The offered statement states that the rock hits the water at various times and with equal velocity.
What is a speed set of questions?The number of kilometers reached to the time needed to travel that distance is known as speed. Since speed simply has a part and no magnitude, it is a proportionality constant.
Briefing:
If we ignore air resistance due to the energy conservation, then the velocity of both stones would have to be equal because energy is a finite resource. They will each have the same sum of kinetic and potential energies at the beginning, hence the potential and the kinetic energies must be identical at the end, this happens when they reach the ground. Potential energy will change into kinetic energy.
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a stuntman is being pulled along a rough road at a constant velocity, by a cable attached to a moving truck. the cable is parallel to the ground. the mass of the stuntman is 109 kg, and the coefficient of kinetic friction between the road and him is 0.870. find the tension in the cable.pdf
The tension in the cable is 929.334 N.
Solution:
The net force in the horizontal direction is T - F = 0.
Resolving vertically,
N = mg
The relationship between friction and reaction force is
[tex]F = \mu_{k}N[/tex]
[tex]T - \mu_{k} N = 0[/tex]
[tex]T = \mu_{k} mg[/tex]
= [tex](0.870)(109 kg) \times 9.8 \frac{m}{s^{2}}=(0.870)(109kg)[/tex] x 9.8ms²
N = 929.334N.
Tension refers to the force transmitted when a cable, rope, wire, or cord is knotted by forces acting on both ends. The cord is unidirectional along its length and pulls the object evenly at both ends of the cord. As lift increases, the total stress equals the sum of weight and force due to acceleration. As the lift is lowered, the total stress equals the difference in weight and force due to acceleration.
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How can friends, family members, or teammates
increase the likelihood of you reaching your goals?
a ferris wheel starts from rest and builds up to a final angular speed of 1.9 rad/s while rotating through an angular displacement of 4.9 rad. what is its average angular acceleration?
The average angular acceleration of Ferris wheel is 0.368m/s².
According to their position on the Ferris wheel, riders will feel "heavier" or "lighter" depending on the physics of the Ferris wheel, which is directly related to centripetal acceleration.The passenger gondolas (seats) for the ferris wheel are attached to the rim of an upright wheel. At the support where they are connected to the Ferris wheel, these gondolas can freely pivot. As a result, while the Ferris wheel is spinning, the gondolas always hang downward.ω=1.9rad/s
α=4.9rad
To find angular acceleration.
[tex]w^2=2\alpha s[/tex]
To find α:-
[tex]\alpha =\frac{w^2}{2s}[/tex]
=1.9 x 1.9/9.8
=0.368m/s²
To find angular acceleration-
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what do we mean by the halo of a galaxy? (a) it is the central region that is crowded with stars. (b) it is a large, roughly spherical region surrounding the disk. (c) it is the pancake-shaped region in which spiral arms are found.
A galaxy's halo is a large, generally spherical area that surrounds the disk.
Solution b is accurate.
What is Halo Galaxy?An extended, approximately spherical component of a galaxy that extends beyond the primary, visible component is called a galactic halo. The halo is made up of several distinctive galaxy parts, including: the halo of a star. a galaxy's corona (hot gas, i.e. a plasma)
The term "halo" refers to a ring of light that seems to surround the sun or moon and is caused by the refraction or reflection of light by atmospheric ice particles.
Globular clusters and other aging stars can be found in the galactic halo, a region of the galaxy that extends far above and below the galactic disk. - Roughly round; somewhat flattened. - Only includes old stars. - is free of gas and dust.
Thus halo galaxy is a large, roughly spherical region surrounding the disk (option B is correct)
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A block of iron has the dimensions of 3. 00 cm x 3. 00 cm x 3. 00 cm. It has a mass of 213 g. When placed in water, the block sinks. What volume of water did it displace? 213 cm 3 0. 127 cm 3 7. 89 cm 3 27. 0 cm 3.
When the block of iron is placed in water the volume of water that is displaced is 27.0 cm³
Hence, Option D is correct.
Explain in detail.
The volume water that is displaced is equal to volume of block of the ironvolume of block of iron = length x width x height length= 3 cm width = 3 cm height = 3 cmtherefore the volume displaced = 27 cm³ since the volume of water displaced is equal to volume of block.
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A 90 g mass is attached to one end of a 10-cm-long spring. The other end of the spring is connected to a frictionless pivot on a frictionless, horizontal surface. Spinning the mass around in a circle at 90 rpm causes the spring to stretch to a length of 12 cm.
The spring constant of the spring is 6.66 N/m.
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity.
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
The rotational speed of the 90 g = 0.09 kg mass is: ω = 90 rpm
= 90×2π/60 radian/second.
= 3π radian/second.
So centripetal force acting on the spring = mω²r
This causes the spring to stretch to a length of 12 cm = 0.12 m.
Hence, spring constant: k = mω²r/0.12 = 0.09×(3π)²×0.10/0.12 N/m = 6.66 N/m.
Hence, the spring constant of the spring is 6.66 N/m.
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in sec. 10.6 of the experiment, your ear simultaneously hears waves from different sources, so it can hear beats from the two speakers. suppose one speaker is driven at 590 hz and the other at 560 hz. what is the beat frequency (in hz)?
It can hear the two speakers' beats because of the frequency of 30 Hz. Consider driving one speaker at 590 Hz and another at 560 Hz.
Why not offer an example of frequency?The quantity of observations that take place during a specific predetermined timeframe is the frequency of the a class interval. Therefore, if 20 individuals between the ages of 5 and 9 are found in the data from our study, the frequency again for 5–9 age range is 20.
What is the purpose of frequency?The temporal rate of evolution seen in oscillatory & periodic events, such as vibrations, speech recordings (sound), radio frequencies, and light, is specified by the frequency, an essential parameter in science and engineering.
Briefing:Beat frequency f = f₂ - f₁
F₂ = 590 Hz
F₁ = 560 Hz
f = 590 - 560
f = 30 Hz
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A mover is trying to lift a piano (slowly) up to a second-story apartment. He use a pulley and ropes to decrease the force needed to raise a heavy load (Figure 1) Figure 1 of 1 B mg Part A But for every meter the load is raised, how much rope must be pulled up? Account for this, using energy concepts O For each meter of the load is raised, 2 m of rope must be pulled up. O For each meter of the load is raised, 2.5 m of rope must be pulled up For each meter of the load is raised, 1.5 m of rope must be pulled up. O For each meter of the load is raised, 0.5 m of rope must be pulled up. Submit Request Answer Provide Feedback
Two metres of rope must be raised in order to move the burden every metre.
Explain why two metres of rope should be raised.
Assuming no dissipative forces are at work over the rope.
The effort is used to draw upward on the rope's free end while the load is hung from the pulley block. The effort required is just half the amount of the load because the load is now suspended from two ropes, each of which is bearing half of the weight.
Hence, two metres of rope must be raised in order to move the burden every metre.
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1. (10 points) when ashley sat on a rotating stool holding a set of weights close to her body, her rate of rotation changed when she moved the weights away from her body. did her rate or rotation slow down or speed up? why did this occur? did this violate the conservation of energy?
Moment of inertia decreases. due to friction effects associated with the tides driven by the Moon.
Conservation of energy Physics. a fundamental regulation of physics and chemistry stating that the whole power of an isolated system is steady despite inner modifications. it's far most normally expressed as electricity can neither be created nor destroyed and is the basis of the first law of thermodynamics.
According to the regulation of conservation of electricity, electricity can not be created or destroyed. it is able to, however, be converted from one shape to some other. whilst all kinds of strength are considered, the full strength of an isolated gadget stays consistent.
The longer we pass without making enormous adjustments, the greater the risk of world warming and climate exchange come to be in our everyday lives. whilst we burn fossil fuels, they devise an awesome amount of greenhouse gas emissions.
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go to the exploring waves discussion and post an answer to this question: waves are used in many practical applications to support work, entertainment, and health. one example is the use of ultrasound imaging to safely track the development of a growing fetus. what is a specific example of a practical application of waves in medicine, entertainment, safety, or other fields? provide a brief explanation of how the properties of waves are useful to that application. in your explanation, make sure you use at least four of the terms about waves introduced in this lesson. respond to at least one other person and explain why you agree or disagree with their comment. make a copy of your discussion post and response, and paste these items into 06.02 exploring waves discussion assessment.
A specific example of a practical application of waves in medicine is the capturing of body structures to detect abnormalities in them.
Abnormality is the giant deviation from normally usual patterns of conduct, emotion, or notion, same time as normality is the absence of illness and the presence of a country of nicely being otherwise referred to as normalcy. It may be hard to attract the line between regular and strange behaviors, specifically in management.
Abnormality consists of 3 extraordinary classes; they're subnormal, supernormal, and paranormal. The technology of unusual psychology studies two types of behaviors: adaptive and maladaptive behaviors.
Apart from genes, similarly, organic elements that contribute effectively to the abnormality of 1's behavior are neurotransmitters and hormones. Imbalance in neurotransmitters like GABA, norepinephrine, and many others., causes unusual neural plasticity or mental dysfunction.
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a grating with 532 lines/mm is illuminated with light of wavelength 565 nm. what is the angular separation between the two lines formed in order m
The angular separation is 77.8°.
What is angular separation?
It is the angle between two point objects or sightlines, as seen from an observer. It is denoted by θ.
What is bragg's law?
Bragg's law states that "The reflected x-ray beam has the same angle of scattering as the incident beam when an x-ray beam strikes a crystal at an angle. When the path difference (d) is equal to the wavelength's whole number (n), constructive interference will result."
nλ = 2d sin θ
Separation of 532 lines = 1 mm, so the slit separation is,
d= 1 / 532 mm
=[tex](1.8 * 10^-^3mm) (\frac{10^-^3m}{1 mm)}[/tex] = [tex]1.8 * 10^-^6[/tex] m
The Bragg's equation is,
d sinθ = nλ
Rewrite the Bragg's equation for θ
θ = [tex]sin^-^1[/tex] [mλ / d ]
Thus, the angle of diffraction is,
θ = [tex]sin^-^1 [\frac{2(565 * 10^-^9) }{1.8 * 10^-^6}][/tex]
= 38.89°
Angular separation = 2θ
=2(38.89)°
= 77.78°
≅ 77.8°
The angular separation is 77.8°.
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in the proton-proton chain, the mass of four protons is slightly greater than the mass of a helium nucleus. explain what happens to this "lost" mass.
The lost mass or mass defect that results in the mass of four protons being slightly greater than the mass of a helium nucleus is due to the conversion of matter to energy.
What is the lost mass in a nucleus of atoms?The lost mass or the mass defect is the difference in mass that is observed when the mass atoms of elements are compared to the sum of the mass of the constituents of all the particles in the nucleus of the atom.
For example, the mass of four protons is slightly greater than the mass of a helium nucleus that is also composed of four protons.
This loss in mass is known as the mass defect.
The loss in mass or mass defect is a result of the conversion of some of the mass of the particles to energy.
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an uncharged capacitor and a resistor are connected in series to a source of emf. if e 5 9.00 v, c 5 20.0 mf, and r 5 100 v, find (a) the time constant of the circuit, (b) the maximum charge on the capacitor, and (c) the charge on the capacitor at a time equal to one time constant after the battery is connected.
a)The time constant of the circuit is 2sec.
b)The maximum charge on the capacitor is 0.18C
c)The charge on the capacitor at one time constant is 0.18×(1-(1/[tex]e^\frac{t}{500}[/tex]).
a)We have resistor resistance 100ohm,capacitor capacitance as 20mf and EMF value as 9V.
We know very well that the time constant of the circuit is defined as the product of Resistance and Capacitance, or in other words
τ=R×C
Therefore,τ=100ohm×20×10⁻³F
=>τ=2sec.
b)The maximum charge on the capacitor is defined as the product of capacitance and voltage applied by the battery.
In other words, Q=C×E
=>Q=20×10⁻³F×9V
=>Q= 180×10⁻³C
=>Q=0.18C
c)Now,we need to find the charge on the capacitor at one constant time.We know very well that charge on the capacitor at any given time is represented by
q(t)=q₀(1−1 /[tex]e\frac{t}{RC}[/tex])
where q₀ is the maximum charge induced on the capacitor
Therefore, q(t)=0.18×(1-(1/[tex]e^\frac{t}{100.5}[/tex])
=>q(t)=0.18×(1-(1/[tex]e^\frac{t}{500}[/tex])
Hence, a)time constant is 2sec,b)maximum charge is 0.18C and c)charge at one time constant on capacitor is q(t)=0.18×(1-(1/[tex]e^\frac{t}{500}[/tex]).
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if electromagnetic radiation a has a lower frequency than electromagnetic radiation b, then compared to b, the wavelength of a is:____.
when testing the strength of grade a cotton fabric covering an aircraft that requires only intermediate grade, the minimum acceptable strength the fabric must have is
B- 70 percent of the original strength for intermediate fabric.
What is Fabric covering?
Fabrics are adaptable and employed in a wide range of industries, including clothing, agriculture, the military, and obviously the healthcare sector. More than you would imagine, specialty textiles are a part of our daily life. These textiles are generally flame resistant, mould and mildew resistant, and particularly treated with antibacterial properties for the healthcare sector. Why, I presume you ask? Because textiles used often in the medical field need to be antimicrobial and stain resistant from the start, this will help prevent bacteria from growing on the fabric surface.
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A slate falls from the roof of a height-rise building. Find how far it falls
a. In the first second
b. In the first two seconds
c. During the third second
In the first second, a slate drops from the roof of a tall building.
Explain about the seconds?Second is the standard unit of time in the International System of Units (SI) (s or sec). In decimal form, one cycle of radiation, or 9,192,631,770 (9.192631770 x 109), is equal to one second. This radiation is produced as the cesium-133 atom moves between two levels.
The symbol for a second, or s, is used to denote SI time. It is described as the fixed numerical value of the cesium frequency, vCs, which is the unaltered ground-state hyperfine transition frequency of the cesium 133 atom. The unit Hz, which is equivalent to s-1, is used to express this frequency. The second is the unit of time measurement.
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Shown below are the four terrestrial planets of our solar system. Assume that all the planets started out equally hot inside. Rank the planets based on their expected cooling rates, from fastest cooling to slowest cooling.MercuryMarsVenusEarth
The rank of the terrestrial planets based on their expected cooling rates, from fastest cooling to slowest cooling is as follows -
mercury , Mars, Venus, Earth
Mercury - It is the smallest terrestrial planet in the solar system. It has a thin atmosphere, which causes it to swing between burning and freezing temperatures.
Mars - It is less dense than Earth and has a smaller magnetic field, which is a indication of a solid core rather than a liquid one. Mars is known to have water ice and organics- some of the ingredients for living things.
Venus - It is about the same size as Earth and has a thick, toxic carbon-monoxide (CO) dominated atmosphere that traps heat, making it the hottest planet in the solar system.
Earth - Out of the four terrestrial planets, Earth is the largest and has regular seasons for much of it surface; regions closer to the equator tend to stay warm, while spots closer to the poles are cooler and in the winter, icy.
Therefore, the cooling rate of terrestrial planets is Mars, Earth, Venus, Mercury
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a solid cylinder with a mass of 5 kg and a radius of 30 cm is rolling on a flat surface. the cylinder rolls with a speed of 2 m/s. what its kinetic energy?
The total kinetic energy of a cylinder is 15 J.
Given that, mass = 5 kg
Radius of the cylinder= 30 cm = 30/100 m = 0.3 m
Speed = 2 m/s
Ut = Uk + Ur
where, Uk - translation kinetic energy
Ur - rotational kinetic energy
I is the moment of inertia of the solid cylinder
⇒ 1/2 mv² + 1/2 Iω²
⇒ 1/2 mv² + 1/2 [1/2 m r² * (v/r)²]
⇒ 1/2* 5 * (2)² + 1/2 [1/2* 5 *(0.3)² * (2/0.3)²]
⇒ 10 + 1/2*1/2*5* (0.3)²* 4 / (0.3)²
⇒ 10 + 5 = 15 J
Thus, the total kinetic energy is 15 J.
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A person can see objects clearly only if they are between 0.6 m and 4 m from her eyes. Her optometrist prescribes bifocals that enable her to see distant objects through the top half of the lenses and read papers at a distance of 0.25 m through the lower half. What are the respective powers of the top and bottom lenses?a. -0.25 dB (top lens); +5.7 dB (bottom lens)b. +2.3 dB (top lens); -3.3 dB (bottom lens)c. +4 dB (top lens); -1.7 dB (bottom lens)d. -5.7 dB (top lens); +0.25 dB (bottom lens)e. -0.25 dB (top lens); +2.3 dB (bottom lens)
A person can see objects clearly only if they are between 0.6 m and 4 m from her eyes. Her optometrist prescribes bifocals that enable her to see distant objects through the top half of the lenses and read papers at a distance of 0.25 m through the lower half. What are the respective powers of the top and bottom lenses?a. -0.25 dB (top lens); +5.7 dB (bottom lens)b. +2.3 dB (top lens); -3.3 dB (bottom lens)c. +4 dB (top lens); -1.7 dB (bottom lens)d. -5.7 dB (top lens); +0.25 dB (bottom lens)e. -0.25 dB (top lens); +2.3 dB (bottom lens).
e. -0.25 dB (top lens); +2.3 dB (bottom lens)
docs of optometry (O.D.s/optometrists), the usa's number one eye health care carriers, are the frontline of eye and vision care. doctors of optometry are essential fitness care companies and are diagnosed as physicians underneath Medicare. They study, diagnose, treat and control illnesses and issues of the attention.
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a jeweler is wearing a 20 d magnifying lens directly in front of his eye. if his near point is a typical 25 cm, how close can he hold a gem that he is inspecting?
If his near point is a typical 25cm, he must hold the gem that he is inspecting at 4.17cm in front of the magnifying lens that the jeweler is wearing.
What is magnifying lens (magnifying glass)?It is a convex lens that is used to produce a magnified image of an object. The lens is usually mounted in a frame with a handle or wear it like an eyeglasses in front of our eye.
How to calculate, how close can he hold a gem that he is inspecting?
First, let's calculate the focal length of the lens.
f = 1 / P
= 1 / 20D
= 0.05m * ( 10^2 cm / 1m)
= 5cm
Convex lens will create a virtual image of a nearby object. Therefore, the image distance is taken as negative, di = -25cm
The position where the gem can be held is calculated with this formula :
1 / f = 1 / do + 1 / di
1 / do = 1 / f - 1 / di
= (1 / 5cm) - (1 / -25cm)
do = 4.17cm
Therefore, the jeweler needs to hold the gem at 4.17cm.
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a flat, circular loop has 17 turns. the radius of the loop is 11.0 cm and the current through the wire is 0.58 a. determine the magnitude of the magnetic field at the center of the loop (in t).
The magnitude of the magnetic field at the center of the loop 6.28 × 10⁻⁵ T.
A magnetic field is a vector subject that describes the magnetic effect on moving electric charges, electric currents, and magnetic materials. A transferring price in a magnetic area stories a pressure perpendicular to its very own pace and to the magnetic discipline.
calculation:-
Given;
Number of turns n = 17 turns
radius = 11 cm = 0.11m
current i = 0.58 A
Magnetic field at the centre of the loop is
B = μ₀nI//2r
B = 4π × 10⁻⁷ × 17 × 0.58 / 2× 0.11
= 628.4 × 10⁻⁷ T
= 6.28 × 10⁻⁵ T
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric-powered currents, and magnetic substances. A transferring rate in a magnetic field story a pressure perpendicular to its own velocity and to the magnetic area.
The magnetic field is the place around a magnet wherein the impact of magnetism is felt. We use the magnetic discipline as a tool to explain how the magnetic force is shipped in the area around and inside something magnetic in nature.
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a particle is moving with a constant velocity in the x-direction. when the particle reaches the origin, a constant force is exerted on it in the y-direction. which of the following graphs best shows the path the particle will follow?
Parabolic Up. Since the force is in the y-direction, the particle will continue to move at a constant speed in the x-direction and accelerate in the y-direction. This creates a parabolic path around y-axis.
Force is the power that changes the motion of an item. A force can purpose an object with mass to alternate its pace. Pressure also can be described intuitively as a push or a pull. A force has both value and path, making it a vector quantity.
Pressure is a push or a pull and it affects us in our daily lives because, without force, people might not be capable of open and near stuff or lifting up their arms or legs.
Variety of Forces :
* Muscular Forces, muscular tissues feature to produce an ensuing force which is referred to as 'muscular force'.
* Frictional Forces, while an item modifications its national motion, 'frictional pressure' acts upon it.
* Carried out pressure.
* Tension force.
* Spring force.
* Gravitational pressure.
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use newton's method to approximate the zero(s) of the function. continue the iterations until two successive approximations differ by less than 0.001. then find the zero(s) to three decimal places using a graphing utility and compare the results. f(x)
Only one genuine zero exists, and it is found at x = 1.359. newton's method to approximate the zero(s) of the function
The first three decimal places were repeated in the solution after the fourth iteration. I began by assuming that x = 1 was the answer to the Newton's Method formula.
When I entered 1 for x, I received a zero of 5/3.
I entered 5/3 and repeated the process to get 997/687.
I was able to get 1.36976 by plugging in 997/687 and repeating the process.
I entered 1.36976 and repeated the process to get 1.359454.
I entered 1.359454 and repeated the process to get 1.359304.
There was no need to go any further because we are only interested in accuracy to three decimal places.
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what is the minimum coefficient of friction between the tires and the road that the car could have and still make the turn?
The minimum coefficient of friction between the tires and the road that the car could have and still make the turn is 0.7 for dry roads and 0.4 for wet roads.
The value of minimum coefficient of friction is usually between 0 and 1 but can be greater than one. A value of zero means there is no friction between the objects such is possible with a lubricant material . All objects, should have friction between them when they come in contact with each other.
The coefficient of friction is as low as 0.05 between dry sliding surfaces will be achieved when the mechanical interconnections are removed. This outcome has been attained based on a theoretical model of an ideal surface for low friction.
The coefficient of friction having value 1 is a perfect positive correlation. A coefficient of correlation zero means there is no linear relationship. Correlation coefficients are used in science to assess the degree of association between two variables, factors, or data sets.
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in a series circuit with three bulbs, adding another bulb will a. make the nearest bulb brighter. b. make some of the bulbs dimmer. c. make all the bulbs brighter. d. make all the bulbs dimmer. please select the best answer from the choices provided a b c d
The addition of a fourth bulb will cause some of the three lights in a series circuit to become dim.
What does an electrical bulb do?A wire filament is used in an electronic bulb, a compact and basic light source that emits light when power is applied. The illustration below shows the incandescent light bulb's construction. Three essential components make up the light bulb. the thread. glass lightbulb
Is a light a bulb?An electrical device that generates light is known as an electric light, lamp, or lightbulb. The most prevalent type of artificial illumination is this. A lamp's base, which is often composed of ceramic, metal, glass, or plastic, attaches it in the socket of such a lighting system, which is also frequently referred to as a "lamp."
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a particle of mass 0.195 ???? carries a charge of −2.50×10ି଼ ????. the particle is given an initial horizontal velocity that is due north and has a magnitude of 4.00×10ସ ௦. what are the magnitude and direction of the minimum magnetic field that will keep the particle moving in the earth’s gravitational field in the same horizontal, northward direction?
The magnitude and direction of the minimum magnetic field that will keep the particle moving in the earth’s gravitational field in the same horizontal, northward direction is 1.911 Tesla.
Velocity v = 4×[tex]10^{4}[/tex]
Charge q = 2.5 × [tex]10^{-8}[/tex]
Mass of particle m= 0.195 g = 0.195 × [tex]10^{-3}[/tex] kg
Using the concept of Lorentz force
mg=Bvq
B = mg/vq
Substituting the values
B= 0.195 × [tex]10^{-3}[/tex] × 9.8/4×[tex]10^{4}[/tex]×2.5×[tex]10^{-8}[/tex]
B= 1.911 Tesla
Therefore, To produce upward force, using right hand value and taking particle in negative charge then the magnetic field has to be point in eastwards.
What is gravitational field?
In physics, a gravitational field is a model used to describe the effect of one massive object spreading out in space around it and creating a force on another massive object. Gravitational fields are used to describe gravitational phenomena and are measured in Newtons per kilogram.
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Which states of matter are required for energy transfer to occur when radiant energy is the source?.
No state of matter is required for energy transfer to occur when radiant energy is the source.
Which states of matter are required for energy transfer when radiant energy is the source?When radiant energy is the source, it means we are talking about energy transfer by radiation, so matter is not needed for the energy to be transferred.
An example of this is the Sun as it heats up the Earth by radiation, even through the vacuum of outer space, where there is almost no matter.
Radiant energy is used for radiant heating that can be generated electrically by infrared lamps, or can be absorbed from sunlight and is used to heat water.
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Nuclear decay occurs according to first-order kinetics. What is the half-life of polonium-218 if a sample decays from 55. 4 g to 31. 7 g in 2. 50 minutes?.
The half-life of polonium-218 if a sample decays from 55. 4 g to 31. 7 g in 2. 50 minutes is 3.5 minutes.
Rate of first order reaction is given by:[tex]kt = 2.303 * log(R'/R)[/tex]
Where , k = rate of reaction
t= time = 2.5 minutes
R= final amount = 31.7g
R'= initial amount = 55.4g
Putting these values in above equation we get k = 0.22
Now half life of a first order reaction is given by: 0.693/k
Putting k= 0.22 , we get half life = 3.5 minutes.
So the half-life of polonium-218 if a sample decays from 55. 4 g to 31. 7 g in 2. 50 minutes is 3.5 minutes.
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A cyclist is travelling along a track at 8 m/s when a rabbit runs out in front of them. they stop their bike in 1.6 seconds. calculate their deceleration.
The deceleration experienced by the cyclist is -5 m/s. Deceleration is also called negative acceleration.
What is deceleration?Deceleration is the term used to describe a decrease in speed as the body moves away from the beginning place. The opposite of acceleration is deceleration.
Given,
Initial velocity (V₁) = 8 m/s
Final velocity (V₂) = 0 m/s (Since the bike was stopped).
Time taken for the velocity drop (t) = 1.6 seconds
We know,
[tex]deceleration=\frac{V_{2}-V_{1} }{t} \\[/tex]
Substituting the values we get,
[tex]deceleration= \frac{0-8}{1.6}[/tex]
[tex]= -5 m/s[/tex]
Hence, the deceleration experienced by the cyclist is -5 m/s.
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The right answer is "-1.5 m/s²"
Answer explanation:
Acceleration = change in velocity / time
= (4 m/s – 7 m/s) / 2 s = -1.5 m/s2.
The acceleration is negative because the bike is slowing down.(decelarating)
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a 2800. kg rollercoaster is traveling at 18.5 m/s along its track. what is the largest radius loop (in m) that the coaster could successfully go around at that speed?
The Radius loop of 34.88m that coaster could go around with speed of 18.5m/s.
Mass of rollercoaster =2800kg
Speed is 18.5m/s
On a roller coaster, the so-called clothoid loops are the most obvious place where centripetal acceleration takes place. A spiral segment with a variable radius is called a clothoid. The radius at the bottom of a clothoid loop is significantly larger than the radius at the top, in contrast to a circular loop where the radius is a constant value.A clothoid's curvature is less at the bottom of the loop than it is at the top. We will characterize a clothoid loop as being made up of a number of circular sections that overlap or are adjacent to one another in order to simplify our analysis of the physics of clothoid loops.[tex]V=\sqrt{gR}\\ \\V=speed=18.5m/s\\\\g=gravity=9.81m/s^2\\\\R=radius[/tex]
Calculation- squaring both sides of equation.
[tex]V^2=gR\\\\R=V^2/g\\\\R=18.5^2/9.81\\\\R=342.25/9.81\\\\R=34.88m[/tex]
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