in the town of centralburg (figure 1), which is laid out in a uniform block grid, the grocery store is three blocks east and four blocks north of the post office. which of the following is a correct equation for the quantities represented in this scenario?
a. tan (θ) = dn/de
b. sin (θ) = dn/de
c. θ = dn/de
d. arctan (θ) = dn/de
Answers
The correct equation for the quantity represented in the centralburg city scenario laid out in a uniform grid of blocks, the grocery store is three blocks east and four blocks north of the post office is tan (θ) = dn/de (option A)
Take a look at the image below (figure 1)
To determine tan (θ) = opposite side/ adjacent side.
Now, according to the figure,
The angle's opposite side is dn and the adjacent sides is de.
A right-angled triangle serves as the foundation for the three primary trigonometric functions: sine, cosine, and tangent.
The opposite side, adjacent side, and hypotenuse of a triangle are denoted by:
The terms "opposite" and "adjacent" refer to the opposing and adjacent angles.
Put these values into the formula now,
Which results in the equation,
tan (θ) = dn/de
Now, it is clear from the options provided that option A is correct.
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Related Questions
Explain the sources of instrumental errors
Answers
Answer:
A pH meter that reads 0.5 off or a calculator that rounds incorrectly would be the source of instrumental errors.
a steel pad supporting heavy machinery rests on four short, hollow, cast iron piers (see figure). the ultimate strength of the cast iron in compression is 50 ksi. the outer diameter of the piers is d 5 4.5 in., and the wall thickness is t 5 0.40 in. using a factor of safety of 3.5 with respect to the ultimate strength, determine the total load p that can be supported by the pad.
Answers
Respect to the ultimate strength, determine the total load p=294k that can be supported by the pad.
What is meant by strength?
Strength is frequently described as "the maximal force that a muscle or set of muscles can exert during a single contraction."Positive character characteristics or abilities are referred to as strengths. Knowledge, characteristics, abilities, and talents are examples of strengths. In contrast, weaknesses are shortcomings.Your strengths should typically be abilities that are reinforced by experience. If communication is one of your strengths, for instance, think back to a time when you used it to accomplish a task or solve a problem.Self-motivation, listening skills, and the ability to do tasks correctly and swiftly are some of my strongest traits.σ U =50ksi
n=3.5
σ allow = nσ /U = 50ksi/3.5 =14.29ksi
d=4.5in.
t=0.4in.
[tex]d_{0}[/tex] =d−2t=3.7in.
A= π/4 [tex](d^{2} -d^{2} _{0})[/tex] = π/4[[tex](4.5in.)^{2} (3.7in.) ^{2}[/tex] ]=5.152[tex]in.^{2}[/tex]
P 1 = allowable load on one pier
P 1 =σ allowA =(14.29ksi)(5.152[tex]in.^{2}[/tex])=73.62k
Total load P = [tex]4P_{1}[/tex]=294k
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How to find the greatest impulse
Answers
The impulse is equal to the average net external force times the length of time it takes for that force to act, as shown by the equation.
How do you calculate the impulse?p = F net t. Fnet t Fnet The impulse-momentum theorem describes the relationship between the quantities t and.The impulse is equal to the average net external force times the length of time it takes for that force to act, as shown by the equation.The momentum shift is equivalent to it.Momentum changes more dramatically the stronger the stimulus.Either the force's output or the time span over which it acts can be altered to alter the impulse.Momentum change is equivalent to impulse.Mv - mu = ft.The change in momentum has the same area under a force-time graph as the force.To learn more about impulse refer
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What fraction of its initial kinetic energy is lost?
Express your answer using two significant figures.
K lost/ K initial=?
Answers
The fraction of its initial kinetic energy lost can be estimated to be 0.10 to 0.20.
What is initial kinetic energy?Initial kinetic energy is the energy possessed by an object due to its motion. It is the energy of an object before any other external forces, such as gravity, friction, or air resistance, act upon it. Kinetic energy is a scalar quantity, meaning it has magnitude but not direction.
The fraction of kinetic energy lost will depend on the nature of the collision and the amount of energy dissipated. Generally, it is estimated that about 10% to 20% of the initial kinetic energy is lost in a collision. Therefore, the fraction of its initial kinetic energy lost can be estimated to be 0.10 to 0.20.
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Occurs when the type, degree, and duration of force employed was not necessary or appropriate.
Answers
The type, degree, and duration of force that is employed during the moment was not necessary.
in mechanics, any action that seeks to preserve, modify, or deform a body's motion. Isaac Newton's three laws of motion, which are outlined in his Principia Mathematica, are frequently used to illustrate the concept of force (1687).
Simple people with simple minds teach simple subjects, like physics. The first thing physicists do when they examine an object is to simplify it. A book is a box, not a collection of paper sheets attached with glue and string. A automobile is a box; it doesn't have rotating rubber tires, six-way adjustable seats, lots of cup holders, or a rear window defogger. A human is not formed of bone, muscle, skin, and hair; rather, they are a box with two arms, two legs, and a head. This is the start of a free body diagram, a style of drawing popular among engineers and physicists.
The foundation of physics is the logical process of analysis, which involves dissecting complex circumstances into a collection of smaller ones.
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you have a lightweight spring whose unstretched length is 4.0 cm . first, you attach one end of the spring to the ceiling and hang a 2.6 g mass from it. this stretches the spring to a length of 5.1 cm . you then attach two small plastic beads to the opposite ends of the spring, lay the spring on a frictionless table, and give each plastic bead the same charge. this stretches the spring to a length of 4.4 cm . What is the magnitude of the charge (in nC) on each bead?
Answers
Magnitude of the charge on each bead is calculated as 14.7 nC
What is charge?In physics, charge is a characteristic of unit of matter that expresses the extent to which it has more or fewer electrons than protons.
As, F = kΔL, where F is the force, k is the spring constant, and ΔL is the change in length of the spring.
Given mass is 2.6 gm and unstretched length is 4.0 cm .
So, F = mg = 2.6g * 9.8 m/s^2
ΔL = 5.1 cm - 4 cm = 1.1 cm
Hence, k = F/ΔL = (2.6*9.8)/(0.011) = 469.09 N/m
ΔL = 4.4 cm - 4 cm = 0.4 cm
F = kΔL = 469.09 N/m * 0.4 cm = 187.63 N
As we know, q = F/E
q = 187.63 N / (1/(4π8.85410^-12)) = 1.4710^-8 C
So, the magnitude of the charge on each bead is 1.4710^-8 Coulombs, or 1.4710^-8 * 10^9 = 14.7 nC
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a person wants to transmit an audio file from a device to a second device. which of the following scenarios best demonstrates the use of lossless compression of the original file? What is the speed of the block immediately after the bullet exits?
Answers
The answer is that A device compresses the audio file before transmitting it to a second device. The second device restores the compressed file to its original version.
What is an compresses an audio file?To compresses an audio file is a term that connote the act of making an audio file to be smaller in size so as to fit into a given device or app. Note that the option that best demonstrates the use of lossless compression of the original file is that A device compresses the audio file before transmitting it to a second device. The second device restores the compressed file to its original version before playing it and as such, option A is correct.
Here,
The solution is that before sending the audio file to a second device, A compresses it. The second device converts the compressed file back to its original state.
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A beachgoer in Florida notices the waves crashing ashore are spaced 13 meters apart and hit the shore every 6 s. How fast (in m/s) are the waves traveling?
Answers
The speed of the waves at the beach in Florida is 2.167 m.s.
What is the wavelength of the wave?The wavelength of a wave is the distance between successive points in a wave.
The wavelength of the given wave is obtained as follows:
Wavelenegh of the wave = 13 meters
The frequency of the wave is 1/6 per second
The wavelength, speed, and frequency of the wave is related as follows;
The velocity of a wave = wavelength * frequency
The speed or velocity of the wave = 13 * 1/6
The speed or velocity of the wave = 2.176 m/s
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what is the direction of the acceleration of the object at moment 5? enter the letter of the arrow with this direction from the compass rose in the figure. type z if the acceleration vector has zero length.
Answers
The direction of the acceleration of the pendulum at moment 5 is towards A (center), which is perpendicular to the direction of motion of the bob.
There is no any component of force acting along the tangent direction, when the bob is at the equilibrium mid-position as the string is completely vertical. Restoring force is momentarily absent in the bob when it is moving through the equilibrium position. The restoring force is only required when the pendulum bob has been slightly displaced away from the equilibrium position.
In the equilibrium position, the tension force is greater than the perpendicular component of gravity when the bob moves through this equilibrium position. As the bob continues its motion along a circular arc, so there must be a net centripetal force towards the center. So the direction will be towards A.
--The given question is incomplete, the complete question is:
"what is the direction of the acceleration of the object at moment 5? enter the letter of the arrow with this direction from the compass rose in the figure. type z if the acceleration vector has zero length."
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Which of the following practices are common ways in which journalists misrepresent research studies in their media articles?
Answers
Journalists frequently misinterpret research studies in their media articles in a number of ways. Such practices can lead to inaccurate and potentially harmful messages about scientific research.
Misinterpretation of research studies occurs in several ways:
First, journalists may inaccurately represent the findings of a study, either by overstating its conclusion or by misinterpreting its results. For example, they may suggest that a study shows a causative relationship between two variables when the actual findings only show a correlation.
Second, journalists may fail to provide enough context for readers to understand the research. This includes not providing enough information about the study sample and design, as well as failing to explain the statistical methods used in the analysis.
Third, journalists may selectively report on research studies, emphasizing those that are most sensational or that support a particular narrative. By omitting certain study results, they may give an incomplete picture of the research at hand.
Finally, journalists may report on studies that contain weak or unreliable evidence. This is particularly problematic when the research is based on a small sample size or uses methods that are not well-validated.
In summary, journalists are prone to misrepresenting research studies by giving an incomplete account of the findings, failing to provide adequate context, selectively reporting on studies, and relying on unreliable evidence. Such practices can lead to inaccurate and potentially harmful messages about scientific research.
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the charge on a nonconducting rod increases linearly from end a to end b. the rod is bent in a circle so that ends a and b almost meet very near the top of the circle (figure 1). figure1 of 1 a positively charged rod a b is bent into a ring so that its ends almost meet at the top of the ring. end b is on the left, end a is on the right. the center of the ring is marked by a black dot. a dashed horizontal line passes through the black dot. part a what is the direction of the electric field at the center of the circle? (hint: consider contributions from diametrically opposite segments!)
Answers
A uniformly charged ring has zero electric field at its center. Radially inwards toward negative point charge and outwards from positive charge is the electric field.
Which way does the electric field point in the center of a charged circular loop?Radially inwards toward negative point charge and outwards from positive charge is the electric field.A uniformly charged ring has zero electric field at its center.Both of the electric fields that are donated to the dipole are pointing in the same general direction—that is, toward the negative charge—in the middle of the dipole.The electric field's strength can be calculated using the equation E = k | Q | r 2 by using the formula. The charge's sign—negative in this instance—determines the direction of the electric field.To learn more about electric field refer to:
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How are atoms molecules, compounds, and pure substances
related?
Answers
Elements are most simply made up of atoms. A pure element will only have one type of atom, for example, a pure chunk of gold will only have gold atoms, making it chemically pure.
Two identical atoms bonded chemically, most frequently by covalent bonds, to form a molecule. Halogens are typically diatomic molecules; for example, chlorine is known as Cl2.
A pure substance is made up of various elements that have been chemically combined. Ionic chemicals that are connected by ionic bonds are the most common way to observe this. Please remember that a compound is not the same as a mixture! Keep in mind that a combination is not linked chemically.
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What is the average velocity of the marble?
note that 2 frames is one second
Answers
The average velocity of the marble based on the image is 2.75 m/s.
What is average velocity?The ratio of the change in position or displacement (x) and the time periods (t) during which the displacement happens is known as average velocity.
Mathematically;
average velocity = ∆x / ∆twhere;
∆x = change in position or displacement∆x = change in timeThe change in the displacement of the marble, ∆x = 7 m - (-4) m
The change in the displacement of the marble, ∆x = 11 m
The change in time, ∆x = 8/2 seconds
The change in time, ∆x = 4 seconds
The average velocity of the marble = 11 m / 4 seconds
The average velocity of the marble = 2.75 m/s
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A particle is launched with a horizontal velocity v0 = 0.55 m /s from the 30° position shown and then slides without friction along the funnel-like surface. Determine the angle θ which its velocity vector makes with the horizontal as the particle passes level O-O. The value of r is 0.9 m. [
Answers
The angle its final velocity makes with the horizontal is 60⁰.
What is the time of motion of the particle?
The time taken for the particle to travel through the 0.9 m radius is calculated by applying the following equation.
t = ( 2v sin (θ) ) / g
where;
v is the initial velocity θ is the angle of projectiong is acceleration due to gravityt = ( 2 x 0.55 x sin 30 ) / ( 9.8 )
t = 0.056 s
The final vertical velocity is calculated as follows;
Vy = Vi + gt
Vy = ( 0.55 x sin 30 ) + (9.8 x 0.056 )
Vy = 0.82 m/s
The final horizontal velocity is calculated as follows;
Vx = V cos (30)
Vx = 0.55 m/s x cos ( 30 )
Vx = 0.48 m/s
The angle made with the horizontal is calculated as;
θ = arc tan ( Vy / Vx )
θ = arc tan ( 0.82 / 0.48 )
θ = 59.7⁰ ≈ 60⁰
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A 500 kg roller coaster car starts from rest at point A and moves down the curved track._ The speed of the car at the point C is 10 m/s. Calculate the energy loss due to friction from A to C
Answers
The appropriate values into the equation: E = (500 kg) (9.81 m/s2) (change in height between A and C).
What is equation?An equation is a mathematical statement that expresses the relationship between two or more variables. It is composed of algebraic expressions, including constants, coefficients, variables, and operators, arranged in a particular order.
The energy loss due to friction from A to C can be calculated using the equation E = mgh, where m is the mass of the car (500 kg), g is the acceleration due to gravity (9.81 m/s2), and h is the change in height between points A and C.
Assuming that the track is level between A and C,
then the change in height is zero and the energy loss due to friction is also zero. If, however,
the track is not level and there is a change in height between A and C,
then the energy loss due to friction can be calculated by plugging in the appropriate values into the equation: E = (500 kg) (9.81 m/s2) (change in height between A and C).
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In physics, the amount of work done on an object is the product of ______________.
Answers
Answer:
In physics, the amount of work done on an object is the product of the force applied to the object and the distance over which the force is applied, also known as the force's displacement. Mathematically, it is represented as W = F * d.
Explanation:
if the total number of joints (n) in a simple truss is three (3), calculate the total number of members (m) in the truss.
Answers
If the total number of joints in a simple truss is three, the total number of members in the truss is three.
What is truss?In engineering, a truss is a structural member made of straight pieces of metal or wood that are joined together to form a series of triangles that lie in a single plane. Roofs, bridges, and towers are the most common structures that use trusses. Truss structures are classified into three types: simple, planar, and space frame. Various truss varieties have been developed over the years within these three basic types. A framework is made up of straight members joined at their ends to form a truss structure. Trusses can support both moving and stationary loads. Trusses are commonly used in roof supports, bridges, and other similar structures.
Here,
m=2j-3
j=3
m=2*3-3
m=3
The total number of members in the truss is 3 if the total number of joints in a simple truss is three.
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A 65.2 kg base runner begins his slide into second base while moving at a speed of 4.93 m/s. He slides so that his speed is zero just as he reaches the base. The acceleration of gravity is 9.8 m/s². What is the magnitude of the mechanical energy lost due to friction acting on the run- ner? Answer in units of J.
Answers
Answer:
about 792 J
Explanation:
You want the mechanical energy lost by a 65.2 kg base runner who slides into second base from a speed of 4.93 m/s, reaching the base with a speed of 0.
Kinetic energyThe runner's kinetic energy is ...
KE = 1/2mv²
KE = 1/2(65.2 kg)(4.93 m/s)² = 792.33974 J
As the runner slides into second base, his speed decreases to zero, so all of his kinetic energy is lost to friction.
The energy lost to friction is about 792 J.
how can a simple fixed pulley make a job easier
a. by decreasing the work done
b. by changing the direction at which the force needs to be applied
c. by decreasing the distance that the force needs to be applied
d. by decreasing the force required to lift the object
Answers
It is considerably easier for us to move objects thanks to simple machinery called pulleys that can shift the direction of force. The amount of force necessary to lift something up is reduced by this procedure. Option d
What does a scientific force mean?A clear meaning is attached to the word "force." The terms "push" and "pull" are perfectly acceptable at this level to describe forces. An object does not have a force inside of it or within it.
Who or what is force?A massed item changes its velocity in response to a push or pull. A body can change its state of rest or motion when an external force acts on it. It is directed and has a magnitude.
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if your hot pot has a power rating of 600 watts, show how to find how long it will take to complete the process. (make sure you are comfortable using standard units of energy, and that you understand the relation of power to energy. hint: what are watts?)
Answers
It will take 91.125 sec (approximately 1 min and 30 sec) to complete the process using a hot pot with a power rating of 600 watts.
How does the conversion process of ice to water occur?The process of converting 150 pieces of ice at -15 degrees Celsius into liquid water at 50 degrees Celsius is an endothermic process, meaning that heat is absorbed by the system. To represent this process in an energy-interaction diagram, we would start with the initial state of the ice at -15 degrees Celsius, with the horizontal axis representing the amount of energy absorbed by the system (in joules) and the vertical axis representing the temperature. As heat is added to the system, the temperature of the ice will increase, and the energy absorbed by the system will also increase. The process will continue until the ice has completely melted and reached a temperature of 50 degrees Celsius, at which point the energy absorbed by the system will reach its maximum value.
The amount of heat added to the system to complete this process can be calculated using the formula:
Q = mcΔT
where Q is the heat added (in joules), m is the mass of the ice (in kilograms), c is the specific heat capacity of ice (about 2.1 J/gC), and ΔT is the change in temperature (50 - (-15) = 65 degrees Celsius). The heat absorbed by the system is therefore calculated as follows:
Q = 150 pieces × 0.02 (kg/piece) × 2.1 (J/g*C) × 65(C) = 54675 J
It will take 91.125 sec (approximately 1 min and 30 sec) to complete the process using a hot pot with a power rating of 600 watts.
How does the conversion process of ice to water occur?The process of converting 150 pieces of ice at -15 degrees Celsius into liquid water at 50 degrees Celsius is an endothermic process, meaning that heat is absorbed by the system. To represent this process in an energy-interaction diagram, we would start with the initial state of the ice at -15 degrees Celsius, with the horizontal axis representing the amount of energy absorbed by the system (in joules) and the vertical axis representing the temperature. As heat is added to the system, the temperature of the ice will increase, and the energy absorbed by the system will also increase. The process will continue until the ice has completely melted and reached a temperature of 50 degrees Celsius, at which point the energy absorbed by the system will reach its maximum value.
The amount of heat added to the system to complete this process can be calculated using the formula:
Q = mcΔT
where Q is the heat added (in joules), m is the mass of the ice (in kilograms), c is the specific heat capacity of ice (about 2.1 J/gC), and ΔT is the change in temperature (50 - (-15) = 65 degrees Celsius). The heat absorbed by the system is therefore calculated as follows:
Q = 150 pieces × 0.02 (kg/piece) × 2.1 (J/g*C) × 65(C) = 54675 J
To find out how long it will take to complete the process using a hot pot with a power rating of 600 watts, you can use the formula:
time (in seconds) = energy (in joules) / power (in watts)
time = 54675 J / 600 W = 91.125 sec (approximately 1 min and 30 sec)
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the rigid bar efg is supported by the truss system shown. knowing that the member cg is a solid circular rod of 0.75-in. diameter, determine teh normal stress in cg
Answers
Normal stress in CG is 13.58 Ksi
When the deforming force is applied to an item, it deforms. The object will generate an opposing force from within to revert to its previous dimensions and shape. This restoring force will be applied in the opposite direction and have the same magnitude as the deforming force.Stress is a term used to describe how much of this restorative force is produced per unit area of the material. When the path of the deforming force is perpendicular to the body's cross-sectional area, stress is said to be normal stress. If the wire's length or the body's volume changes, the stress level will remain normal.
Using the portion EFCGB as a free body ,
∑[tex]F_{y} =0 :[/tex]
[tex]\frac{3}{5}F_{AE}[/tex]-3600=0
[tex]F_{AE}[/tex]=6000 lb
Using beam EFG as a free body ,
+[tex]M_{F} =[/tex]0 ,
-(4) [tex]\frac{3}{5}F_{AE}[/tex] + (4)[tex]\frac{3}{5}F_{cc}[/tex] = 0
[tex]F_{cc} =F_{AE} =[/tex]6000lb
cross section area of member CG :
[tex]A_{CG}=\frac{\pi}{4} d^{2}[/tex]= [tex]\frac{\pi}{4} (0.75)^{2}[/tex]
[tex]A_{CG}=0.44179 \:in^{2}[/tex]
Let the normal stress is 'B'
Normal stress in CG
[tex]B_{CG} =\frac{ F_{CG} }{ A_{CG} }[/tex] = [tex]\frac{6000 }{0.44179 }[/tex] = 13,580 psi
[tex]B_{CG} =[/tex] 13.58 Ksi
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If 240 million people in the United States jumped up into the air simultaneously pushing off the earth with an average force of 800 N each for 0.10 s, what would happen to the 5.98x10^24 kg earth?
Answers
when 270 million people jump at the same time the Earth will move at 1.3 m/s.
What is average force?The vector quantity of a force. It is a quantity with both magnitude and direction, hence.
We must specify both the size and the direction of the force operating on an object in order to adequately understand it. The average force is the force applied by an item traveling over a specific period of time at a defined rate of speed, or velocity.
This velocity is not instantaneous or precisely calculated, as the word "average" indicates. As a result, the average force is determined by multiplying the body's mass by the object's average velocity during the specified period of time.
Therefore, when 270 million people jump at the same time the Earth will move at 1.3 m/s.
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two Casa distance to kilometer apart on a straight line if they are moving towards each other at 10 km per hour in 30 km per hour respectively how long it does say take to reach at their passing point
Answers
The four different forms of speed are as follows: uniform speed. variable rate Typical rate.
What is the meaning of relative speed?The speed of one moving body in relation to another is known as relative speed. When two bodies are moving in the same direction, their difference is used to calculate their relative speed. The relative speed, however, is determined by summing the speeds of the two bodies when they are going in the opposite direction.Speed is a talent. It takes a lot of technical expertise to constantly use one's body's capabilities to its fullest capacity.Velocity, as opposed to speed, refers to the pace and direction of an object's movement as it moves down a path. In other words, whereas velocity is a vector, speed is a scalar quantity.To learn more about speed refer to:
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999mm is added to 100 we get
Answers
999mm is added to 100m, we get 100999m.
What is the Conversion of units?A unit conversion is defined as the same property as a different unit of measurement such that time can be expressed in minutes instead of hours, while distance can be expressed in miles to kilometers or feet or lengths which can be converted to any other measurement.
In the above given information,
We have two numbers which are 999mm and 100m
So, we have to convert 100m into mm.
we know, 1cm=10mm
1m=100cm=100×10=1000mm
100m will be=100×1000=100000mm
Now, after adding 999m with 100000mm,
999mm+100000mm =100999mm
Hence, when 999mm is added to 100m we get 100999m.
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the built-up shaft consists of a pipe ab and solid rod bc. the pipe has an inner diameter of 20 mm and outer diameter of 28 mm. the rod has a diameter of 12 mm. determine the average normal stress at points d and e and represent the stress on a volume element located at each of these points.
Answers
In order to determine the average normal stress at points D and E, we need to know the applied loading and the cross-sectional areas of the pipe and rod at these points.
It is assumed that pipe AB and solid rod BC form a built-up shaft that is subjected to an axial load, represented by P. The average normal stress at point D, which is located on the pipe, can be calculated by:
σD = P/A
Where A is the cross-sectional area of the pipe at point D. The cross-sectional area of the pipe can be calculated by:
A = π/4 * (D_o^2 - D_i^2)
Where D_o is the outer diameter of the pipe and D_i is the inner diameter of the pipe
The average normal stress at point E, which is located on the rod, can be calculated by:
σE = P/A
Where A is the cross-sectional area of the rod at point E. The cross-sectional area of the rod can be calculated by:
A = π/4 * D_r^2
Where D_r is the diameter of the rod
Therefore, by substituting the given values into the above equations we can calculate the average normal stress at points D and E.
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a cup of hot tea initially at 95*c, cools to 75*c, in 5.0 minutes when sittinf in 25*c surroundings. use newton's law of cooling to determine how long it will take to cool to 35*c
Answers
According to Newton's law of cooling, the rate of cooling is inversely related to the temperature differential between the object and its surroundings. For this, the equation is:
dT/dt = k (T - Ts) (T - Ts)
where T is the object's temperature, Ts is the environment's temperature, and k is the cooling constant. where dT/dt is the rate of change in temperature.
This equation can be used to calculate the cooling constant k for the cup of tea. We know that the temperature started off at 95 degrees Celsius, dropped to 75 degrees Celsius, and took 5 minutes to cool down.
95 - 75 = 20, dT/dt = k (20), dT/dt = k (20) *(1/5), and dT/dt = 4k.
Then, we can determine how long it will take for the temperature to cool to the desired level by using this cooling constant and the target temperature (35°C).
35 - 75 = -40\s-40 = 4k(t) (t)
t = -40 / 4k
We are unable to solve for t since we lack the value for k. But if we assume that the cooling rate is comparable to the rate we currently know, we can come up with an estimate. If we assume that the rate of cooling is constant, we can calculate how long it will take for the tea to cool from 75 to 35 degrees by using the rate of cooling from 95 to 75 degrees.
t = -40/20 equals 2 minutes.
It would take around 2 minutes to cool the tea from 75c to 35c under the assumption of similar cooling rate.
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in an electric circuit, a single wire is connected to three branches that contain resistors. the three branches then connect back to a single wire. the current in each of the single wires is the same. conservation of which of the following best explains this phenomenon?
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The current in each of the single wires being the same in an electric circuit with a single wire connected to three branches that contain resistors and then connecting back to a single wire is explained by the conservation of charge.
What is conservation of charge?Conservation of charge states that total charge in an isolated system remains constant. In electric circuit, charge flows through circuit in the form of electric current. Therefore, amount of charge flowing into any point in the circuit must be equal to the amount of charge flowing out of that point.
This means that current flowing into a branch in the circuit must be equal to the current flowing out of that branch. As the current in the single wire connected to the three branches is the same, current flowing into and out of each branch must also be the same, as per the conservation of charge principle.
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a 64.0-kg bungee jumper steps off a bridge with a light bungee cord tied to her and to the bridge. the unstretched length of the cord is 15.0 m. the jumper reaches reaches the bottom of her motion 41.0 m below the bridge before bouncing back. we wish to find the time interval between her leaving the bridge and her arriving at the bottom of her motion. her overall motion can be separated into an 15.0-m free-fall and a 26.0-m section of simple harmonic oscillation.
Answers
The free-fall and oscillation sections, which is [tex]$3.02 \ s + 2.01 \ s = 5.03 \ s$[/tex].
What is oscillation sections?Oscillation sections are sections of a waveform that repeat themselves over a certain period of time. This period of time is known as the oscillation period and is typically measured in seconds or milliseconds.
The time interval between the bungee jumper leaving the bridge and reaching the bottom of her motion can be found by summing the time intervals associated with the free-fall and oscillation sections of the motion.
The time interval associated with the 15.0 m free-fall can be found using the equation for the time it takes an object to fall a given distance, which is:
[tex]$t_{fall} = \sqrt{\frac{2d}{g}}$[/tex]
where d is the distance fallen and g is the acceleration due to gravity, which is [tex]9.81 m/s$^2$.[/tex]
Therefore, the time interval associated with the free-fall can be calculated as follows:
[tex]$t_{fall} = \sqrt{\frac{2 \cdot 15.0 \ m}{9.81 \ m/s^2}} = 3.02 \ s$[/tex]
The time interval associated with the 26.0 m of oscillation can be found using the equation for the period of a simple harmonic oscillator, which is:
[tex]$T = 2 \pi \sqrt{\frac{m}{k}}$[/tex]
where $m$ is the mass of the object and k is the spring constant.
In this case, the mass of the object is 64.0 kg, and the spring constant is the force of gravity acting on the jumper, which is [tex]$mg = 64.0 \ kg \cdot 9.81 \ m/s^2 = 628.64 \ N/m$[/tex]
Therefore, the time interval associated with the oscillation can be calculated as follows:
[tex]$T = 2 \pi \sqrt{\frac{64.0 \ kg}{628.64 \ N/m}} = 2.01 \ s$[/tex]
The total time interval between the bungee jumper leaving the bridge and reaching the bottom of her motion is the sum of the time intervals for the free-fall and oscillation sections, which is [tex]$3.02 \ s + 2.01 \ s = 5.03 \ s$[/tex].
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figure 22-53 shows two concentric rings, of radii r and r 3.00r, that lie on the same plane. point p lies on the central z axis, at distance d 2.00r from the center of the rings. the smaller ring has uniformly distributed charge q. in terms of q, what is the uni- formly distributed charge on the larger ring if the
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Symmetry: According to the problem the charge on the larger ring is 4q.
What is Symmetry?Symmetry is a type of balanced arrangement of parts or elements of a whole. It is a fundamental concept in mathematics, art, and nature. Symmetry can be seen in everyday objects, such as a human face, a butterfly, a snowflake, and a fingerprint.
This is because of the symmetry of the system. The electric field due to the smaller ring at point P is the same as the electric field due to the larger ring at point P, since the distance from point P to the center of both rings is the same. Since the charge on the smaller ring is q, the charge on the larger ring must also be q in order to produce the same electric field. Since the larger ring has four times the area of the smaller ring, the charge on the larger ring must also be four times that of the smaller ring, which is 4q.
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water flows with speed v through a horizontal, cylindrical pipe. which of the following changes in the geometry of the pipe will double the speed of the water in the pipe?
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Halving the area of the pipe will double the speed of the water in the pipe. Therefore, option(c) is the correct answer.
Given,
initial flow speed, V₁ = v
let's area, A₁ = A
Now, to double the speed of the water flow
V₂ = 2v
we know that,
using continuity equation of flow:
A₁V₁ = A₂V₂
or A x v = A₂ x 2v
A₂ = A/2 or A₁/2
Therefore, By Halving the area of the pipe will double the speed of the water in the pipe.
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The complete question is:
water flows with speed v through a horizontal, cylindrical pipe. which of the following changes in the geometry of the pipe will double the speed of the water in the pipe?
(a) Doubling the area of the pipe
(b) Doubling the radius of the pipe
(c) Halving the area of the pipe
(d) Halving the radius of the pipe