Answer:
ρ_ x > ρ_ y
Explanation:
The pressure in a fluid depends on its depth with the equation
P = ρ g h
For two points at the same depth there may be several possibilities,
- the pressure is the same if the density of the fluid is equal in the two points
- The pressure is different if the fluid density is different at each point
In this case, as the point x has greater pressure than the point, the density of the fluid in Des is greater than the density of the fluid in Y
ρ_ x > ρ_ y
A closed system consists of 0.4 kmol of propane occupying a volume of 10 m3 . Determine
(a) the weight of the system, in N, and
(b) the mass-based specific volume, in m3 /kmol and m3 /kg respectively. Let g = 9.81 m/s2 .
Answer:
Kinetic
Explanation:
Final answer:
The weight of the closed system of propane is 173.04 N. The mass-based specific volume is 25 m³/kmol and 0.567 m³/kg.
Explanation:
To answer the student's question about the weight and the mass-based specific volume of a closed system of propane:
To find the weight of the system in Newtons, we first need to calculate the mass of the propane.Propane has a molar mass of approximately 44.1 kg/kmol. Since the system has 0.4 kmol of propane, the mass (m) is:
m = 0.4 kmol × 44.1 kg/kmol = 17.64 kg
Now, the weight (W) in Newtons can be calculated using the gravitational acceleration (g = 9.81 m/s2):
W = m × g = 17.64 kg × 9.81 m/s2 = 173.04 N
For the mass-based specific volume in m3/kmol and m3/kg:The specific volume (vsp) in m3/kmol is simply the volume divided by the number of kmols:
vsp = V / n = 10 m3 / 0.4 kmol = 25 m3/kmol
For m3/kg, we divide the specific volume by the molar mass of propane:
vsp = 25 m3/kmol ÷ 44.1 kg/kmol = 0.567 m3/kg
A particular brand of gasoline has a density of 0.737 g/mLg/mL at 25 ∘C∘C. How many grams of this gasoline would fill a 14.9 galgal tank ( 1US gal=3.78L1US gal=3.78L )?
Answer:
The answer to your question is Mass = 41230.7 g or 41.23 kg
Explanation:
Data
density = 0.737 g/ml
mass = ?
volume = 14.9 gal
1 gal = 3.78 l
Process
1.- Convert gallons to liters
1 gal ---------------- 3.78 l
14.8 gal ------------- x
x = 55.94 l
2.- Convert liters to milliliters
1 l ------------------- 1000 ml
55.94 l --------------- x
x = (55.94 x 1000) / 1
x = 55944 ml
3.- Calculate the mass
Formula
density = [tex]\frac{mass}{volume}[/tex]
Solve for mass
Mass = density x volume
Substitution
Mass = 0.737 x 55944
Simplification and result
Mass = 41230.7 g or 41.23 kg
The speed of a certain electron is 995 km s−1 . If the uncertainty in its momentum is to be reduced to 0.0010 per cent, what uncertainty in its location must be tolerated?
Answer:
The uncertainty in the location that must be tolerated is [tex]1.163 * 10^{-5} m[/tex]
Explanation:
From the uncertainty Principle,
Δ[tex]_{y}[/tex] Δ[tex]_{p}[/tex] [tex]= \frac{h}{2\pi }[/tex]
The momentum P[tex]_{y}[/tex] = (mass of electron)(speed of electron)
= [tex](9.109 * 10^{-31}kg)(995 * 10^{3} m/s)[/tex]
= [tex]9.0638 * 10^{-25}kgm/s[/tex]
If the uncertainty is reduced to a 0.0010%, then momentum
= [tex]9.068 * 10^{-30}kgm/s[/tex]
Thus the uncertainty in the position would be:
Δ[tex]_{y} = \frac{h}{2\pi } * \frac{1}{9.068 * 10^{-30} }[/tex]
Δ[tex]_{y} \geq 1.163 * 10^{-5}m[/tex]
The uncertainty in location of the electron can be calculated using Heisenberg's Uncertainty Principle, which stipulates a product of the uncertainties in position and momentum to be at least half of reduced Planck's constant. Uncertainty in momentum is given as 0.0010% of the electron's momentum. Careful consideration of quantities and units is essential.
Explanation:This question revolves around Heisenberg's Uncertainty Principle. According to this principle, the product of the uncertainty in the position, denoted by Δx, and the uncertainty in momentum, denoted by Δp, has a minimum value dictated by Planck's constant, h. Mathematically, it is represented as Δx * Δp ≥ ħ/2, where ħ is the reduced Planck's constant, ħ=h/(2π). The speed of the electron, v, is related to its momentum, p, through mass, m, as p=mv. Therefore, the uncertainty in momentum, Δp, can be calculated as 0.0010% of p. Once we find Δp, using the Uncertainty Principle, we can find the minimum required uncertainty in the electron's location, Δx. In such problems, considering mass and speed of electron and appropriate units for constants are crucial for
correct computation
. Make sure to consider them appropriately.
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Which of the following was NOT considered a key characteristic of the genetic material even before nucleic acids were identified as the genetic material?
Genetic material must encode the phenotype.
Genetic material must encode complex information.
Genetic material must be copied accurately.
Genetic material must have a complex structure.
These are all key characteristics of genetic material.
Answer:
D:Genetic material must have a complex structure.
Before DNA was identified as the genetic material, a complex structure was not considered a key characteristic of genetic material. Proteins, with their diverse amino acids, were initially thought to be the genetic carriers due to their apparent structural complexity compared to DNA's four nucleotides.
Explanation:The one characteristic that was NOT considered a key attribute of the genetic material before nucleic acids were identified is that the genetic material must have a complex structure. Historically, even though DNA does have a complex structure, early scientific thought leaned towards proteins as the biomolecules with sufficient complexity to encode genetic information. This belief was due to proteins being composed of 20 different amino acids, allowing for a high degree of variability and complexity, while DNA, composed of only four nucleotides, seemed too simple to account for the vast genetic diversity observed in living organisms.
It wasn't until the transformative experiments of Avery, McCarty, McLeod, and eventually the definitive work of Hershey and Chase, that DNA was confirmed to be the genetic material. The initial complexity perceived in proteins overshadowed the abstract concept of steep structural complexity in DNA. Afterward, it was understood that through the processes of replication and expression, DNA's arrangement of four bases could indeed encode and express the complexity necessary for life.
When Earth catches up to a slower-moving outer planet and passes it in its orbit the planet
a.exhibits retrograde motion.
b. slows down because it feels Earth's gravitational pull.
c. decreases in brightness as it passes through Earth's shadow.
d. moves into a more elliptical orbit.
Answer:
a. exhibits retrograde motion.
Explanation:
When earth catches up to a slower moving outer planets like for example Saturn and jupitar they seems to show the retrograde motion which is actually an illusion but there exits the real retrograde motion too in some cases. In retrograde motion planets appears to move in the backward direction like from east to west rather then from west to east in the sky.
In a typical coal-fired power plant, 2,460kWh of electricity can be produced per ton of coal burned. Calculate how many tons of coal would have to be burned in a typical coal-fired power plant to provide the electricity for a typical house in the United States for a year. Show your work.
4.472 tonnes of coal burned
Explanation:
The electricity consumption for a typical house in the United States for a year is approximated as 11,000 kWh.
Given that a typical coal-fired power plant produces 2,460 kWh of electricity per ton of coal burned then;
2460 kWh = 1 ton of coal burned
11,000 kWh =?
cross-product
(11,000*1)÷ 2460 = 4.472 tonnes of coal burned
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The amount of coal required to be burned in a typical coal-fired power plant to provide the electricity for a typical house in the United States for a year will be 4.472 tonnes.
Given data:
The electricity produced per ton of coal burn is, E = 2,460 kWh.
The given problem is based on the Energy consumption. The energy consumption is the energy utilized to perform various actions such as manufacturing, welding, inhabiting, and many more.
The electricity consumption for a typical house in the United States for a year is approximated as 11,000 kWh.
And as per the given question,
2460 kWh = 1 ton of coal burned
So for 11,000 kWh, the amount of coal need to be burned is,
= 11000/2460
= 4.472 tonnes of coal
Thus, we can conclude that amount of coal required to be burned in a typical coal-fired power plant to provide the electricity for a typical house in the United States for a year will be 4.472 tonnes.
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What should the Architect do to ensure Field-Level Security is enforced on a custom Visualforce page using the Standard Lead Controller?
Answer:
the Architect should use {!$FieldType.lead.accessible} expression within the Visualforce page.
Explanation:
Visualforce is a framework that allows developers to build complex, user friendly interfaces that can be hosted primarily on the Lightning Platform
Controllers provide access to the data that should be displayed in a page, and can modify component behavior. a number of standard controllers are provided by The Lightning platform that contain functionality and logic that which are used for standard Salesforce pages
The Architect should Use the expression {!$FieldType.lead.accessible} within the Visualforce page.
To enforce Field-Level Security on a custom Visualforce page using the Standard Lead Controller, the Architect should define the page with the 'standardController' attribute set to 'Lead' and the 'extensions' attribute set to the appropriate Lead Controller extension. The 'with sharing' keyword should be used in the extension to enforce field-level security.
Explanation:To ensure Field-Level Security is enforced on a custom Visualforce page using the Standard Lead Controller, the Architect should define the Visualforce page with the 'standardController' attribute set to 'Lead' and the 'extensions' attribute set to the appropriate Lead Controller extension. Within the extension, the Architect can use the 'with sharing' keyword to enforce field-level security.
For example:
<apex:page standardController='Lead' extensions='LeadControllerExtension'>...</apex:page>public with sharing class LeadControllerExtension { ... }The 'with sharing' keyword ensures that the Visualforce page adheres to the Org-wide default settings and user's record-level access. This means that any field-level security restrictions defined for the Lead object will be enforced on the page.
What equation gives the position at a specific time for an object with constant acceleration?
Answer:
[tex]x = x_{0}+v_{0}t+\frac{1}{2}at^{2}[/tex] equation gives the position at a specific time for an object with constant acceleration
Explanation:
[tex]x = x_{0}+v_{0}t+\frac{1}{2}at^{2}[/tex] equation gives the position at specific time for an object having constant acceleration. Constant acceleration is referred as the change of velocity with respect to the time is known as the acceleration, but when the velocity changes occurs at constant rate this rate is termed as the constant acceleration. The constant acceleration can never be zero. The velocity changes but that change occurs in the consistently. The acceleration is affected by the mass.
A spring has a force constant of525.6 N/m. Find the potential energy stored in thespring when thespring is...
a) stretched 4.08 cm fromequilibrium. Answer in units of J
b)compressed 2.17 cm from equilibrium. Answer in units ofJ
c) unstretched. Answer in units ofJ
A tennis player swings her 1000 g racket with a speed of 15.0 m/s. She hits a 60 g tennis ball that was approaching her at a speed of 18.0 m/s. The ball rebounds at 40.0 m/s.
Part A) How fast is her racket moving immediately after the impact? You can ignore the interaction of the racket with her hand for the brief duration of the collision.
_________m/s
Part B) If the tennis ball and racket are in contact for 7.00 , what is the average force that the racket exerts on the ball?
_________N
Final answer:
The racket is moving at a speed of 15 m/s immediately after the impact. The average force that the racket exerts on the ball is 0.189 N.
Explanation:
Part A:
To calculate the racket's speed immediately after the impact, we can use the principle of conservation of momentum. The momentum before the impact is equal to the momentum after the impact.
The momentum before the impact is given by the product of the racket's mass and its initial speed:
Momentum before = (0.001 kg)(15.0 m/s) = 0.015 kg·m/s
The momentum after the impact is equal to the product of the racket's final speed (which is what we need to find) and its mass:
Momentum after = (0.001 kg)(v)
Since the momentum is conserved, we can equate the two expressions:
0.015 kg·m/s = (0.001 kg)(v)
Simplifying this equation gives:
v = 15 m/s
Therefore, the racket is moving at a speed of 15 m/s immediately after the impact.
Part B:
To find the average force that the racket exerts on the ball, we can use the impulse-momentum principle. The impulse exerted on the ball is equal to the change in momentum of the ball:
Impulse = change in momentum
The change in momentum can be calculated using the formula:
change in momentum = (final momentum) - (initial momentum)
The initial momentum of the ball is given by the product of its mass and its initial speed:
Initial momentum = (0.060 kg)(18.0 m/s) = 1.08 kg·m/s
The final momentum of the ball is given by the product of its mass and its final speed:
Final momentum = (0.060 kg)(40.0 m/s) = 2.4 kg·m/s
Substituting these values into the formula, we have:
Impulse = 2.4 kg·m/s - 1.08 kg·m/s
Impulse = 1.32 kg·m/s
Since impulse is equal to the average force multiplied by the time of contact, we can rearrange the formula to solve for the average force:
Average force = Impulse / Time of contact
Substituting the values for impulse and the given time of contact, we have:
Average force = 1.32 kg·m/s / 7.00 s
Average force = 0.189 N
If you ignore air resistance after an initial force launches a projectile, name all forces acting on it as it moves through the air. What does this force cause the object to do?
Answer:
Neglecting air resistance, the only force acting on a projectile is gravity.
This force causes the object to accelerate.
Explanation:
As a projectile moves upward, there is a downward force and a downward acceleration due to force of gravity. That is, as the object is moving upward, force of gravity acting on the projectile is causing a steady slowing down of the projectile.
Hence, Gravity is the downward force upon a projectile that influences its vertical motion and causes the parabolic trajectory that is characteristic of projectiles.
From Newton's law of motion, it suggest that force is required to cause an acceleration and not motion. Therefore, force of gravity causes the object to accelerate downwards.
Two technicians are discussing voltage drop testing. Technician A says that the voltmeter should be connected in series with the circuit you are testing. Technician B says that the voltmeter should be connected in parallel with the circuit you are testing. Who is correct?
Technician B is correct. A voltmeter should be connected in parallel with the component or section of a circuit that is being tested, while an ammeter should be connected in series.
Explanation:Technician B is correct when it comes to assessing the method of connecting a voltmeter. A voltmeter is designed to measure the voltage across elements of a circuit and is placed in parallel with the component or section of the circuit that is being tested. In this configuration, the voltmeter receives the full voltage.
On the other hand, Technician A is confusing a voltmeter with an ammeter. An ammeter, which measures the current flowing through a given branch of an electric circuit, should be connected in series in order to get a measure of the full current passing through that branch. The ammeter has a small resistance to limit its impact on the circuit.
By contrast, a voltmeter has to have a large resistance as it is connected in parallel and thus should have minimal impact on the circuit being tested.
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A particle with a mass of 9.00 ✕ 10-20 kg is vibrating with simple harmonic motion with a period of 3.00 ✕ 10-5 s and a maximum speed of 7.00 ✕ 103 m/s. (a) Calculate the angular frequency of the particle. rad/s (b) Calculate the maximum displacement of the particle.
Answer:
(a) [tex]\omega=2.09*10^{5}\frac{rad}{s}[/tex]
(b) [tex]A_{max}=0.033m[/tex]
Explanation:
(a) The angular frequency is defined as:
[tex]\omega=2\pi f[/tex]
Here f is the frequency of the particle, which is inversely proportional to its period:
[tex]f=\frac{1}{T}[/tex]
Replacing, we have:
[tex]\omega=\frac{2\pi}{T}\\\omega=\frac{2\pi}{3*10^{-5}s}\\\omega=2.09*10^{5}\frac{rad}{s}[/tex]
(b) The maximum displacement is given by:
[tex]A_{max}=\frac{v_{max}}{\omega}\\A_{max}=\frac{7*10^3\frac{m}{s}}{2.09*10^5\frac{rad}{s}}\\A_{max}=0.033m[/tex]
The Goodyear blimp Spirit of Akron is 62.6m long and contains 7023m^3 of helium. When the temperature of the helium is 285 K, its absolute pressure is 112 kPa. Find the mass of the helium in the blimp.
Answer:
1328.7032 kg
Explanation:
P = Pressure = 112 kPa
T = Temperature = 285 K
V = Volume = 7023 m³
R = Gas constant = 8.314 J/mol K
From the ideal gas law we have
[tex]PV=nRT\\\Rightarrow n=\dfrac{PV}{RT}\\\Rightarrow n=\dfrac{112000\times 7023}{8.314\times 285}\\\Rightarrow n=331960.04203\ moles[/tex]
The mass of gas is given by
[tex]m=n\times MW_{He}\\\Rightarrow m=331960.04203\times 4.0026\times 10^{-3}\\\Rightarrow m=1328.70326\ kg[/tex]
The mass of helium in the blimp is 1328.7032 kg
By applying the ideal gas law, we determined the number of moles of helium in the blimp. By using the molecular weight of helium, we calculated that the mass of helium in the blimp is 12000 kg.
Explanation:We can use the ideal gas law to solve this problem. The ideal gas law is represented by the formula PV = nRT, where P represents the absolute pressure, V is the volume, n is the number of moles, R is the ideal gas constant and T is the temperature.
Based on the given values, we have P = 112 kPa, V = 7023 m^3, R = 8.31 (J/mol.K), and T = 285 K. We need to calculate n (number of moles) first.
Transforming the formula, we get n = PV/RT. Substituting the given values, n = (112,000 Pa * 7023 m^3) / (8.31 J / (mol. K) * 285 K) which gives us n = 3.0 * 10^6 moles.
Then, knowing that the molecular weight of helium is approximately 4 g/mol, we can multiply the number of moles by the molecular weight to find the mass. So, the mass is m = n * Molecular weight = 3.0 * 10^6 moles * 4 g/mol = 12 * 10^6 g or 12000 kg.
Therefore, the mass of the helium in the blimp is 12000 kg.
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A 6.0-cm-diameter horizontal pipe gradually narrows to 4.5 cm. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 31.0 kPa and 24.0 kPa, respectively. What is the volume rate of flow?
Answer:
0.0072 m³/s
Explanation:
Using Bernoulli's law
P₁ + 1/2ρv₁² = P₂ + 1/2ρv₂ since the pipe is horizontal
1/2ρv₂² - 1/2ρv₁² = P₁ - P₂
flow rate is constant
A₁v₁ = A₂v₂
A₁ = πr₁² = π (0.06/2)² = 0.0028278 m²
A₂ = πr₂² = π (0.0225)² = 0.00159 m²
v₁ = (A₂ / A₁)v₂
v₁ = (0.00159 m²/ 0.0028278 m²) v₂ = 0.562 v₂
substitute v₁ into the Bernoulli's equation
1/2ρv₂² - 1/2ρv₁² = P₁ - P₂
500 ( 1 - 0.3161 ) v₂² = (31.0 - 24 ) × 10³ Pa
341.924 v₂² = 7000
v₂² = 20.472
v₂ = √ 20.472 = 4.525 m/s
volume follow rate = 0.00159 m² × 4.525 m/s = 0.0072 m³/s
[tex]0.0072 \;\rm m^{3}/s[/tex]The volume flow rate at the exit of the pipe is [tex]0.0072 \;\rm m^{3}/s[/tex].
Given data:
The initial diameter of horizontal pipe is, d = 6.0 cm.
The final diameter of pipe is, d' = 4.5 cm.
The gauge pressure at inner section is, P = 31.0 kPa.
The gauge pressure at outer section is, P' = 24.0 kPa.
Applying the Bernoulli's concept, which says the total pressure energy and kinetic energy throughout the flow remains constant .
So, for the horizontal pipe, the expression is,
[tex]P + \dfrac{1}{2} \rho v^{2} = P' + \dfrac{1}{2} \rho v'^{2}[/tex] ............................................(1)
Here, [tex]\rho[/tex] is the density of water throughout the flow, which remains constant.
Now, apply the continuity equation as,
[tex]A\times v = A' \times v'\\\\(\pi/4 \times d^{2}) \times v = (\pi/4 \times d'^{2}) \times v'\\\\ d^{2} \times v = d'^{2} \times v'\\\\v/v' = 0.045^{2}/0.006^{2}\\\\v = 0.5625\times v'[/tex]
Now substitute the value in equation (1) as,
[tex]P -P' = \dfrac{1}{2} \rho v'^{2} - \dfrac{1}{2} \rho v^{2}\\\\(31 -24) \times 10^{3} \;\rm Pa = \dfrac{1}{2} \times 1000 v'^{2} - \dfrac{1}{2} \times 1000 (0.5625 v')^{2}\\v' = 4.52 \;\rm m/s[/tex]
Then the flow rate is calculated as,
[tex]Q' = A' \times v'\\\\Q' = (\pi /4) d'^{2} \times v'\\Q' = (\pi /4) \times 0.06'^{2} \times 4.52\\\\Q' = 0.0072 \;\rm m^{3}/s[/tex]
Thus, the required value of volume flow rate is, [tex]0.0072 \;\rm m^{3}/s[/tex].
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Jaclyn plays singles for South's varsity tennis team. During the match against North, Jaclyn won the sudden death tiebreaker point with a cross-court passing shot. The 57.5-gram ball hit her racket with a northward velocity of 26.7 m/s. Upon impact with her 331-gram racket, the ball rebounded in the exact opposite direction (and along the same general trajectory) with a speed of 29.5 m/s.
A. Determine the pre-collision momentum of the ball.
B. Determine the post-collision momentum of the ball.
C. Determine the momentum change of the ball.
D. Determine the velocity change of the racket.
Answer:
A) pbin = 1.535 Kgm/s (+)
B) pbf = 1.696 Kgm/s (-)
C) Δp = 3.3925 Kgm/s
D) Δvr = 10.249 m/s
Explanation:
Given
Mass of the ball: m = 57.5 g = 0.0575 Kg
Initial speed of the ball: vbi = 26.7 m/s
Mass of the racket: M = 331 g = 0.331 Kg
Final speed of the ball: vbf = 29.5 m/s
A) We use the formula
pbin = m*vbi = 0.0575 Kg*26.7 m/s = 1.535 Kgm/s (+)
B) pbf = m*vbf = 0.0575 Kg*29.5 m/s = 1.696 Kgm/s (-)
C) We use the equation
Δp = pbf - pbin = 1.696 Kgm/s - (-1.535 Kgm/s) = 3.3925 Kgm/s
D) Knowing that
Δp = 3.3925 Kgm/s
we can say that
Δp = M*Δvr
⇒ Δvr = Δp / M
⇒ Δvr = 3.3925 Kgm/s / 0.331 Kg
⇒ Δvr = 10.249 m/s
Stacy travels 5 times as fast as Eric. Traveling in opposite directions, they are 336 miles apart after 4 hours. Find their rates of travel.
Final answer:
To find their rates of travel, represent Eric's rate as E and Stacy's as 5E. Since together they cover 336 miles in 4 hours, the equation 4E + 20E = 336 leads to Eric's rate of 14 mph and Stacy's rate of 70 mph.
Explanation:
Stacy and Eric travel in opposite directions and collectively cover 336 miles in 4 hours. Since Stacy travels 5 times as fast as Eric, we can set up equations to represent their speeds and use these to find the rates of travel for both.
Let E represent Eric's rate of travel. Then 5E represents Stacy's rate of travel. Since distance equals rate times time, we can set up the equation E x 4 hours + 5E x 4 hours = 336 miles.
Combining terms, we get 4E + 20E = 336, which simplifies to 24E = 336. Dividing both sides by 24 gives us E = 14. So, Eric travels at 14 miles per hour, and Stacy travels at 5 times that rate, which is 70 miles per hour.
A small ball is attached to one end of a spring that has an un- strained length of 0.200 m. The spring is held by the other end, and the ball is whirled around in a horizontal circle at a speed of 3.00 m/s. The spring remains nearly parallel to the ground during the motion and is observed to stretch by 0.010 m. By how much would the spring stretch if it were attached to the ceiling and the ball allowed to hang straight down, motionless?
Answer:
[tex]\Delta x=0.002287\ m=2.287\ mm[/tex]
Explanation:
Given:
un-stretched length of the spring, [tex]l=0.2\ m[/tex]speed of revolution of the ball in horizontal plane, [tex]v=3\ m.s^{-1}[/tex]length stretch during the motion, [tex]\Delta l=0.01\ m[/tex]Now the radius of revolution of the ball:
[tex]r=l+\Delta l[/tex]
[tex]r=0.2+0.01[/tex]
[tex]r=0.21\ m[/tex]
Now in this case the centrifugal force is equal to the spring force:
[tex]F_c=F_s[/tex]
[tex]m.\frac{v^2}{r} =k.\Delta l[/tex]
where:
m = mass of the ball
k = spring constant
[tex]m\times \frac{3^2}{0.21} =k\times 0.01[/tex]
[tex]k=(4285.714\times m)\ N.m^{-1}[/tex]
Now the extension in the spring upon hanging the ball motionless:
[tex]m.g=k.\Delta x[/tex]
[tex]9.8\times m=(4285.714\times m)\times \Delta x[/tex]
[tex]\Delta x=0.002287\ m=2.287\ mm[/tex]
When two point charges are a distance dd part, the electric force that each one feels from the other has magnitude F.F . In order to make this force twice as strong, the distance would have to be changed to _____
Answer:
In order to make this force twice as strong, F' = 2 F, the distance would have to be changed to half i.e. r' = r/2.
Explanation :
The electric force between two point charges is directly proportional to the product of charges and inversely proportional to the square of the distance between charges. It is given by :
[tex]F=\dfrac{kq_1q_2}{r^2}[/tex]
r is the separation between charges
[tex]F\propto \dfrac{1}{r^2}[/tex]
[tex]r=\sqrt{\dfrac{1}{F}}[/tex]
If F'= 2F
[tex]r'=\dfrac{1}{\sqrt{2F} }[/tex]
In order to make this force twice as strong, F' = 2 F, the distance would have to be changed to half i.e. [tex]r'=\dfrac{1}{\sqrt{2F} }[/tex]. Hence, this is the required solution.
You find a featureless black slab. There are two arms marked In and OUT. You find that moving the IN arm 20 inches causes the OUT arm to move 5 inches. You find that a 10 lb. pull on IN lifts 30 lbs. on OUT. What is the AMA?a. 1
b. 4
c. 3
d. 1/3
Answer:
c. 3
Explanation:
Given:
displacement in the input arm, [tex]d_i=20\ in[/tex]corresponding displacement in the output arm, [tex]d_o=5\ in[/tex]load on the output arm, [tex]F_o=30\ lbs[/tex]corresponding load on the input arm, [tex]F_i=10\ lbs[/tex]Since AMA i.e. actual mechanical advantage is defined as the ratio of the output force to the input force on a simple machine. This takes into account the losses occurred.
Now, mathematically:
[tex]AMA=\frac{F_o}{F_i}[/tex]
[tex]AMA=\frac{30}{10}[/tex]
[tex]AMA=3[/tex]
Answer:
kuh
Explanation:
The total electric flux through a closed cylindrical (length = 1.2 m , diameter = 0.20 m) surface is equal to −5 0. Nm / C^2. Determine the net charge within the cylinder in pC? (εo = 8.85z10^-12)
a) – 71
b) – 62
c) – 53
d) – 44
e) –16
Final answer:
The net charge within the cylinder, given the electric flux of -50 Nm²/C² and the permittivity of free space, is -44 picocoulombs (pC).
Explanation:
The question asks to determine the net charge within a cylindrical surface given the total electric flux and the electrical permittivity of free space. According to Gauss's law, the electric flux (φ) through a closed surface is equal to the net charge (Q) enclosed by the surface divided by the permittivity of free space (ε0). The formula is φ = Q / ε0. Given the electric flux is -50 Nm2/C2 and ε0 = 8.85 x 10-12 C2/Nm2, we can solve for Q:
Q = φ x ε0
Q = (-50 Nm2/C2)(8.85 x 10-12 C2/Nm2)
Q = -4.425 x 10-10 C
To convert this to picocoulombs (pC), we multiply by 1012 pC/C:
Q = -4.425 x 10-10 C x 1012 pC/C = -442.5 pC
The closest answer to -442.5 pC is -44 pC, so the correct answer is (d) -44.
Both a gage and a manometer are attached to a gas tank to measure its pressure. If the reading on the pressure gage is 80 kPa, determine the distance between the two fluid levels of the manometer if the fluid is
(a) mercury (r 5 13,600 kg/m3) or
(b) water (r 5 1000 kg/m3).
To determine the distance between the two fluid levels of the manometer, we use the equation P = ρgh. For mercury, the density is 13,600 kg/m3, and for water, the density is 1000 kg/m3.
Explanation:To determine the distance between the two fluid levels of the manometer, we need to consider two cases: one with mercury and one with water.
(a) For mercury, we can use the equation P = ρgh, where P is the pressure difference, ρ is the density of mercury, g is the acceleration due to gravity, and h is the height difference between the two fluid levels. Rearranging the equation, we have h = P / (ρg). Plugging in the values of P = 80 kPa, ρ = 13,600 kg/m3, and g = 9.8 m/s2, we can calculate the value of h in meters.
(b) For water, we can use the same equation P = ρgh, but with the density of water. Plugging in the values of P = 80 kPa, ρ = 1000 kg/m3, and g = 9.8 m/s2, we can calculate the value of h in meters.
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A sealed tank containing seawater to a height of 10.7 m also contains air above the water at a gauge pressure of 3.20 atm. Water flows out from the bottom through a small hole. How fast is this water moving?
The water was moving out from the bottom at a velocity of 29 m/s
Applying Bernoulli's equation:
P + ρgh + (1/2)ρv² = constant
P is pressure, g is acceleration due to gravity, h is height, v is velocity, ρ is density.
At top:
P = 3.20 atm = 3.20 * 101300 Pa, ρ = 1025 kg/m³, v = 0, g = 9.81 m/s, h = 10.7 m, hence:
P + ρgh + (1/2)ρv² = ( 3.20 * 101300) + (1025 * 9.81 * 10.7) + 0
At bottom:
h = 0, P = 0
P + ρgh + (1/2)ρv² = 0 + 0 + (1/2* 1025)v²
Equating top and bottom:
( 3.20 * 101300) + (1025 * 9.81 * 10.7) = (1/2* 1025)v²
v = 29 m/s
The water was moving out from the bottom at a velocity of 29 m/s
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To calculate the speed of the water flowing out of the tank, we can use Bernoulli's equation. Plugging in the given values and solving for the final velocity, we can determine the speed of the water.
Explanation:To determine how fast the water is moving, we can use Bernoulli's equation which relates the pressure, velocity, and height of a flowing fluid.
Bernoulli's equation:P1 + 1/2 ρv12 + ρgh1 = P2 + 1/2 ρv22 + ρgh2
Where:
P1 = initial pressure of the waterv1 = initial velocity of the water (0 m/s, since it is at rest)ρ = density of the waterg = acceleration due to gravity (9.8 m/s2)h1 = initial height of the water (10.7 m)P2 = gauge pressure (3.20 atm)v2 = final velocity of the water (unknown)h2 = final height of the water (0 m)Plugging in the values, we can solve for v2:
3.20 atm + 0 + (1000 kg/m3)(9.8 m/s2)(10.7 m) = 1 atm + 1/2(1000 kg/m3)v22 + (1000 kg/m3)(9.8 m/s2)(0 m)
Simplifying the equation, we can solve for v2:
v22 = 2[(3.20 atm - 1 atm) / (1000 kg/m3)]
v2 = √[2(3.20 atm - 1 atm) / (1000 kg/m3)]
Using the equation, we can calculate v2 to find the speed at which the water is flowing.
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An ornament of mass 42.0 g is attached to a vertical ideal spring with a force constant (spring constant) of 33.9 N/m. The ornament is then lowered very slowly until the spring stops stretching. How much does the spring stretch?
Answer:
Extension is 12.14m
Explanation:
mass of ornament=42g,weight of ornament=mg=42*9.8=411.6
Force constant(k)= 33.9N/m
F=ke
e=F/k
F is force, e is extension
F=weight of ornament
e=411.6/33.9
e=12.14m
A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup.
Answer:
The maximum capacity of such cup is
2 × 3.142R^3/9×squareroot3
Explanation:
From the diagram in the attachment,
h= height of the cone, r= radius of the cone,R= radius of the original circular piece of paper
Using pythagorean theorem, we get
r^2+h^2=R^2 => r^2=R^2-h^2
Formular for the volume of a cone is given as V=1/3×(3.142)^2h
Substituting for r^2 when R is a constant
V=1/3(3.142)(R^2-h^2)h
V=1/3(3.142)(R^2-h^3)
V'=0=1/3(3.142)R^2-3h^2)
0=R^2-3h^2
h^2=R^2/3 => h=R/squareroot of 3
V"=1/3(3.142)(0-6)=-2×3.142×h
Negative shows that v is concave
V(R/squareroot of 3)=1/3(3.142)[R^2×R/squareroot 0f 3-(R/squareroot of 3)^3
V=2×3.142×R^3/9× squareroot of 3
To find the maximum capacity of a cone-shaped drinking cup made from a circular piece of paper of radius R, you need to use differential calculus to maximize the volume of the cone, derived from the formula V = (1/3)π*r²h, where r = R*(1- θ/2π) is the radius of the cone and h = sqrt[R² - r²] is its height.
Explanation:The subject of this question is finding the maximum capacity of a cone-shaped drinking cup made from a circular piece of paper of radius R. To find the maximum capacity or volume of such a cup, we need to formulate the problem in terms of mathematical geometry. The volume of a cone, which in this case represents our drinking cup, is given by the formula V = (1/3)π*r²h, where r is the radius of the base circle (which will also be our R), and h is the height of the cone.
The cone is created by cutting out a sector and joining edges CA and CB on the leftover part of the circular paper. Let θ denote the angle of the sector that is cut out (in radians). Since we have subtracted this sector, the circumference of the top circle of the cone is now 2πR*(1-(θ/2π)) = 2πR*(1 - θ/2π) = 2πR - R*θ.
Setting this equal to the circumference of the top of the cone (2πR - R*θ = 2πr, where r is now the radius of the cone), we can solve for r in terms of R and θ: r = R*(1- θ/2π).
The slant height of the cone will be equal to the radius of the initial circular piece of paper, R. Using Pythagorean theorem, the height h of the cone can be expressed as h = sqrt[(R² - r²)] = sqrt[R²(1 - (1- θ/2π)²)].
Substituting the expressions for r and h into the cone volume formula, we get V = (1/3)π[R²(1- θ/2π)]²*sqrt[R²(1 - (1- θ/2π)²)]
This is an expression for the volume V of the cone-shaped drinking cup in terms of R and θ. The task now is to utilize differential calculus to find the maximum of this function V(θ), i.e., we need to find the value of θ (between 0 and 2π) that maximizes the volume V.
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The Vehicle Assembly Building at the Kennedy Space Center in Florida has a volume of 3,666,500 m3. Convert this volume to liters and express the result in standard exponential notation?
Explanation:
The Vehicle Assembly Building at the Kennedy Space Center in Florida has a volume of 3,666,500 m³.
Volume = 3,666,500 m³
1 m³ = 1000 L
So volume = 3,666,500 x 1000 = 3666500000 L
Volume of vehicle Assembly Building at the Kennedy Space Center in Florida = 3666500000 L
Volume of vehicle Assembly Building at the Kennedy Space Center in Florida = 3.67 x 10⁹ L
The volume in liters and in exponential notation is [tex]3.67\times10^{23}[/tex].
To convert the given volume to liters it is necessary to use the following relation of values:
[tex]dm^{3} = L\\ m ^{3} = 1000L[/tex]
Therefore, the following calculation must be performed:
[tex]3,666,500m^{3} \times 1000= xL[/tex]
[tex]x = 3,666,500,000 L[/tex]
Now, to convert to scientific notation, leave the number different from the power of 10 between 1 and 10, so that:
[tex]3,666,500,000 = 3.67 \times 10^{9} L[/tex]
So, the volume in liters and in exponential notation is [tex]3.67\times10^{23}[/tex]
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Michael opens his eyes in the morning to see the alarm clock on his dresser. At that point, his eyes are receiving light energy, which they change into neural messages for the brain. This conversion of one form of energy into another is called _____.
Answer:
Transduction.
Explanation:
Transduction is actually a process which involves the conversion of energies or messages from one kind to another. So in this case the transfer of light energy received by the eyes into the message for the brain is also called as transduction.
The power output, P, of a solar panel varies with the position of the sun. Let P = 10sinθ watts, where θ is the angle between the sun's rays and the panel, 0 ≤ θ ≤ π. On a typical summer day in Ann Arbor, Michigan, the sun rises at 6 am and sets at 8 pm and the angle is θ = πt/14, where t is time in hours since 6 am and 0 ≤ t ≤ 14. (a) Write a formula for a function, f(t), giving the power output of the solar panel (in watts) t hours after 6 am on a typical summer day in Ann Arbor. (b) Graph the function f(t) in part (a) for 0 ≤ t ≤ 14. (c) At what time is the power output greatest? What is the power output at this time? (d) On a typical winter day in Ann Arbor, the sun rises at 8 am and sets at 5 pm. Write a formula for a function, g(t), giving the power output of the solar panel (in watts) t hours after 8 am on a typical winter day.
Final answer:
The function for the power output of a solar panel in Ann Arbor on a summer day is f(t) = 10sin(πt/14), and on a winter day, the function is g(t) = 10sin(π(t+2)/9). The power output is greatest at 1 pm during summer with 10 watts. Graphing reveals the variation of power throughout the day.
Explanation:
Writing a Function for Solar Panel Power Output:
To answer part (a), we start by incorporating θ = πt/14 into the original power output equation P = 10sinθ, leading to a new function f(t) = 10sin(πt/14).
For part (b), graphing f(t) between 0 ≤ t ≤ 14 will show a sinusoidal curve that represents the power output throughout the day.
For part (c), the power output is greatest when θ = π/2, which occurs when t = 7 (1 pm), and the power output at this time is P = 10 watts.
Regarding part (d), for a typical winter day with sunlight from 8 am to 5 pm, the angle for t hours after 8 am needs to be adjusted. We can denote it as θ1 = π(t+2)/9. Thus, a new function g(t) = 10sin(π(t+2)/9) represents the power output on a typical winter day.
What are we calculating when we calculate expected frequencies? What is the reason for calculating expected frequencies the way we do? In laymen’s terms, what do expected frequencies tell us?
Answer:
1. What we calculate when we calculate expected frequency is the predicted frequency that can be obtained from an experiment whose outcome is expected to be true.
2. The reason for using expected frequency is because it is a tool used for doing complex probability calculations and predictions. Also, it serves as a working tool that can be used in place of the observed frequency,when the observed frequency is not available.
3. In probability, expected frequency tell us the possible outcomes of an event.
Say, for example rolling of a fair die.
The probability of getting 1,2....,6 as the outcome is 1/6 but that doesn't mean that when we roll a fair die 6 times, we'll get outcomes of 1-6.
So, the essence of expected frequency is to tell us what to expect in an event (this may or may not turn out to be true).
Final answer:
Expected frequencies estimate how often an event should occur based on a probability distribution, providing a basis for comparing actual outcomes in a data set to determine consistency with expected probabilities.
Explanation:
When we calculate expected frequencies, we are determining how often we anticipate an event will occur based on a probability distribution. To find the expected frequency, one typically multiplies the expected percentage by the total number of observations or the sample size. For instance, if an event has a 10% chance of occurring out of 600 trials, the expected frequency would be 0.10 * 600 = 60.
The reason for calculating expected frequencies in this manner is to provide a basis for comparison with the actual frequencies that occur in a data set. This comparison allows us to determine if the outcomes observed are consistent with the expected probabilities, which can be particularly useful in statistical hypothesis testing, such as the chi-square test.
Expected frequencies give us insight into what we might predict to occur over a long period of trials or observations. They are theoretical estimates that can be appraised against actual outcomes to understand the probability distribution of a given scenario.
If your front lawn is 18.0 feet wide and 20.0 feet long, and each square foot of lawn accumulates 1050 new snowflakes every minute, how much snow, in kilograms, accumulates on your lawn per hour? Assume an average snowflake has a mass of 2.10 mg.
Answer:
47628 kg/hr
Explanation:
Total area = 18*20 =360 ft^(2)
no .of snowflakes per minute = 1050*360 =378000
mass of snowflakes per minute = 378000*2.1*10^(-3) =793.8 kg/min
mass accumulated per hour = 793.8kg/min * 60min/hr =47628 kg/hr