The work done when one mole of a gas expands isothermally from 15 L to 50 L against a constant pressure of 1 atm at 25 °C is -718 cal.
As we know that, work done in isothermal expansion is given as
W = -n RT ln(V₂/V₁) = - 2.303 n RT log(V₂/V₁)
Given,
Number of moles n = 1
Gas constant R = 2 cal
T is constant temperature associated with the process = 25 °C = (25 + 273)K = 298 K
Initial volume V₁ = 15 L
Final volume V₂ = 50 L
W = - 2.303 × 1 × 2 × 298 × log(50/15) = -1372.588 (log10 - log 3) = -1372.588 × 0.523 = -717.86 ≈ -718 cal
Thus, the work done will be -718 cal.
The given question is incomplete. The complete question is ' What will be the work done when one mole of a gas expands isothermally from 15 L to 50 L against a constant pressure of 1 atm at 25 °C ?'
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A cylindrical diving bell, 3.0 m in diameter and 4.0 m tall with an open bottom, is submerged to a depth of 220 m in the ocean. The surface temperature is 25oC, and the temperature 220 m down is 5.0oC. The density of seawater is 1025 kg/m3. How high does the seawater rise in the bell when it is submerged
The seawater will rise by 220m when the bell is submerged in seawater.
Diving bells are large, cylindrical chambers used to allow divers to explore the depths of the ocean. In this particular scenario, a 3.0 m diameter and 4.0 m tall diving bell with an open bottom is submerged to a depth of 220 m.
At this depth, the temperature is significantly cooler than the 25oC temperature near the surface. The density of the seawater is 1025 kg/m3.
Given the temperature difference between the surface and the diving bell's depth, the increase in water pressure will cause the water to rise a measurable amount within the bell. By taking into account the density of the seawater and the temperature difference between the diving bell's depth and the surface, the height of the seawater rise can be calculated.
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For each scenario, explain what distribution would be best to use and why. b. Airplane engines will fail when in flight with probability p. We are interested in computing the probability of at most 1 engine among the 6 failing on the plane.
CDF distribution will be used, Using Binomial Random variable, this problem can be solved.
The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, assessed at x, is the likelihood that X will take a value less than or equal to x in probability theory and statistics.
The PDF is the likelihood that a random variable, let's say X, would take a value exactly equal to x, while the CDF is the likelihood that a random variable will have a value less than or equal to x.
The cumulative distribution function (cdf), which is sometimes abbreviated as F(x), provides the likelihood that the random variable X is less than or equal to x. The function defined by F(x)=P[Xx] is the cumulative distribution function of the random variable X.
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Who first measured longitude?
Hipparchus is the first measured longitude. Hewas the first to specify a certain location using latitude and longitude in a coordinate.
Who is hipperchus?Hipparchus is a Greek astronomer that was live in 190-120 before century. He was the first who specify the location by latitude and longitude. He determine it by proposing an absolute time by lunar eclipse cycle and zero meridian that pass through Rhodes. He calculate it by measuring time between local time to absolute time. At those time, the accuracy is still lack because of the clock is not invented yet. Later in 1530, Gemma Frisius proposed to calculate it with a clock.
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What mass of HI should be present in 0.300 L of solution to obtain a solution with each pH value? Part A pH= 1.20 Part B pH= 1.70 Part C. pH= 2.80
At pH = 1.20, the concentration of HI must be high and the concentration of H+ must be high as well, so HI is mostly in the form of H+ ions.
At pH = 1.70, the concentration of HI is lower and the concentration of H+ is lower as well, so HI is mostly in the form of HI molecules.
At pH = 2.80, the concentration of HI is even lower and the concentration of H+ is even lower as well, so HI is mostly in the form of HI molecules.
MASS OF HITo determine the mass of HI present in a solution at a specific pH, you would need to use the acid dissociation constant (KA) of HI and the concentration of the solution.
Given the pH values, it would be difficult to determine the mass of HI present in 0.300 L of solution without knowing the acid dissociation constant (KA) of HI and the initial concentration of HI in the solution.
The mass of HI refers to the amount of HI (Hydrogen Iodide) present in a solution. It is typically measured in grams. To determine the mass of HI in a solution, you would need to know the concentration of the solution and the volume of the solution. The equation to calculate mass of HI would be: mass = concentration x volume.
It is also important to know that the mass of HI would change depending on the degree of dissociation, the mass of HI would be different in different pH values.
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damping is negligible for a 0.150-kg mass hanging from a light 6.30-n/m spring. the system is driven by a force oscillating with an amplitude of 1.70 n. at what frequency will the force make the mass vibrate with an amplitude of 0.440 m?
A sinusoidal force with an amplitude of 1.70N drives the system = 0.641 Hz if Damping is negligible for a 0.150kg object hanging from a light, 6.30N/m spring.
What is a force in science?In science, the word 'force' has a precise meaning. At this level, it is completely appropriate to describe a force as a push or a pull. A force is not something that an object contains or 'has in it'. A force is exerted on one object by another.
What is balance force?Balanced forces: Balanced forces are those that are opposite in direction and equal in size. Balanced forces are considered to be in a state of equilibrium. When forces are balanced there is no change in direction.
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What is the atmosphere best answer?
The Earth has an outer layer of air that is known as the atmosphere.
The Importance of the Earth's AtmosphereThe Earth's atmosphere is comprised of gases that are essential for life on the planet. It acts as a protective layer, shielding us from the sun's harmful rays and other space particles. It also helps to regulate the temperature of the Earth, making it possible for plants and animals to survive.
Furthermore, the atmosphere contains oxygen, which is essential for humans and other creatures to breathe. The atmosphere also contains water vapor which helps to transfer heat from the equator to the poles, and is also an important factor in weather systems.
The atmosphere is vital for the survival of all living things on Earth. We depend on it for many important functions, such as the production of food, the regulation of temperatures, and the protection of the planet from the harmful rays of the sun.
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What is the volume of a liquid with a mass of 0.254 g and a density of 1.00 g/ml?
0.254 g x (1 g/ml) = 0.254 ml
Imagine that an object is falling through a long straight glass tube held vertical; air has been removed
completely from the tube. The object does not touch the walls of the tube. Will the object experience any
force of friction
No, because of force of friction, the object won't experience any force of friction. It is given that the object does not touch the walls of the tube thus, there will be no force of friction.
How does an object experience friction?When two surfaces glide past one another, a force known as friction is created. Moving objects lose energy and slow down due to the friction force that opposes their motion. A fluid, like air or water, exerts a frictional force on moving objects when they move through it.
Does friction still exist when an object is stationary?Friction is a kind of force that opposes the direction of motion of an object, so it acts on the opposite direction to the actual movement of the object. But, an object doesn't necessarily have to be moving in order to experience the force of friction. When an object is stationary, static friction is in play.
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When a force of p N is applied to a spring, it stretches by q m.
What expression represents the spring constant of the spring?
Enter your answer as an expression with variables, such as x + y, with the appropriate unit.
When a force of P is applied to the spring results in its stretching by q m, the expression for force is written as:
p = -k q or p/q = k
where, the proportionality constant k is called the spring constant.
What is spring constant?For an elastic material like a spring, the force applied on the material is directly proportional to the displacement occurred.
thus, F = - kx
where F is the force , x be the displacement and the proportionality constant k is called the spring constant of the elastic material.
The spring constant can be defined as the force required to stretch an elastic material by one unit. Unit of force is Newton (N) and the displacement if given in meter, the unit of spring constant is N/m.
Given the force applied here is p N. The stretched length of the spring is q m. then,
p ∝ q
p = - k q
and spring constant k = p/q N/m.
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the electric field inside the dome of a highly-charged van de graaff generator is _________.
the electric field inside the dome of a highly-charged Van De Graaff Generator is zero.
About Van De Graaff generatorA Van de Graaff generator is an electrostatic generator which uses a conveyor belt to accumulate electric charge in a hollow metal ball on top of an insulated pole, creating a high electric potential. Producing high voltage in direct current (DC) electricity at a low level. This generator was invented by the American physicist Robert J. Van de Graaff in 1929.
The Van de Graaff generator was originally used as a particle accelerator for physics research, because with its high potential it can be used to accelerate subatomic particles to very high speeds in an evacuation tube. This generator is also a type of powerful accelerator until the discovery of the cyclotron which existed in the early 1930s. The Van de Graaff generator is still used as an accelerator to produce energetic particles and X-rays for nuclear research and nuclear medicine.
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A device that measures absolute air pressure is called a a.manometer b. barometer c. thermometer d. tire gauge
Weather forecasts are made using barometers. An air pressure gauge, or barometer When the barometer reads "rising," the air pressure is rising; when it reads "falling," the air pressure is lowering.
What does barometric mean?Barometric pressure, to put it simply, is the measurement of air pressure in the atmosphere, more particularly, the measurement of the weight exerted by air molecules at a certain location on Earth.
The usage of a barometer:barometer, a tool for calculating atmospheric pressure. A barometer may also be used to determine height since air pressure varies with elevation above or below sea level. Mercury and aneroid barometers are the two primary varieties.
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if the type i error (α) for a given test is to be decreased, then for a fixed sample size n? A) the Type II error (β) will also decrease.B) the Type II error (β) will increase.C) the power of the test will increase.D) a one-tail test must be utilized.
For a fixed sample size n, "the type II error (β) will increase" if the type I error (α) for a given test is to be decreased. Thus, the correct answer is B.
The Type I error, also known as a false positive, is the probability of incorrectly rejecting a null hypothesis when it is actually true. The Type II error, also known as a false negative, is the probability of incorrectly failing to reject a null hypothesis when it is actually false. When the Type I error (α) is decreased for a given test, the probability of making a Type II error (β) increases. This is because decreasing the Type I error rate makes the test more stringent, which in turn makes it harder to reject the null hypothesis. As a result, the power of the test, which is the probability of correctly rejecting a null hypothesis when it is false, may not increase.
Option A is incorrect because decreasing (α) does not necessarily mean that (β) will decrease. Option C is incorrect because increasing the power of the test, or the likelihood of correctly rejecting a false null hypothesis, is not directly related to decreasing (α). Option D is incorrect because the type of test (one-tail or two-tail) is not necessarily related to decreasing (α).
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A block of mass M is at rest on a ramp that is inclined at an angle θ with respect to the horizontal. Frictional forces are considered to be nonnegligible. The block is pushed against a spring and then held in place. The spring is compressed a distance of x1, and the spring is not secured to the block. The block is then released from rest, travels up the incline, and comes to rest after traveling a distance D, as shown above. Which of the following claims correctly describes the energy of the system under consideration from when the block compressed the spring and when the block has traveled a distance D along the incline? Select two answers.
See the image for choices
(B) The mechanical energy of the system consisting of the block does not change
(D) The mechanical energy of the system consisting of the block, spring and Earth increases by ¹/₂kx².
option B and D are the correct answers.
What is law of conservation of energy?
The law of conservation of energy states that energy can neither be created nor destroyed but can be converted from one form to another.
Based on the law of conservation of energy, the total mechanical energy of a system is always conserved.
Mathematically, the formula for conservation of mechanical energy is given as;
M.A = K.E + P.E
where;
K.E is kinetic energyP.E is the potential energy of the systemWhen the block is placed at the given position, its mechanical energy does not change because the change in the kinetic energy of the block is equal to the change in potential energy of the block.
However, by compressing the spring, the block acquires stored elastic potential energy, this increases the total mechanical energy of the block and the entire system.
Mathematically, the formula for the stored elastic potential energy of the spring is given as;
U = ¹/₂kx²
where;
x is the compression of the springk is the spring constantThus, we can conclude the total mechanical energy of the system consisting of the block, spring and Earth increases by the stored elastic potential energy of the spring.
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A sphere and a cylinder have the same radius and height. the volume of the cylinder is 50 feet cubed. a cylinder with height h and radius r. a cylinder with height h and radius r. what is the volume of the sphere? startfraction 50 over 3 endfraction feet cubed startfraction 100 over 3 endfraction feet cubed 75 feet cubed 100 feet cubed
The volume of such sphere is 100/3 cubic feet, according to the provided declaration.
A circle or a sphere?A hemisphere is a three-dimensional object, whereas a rectangle is a two-dimensional figure. In a sphere, all the spots are equally spaced from the center along one of the axes, unlike in a circle where all points are equally spaced from the center along a plane.
If you look at the sphere in this instance, the height is equal to double the radius.
The volume of something like a sphere may be calculated using the formula πr²h. Basically, the height is merely 2r. The modified formula is now πr²2r = 2πr³.
2πr³ = 50
πr³ = 25
r³ = 7.957747155
r = [tex]\sqrt[3]{7.957747155}}[/tex]
r = 1.99
Now that we know how big the radius is, we can calculate the sphere's volume.
= (4 / 3)πr³
= (4/3)π
= (4/3)π * 7.957747155
= (4/3) * π * (25 / π)
= (4/3) * 25
= 100/3 cubic feet.
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The complete question is-
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 50 feet cubed. A cylinder with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere? StartFraction 50 Over 3 EndFraction feet cubed StartFraction 100 Over 3 EndFraction feet cubed 75 feet cubed 100 feet cubed
If sparky starts with a velocity of 0 m/s and runs with a constant
acceleration of 0.75 m/s² for 8 seconds, what is Sparky's total
displacement in meters?
Answer:
0
Explanation:
if Sparkly was falling from somewhere then you coud multiply 0.75x 8, otherwise i think its displacement is 0
How do collisions between molecules transfer energy from a system of reacting substances to its surroundings
Answer:
They cause heat to flow from the system to the surroundings.
Determine the net impulse imparted to the object during the 6-second time interval.
P equals F net t. t F net F net The impulse-momentum theorem is an equation that relates the quantities t and.
According to the equation, the impulse is equal to the average net external force times how long it takes for that force to act.
It is equivalent to the momentum shift.
Without time, how can you discover impulse?You may use our calculator to directly calculate the impulse using the impulse formula J = p by entering the starting and end momentum values.
To compute the impulse using the equation J = mv, you may additionally insert the mass and velocity change of an object.
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What are objects that sink in water called?
A positively buoyant item is one that floats in water. A sinking item is negatively buoyant. To calculate the buoyancy of an item, both its mass and volume * must be known.
What is negatively buoyant?Negative buoyancy occurs when the submerged item is denser than the fluid displaced, causing the object to sink. When the weight of the submerged item equals the fluid displacement, neutral buoyancy occurs. The scuba diver's dive is an excellent illustration of neutral buoyancy. Objects sink because of negative buoyancy. It refers to an item whose weight exceeds that of the liquid it displaces.
Here,
Positive buoyancy refers to an item that floats in water. Sinking objects are negatively buoyant. To calculate an object's buoyancy, both its mass and volume * must be known.
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Wave A and Wave B are mechanical waves. Each wave has the same frequency. Which wave do you think will transfer more energy in 5 minutes? Explain the reason for your choice.
The wave that transfers more energy in 5 minutes is the wave with the larger amplitude.
What is a wave?A wave is an energetic disturbance in a medium that doesn't involve any net particle motion. Elastic deformation, a change in pressure, an electric or magnetic intensity, an electric potential, or a change in temperature are a few examples. A wave is a dynamic disturbance of one or more quantities that propagates.
The amount of energy transferred by a wave is directly proportional to the square of its amplitude. This means that a wave with twice the amplitude of another wave will transfer four times as much energy in a given amount of time. The frequency of the wave has no effect on the amount of energy it transfers
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Compared with a simple galvanometer, an electric motor is _____. A. The coil becomes a stronger electromagnet
B. Circle the wire in closed loops.
C. Much the same with small modifications
D. Similar to that of an interior bar magnet
Compared with a simple galvanometer, an electric motor is Much the same with small modifications.
ABOUT ELECTRIC MOTORAn electric motor is a device for converting electrical energy into mechanical energy. A tool that functions the other way around, converting mechanical energy into electrical energy is called a generator or dynamo. Electric motors can be found in household appliances such as fans, washing machines, water pumps, vacuum cleaners. and much more.
Electric motors that are commonly used in the world Industry are asynchronous electric motors, with two global standards namely IEC and NEMA. metric (millimeter) based IEC asynchronous motors, while imperial (inch) based NEMA electric motors, in applications there are power units in horsepower (hp) and kiloWatt (kW).
IEC electric motors are divided into several classes according to their efficiency, as a standard in the EU, this class division is EFF1, EFF2 and EFF3. EFF1 is the most efficient electric motor, consumes the least amount of energy, while EFF3 is no longer allowed to be used in the EU environment, because it wastes fuel in the power plant and will automatically generate the most carbon emissions, thus polluting the environment even more.
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How does ballistic stretching improve flexibility?
Ballistic stretching works muscles through a variety of motions to increase flexibility. Ballistic stretching before exercise prepares the muscles for high-impact action. Consequently.
A ballistic stretching is what?Ballistic Method It is the oldest technique for stretching exercises. This strategy employs quick movements. A joint or even a muscle can be stretched with only repetitive motions or activities around it. It is essential to warm up properly before beginning such a workout.
Ballistic stretching uses the velocity of a moving person or limb to push an object outside its inherent range of motion. You are "starting to warm up" or stretched by jumping into an extended posture and using your stretched muscles like a springtime to pull yourself out of it.
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You are designing a rotating metal flywheel that will be used to store energy. The flywheel is to be a uniform disk with radius 35. 0 cm. Starting from rest at t = 0, the flywheel rotates with constant angular acceleration 3. 00 rad/s2 about an axis perpendicular to the flywheel at its center.
The thickness that it must have to store 800 J of kinetic energy at t = 8.00 s is calculated to be , h=0.0735m.
What is angular acceleration?The time rate of change of angular velocity is called angular acceleration. It is expressed in radians per second per second. Angular acceleration is also known as rotational acceleration.
Given, radius 23.0 cm and starting from rest at t = 0,
Constant angular acceleration is 3.00 rad/s2
Given , density is 8600 kg/m3, and 800 J of kinetic energy
Generally the equation for the is mathematically given as
N= π r * h * p
= 3.14 * (23 *10^-22) * h * p
= 1428.5 h
E = 1/2 I W²
= 1/2 (NR²/2) W²
800 = 1/2 [(1428.5 *10^-2)²/2]*( 2 *8)²
So, h=0.0735m.
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Note : The question given on the portal is incomplete. here is the complete question.
Question: You are designing a rotating metal flywheel that will be used to store energy. The flywheel is to be a uniform disk with radius 23.0 cm. Starting from rest at t = 0, the flywheel rotates with constant angular acceleration 3.00 rad/s2 about an axis perpendicular to the flywheel at its center. If the flywheel has a density (mass per unit volume) of 8600 kg/m3, what thickness must it have to store 800 J of kinetic energy at t = 8.00 s?
Question 22 of 32
As a warehouse worker pushes a crate across a concrete floor, the force he
applies is not perfectly horizontal, as shown in the image below. If the
coefficient of kinetic friction between the crate and concrete floor is 0.5, what
is the net force on the crate?
Pushing Force
250 N
Weight
345 N
50
Friction Force
If the coefficient of kinetic friction between the crate and the concrete floor is 0.5, then the net force on the crate will be 99N.
What is the calculation of the net force?On resolving the given force and acceleration.Mathematically in the different components and balancing the equation gets.Components in the x-direction.
When all the forces get resolved the y-direction of forces are;
300 sin 10° +N = 445
N = 445-295.4
N = 392.9 N
The normal force is 392.9 N.
The net force on the crate is found by resolving the force in the x-direction;
F = 300 cos 10° - μN
F= 295.44-196.45
F= 98.99
F=99
Hence, the net force on the crate will be 99 N.
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Your question was incomplete most probably your full question was:
As a warehouse worker pushes a crate across a concrete floor, the force he applies is not perfectly horizontal, as shown in the image below. If the coefficient of kinetic friction between the crate and concrete floor is 0.5, what is the net force on the crate?
A. 136 N
B. 99 N
C. 73 N
D. 112 N
the strong force of cohesion at the surface of a liquid?
The cohesive forces between liquid molecules generate the surface tension phenomena.
What is cohesion?In physics, cohesion is defined as the intermolecular attractive force operating between two adjacent sections of a material, most notably a solid or liquid. This is the force that keeps stuff together. Intermolecular forces also exist between two distinct substances that come into contact, a process known as adhesion. Water characteristics cohesion and adhesion explain how water molecules interact with one another. as well as how water molecules interact with other substances such as leaves or even you. Water tends to stick to itself, which is what cohesion means. Water tends to attach to other things, which is what adhesion means. Cohesion is the act of sticking together. If your group of pals goes to the lunchroom as a unit and sits together, you're displaying good cohesiveness.
Here,
The phenomenon known as surface tension is caused by the cohesive forces between liquid molecules.
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A system which undergoes an adiabatic change (i.e., q = 0 which means no change in the system's heat energy) and does work on the surroundings has a. w> 0. AE <0 b. W<< 0, AE <0 c. W<0, AE = 0 d. W>0. AE > 0 e. W<0. AE > 0
A system which undergoes an adiabatic change. The work done and the change in the internal energy are: W>0, AE > 0 (option d)
Adiabatic process is a thermodynamic process in which no heat goes into or out of a system and all internal energy is changed by work.
Adiabatic operations are frequently carried out in an insulated container, where the process occurs too quickly for heat to be transferred. Because heat transfers due to a temperature difference between a system and its surroundings, an adiabatic process can occur even when the system is in thermal equilibrium.
The first law of thermodynamics is:
ΔU = Q + W
Where:
ΔU = change in internal energy
Q = heat transfer
W = work done
In the given problem, the internal energy is represented by AE, hence, we can write:
AE = Q + W
Since there is no change in heat energy, Q = 0, therefore,
AE = W
The work done in an adiabatic process is positive. Therefore, the correct answer is W>0, AE > 0 (option d)
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how is weight affected by buoyant force?
The buoyant force acting on the suspended object exactly equals the object's weight.
Explanation:
If the buoyant force is greater than the object's weight, the object will rise to the surface and float. If the buoyant force is less than the object's weight, the object will sink. If the buoyant force equals the object's weight, the object can remain suspended at its present depth.
Help, I have to deliver it tomorrow What do I have to do?
A state machine is graphically represented by a state diagram. It displays a behavioral model made up of states, transitions, and actions, together with the events that have an impact on these.
What is Intial model Diagram?Additionally, it's one of the 14 UMLs, or Unified Modeling Languages, that are employed for defining, modeling, building, and documenting software systems.
The two types of UML diagrams are structural and behavioral. While behavioral UML diagrams portray the dynamic changes inside a system, structural UML diagrams show the static framework of a system or process.
A state diagram is one kind of behavioral diagram, in case you hadn't guessed.
Therefore, A state machine is graphically represented by a state diagram. It displays a behavioral model made up of states, transitions, and actions, together with the events that have an impact on these.
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the mass of a grain of salt is around 0.06 mg. how many grains of salt would be in 100 grams of sand?
The number of the grains of salt that would be in the total mass of the sand is determined as 1.67 x 10⁶ gains.
What is the number of grains of salt?The number of grains of salt is calculated by dividing the total mass of the sand by the mass of a single grain of salt.
Mathematically, the formula for the number of grains of salt is given as ;
1 grain of salt ----------> 0.06 mg
? grain of salt ------------> 100 g
For the mass of a grain of salt is around 0.06 mg, the number of grains that will be found in 100 grams of sand is calculated as follows;
number of grains of salt = ( mass of the sand ) / ( mass of a single grain of salt )
number of grains of salt = ( 100 g ) / ( 0.06 x 10⁻³ g )
number of grains of salt = 1.67 x 10⁶ gains
Thus, the number of the grains of salt found in the mass of the sand is a function of total mass of the sand and the mass of a single grain of salt.
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on a typical seismogram, ____________ will show the highest amplitudes.
Surface waves will typically have the highest amplitudes on a seismogram.
Seismogram. the recorded seismic waves from an earthquake that were made by a seismograph. The best way for floor waves (L) to travel is through solids, which causes the crust to ripple like ocean waves (maximum destructive) The first waves to be detected after an earthquake are body waves (P & S).
P waves arrive first because they travel at the best velocity because they are compressional waves. The primary, or P, waves travel the fastest and are the first to be recorded by a seismograph. Secondary waves, or S waves, move more slowly.
Rock oscillates perpendicular to the direction of wave propagation in S or shear waves. In rock, S waves typically travel at a speed of around 60% that of P waves, and they always arrive after the P wave.
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A small block of mass M is released from rest at the top of the curved frictionless ramp shown above. The block slides down the ramp and is moving with a speed 3.5vi when it collides with a larger block of mass 1.5 M at rest at the bottom of the incline. The larger block moves to the right at a speed 2vi immediately after the collision.
1. Determine the height h of the ramp from which the small block was released in terms of M, vi, h, and constants.
2. The larger block slides a distance D before coming to rest. Determine the value of the coefficient of kinetic friction µ between the larger block and the surface on which it slides, in terms of M, vi, h, D and constants.
The height of the ramp and the coefficient of kinetic friction found using the principle of conservation of energy are as follows;
1. h ≈ 0.625·[tex]v_i[/tex]²
2. [tex]\dfrac{10}{49} \cdot \dfrac{v_i^2}{D}[/tex]
What is the principle of conservation of energy?The principle of conservation of energy states that energy can only be transformed from one form to another, as energy is neither created nor can energy be destroyed.
Mass of the smaller block = M
Initial height of the smaller block = h
Velocity of the smaller block when it collides with the larger block = 3.5·[tex]v_i[/tex]
Mass of the larger block = 1.5·M
Speed of the larger block just after collision = 2·[tex]v_i[/tex]
1. The potential energy of the smaller block at the top of the ramp = M·g·h
Where;
g = The acceleration due to gravity ≈ 9.81 m/s²
The kinetic energy of the smaller block when it collides with the larger block at rest at the bottom of the incline = 0.5·M·[tex](3.5\cdot v_i)^2[/tex]
According to the principle of conservation of energy, we get;
M·g·h = 0.5·M·[tex](3.5\cdot v_i)^2[/tex] = 0.5·M×12.25·[tex]v_i[/tex]² = 6.125·M·[tex]v_i[/tex]²
M·g·h = 6.125·M·[tex]v_i[/tex]²
h = (6.125÷9.81)·[tex]v_i[/tex]² ≈ 0.625·[tex]v_i[/tex]²
The height of the ramp, h ≈ 0.625·[tex]v_i[/tex]²
2. The frictional force, [tex]F_N[/tex] = Normal reaction × Coefficient of friction
The normal reaction of the larger block on the flat surface = The weight of the larger block
Therefore; [tex]F_N[/tex] = 1.5·M·g = 1.5×9.8×M = 14.7·M
The coefficient of kinetic friction = μ
Therefore, [tex]F_N[/tex] = 14.7·M × μ
The work done due to friction = [tex]F_N[/tex] × D
Therefore; Work due to friction = 14.7·M × μ × D
The kinetic energy of the larger block = 0.5 × 1.5·M × (2·[tex]v_i[/tex])² = 3·M·[tex]v_i[/tex]²
According to the principle of conservation of energy, we get;
14.7·M × μ × D = 3·M·[tex]v_i[/tex]²
14.7 × μ × D = 3·[tex]v_i[/tex]²
μ = 3·[tex]v_i[/tex]² ÷ (14.7 × D) = (10/49)·([tex]v_i[/tex]²/D)
Learn more on the principle of conservation of energy here: https://brainly.com/question/2554432
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