. The moment of inertia of a mass with respect to an axis is defined as the square of the mass times the distance from the axis.
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Two blocks, each of mass m=3.50kg, are hung from the ceiling of an elevator as in above figure. (a) If the elevator moves with an upward acceleration aof magnitude 1.60m/s 2, find the tensions T 1and T 2in the upper and lower strings. (b) If the strings can withstand a maximum tension of 85.0N, what maximum acceleration can the elevator have before a string breaks.
The tension in the upper and lower string is 79.8 N and 39.9 N respectively and the maximum acceleration of the elevator at tension of 85 N is 2.34 m/s².
(a) Mass of blocks = m = 3.5 Kg
Acceleration of the elevator = a = 1.6 m/s²
Gravitational force experienced by both strings = G
= m X g
= 3.5 X 9.8
= 34.3 N
For the lower block, apply Newton's Second Law of Motion,
Net force on the lower block =
= F = T₂ - (m X g)
= (m X a) = T₂ - (m X g)
= T₂ = (m X a) + (m X g)
= T₂ = m X (a + g)
= T₂ = 3.5 X (1.6 + 9.8)
= T₂ = 39.9 N
For the upper block, apply Newton's Second Law of Motion,
Net force on the Upper block =
= F = T₁ - T₂ - (m X g)
= (m X a) = T₁ - T₂ - (m X g)
= T₁ = T₂ + (m X g) + (m X a)
= T₁ = 39.9 + 3.50 X (9.8 + 1.6)
= T₁ = 79.8 N
(b) Now we know that T₁ > T₂, thus the upper string will break before the lower string. So, acceleration will increase when the upper string breaks.
Tension given = T₁ = 85 N
Acceleration = a =
= T₁ = T₂ + (m X g) + (m X a)
But, T₂ = m X (a + g)
Thus,
= T₁ = m X (a + g) + (m X g) + (m X a)
= T₁ = 2 X (m X a) + 2 X (m X g)
= a = (T₁ - ( 2 X (m X g))) / (2 X m)
= a = (85 - [ 2 X ( 3.5 X 9.8)] ) / (2 X 3.5)
= a = 2.34 m/s²
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