One of the several configurations in which matter can exist is a state of matter. In daily life, we can observe four different states of matter: solid, liquid, gas, and plasma.
There are numerous known intermediate states, including liquid crystal, while others, like Bose-Einstein condensates (in extremely cold temperatures), neutron-degenerate matter (in extremely high densities), and quark-gluon plasma, can only exist under very specific circumstances (at extremely high energy). Enthalpy is characterized as the quantity of internal energy and the result of the pressure and volume of a thermodynamic system. Enthalpy is a quality or state function that resembles energy and possesses energy dimensions (and is thus calculated in joules or erg units).The enthalpy H is equal to the product of the system's internal energy E and pressure P multiplied by volume V, or H = E + PV.
The density of the corona is ten million times lower than that of the Sun's surface. The corona is substantially less luminous than the Sun's surface as a result of its low density.To know more about matter
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Find the acceleration a of the particle. Express the acceleration in terms of vi , vf , and s.
The acceleration a of the particle, expressed in terms of vi , vf , and s, is a = (vf² - vi²) / (2s).
What is acceleration of a particle?
The acceleration of a particle is the rate of change of velocity of the particle with time.
Mathematically, the acceleration of any particle can be determined by applying the following kinematic equation.
a = (vf - vi)/t
where;
vf is the final velocity of the particlevi is the initial velocity of the particlet is time of motion of the particleWhen the final velocity of the particle is known, the initial velocity is also known and the distance travelled by the is known as well, then the acceleration of the particle can be calculated by applying the formula for third kinematic equation as shown below.
vf² = vi² + 2as
a = (vf² - vi²) / (2s)
Thus, the acceleration of the particle depends on the final velocity, initial velocity and the distance travelled by the particle.
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consider an element that reaches its first excited state by absorption of 348.9 nm light.348.9 nm light. determine the energy difference in kilojoules per mole between the ground state and the first excited state.
The 348.9 nm light is the light energy and energy difference's in K J /moles between excited and ground states is 343.0 KJ/mol.
Here we have 348.9 nm light :
[tex]ΔE = E1 - E0 \\ΔE = hc/ lambda \\h= 6.626 ×10^34\\c = 3 × 10 ^8\\lambda = 348.9 nm\\ΔE = hc/ lambda = 6.626 ×10^34×3 × 10 ^8÷348.9 nm\\= 5.697 × 10^22 ×6.022 ×10^23 mol^-1 \\= 343.0 KJ /molTherefore the energy difference is 343.0 KJ /mol.[/tex]
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from an astronomical perspective, where would be the best location to put a telescope? group of answer choices on a tall, dry mountain peak close to a large city where there are many astronomers to use it on the west coast of the u.s. very close to sea level (a location like seattle, for example) in a dark spot right on the campus
A tall, dry mountain peak close to a large city would be the best location to put a telescope.
A telescope is a device that focuses a significant amount of light through large-diameter lenses or mirrors to enable the observation of distant objects with extremely weak light.
The following factors must be considered while choosing a telescope's location:
The location must be far from cities and other bright light sources in order to ensure that no neighboring lights interfere with the observation.
To prevent fogging up of the optical surfaces and to lessen the thermal expansion that alters the length of the instrument, the climate should be as stable as possible with minimal temperature variations.
You must pick a location where there is little rain and thus little cloud cover.
We can determine which luxury will be the most appropriate based on these needs.
a) A lot of light is present in the area.
b) There is a lot of wind and humidity.
c) There is enough light.
d) The stable climate, low light levels, and low humidity make this a suitable location.
e) a lot of light and humidity.
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a car moving at 12.0 m/s crashes into a tree and stops in 0.31 s. calculate the force the seat belt exerts on a passenger in the car to bring him to a halt. the mass of the passenger is 70 kg.
Answer:
[tex]\huge\boxed{\sf F=2709.7\ N}[/tex]
Explanation:
Given Data:Velocity = v = 12.0 m/s
Mass = m = 70 kg
Time = 0.31 s
Required:Force = F = ?
Formula:[tex]\displaystyle F=\frac{mv}{t}[/tex]
Solution:Put the given data in the above formula.
[tex]\displaystyle F = \frac{(70)(12)}{0.31} \\\\F=\frac{840}{0.31} \\\\F=2709.7 N\\\\\rule[225]{225}{2}[/tex]
two point masses are placed 10.0 cm apart and attract each other with a force of 10.0 n. find the force of gravitational attraction between the masses when they are placed 5.00 cm apart.
The final gravitational force after they are placed 5cm apart is 40 N.
We need to know about gravitational force to solve this problem. The gravitational force is the force caused by two masses objects. The magnitude of gravitational force can be determined as
F = G.m1.m2 / R²
where F is the gravitational force, G is the gravitational constant (6.674 × 10¯¹¹ Nm²/kg²), m1 and m2 are the mass of the object and R is the radius.
From the question above, we know that
Ra = 10 cm
Rb = 5 cm
Fa = 10 N
The gravitational force is inversely proportional to squared distance. Hence
Fa / Fb = Rb² / Ra²
10 / Fb = 5² / 10²
Fb = 40 N
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when a ping pong ball rolling with a speed of 3.0 mls collides with a bowling balla t rest, the ping pong's speed after the collision will be close to
When a ping pong ball rolling with a speed of 3.0 m / s collides with a bowling ball at rest, the ping pong's speed after the collision will be close to 3 m / s
Let the ping pong ball be 1 and bowling ball be 2.
A ping pong ball weighs 2.7 g and a bowling ball weighs 2.85 kg
m1 = 2.7 g = 0.0027 kg
m2 = 2.85 kg
u1 = 3 m / s
u2 = 0
According to law of conservation of momentum,
m1 u1 + m2 u2 = m1 v1 + m2 v2
Ping pong ball's mass is so less compared to a bowling ball's mass. So the bowling ball will still remain at rest after collision.
v2 = 0
( 0.0027 * 3 ) + 0 = ( 0.0027 * v1 ) + 0
v1 = 3 m / s
Therefore, when a ping pong ball rolling with a speed of 3.0 m / s collides with a bowling ball at rest, the ping pong's speed after the collision will be close to 3 m / s
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write an expression for the horizontal component of the system's initial momentum, pi,x, in terms of m, v1i and v2i.
When an object first begins to move, it has what is known as initial momentum. A mass moving at its initial velocity would have initial momentum.
How do you determine the starting momentum?Because the ball is moving to the left, we may use the equation pi=mvi p I = m v I to calculate the starting momentum, where m is equal to 1 kg and vi is equal to -7 m/s. -7 kgm/s to the left is the initial momentum. Locate the impulse and its course in step two.When an object first begins to move, it has what is known as initial momentum. A bowling ball's initial momentum, for instance, would be the ball's momentum immediately after the bowler releases the ball from his or her hand and starts rolling down the bowling alley.A mass moving at its initial velocity would have initial momentum.To learn more about Initial momentum refer to:
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an object is 15 mm in front of a converging lens, and the image is 4.0 mm behind the lens. what is the focal length of the lens?
3.1578 MM is the focal length of the lens when the image is 4.0 mm behind the lens and the object is 15 mm in front of the converging lens. the length of an optical system's focus point.
Is a measurement of the degree to which the system strongly diverges or converging lens; it is the opposite of the system's optical power. A system's light converges when the focal length is positive, while it diverges when the focal length is negative. The optical centre or axis of a convergent lens is where light is focused. a lens that creates convergent light rays from parallel light rays. Is called converging lens.
If is the lens's focal length, then the calculation for its length is as follows:
1/f = 1/u+1/v = 19/60
f = 60/19 = 3.15789 mm
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two spaceships approaching each other move at very close to the speed of light, each sending a beam of light to the other. each measures the speed of light from the other spaceship as group of answer choices c. slightly less than c. slightly greater than c. much greater than c.
Exactly C ; two spaceships approaching each other move at very close to the speed of light, each sending a beam of light to the other. each measures the speed of light from the other spaceship is 'C'.
A fundamental physical constant, typically abbreviated as c, the speed of light in a vacuum is significant in many branches of physics. 299,792,458 meters per second is the precise speed of light, or c. (approximately 300,000 kilometres per second; 186,000 miles per second; 671 million miles per hour). [Note 3] The special theory of relativity states that the maximum speed at which ordinary matter or energy (and thus any signal carrying information) may move across space is c.
Including visible light, all types of electromagnetic radiation move at the speed of light. Light and other electromagnetic waves will appear to propagate instantly for many practical uses, but for very sensitive measurements over great distances, their finite speed has noticeable impacts.
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True or False a stranded conductor with the same circular-mil rating of a solid conductor has a greater surface area and flexibility than the solid conductor.
It is true that a standard conductor with the same circuit-mil rating of a solid conductor has a greater surface area and flexibility than the solid conductor.
A standard conductor consist of many thin wires of small cross-sectional areas called strands, because of this they can be coiled easily to transport current over long distances. Moreover, the flexibility of the standard conductor increases as the number of strands increase.
This standard conductor has better conductance than the solid conductor because the individual wires together have a greater surface area. This standard conductor is formed by twisting the strands to form layers. This process is called stranding.
The centre of the standard wire is made of steel strand that gives high tensile strength to the conductor and hence is more flexible along with having more surface area than the solid conductor.
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what volume of butane (C4H10) is required to produce 97.2 liters of water according to the following reaction? (all gases are at the same temperature and pressure.)
19.44 L volume of butane (C4H10) is required to produce 97.2 liters of water according to the following reaction.
What is Avogadro's Law ?The same quantity of any ideal gas will have the same volume at the same temperature and pressure, according to Avogadro's law. In other words, the volume is unaffected by the gas's composition. This is due to the fact that in ideal gases, the relative importance of each gas particle's size to the gas's overall volume is negligible (since the particles are so far apart from each other in the gaseous state).No of the size or molar mass of the gas, there are always the same amount of molecules or atoms in a given volume of a perfect gas. The mathematical formulation of Avogadro's Law is as follows: Where V is the gas's volume, n is its moles, and k is a proportionality constant, we get Vn=k.Given details :
First thing is you need a correctly balanced equation for this reaction:
2C4H10 + 13O2 ==> 8CO2 + 10H2O ... balanced equation
Since all are at the same temperature and pressure, the coefficients serve to not only tell us the moles of each, but also tell us the volume (liters) of each. Using dimensional analysis and the stoichiometry of the balanced equation, we can find the volume of C4H10 needed to produce 97.2 liters of H2O.
97.2 L H2O x 2 L C4H10 / 10 L H2O = 19.44 L of C4H10 required.
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A weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by
y=1/3sin2t+1/4cos2t
y=1/3sin2t+1/4cos2t
where y is the distance from equilibrium (in feet) and t is the time (in seconds). Use the identity
asin Bθ + b cosBθ = √a^2+b^2 sin(Bθ+C)
asinBθ+bcosBθ=√a 2
+b 2
sin(Bθ+C)
where C = arctan (b/a), a > 0, to write the model in the form
y=√a^2+b^2 sin(Bt+C)
y=√a 2
+b 2
sin(Bt+C)
A weight is attached to a spring suspended vertically from a ceiling.
The given model y = 1/3 sin2t + 1/4 cos 2t is to be written in the form y = √(a² + b²) sin (Bt+C) is 5/12 * sin(2t + 0.6435).
Given equation of y = 1/3 sin2t + 1/4 cos 2t
We know the identity, a sin Bθ + b cos Bθ = √a²+b² * sin(Bθ + C), C = arctan(b/a).
In our case, a = 1/3, b = 1/4, θ = t, B = 2
So we get, y = √(1/3)² + (1/4)² * sin[ 2t + arctan (1/4 ÷ 1/3)]
= √(25/144)* sin [2t + arctan (0.75)]
= 5/12 * sin(2t + 0.6435)
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The National High Magnetic Field Laboratory holds the world record for creating the strongest magnetic field. For brief periods of time, their largest multi-shot pulsed magnet can produce magnetic fields in excess of 85 T. To see if such a strong magnetic field could pose health risks for nearby workers, calculate the maximum acceleration the field could produce for Na ions (of mass 3.8 * 10-26 kg) in blood traveling through the aorta. The speed of blood is highly variable, but 35 cm/s is reasonable in the aorta.Would you guess that the acceleration you found above would be dangerous for workers to be near such a large magnetic field?
Their greatest multi-shot pulsating magnet can generate magnetic properties in excess of 85 t for short amounts of time, to see if such a powerful magnetic field might.
What is a magnet, please?A magnet is any item that generates its own magnetic field and interacts with other magnetic fields. A magnet has two poles, the north pole as well as the south pole. The magnetic field of a magnet is depicted by field lines that start at its north pole but stop at its south pole.
What is in a magnet?Most permanent magnets have iron, chromium, and cobalt as their principal metals. Cobalt, nickel, and aluminium are combined to form the alloy known as Alnico.
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To outside observers at rest, the overall sizes of objects traveling at relativistic speeds are.
To outside observers at rest, the overall sizes of objects traveling at relativistic speeds are smaller.
The relativistic speed, "c," or the mathematical sign for light speed, is roughly 186,282 miles per second. Relativistic speed, then, is the speed at which such effects become essential for getting the appropriate level of measurement precision for the event in question. the differences between values calculated using theories based on relativity.
Generally speaking, sizes of items refer to a thing's size or magnitude. Geometrical size or spatial size is a more precise phrase that can be used to refer to area, volume, or linear dimensions. When a range of densities is assumed, mass can also be used to determine size. Actual file space on a disc is represented by object sizes. The logical and physical dimensions of a file can coincide.
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Which equation represents a line that passes through 4 1 and has a slope of?.
The equation that represent the line is 9x - 12 y =32
We are given that ,
x₁ = 4, y₁= 1/3 , m = 3/4
Where,
m = slope of the line
Then the equation of line can be given as,
(y - y₁) = m (x - x₁)
3y -1 = 9/4 (x-4)
12 y - 4 = 9x - 36
9x - 12y = - 4 + 36
9x - 12y = 32
note- the given questions is incomplete therefore the complete question is,
Which equation represents a line that passes through (4, 1/3) and has a slope of 3/4
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what is the radius of curvature of the path of the proton in the above question if the magnitude of the field is 0.80 t?
Proton route curvature has a 9.9mm radius of curvature.
Which magnitude do you mean?Magnitude is simply "distance or amount," according to the definition given in physics. It shows how an item moves while it is in motion, whether that movement is absolute, relative, or of a certain magnitude. It serves as a method to convey something is really size and scope. Magnitude is a broad term used in physics to describe size or distance.
What is an illustration of magnitude?Size can be described as magnitude. A automobile is travelling quicker than a bike, for instance, in terms of speed. The automobile is now moving faster than the bike in this situation by a significant margin. It communicates the absolute size or direction.
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Why is there no liquid metallic hydrogen zone in the interiors of uranus or neptune?.
The pressure is too low for hydrogen to be metallic.
What is metallic hydrogen zone ?Hydrogen exists in a phase known as metallic hydrogen, where it exhibits electrical conductivity. Eugene Wigner and Hillard Bell Huntington made a theoretical prediction about this phase in 1935.
The layer on Saturn is smaller than that of Jupiter because Saturn does not produce the pressure required for metallic hydrogen in as much of its volume as Jupiter does, whereas Uranus and Neptune are too small to generate the pressures required for this layer.
Because they are smaller than Jupiter and Saturn, neither has the deep metallic hydrogen mantles that can be found on those planets. Uranus and Neptune are frequently referred to as Ice Giants to distinguish them from the Gas Giants, Jupiter and Saturn, because they are mostly composed of ices and lack deep hydrogen mantles.
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(part a) when the spring is stretched to its farthest position and the block comes momentarily to rest, how much potential energy is stored in the spring?
Although the spring force has a negative sign and is a restoring force, the elastic potential energy cannot be negative.
what is potential energy ?
Potential energy is the energy stored by an item as a result of its location relative to other objects, internal tensions, electric charge, or other reasons.
The gravitational potential energy of an item, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field are all examples of common forms of potential energy. The joule, denoted by the sign J, is the unit of energy in the International System of Units (SI). is the energy stored by an item as a result of its location relative to other objects, internal tensions, electric charge, or other reasons.
The gravitational potential energy of an item, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field are all examples of common forms of potential energy. The joule, denoted by the sign J, is the unit of energy in the International System of Units (SI).
Although the spring force has a negative sign and is a restoring force, the elastic potential energy cannot be negative. Positive potential energy is stored in the spring as soon as it is stretched or compressed.
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The mass fractions of total ferrite and total cementite in an iron-carbon alloy are 0. 88 and 0. 12, respectively. Is this a hypoeutectoid or hypereutectoid alloy? why?.
This is a hypoeutectoid alloy because the mass fraction of carbon is less than the eutectoid composition of 0.8%.
What is hypoeutectoid?
The ductility of the eutectoid alloy has decreased by the a factor of three, while that of the hypoeutectoid steel has decreased by the a factor of three. The additional, fragile cementite just on pearlite grain boundaries in hyper-eutectoid alloys reduces the alloy's ductility even more. The proeutectoid cementite limits fracture to the fragile grain boundary zone and limits plastic deformation to a ferrite lamellae inside the pearlite. Such alloys must be chosen for their composition to balance such properties to the requirements of the design in order to be used in light-strong structures. Although a front fork on the a bicycle must meet certain requirements, one of those requirements is high toughness, which necessitates tailoring this same carbon content to provide the required ductility.
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should the average velocity of the glider change or stay about the same as you decrease the displacement between the two photogates?
The average velocity should stay about the same as you decrease the displacement between the two photogates.
What distinguishes distance from displacement?Distance is the length of any path connecting any two places. When measured along the shortest path between any two points, displacement is the direct distance between them.
What does velocity displacement mean?The vector difference between an object's initial and finishing coordinates is known as displacement. The distance the thing has travelled may be substantially different from that. The pace at which displacement alters over time is known as velocity. It is also a vector.
Does displacement have a scalar value?False—distance is a vector quantity. It calculates the length and direction of a hypothetical motion in a straight line from the starting point to the destination of the point.
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a tire has a tread pattern with a crevice every 2.00 cm. each crevice makes a single vibration as the tire moves. what is the frequency of these vibrations if the car moves at 24 m/s?'
The frequency of these vibrations if the car moves at 24 m/s is 1500 Hz
It is given that
Wavelength = 2.00 cm = 0.02 m
velocity = 24 m/s
Frequency = v x λ
Frequency = 0.02 x 24 = 1500 Hz
What is frequency ?Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as temporal frequency to emphasize the contrast to spatial frequency, and ordinary frequency to emphasize the contrast to angular frequency
Hence, the frequency of these vibrations if the car moves at 24 m/s is 1500 Hz
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. find the maximum number of lines per centimeter a diffraction grating can have and produce a first-order maximum for the smallest wavelength of visible light.
14,300 lines per centimeter .The reciprocal of the shortest distance between two adjacent slits, which is the maximum number of lines per centimeter,
How much visible light has the shortest wavelength?Justification: 400 nm to 400 nm. The reciprocal of the shortest distance between two adjacent slits, which is the maximum number of lines per centimeter, can be found using the following equation.
mλ = dsin (θ)
The order of diffraction, m, is represented in this equation.
denotes the incident light's wavelength.
The separation of the two slits' centers is measured in terms of d.
The angle at which the mth order would diffract is given by,.
Utilizing the visible spectrum's maximum wavelength of 700 nm, we can determine the smallest spacing necessary to observe one full order of the visible spectrum.
d = mλ / sin (θ)
In order for sin () to be the greatest and the distance d to be the smallest,
Therefore, 700 nm is the minimum separation that would allow for the capability of detecting the full first order of the visible area spectra. Using this information, we can find the maximum number of lines per centimeter, which is the reciprocal of the number of lines per cm.
n = 1/d = 1, 430,000 lines per m, or 14,300 lines per cm.
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a weight suspended from a spring is seen to bob up and down over a distance of 30 cmcm twice each second. what is its frequency?
A weight suspended from a spring is seen to bob up and down over a distance of 30 cm twice each second then the frequency is 0.5 sec.
What is frequency?
"Frequency" is the term used to describe the number of waves that pass through a fixed point in a given amount of time. It also specifies the quantity of vibrations or cycles that a body in periodic motion produces in a predetermined period of time.
What is suspended?
A mass that is suspended on a spring hangs in its resting position. After being pulled below its rest position and then released, a mass starts to vibrate up and down.
Frequency(f) = 2 bobs/sec =2 Hz
Time period(T) = 1/f
= 0.5 sec
Therefore, a weight suspended from a spring is seen to bob up and down over a distance of 30 cm twice each second then the frequency is 0.5 sec.
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Dr. Bennett decides to take a vacation to outer space. He finds a nice planet with a beach and stops for a while. He can't decide if he feels heavier or lighter here, 2250 so he makes a simple pendulum to measure g. The pendulum is 0.7 m long and completes 96 cycles in 114 seconds UNITS STATS HELP PREFERENCES NOTES Part IMAGES DISCUSS Description Answer Save Status 16.67 pts. 100% A. What is the value of g on this mysterious planet? |(include units with answer) # tries: 0 Show Details Format Check 2% try penalty Hints: 0,0
The value of accelration due to gravity on this planet is 19.59 m/s², so Dr. Bennett should feel heavier on this planet.
The length of the pendulum of Dr. Bennett is 0.7m.
The pendulum completes 96 cycles in 114 seconds.
So, we can write,
96 cycle = 114 seconds
1 cycle = 114/96 seconds.
Time taken by the pendulum to complete one cycle is the time period of the pendulum.
The time period of the pendulum is given by,
T = 2π√(l/g)
Putting values,
114/96 = 2π√(0.7/g)
g = 19.59 m/s².
The value of acceleration due to gravity on this planet is 19.59 m/s².
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the door sill or curb around a liquid-cooled transformer installed to protect a transformer vault doorway shall not be less than an approved height sufficient to confine the oil from the largest transformer in the vault, and shall in no case be less than ? high.
The door sill or curb around a liquid-cooled transformer installed to protect a transformer vault doorway shall not be less than 4 inches high.
This minimum requirement is mentioned in the article 430.43 issued by National Electrical Code. It provides Effluent limitations guidelines representing the degree of effluent reduction attainable by the application of the best conventional pollutant control technology (BCT).
The article is contained within subpart D - Dissolving Sulfite Subcategory, which is contained in Part 430 - the pulp, paper and paperboard point source category. The title is 40 - Protection of Environment.
Therefore, the door sill or curb around a liquid-cooled transformer installed to protect a transformer vault doorway shall not be less than an approved height sufficient to confine the oil from the largest transformer in the vault, and shall in no case be less than 4 inches height
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The magnitude, m, of an earthquake is represented by the equation m=23logee0 where e is the amount of energy released by the earthquake in joules and e0=104. 4 is the assigned minimal measure released by an earthquake. Which equation could be used to find the amount of energy released by an earthquake with a magnitude of 2. 7?.
The amount of energy released by an earthquake is [tex]2.8 * 10^{8}[/tex].
What is magnitute of earthquake?
Magnitude is the most commonly used measure of an earthquake's size. It is a measurement of the magnitude of the source for a single earthquake. As a result, it is the same regardless of how or where you perceive it, and the following calculation can be defined:
[tex]magnitude M = \frac{2}{3} log \frac{E}{Eo}[/tex]
where,
E = amount of energy released
Eo = [tex]10^{4.4}[/tex]
As M = 2.7
[tex]M = \frac{2}{3} log \frac{E}{Eo} \\\\2.7 = \frac{2}{3} log \frac{E}{10^{4.4} }\\\\4.05 = log \frac{E}{10^{4.4} }\\\\10^{4.05} = \frac{E}{10^{4.4} }\\\\E = 10^{4.05} * 10^{4.4} \\\\[/tex]
[tex]E = 2.8 * 10^{8}[/tex]
The amount of energy released by an earthquake is [tex]2.8 * 10^{8}[/tex].
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Do quotas increase domestic price?.
An import quota will increase the domestic price and, in the case of a large country, reduce the foreign price.
A quota is a restriction to the amount entering a rustic. With no alternate, equilibrium marketplace price within the USA will exist on the charge which equates domestic demand and home delivery, at P, and with output at Q. However, the arena price is possible to decrease, at P1, then the rate in a rustic that doesn't exchange.
An import quota is a restriction on the total quantity of imports that can be brought into a country in a given time period. It is a non-tariff barrier.
The main advantage of a quota is that it keeps the number of imports unchanged even if demand for imported articles increases.
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How fast would a light beam appear to einstein if he were traveling in the same direction at 90% of the speed of light?.
If Einstein were traveling in the same direction of a light beam at 90% of the speed of light, the light beam would be travelling at 10% of speed of light.
Speed of light, c = 3 * 10⁸ m / s
90 % of Speed of light = 3 * 10⁸ * 0.9
90 % of Speed of light = 2.7 * 10⁸ m / s
Relative speed = 3 * 10⁸ - 2.7 * 10⁸
Relative speed = 0.3 * 10⁸ m / s
Relative speed = 0.1 c = 10% of speed of light
Relative speed of one object with respect to another is the difference in speeds of both objects if they are travelling in same direction. Relative speed of one object with respect to another is the sum of speeds of both objects if they are travelling in opposite direction.
Therefore, if Einstein were traveling in the same direction of a light beam at 90% of the speed of light, the light beam would be travelling at 10% of speed of light.
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A solid sphere, hollow sphere, solid cylinder, hollow cylinder and ring each of mass M and radius R are simultaneously released at rest from top of incline and object rolls down the incline then match Column-I and Column-ll.
List 1
Time taken to reach bottom is maximum for
Angular acceleration maximum for
Kinetic energy at bottom is same for
Rotational kinetic energy is maximum for
List 2
Solid sphere
Hollow cylinder
Hollow sphere
Ring
Solid cylinder
The motion of rolling down involves many factors like mass, radius, gravitation, etc.
This all indicates about the moment of inertia.
The moment of inertia is a measurement of how much the object resists angular rotation.
Inertia is a property of object by which it tries to come in to rest when an external force is applied on the object. When the object is rotating then in that case the inertia acting on the body , which tries to resist its motion is called moment of inertia.
It is calculated by Mass M, Radius R and Length L.
The moment of inertia of solid sphere is 2/5 MR²The moment of inertia of hollow cylinder is 1 ⁄2 M (r₂² + r₁²).The moment of inertia of hollow sphere is 2/3 MR²The moment of inertia of ring is MR²The moment of inertia of solid cylinder is 1/2 (MR²)As the moment of inertia is the resistance to rotational motion we see that the object with least moment of inertia will reach the bottom first.
Matching the two columns, we get:
a) Time taken to reach the bottom is maximum for ring.
We also know the larger the moment of inertia, the smaller is the angular acceleration.
b) Angular acceleration is maximum for solid sphere.
c) Kinetic energy at the bottom is same for hollow and solid cylinder.
d) Rotational kinetic energy is maximum for solid sphere.
Therefore, after matching all these columns we get that these are directly related to moment of inertia.
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A rocket rises at 5 ft/s between 0 and 10 seconds. Afterwards it rises at 15 ft/s for another 15 seconds. Use one loop to calculate the rockets height at the end of the 25 seconds. Use h as the variable for height.
The rockets height at the end of the 25 seconds is 275 ft.
What is the height risen by the rocket at the end of 25 seconds?The height risen by the rocket at the end of the 25 seconds is calculated by applying the following kinematic equation.
h = h1 + h2
where;
h1 is the height risen in the first 10 secondsh2 is the height risen in the next 15 secondstotal time of motion, 10 seconds + 15 seconds = 25 seconds
h = v₁t₁ + v₂t₂
where;'
v represents velocityt represents time of motionThe rockets height at the end of the 25 seconds is calculated as;
h = (10 s x 5 ft/s) + (15 s x 15 ft/s)
h = 50 ft + 225 ft
h = 275 ft
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