The problems ask to find and plot z[n] = x[2–2n] using [tex]a^{u[n]}[/tex] the function, reconstruct a[n] using linear interpolation and time scaling transformations, and find no and ni such that [n] = p[n+ni) is odd and sketch x[n] for the signal p[n] = u[n+ 7] – u[n+ 3] – u[n + no] + u[n +2].
For the first problem, it is important to make sure that you label the heights and times in the sketch. This is important to ensure that when you are solving the problem, you are paying attention to the different points on the graph and how they interact with one another. To begin with, you can use a combination of transformations to find and plot z[n] = x [2–2n). It is possible to use a transformation like [tex]a^{u[n]}[/tex] where a > 1 to manipulate the x[n] into the desired shape.For the second problem, the signal x[n] and two series of time scaling transformations for x[n] are given below. In order to reconstruct a[n] with each series of transformations, you can use linear interpolation to calculate the interpolated values. You will also need to determine if both series of transformations are invertible or not. To do this, you can inspect the series and see if each transformation is reversible.Finally, for the third problem, in order to find no and nį such that [n] = p[n+ni) is odd, you can start by inspecting the signal p[n] = u[n+ 7] – u[n+ 3] – u[n + no] + u[n +2]. From here, you can then use algebraic manipulation to determine the no and nį. Once these are found, you can sketch x[n], which will be a step function.To learn more about transformations at
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The question is -
For problems asking for a sketch, be sure to label heights and times. Show intermediate steps of your work. 1. Combinations of transformations: Let x[n] = a^u[n], where a > 1, find and plot z[n] = x [2–2n). 2. Example of noninvertible transformations: The signal x[n] and two series of time scaling transformations for x[n] are provided below. Try to reconstruct a[n] with each series of transformations. Are both series of transformations invertible? Use linear interpolation if you need to and write down the general formula for calculating the interpolated values. x[n] n -2 -1 0 1 2 3 4 5 5 x[3n] x/r/3] x[n/3] x[n] x[n] x[n/3] x[3n] x[n] x[n] 3. Even/Odd + Step Function: For the signal p[n] = u[n+ 7] – u[n+ 3] – u[n + no] + u[n +2], find no and nį such that [n] = p[n+ni) is odd and sketch x[n].
find the time-domain voltage over the capacitor using phasor domain techniques. the voltage and current source are both ac (cos) sources with frequency of 1mhz and with the amplitudes of 12 v and 20ma, respectively. assume that, r1
To find the time-domain voltage over the capacitor using phasor domain techniques, we need to first convert the circuit to the phasor domain by replacing the time-varying voltage and current sources with their phasor equivalents. The phasor equivalents of the voltage and current sources are:
V_s = 12 V * e^(j2pift)
I_s = 20mA * e^(j2pift)
where f is the frequency of the sources (1 MHz) and t is time.
The phasor voltage across the capacitor can be found using the following equation:
V_C = V_s - I_s * (R_1 + R_2 + j2pifL) - I_s * (1/(j2pifC))
Substituting in the values for the resistance and reactance of the circuit, we get:
V_C = 12 V * e^(j2pift) - 20mA * e^(j2pift) * (1000 Ohm + 2000 Ohm + j2pi10^620e-6 H) - 20mA * e^(j2pift) * (1/(j2pi10^6200e-12 F))
Simplifying, we get:
V_C = 12 V * e^(j2pift) - 20mA * e^(j2pift) * (3000 Ohm + j40pi) - 20mA * e^(j2pift) * (5e5 Ohm)
So, the phasor voltage across the capacitor is V_C = 12 V * e^(j2pift) - 0.02 A * e^(j2pift) * (3000 Ohm + j40pi) - 0.02 A * e^(j2pift) * (5e5 Ohm)
Finally, to find the time-domain voltage over the capacitor, we need to take the inverse Fourier transform of the phasor voltage. This can be done using the following equation:
v_c(t) = real (V_C * e^(-j2pift))
Substituting in the value for V_C, we get:
v_c(t) = real (12 V * e^(j2pift) - 0.02 A * e^(j2pift) * (3000 Ohm + j40pi) - 0.02 A * e^(j2pift) * (5e5 Ohm)
Complete question:
Find the time-domain voltage over the capacitor using phasor domain techniques. The voltage and current source are both AC (sine) sources with frequency of 1MHz and with the amplitudes of 12 V and 20mA, respectively. Assume that, R_1 = 1 k Ohm, R_2 = 2k Ohm, C = 200pF, and L = 20mu H.
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An object attached to a spring vibrates with simple harmonic motion as described by the figure below.
For this motion, find the following.
(a) the amplitude
(b) the period
(c) the angular frequency
(d) the maximum speed
(e) the maximum acceleration
(f) an equation for its position x in terms of a sine function (Do this on paper. Your instructor may ask you to turn in this work.)
The graph provided is a displacement-time graph. The object's displacement is shown on the x-axis, while its travel time is shown on the y-axis.
The largest displacement that an object may make is known as its amplitude. The maximum displacement made by the object is 2 cm.
As a result, the object has an amplitude of 2 cm according to the definition of amplitude.
The amplitude of the object depends on the displacement made by the object. The maximum displacement is made when the object moves to an extreme position in an oscillation.
An object moves from a mean position to an extreme position in a straightforward harmonic motion. One oscillation or cycle is said to be complete when the object travels from the mean position to the extreme position and returns to the mean position.
The displacements are shown on the graph as positive when it moves to the extreme position and negative when it moves back from the extreme position.
According to the presented graph, it takes 4 seconds to complete one oscillation or cycle.
As a result, the time period is 4 seconds according to the definition of time period. Therefore, the time period as ω = 2π/T.
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kicked the ball in the air with an initial velocity of 12m/s at an angle of 40° above the horizontal. If the ball travels a horizontal distance of 15m , how long will it fly in the air?
The soccer ball rose 5.24 meters in the air.
VO =?, max H =?, range = 25m, angle A = 40°
Projectile motion is being used in this situation. Range = vo2 * sin 2A / g is the formula for range. calculating the initial velocity vo's square and its original value.
Range is equal to vo2*sin2A/g.
VO2 * SIN (2 * 40°) / 9.8 m/s = 25 m
vo2 = sin 80° / 9.8 m/s / 25 m
2 vo = 15.77 m/s and 2 vo = 248.8 (m/s) respectively.
The ball's starting speed is 15.77 m/s.
The height of the object, max H, can be calculated as follows: max H = vo * (sin A) * 2g max H = 248.8 (m/s) * (sin 40°) * 19.6 m/s * 2g max H = 5.24 meters
The soccer ball rose 5.24 meters in the air.
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Some crosswalks timers are set in consideration that persons older than 65 walk at an average pace of 2.9 ft/sec. Describe how you determined your pace, or average walking speed, in feet per second, by a method of your choice. How does your pace compare to the average pace of persons older than 65?
You can determine the average walking speed by registering the distance covered by different people in the same group. My pace is higher than people older than 65.
How to determine the walking pace?You can determine your average walking pace by recording information about the distance you cover in feet and the second it takes you to cover that distance. Here is an example:
450 feet / 100 seconds = 4.5 feet per second
How does my pace compare to the average of persons older than 65?My pace is faster than the walking pace of someone who is 65.
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scallops use muscles to close their shells. opening the shell is another story--muscles can only pull, they can't push. instead of muscles, the shell is opened by a spring, a pad of a very elastic biological material called abductin. when the shell closes, the pad compresses; a restoring force then pushes the shell back open. the energy to open the shell comes from the elastic energy that was stored when the shell was closed. (figure 1) shows smoothed data for the restoring force of an abductin pad versus the compression. when the shell closes, the pad compresses by 0.15 mm. How much elastic potential energy is stored?
10J elastic potential energy is stored.
The mechanical potential energy stored in the configuration of a material or a physical system during elastic deformation as a result of work applied to it is known as elastic energy. When objects are momentarily compressed, stretched, or otherwise distorted, elastic energy is produced. Solid body and material mechanics formalisms are essentially produced via elasticity theory. Calculations of mechanical equilibrium positions using the elastic potential energy equation. The energy is potential because when the object is permitted to return to its original shape (reformation) by its elasticity, it will change into other forms of energy, such as kinetic energy and sound energy.
compression = expansion
force=2.5N
K= [tex]\frac{F}{x}[/tex]=[tex]\frac{2.5N}{0.2\times10^{-3} }=1.25\times10^4 N/m[/tex]
compression=0.15mm
Energy= [tex]\frac{1}{2}Kx^{2}[/tex]
Energy= [tex]\frac{1}{2}1.25\times 10^{-4}( 2.25\times10^{-10})J[/tex]
Energy=[tex]1.40625\times 10^{-4}\\[/tex]joules
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In video 1 for Chapter 17, how does the fringe spacing change when the distance between the slits, d, is increased?
The fringes get farther apart.
The fringe spacing stays the same.
The fringes get closer together.
It depends on how wide the slits are.
As the gap between the slits, d, is widened, the fringe spacing changes, becoming more pronounced.
How would you define distance in plain English?Distance is an object's overall motion in a directionless fashion. Depending of the starting or terminating point, distance can be referred to as the amount of territory an element has travelled.
The purpose of distance calculationWe can find out an object's actual size by knowing how far away it is. The area an object occupies in space above us can be measured. Once we know how far away it is, we can calculate its true size. An thing appears smaller the further away it is.
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a 1200 kg safe is 2.1 m above a heavy-duty spring when the rope holding the safe breaks. the safe hits the spring and compresses it 56 cm . What is the spring constant.
When a 1200 kilogram safe is 2.1 m above a heavy-duty spring and the rope holding the safe breaks, the spring constant is 199,136 N/m (roughly 200 kN/m). The safe collides with the spring, compressing it by 56 cm.
What is kinetic energy?In physics, an object's kinetic energy is the energy it has as a result of its motion. It is defined as the amount of work required to accelerate a body of a given mass from rest to a certain velocity. The body retains its kinetic energy after gaining it during acceleration until its speed changes. Kinetic energy is the energy that an item has as a result of its movement. If we wish to accelerate an item, we must apply force to it. Using force demands us to put in effort. After work is completed, energy is transferred to the item, and the thing moves at a new constant speed.
Here,
The spring constant is 200kN/m.
The work done on the spring by the the free falling safe is equal to the kinetic energy of the spring:
W1 =1/2kx²
The work done on the safe by gravity is the potential energy of the spring:
W2 = (mass of safe) x g x (height)
= 1000kg x 9.8 m/s^2 x (2 + 0.54)m
=1000kg x 9.8 m/s^2 x (2.54)m
= 24,892 N-m
W2 = W1 =24892 N-m
W=1/2kx²
Therefore, k = 199136 kN/m.
The spring constant is 199,136 N/m approximately 200 kN/m when a 1200 kg safe is 2.1 m above a heavy-duty spring when the rope holding the safe breaks. the safe hits the spring and compresses it 56 cm.
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a student conducted an experiment where they burned a 5g strip of magnesium metal in an open flame. the result was a 3.5g of white ash collected in a crucible, a bright white flame, and smoke.
This experiment undoubtedly brought about the ignition of magnesium metal, which is an exceptionally receptive metal that promptly consumes within the sight of oxygen.
The ash gathered in the crucible is logical to the excess buildup of the magnesium after it has gone through ignition. The bright white fire and smoke are likewise normal for magnesium consumption.
As the metal consumes at a high temperature and produces a bright light. The ash gathered in the crucible is in all probability magnesium oxide, which is a white fine substance.
The weight of the ash(3.5g) is not exactly the underlying load of the magnesium strip (5g), this is because of the deficiency of magnesium as a gas during the burning system.
The contrast between the weight of the ash and the underlying load of the magnesium strip addresses the weight of the magnesium that was lost as a gas during the combustion.
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assuming that each cubic centimeter of water has a mass of exactly 1 g, find the mass of 1.87 cubic meter of water.
Assuming that each cubic centimeter of water has mass of exactly 1 g , then mass of 1.87 cubic meter of water is 1.87 kg.
What is mass?We define mass as measure of the amount of matter in a body. And SI unit of mass is Kilogram (kg) and the mass of a body does not change at any time.
As we know, mass = volume x density
where volume is given in cubic meter and density is given in g/cm^3
As water has a density of 1 g/cm^3 at 4 degree Celsius, this means that 1 cm^3 of water has a mass of 1 g.
So, mass = 1.87 m^3 x 1 g/cm^3 = 1.87 kg
Therefore, the mass of 1.87 cubic meter of water is 1.87 kg.
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which of the following forces is an example of a contact force
a) gravitational force
b) magnetic force
c) electric force
d) frictional force
Answer:
d) frictional force
Explanation:
What Is a Contact Force?
Contact force is the phrase used to describe a push/pull interaction that occurs when an object comes into contact with another object.
The only force where there is contact between two bodies in the answer choices is frictional force
Answer
d) frictional force
An object is thrown straight up. Which of the following is true about
the sign of work
done by the gravitational force while the object moves up and then
down?
A.Work is positive on the way up, work is positive on the way down
B. Work is negative on the way up, work is negative on the way down
C.Work is negative on the way up, work is positive on the way down
D.Work is positive on the way up, work is negative on the way down E.
Work is zero the way up, work is zero on tâ
The correct option is C. Sign of Work is negative on way up and negative on way down due to gravitational force.
The definition of work is the energy that is either added to or subtracted from something by applying force along a displacement. For a constant force acting in the same direction as the motion, the work is simply equal to the product of the force's magnitude and the distance travelled.
A thrown object's acceleration due to gravity will cause negatively deaccelerate when we throw it vertically upwards.
We represented deacceleration by a (-) sign.
Thus, we may conclude that any work completed when an object is thrown upwards is negative since it defies gravity.
Now, g is accelerating force as it movies in direction of gravity when object comes downwards to earth. Work done when object moves down is positive.
Consequently, the best option will be option (C)
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Infant brain mapping is being used to assess perceptual and cognitive activities including which of the following?
Language
Hearing
Vision
Infant brain mapping is being used to assess perceptual and cognitive activities including Vision, Hearing, and Language.
The very early offspring of humans are called infants or babies. Infant is a formal or specialized synonym for the phrase baby. It comes from the Latin word infants, which means "unable to talk" or "speechless." Other organisms' young may also be referred to by the names.
In everyday speech, an infant that is only a few hours, days, or even a few weeks old is referred to as a newborn. In medical contexts, an infant in the first 28 days following delivery is referred to as a newborn or neonate (from the Latin neonates, newborn); the word is applicable to premature, full-term, and postmature newborns.
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What effect does increasing the moon’s mass have on the earth?
Answer:
Explanation:
If the moon doubled in mass, that means that the Earth will not experience a total solar eclipse like today also, if it doubled in mass, tide waves would increase in size, as the moon would be bigger and would have a bigger gravitational pull
an object's elevation is a perspective cue to . group of answer choices distance shape shadowing size
A monocular cue called linear perspective helps us understand the depth and distance of an object.
Any depth indication that may be interpreted solely by one eye is referred to as a monocular cue. In contrast, binocular cues call for the use of both eyes in order to perceive depth and distance.
Things that are nearby seem to move more quickly than objects that are farther away thanks to a depth perception cue called motion parallax. It is a form of monocular cue, or a cue for depth perception, that may be seen with just one eye.
Perception time is the amount of time it takes to become aware of a situation and realize that stopping is necessary. About three-quarters of a second may pass during this. Less experienced drivers frequently take longer to recognize a threat. The distance a car goes during this time is called perception distance.
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Landon and Jocelyn are partners in pair figure skating. Last weekend, they perfected the death spiral element for inclusion in their upcoming competition. During this maneuver, Landon holds Jocelyn by the hand and swings her in a circle while she maintains her blades on the ice, stretched out in a nearly horizontal orientation. Determine the net force that must be applied to Jocelyn (m = 47.3 kg) if her center of mass rotates in a circle with a radius of 0.915 m once every 1.13 seconds.
The net force that must be applied to Jocelyn is 139 Newton.
How to calculate the net force?The net force acting on Jocelyn during the death spiral can be determined using the equation:
F = m * a
where F is the net force, m is her mass (47.3 kg), and a is her centripetal acceleration.
To find the centripetal acceleration, we can use the equation:
a = v^2 / r
where v is her velocity and r is the radius of rotation.
We know that Jocelyn completes one rotation every 1.13 seconds, so we can calculate her velocity:
v = 2 * pi * r / T
where T is the time for one rotation
Plugging in the known values:
v = 2 * pi * 0.915 m / 1.13 s
v = 5.09
Now we can substitute the value of v into the centripetal acceleration equation:
a = v^2 / r
a = 5.09² / 0.915
a = 28.3
F = ma
F = 47.3 × 28.3
F = 1339 Newton
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after being kicked, a soccer ball flies upward into the air, slowing down as it reaches its maximum height.T/F
False. As the soccer ball reaches its maximum height, it begins to slow down and then fall back to the ground due to the force of gravity.
What is gravity?Gravity is a natural force of attraction that exists between any two objects with mass. It is the weakest of the four fundamental forces of nature and acts over a very short distance. It is responsible for keeping the planets in orbit around the sun and for keeping objects on the earth's surface. Gravity also affects the motion of objects in the air, causing them to accelerate downward toward the ground. In addition, gravity affects the tides and other oceanic phenomena. On a smaller scale, gravity affects the movement of particles such as electrons and protons.
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002 (part 2 of 3) 10.0 points what is the magnitude of the potential difference vy x across the terminals y and x of the battery? answer in units of v. answer in units of v. 003 (part 3 of 3) 10.0 points what power is dissipated by the internal resistance of the battery? answer in units of w. answer in units of w.
The power dissipated by the battery is 100V2/R.
What is power dissipated?Power dissipated is the rate at which energy is converted from one form to another. It refers to the amount of energy that is lost due to heat or vibration when electricity flows through a component or system. Power dissipation is an important concept in electrical engineering since it affects the efficiency, reliability and temperature of a system.
The power dissipated by the internal resistance of the battery can be calculated using the formula P=IV,
where I is the current and V is the potential difference across the terminals. Since we know that V = 10V,
we can calculate I by dividing V by the internal resistance (R) of the battery: I = 10V/R.
The power dissipated by the battery is then given by P = IV = (10V/R)*(10V) = 100V2/R.
Thus,
In units of watts, the power dissipated by the battery is 100V2/R.
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Which of the following describes a benefit of the fact that oll never wears out?
Because oll never wears out, it can be used again and again.
Because oll never wears out, farmers will never run out of it.
Because oll never wears out, it never needs to be replaced.
O Because oll never wears out, its cost remains low.
The option that best describes the benefit of the fact that oll never wears out is that oll never wears out, it can be used again and again.
The correct option is A.
What is the benefit of durability in materials?Durability is the ability of material to last in usage for a long time.
Duravle materials provides benefits to the owners in that it:
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A taxi hurries 95 km in 1 7/12 hours. What is its average speed in kilometers per hour?
85.83 km/hr is the average speed it travels at.
Explain about the speed.An object's speed can be determined if you are aware of the distance it covers in a given period of time. An automobile, for instance, is moving at a pace of 70 miles per hour if it covers 70 miles in an hour (miles per hour).
Speed (or rate, r) is a scalar quantity that represents the amount of distance travelled (d) over the amount of time changed (t), as shown by the equation r = d/t.
Distance divided by time can be used to calculate speed. The speed is determined by dividing the distance travelled (say, 3 meters) by the passing time (say, 3 seconds) (one meter per second) Speed is hence the rate at which an object's position changes in any direction.
By converting 7/12 to a decimal (7/12 = 0.58), you may determine how many hours are in total.
1 plus 0.58 equals 1.58 hours when you add up the total time.
Subtract the overall time from the entire distance (95km) (1.58 hours).
The result, 95 kilometers divided by 1.58 hours, is 85.83 km/h, which is the average speed.
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some psychologists believe that eating disorders representative fence against unconscious conflicts related to sexual development. These psychologists have adopted a _____ approach to eating disorders.
Some psychologists believe that eating disorders represent a defense against unconscious conflicts related to sexual development. These psychologists have adopted a Psychoanalytic approach to eating disorders.
What is a Psychoanalytic approach?A psychoanalytic approach is based on the idea that our unconscious thoughts, feelings, and motivations can have a powerful influence on our behavior by focusing on helping individuals to gain insight into their unconscious processes, recognize and resolve conflicts, and modify their behavior.
Therefore, with this data, we can see that a Psychoanalytic approach is based on unconscious mental processes to develop a cure.
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Tension force has units of ________. Check all that apply.
Answer:
Newton (N)
Explanation:
At what distance of 1m from the source intensity of sound is 2 w / m² . What is the power of this wave
Answer:
25.13274 W (WATT) (Sound Power of the Sound Source)
134.002 dB (Sound Power Level)
An object's speed is 3.6 m/s with a momentum of 180 kgm/s. What is the mass of the object?
Answer:
To solve the problem we must know the concept of momentum.
What is Momentum?
Momentum is defined as the product of the mass of an object and the velocity of an object. It is a vector quantity.
$$\rm{Momentum = velocity \times Mass$$
The mass of the object is 50 kg.
Given to us
velocity of the object = 3.60 m/s
momentum of the object = 180 kg m/s
Mass of the object
We know that momentum is the product of the mass of the object and the velocity of the object,
$$\rm{Momentum = velocity \times Mass$$
Substitute the values,
180 = 3.60 \times \rm Mass180=3.60×Mass
\rm Mass = \dfrac{180\ kg\ m/s}{3.6\ m/s}Mass=
3.6 m/s
180 kg m/s
\rm Mass = 50\ kgMass=50 kg
Hence, the mass of the object is 50 kg.
Each choice below describes how a few astronomical phenomena are related to time periods. Which list is entirely correct? (Careful: some lists are partially correct.) A) Earth's rotation defines a day.The cycle of the Moon's phases takes about a month.Earth's orbit defines a year.Earth's cycle of axis precession takes 26,000 years. B) Earth's rotation defines a day.The cycle of the Moon's phases takes about a week.Earth's orbit defines a year.Earth's cycle of axis precession defines a month. C) Earth's rotation defines a day.The Sun's rotation defines a week.The Moon's rotation defines a month.Earth's orbit defines a year.D) Earth's rotation defines a day.The saros cycle of eclipses defines a month.Earth's orbit defines a year.Earth's cycle of axis precession takes 26,000 years.
The correct list is D) Earth's rotation defines a day. The saros cycle of eclipses defines a month.
What is Earth's rotation?Earth's rotation is the rotation of the planet around its own axis. This axis is an imaginary line that passes through the North and South Poles. Earth rotates from west to east, which is why the Sun appears to rise in the east and set in the west. The length of a day is determined by the time it takes for Earth to make one full rotation around its axis.
Earth's orbit defines a year.Earth's cycle of axis precession takes 26,000 years. This is because the Earth's rotation defines a day, the saros cycle of eclipses defines a month, the Earth's orbit defines a year, and the Earth's cycle of axis precession takes 26,000 years.
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A bottle with a volume of 195 U. S. fluid gallons is filled at the rate of 1.7 g/min. (Water has a density of 1000 kg/m3, and 1 U.S. fluid gallon = 231 in.3.) How long does the filling take?
The time that have been taken by the liquid is 4.4 * 10^5 min.
How long does it take to be filled?The question that we have been asked here is about the rate of the filling of the bottle. We can see that we have been given the volume of the bottle clearly.
We know that the volume of the solution that we have is 195 U. S. fluid gallons or 0.74 m^3. Then we have that;
Density = mass/volume
mass = Density * volume
= 0.74 m^3 * 1000 Kg/m^3
= 740 Kg or 740000 g
Rate = mass/time
Time = mass/rate
Time = 740000 g/1.7 g/min.
= 4.4 * 10^5 min
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Calculate the increase in length of a 40 cm brass rod that is heated from 30 ° C to 50 ° C ( linear expansion of Brass is 1.9 x 10³8¹¹ )
a. 0.015 cm b.0.051 cm c.1.9 cm d. 15.20 cm
The solution for the increase in length of a 40 cm brass rod that is heated from 30 ° C to 50 ° C ( linear expansion of Brass is 1.9 x 10³8¹¹ ) is
0.051 cm. In this case Option B is correct.
Linear Expansion Theory: What Is It?
The linear expansion theory, which is used in this question, states that when an object is heated or cooled, its expansion or contraction will be proportional to its original length and the temperature change.
First, determine Brass' linear expansion (1.9 x 108 11).
Step 2: Determine how long the 40 cm brass rod will grow. Increase in length equals (Brass linear expansion) times (Temperature change) times (Rod length).
(1.9 x 108 11) x (20°C) x (40 cm) length increase
Step 3: Determine the lengthening.
lengthening equals 0.051 cm
Response: 0.051 cm
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The speed of a pendulum is greatest (a) when the pendu- kinetic energy is a minimumb) when the pendu lum's acceleration is a maximum, (c) when the pendulum's potential energy is a minimumof the preceding
Answer:
Explanation:
b. when the pendulum's acceleration is a maximum.
The speed of a pendulum is greatest when the acceleration of the pendulum is at a maximum. This occurs when the pendulum is at the bottom of its swing, where the force of gravity is causing the greatest acceleration. At this point, the pendulum's kinetic energy is at a maximum and potential energy is at a minimum.
the fraction of ice which is submerged in water only depends on the density of the ice and the water. for this problem, assume the density of ice is 928.5 kg/m3.
0.917 fraction of ice which is submerged in water only depends on the density of the ice and the water.
What is density?The density of a material is its mass per unit volume. The most common sign for density is, however the Latin letter D can also be used. The density of a substance is the measure of how densely it is packed together. It is expressed as mass per unit volume. Symbol for density: D or Formula for Density: = m/V, where is the density, m is the object's mass, and V is the object's volume. The density of something describes how compact or dense it is. Let's say you have two boxes, one huge and one tiny. They both, however, weigh the same. That means the small box has a higher density than the large box. Density also tells how concentrated or crowded something is.
Here,
The density of the ice and the water have no effect on the 0.917 proportion of ice that is submerged in water.
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The Kingda Ka roller coaster in New Jersey is the world's tallest ride of its kind. As the passenger cars are launched from rest at the start, they are accelerated uniformly to a speed of 57 m/s (128 mph) in just 3.5 s. (Assume the cars are launched in the positive horizontal direction. Indicate the direction with the sign of your answer where appropriate.)
(a) What is the acceleration experienced by passengers on this ride in m/s2?
m/s2
What is the acceleration experienced by passengers on this ride in g's?
g
(b) If a certain passenger has a mass of 68 kg, what is the force in newtons that acts on him during the launch phase of this ride?
N
What is the force in pounds that acts on him during the launch phase of this ride?
lb
a) The acceleration is 16.3 m/s^2
b) The acceleration is 1.66 g
c) The force that acts is 666.4 N
d) The force in pounds is 149.8 pounds
What is the acceleration?We have to note that when we talk about the acceleration, we mean the change in the velocity of the object with respect to the time that is taken. In the case of the problem that we have here, we are told that the passenger cars are launched from rest at the start, they are accelerated uniformly to a speed of 57 m/s (128 mph) in just 3.5 s.
Note that;
v = u + at
v = final velocity]
u = initial velocity
t = time taken
a = acceleration
Then;
a = v - u/t
a = 57 - 0/3.5
a = 16.3 m/s^2
The acceleration in g's is 16.3 m/s^2/9.8 m/s^2 = 1.66 g
The force that acts on the passenger is; 68 Kg * 9.8 m/s^2 = 666.4 N
The weight in pounds of the passenger is 149.8 Pounds
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problem 1-45: the column is made of concrete having a density of 2.30 mg/m3 . at its top b it is subjected to an axial compressive force of 15 kn. determine the average normal stress in the column as a function of the distance z measured from its base.
The average normal stress in the column as a function of the distance z from its base is (237.68 - 21.43z) kPa or (237,684.54 - 21,431.12z) Pa.
The full question is in the attachment. There is a weight force that works in the concrete column. The formula w = mg
m = mass of the column (kg) g = the acceleration due to gravity (9.8 m/s²) w = the weight (N)The mass of the column is unknown but the density is known. The formula for density ρ = m ÷ V
m = ρV
ρ = the density = 2.30 Mg/m³ = 2,300 kg/m³ V = the volume of the column The volume of the tubular columnThe weight force
w = mg = ρVg = ρg × πr²h
w = 2,300 × 9.8 × 3.14 × 0.18² × (4 - z)
w = 2,293.13 (4 - z)
w = (9,172.52 - 2,293.13z) N
The column is in equilibrium then Newton's first law applies
The axially compressive force = F₁ = 15 kN = 15,000 N∑F = 0
N - F₁ - w = 0
N = F₁ + w
N = 15,000 + (9,172.52 - 2,293.13z)
N = (24,172.52 - 2,293.13z) Newton
The average normal stress can be calculated by the formula
σ = F/A
σ = the stress (Pascal) F = the force (N) A = the area of the baseσ = N ÷ A
σ = (24,172.52 - 2,293.13z) ÷ 0.1017
σ = (237,684.54 - 21,431.12z) Pascal
σ = (237.68 - 21.43z) kPa
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