Answer:
As we need to use a nested loop in our function,hence push $ra
pop $ra
jal nested_function_label
nop is the correct option.
A sheet of gold leaf has a thickness of 0.125 micrometer. A gold atom has a radius of 174pm. Approximately how many layers of atoms are there in the sheet?
Final answer:
To calculate the number of gold atom layers in a 0.125 micrometer thick gold leaf, convert the thickness to picometers and divide by the diameter of a gold atom, which is twice its radius of 174pm, resulting in approximately 359 layers.
Explanation:
The question "A sheet of gold leaf has a thickness of 0.125 micrometer. A gold atom has a radius of 174pm. Approximately how many layers of atoms are there in the sheet?" is asking us to calculate the number of gold atom layers in a given thickness of a gold leaf.
First, we need to convert the given thickness of the gold leaf from micrometers to picometers to match the atomic radius unit. There are 1,000,000 picometers in a micrometer, so 0.125 micrometers is equal to 125,000 picometers. Since the diameter of a gold atom is twice the radius, we have a diameter of 174pm x 2 = 348pm. Now, to find out how many atoms can fit in the thickness, we divide the total thickness by the diameter of one atom:
125,000 pm / 348 pm ~= 359 layers of atoms
Therefore, there are approximately 359 layers of gold atoms in the sheet of gold leaf.
There are approximately 20 layers of atoms in the sheet of gold leaf.
To determine the number of layers of atoms in the sheet of gold leaf, we need to compare the thickness of the sheet with the diameter of a single gold atom.
First, we convert the thickness of the gold leaf from micrometers to picometers (pm) to match the units of the gold atom's diameter.
Since 1 micrometer is equal to 1000 picometers, the thickness of the gold leaf in picometers is:
[tex]\[ 0.125 \times 1000 = 125 \text{ pm} \][/tex]
Next, we need to consider the diameter of a gold atom, which is twice the radius.
Given that the radius is 174 pm, the diameter is:
Using the FCC packing efficiency of 74%, we get:
[tex]\[ \frac{1}{0.74} \approx 1.35 \][/tex]
Again, rounding up to the nearest whole number, we get 2 layers.
Therefore, considering the packing efficiency of gold atoms in the sheet, there are approximately 20 layers of atoms in the sheet of gold leaf.
When musicians tune their instruments, they listen for "beats" in the sound the instruments produce when matched to a standard pitch. These beats are moments when the sound becomes louder, then softer, then louder again. Musicians adjust the pitch of their instruments until they do not hear any more beats in the tuning process. Which statements explain the phenomenon described in the scenario? Check all that apply. 1.The moments of loudness represent constructive interference. 2.The tuning process depends on diffraction. 3.The moments of softness represent destructive interference. 4.The beats are produced by reflections. 5.The instrument is tuned when the frequencies of the standard and the instrument align.
Answer:
1. The moments of loudness represent constructive interference.
3.The moments of softness represent destructive interference.
5. The instrument is tuned when the frequencies of the standard and the instrument align.
Explanation:
Beats are the periodic and repeating fluctuations heard in the intensity of a sound when two sound waves of very similar frequencies interfere with one another.
Constructive interference is the process whereby two waves of identical wavelength that are in phase form a new wave with an amplitude equal to the sum of their individual amplitudes.
In the case of musical instruments, the loudness is due to a wave of larger amplitude formed as a result of the constructive interference of two waves that are in phase
Destructive Interference is the interference of two waves of equal frequency and opposite phase, resulting in the formation of a wave of lesser amplitude or even total cancellation.
The softness in sound is due to the destructive interference of two waves in opposite phase.
When there is an alignment in the frequency of the standard and the instrument, the instrument is tuned
Answer:
1. The moments of loudness represent constructive interference.
3.The moments of softness represent destructive interference.
5. The instrument is tuned when the frequencies of the standard and the instrument align.
Explanation:
Nuclear power stations transfer useful energy to other energy stores. How is this useful energy carried from the power stations?
I
Nuclear power stations transfer energy by nuclear fission to heat water, producing steam. This steam drives turbines connected to generators, producing electricity. The electricity is transported through power lines across the national grid.
Explanation:In a nuclear power station, the useful energy is primarily carried from the power plant through the national grid system. Here's how it works: nuclear power stations transfer energy via a process called nuclear fission where atoms are split, releasing a large amount of energy. This energy is used to heat up water, even to the point of converting it to steam. The steam drives the turbines which are connected to generators. These generators produce electricity, which is then distributed through power lines across the national grid, reaching homes, factories, offices and so on.
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An apple in a tree has a gravitational store of 8J. As it falls, it accelerates constantly until it hits the ground. What is the apple’s maximum kinetic energy store? Explain your answer.
Answer:
Explanation:
Given that on the tree the gravitational energy stored is 8J
Then, mgh = 8J.
The apple begins to fall and hit the ground, what is the maximum kinetic energy?
Using conservation of energy, as the above is about to hit the ground, the apple is at is maximum speed, and the height then is 0m, so the potential energy at the ground is zero, so all the potential of the apple at the too of the tree is converted to kinetic energy as it is about to hits the ground. Along the way to the ground, both the Kinetic energy and potential energy is conserved, it is notice that at the top of the tree, the apple has only potential energy since velocity is zero at top, and at the bottom of the tree the apple has only kinetic energy since potential energy is zero(height=0)
So,
K.E(max) = 8J
When the batter hit the foul ball, the baseball moved upward to a delighted fan in the top deck.
A. KE increases and PE increases.
B> KE increases and PE decreases.
C. KE decreases and PE increases.
D. KE decreases and PE decreases.
We can see here that the correct answer is: A. KE increases and PE increases.
As the ball moves upward against gravity, its height increases, indicating a rise in its potential energy (PE). Since the ball moves, its speed increases, implying an increase in its kinetic energy (KE) as well.
KE (kinetic energy) is the energy possessed by an object due to its motion. When the batter hits the foul ball, the baseball is set in motion, and its kinetic energy increases as it moves upward.
PE (potential energy) is the energy possessed by an object due to its position or condition.
Technician A says that failure analysis will assist the technician in determining whether it is more cost effective to replace rather than repair an engine. Technician B says that when an engine fails under warranty, the manufacturer may want it back for complete analysis of why it failed. Who is correct?
Final answer:
Both Technician A, who speaks about failure analysis for cost effectiveness, and Technician B, who discusses manufacturers' interest in analyzing engine failures under warranty, are correct. These considerations involve complex decision-making in modern automotive engineering, influenced by sophisticated technology and warranty strategies.
Explanation:
Both Technician A and Technician B are correct in their statements. Technician A remarks that a failure analysis is beneficial for determining the most cost-effective option between repairing or replacing an engine. Modern engine complexities mean assessment is critical for understanding the financial impacts of such decisions. Meanwhile, Technician B highlights the interest manufacturers may have in retrieving a failed engine under warranty for complete analysis to understand the failure reasons and improve future manufacturing processes.
Modern car engines have become sophisticated computer-controlled systems, and professionals often require expensive computerized equipment to carry out repairs. This necessity can change the business dynamics for auto repair shops. Warranties also play a significant role, helping to distinguish between higher and lower quality cars, with longer warranties often indicating confidence from the manufacturer in the vehicle's reliability.
Final answer:
Both Technician A and Technician B are correct; Technician A emphasizes the importance of a cost-benefit analysis, while Technician B points out the manufacturer's need for quality control and improvement.
Explanation:
The question revolves around the roles and statements made by two hypothetical technicians, Technician A and Technician B, in the context of engine failure analysis in the automotive industry. Technician A contends that failure analysis is beneficial for determining if it is more cost-effective to replace rather than repair an engine, which is a question of balancing the costs of new equipment against the costs and risks of continued equipment failure. Technician B states that when an engine fails while under warranty, the manufacturer might request the engine to determine the cause of failure, which is a matter of quality control and learning from product errors to prevent future occurrences.
In this scenario, both Technician A and Technician B are correct. Technician A highlights the importance of a cost-benefit analysis when deciding to repair or replace an engine. Technician B discusses the manufacturer's interest in warranty cases which is crucial for improving the product and maintaining customer satisfaction and safety.
Killer whales are known to reach 32 ft in length and have a mass of over 8,000 kg. They are also very quick, able to accelerate up to 30 mi/h in a matter of seconds. Disregarding the considerable drag force of the water, calculate the average power a killer whale named Shamu with mass 8.00 x 103 kg would need to generate to reach a speed of 12 m/s in 6 s
Answer:
Power, P = 96 kW
Explanation:
Mass of Shamu, m = 8000 kg
Initial velocity, u = 0
Final velocity, v = 12 m/s
We need to find the average power of the whale. It is equal to the work done per unit time. Work done is equal to the change in kinetic energy. So,
[tex]P=\dfrac{\Delta K}{t}\\\\P=\dfrac{mv^2}{2t}\\\\P=\dfrac{8000\times 12^2}{2\times 6}\\\\P=96000\ W[/tex]
or
P = 96 kW
So, the average power of the killer whale is 96 kW.
Final answer:
To calculate the average power Shamu the killer whale needs to generate to reach a speed of 12 m/s in 6 seconds, we first find the acceleration and then use it to calculate the work done. Dividing the work by the time gives us the average power, which is 96 kilowatts (kW).
Explanation:
The question asks us to calculate the average power required for a killer whale named Shamu to accelerate up to a speed of 12 m/s in 6 seconds, ignoring the drag of water. To find the power, we first need to calculate the work done in accelerating Shamu, and then divide that work by the time taken to find the average power.
Calculating Work Done
Work done is given by the equation:
Work = Force × Distance
First, we need the acceleration, which can be found using the equation:
Acceleration (a) = (Final speed - Initial speed) / Time
Since Shamu is starting from rest, the initial speed is 0. Thus, the acceleration is:
a = (12 m/s - 0 m/s) / 6 s = 2 m/s²
Next, we use Newton's second law to find the force:
Force = Mass × Acceleration
Force = 8.00 × 10³ kg × 2 m/s² = 16,000 N
Now we find the distance covered using the equation:
Distance = (Initial speed + Final speed) / 2 × Time
Distance = (0 + 12 m/s) / 2 × 6 s = 36 m
Thus, work done = 16,000 N × 36 m = 576,000 J
Calculating Average Power
Average power is work done divided by time:
Power = Work / Time
Power = 576,000 J / 6 s = 96,000 W or 96 kW
The average power generated by Shamu to reach the required speed is 96 kilowatts (kW).
In a laundromat, during the spin-dry cycle of a washer, the rotating tub goes from rest to its maximum angular speed of 4.7 rev/s in 8.3 s. You lift the lid of the washer and notice that the tub decelerates and comes to a stop in 17.5 s. Assuming that the tub rotates with constant angular acceleration while it is starting and stopping, determine the total number of revolutions undergone by the tub during this entire time interval.
Answer:
Number of revolutions = Δθ = 60.63 revs
Explanation:
The angular acceleration of the washer is given by
α = (ωf - ωi)/Δt
Where ωf is the initial angular speed, ωi is the final angular speed and Δt is the interval of time during this acceleration.
α = (4.7 - 0)/8.3
α = 0.56 rev/s²
As we know from the equation of kinematics,
2αΔθ = ωf² - ωi²
Where Δθ is the change in angular displacement of the washer.
Δθ = (ωf² - ωi²)/2α
Δθ = (4.7² - 0²)/2*0.56
Δθ = 19.72 revs
Now the tub decelerates and comes to a stop in 17.5 s
α = (ωf - ωi)/Δt
α = (-4.7 - 0)/17.5
α = -0.27 rev/s²
the corresponding change in angular displacement of the washer is
Δθ = (ωf² - ωi²)/2α
Δθ = (0² - 4.7²)/2*-0.27
Δθ = 40.91 revs
Therefore, the total number of revolutions undergone by the tub during this entire time interval is
Δθ = 19.72 + 40.91
Δθ = 60.63 revs
Two technicians are discussing a problem where the brake pedal travels too far before the vehicle starts to slow. Technician A says that the brakes may be out of adjustment. Technician B says that one circuit from the master cylinder may be leaking or defective. Which technician is correct?
Answer:
Technician A
Explanation:
If Technician B was correct, and the master cylinder is defective - then no braking action would occur.
This is not true however, as some breaking action eventually occurs, meaning it must be out of adjustment.
Both Technician A, suggesting the brakes are out of adjustment, and Technician B, suggesting a leak or defect in the master cylinder, could be correct in the scenario of extended brake pedal travel before the vehicle slows.
Explanation:Both Technician A and Technician B could be correct in diagnosing a problem where the brake pedal travels too far before the vehicle starts to slow down. Technician A suggests that the brakes may be out of adjustment. If the brakes are not properly adjusted, the brake pads or shoes may be too far from the rotor or drum, causing the pedal to travel further before the pads make contact and slow the vehicle.
Technician B considers a hydraulic issue, proposing that one circuit from the master cylinder may be leaking or defective. In a hydraulic brake system, if there is a leak or a defect in one of the cylinders, it could result in a loss of pressure when the brake pedal is applied. This loss of pressure means the braking force is not adequately transmitted to the brake pads, leading to increased pedal travel.
Hydraulic brakes use Pascal's principle, where pressure applied to a confined fluid is transmitted undiminished in all directions. The master cylinder, when the brake pedal is applied, generates pressure that is transferred to the slave cylinders located at each wheel. If the master cylinder is compromised or out of adjustment, the result is insufficient pressure and force at the slave cylinders, hence longer pedal travel before effective braking occurs.
PLEASEEEE ANSWERRR FASTT!!! Summarize the contributions that Ellen Swallow Richards made to help
clean up the Earth. *
Answer:
Ellen tested the water in Massachusetts and it had way too much chlorine. She talked to the city and got them to stop dumping waste and garbage into the water.
Explanation:
oh btw im in 5th grade and i get these kind of questions your welcome
Suppose a dolphin sends out a series of clicks that are reflected back from the bottom of the ocean 80 m below. How much time elapses before the dolphin hears the echoes of the clicks? (The speed of sound in seawater is approximately 1530 m/s.)
Answer:
Time, t = 0.104 seconds
Explanation:
Frequency of the click of the Dolphin, f = 55.3 kHz
A dolphin sends out a series of clicks that are reflected back from the bottom of the ocean 80 m below, d = 80 m
The speed of sound in seawater is, v = 1530 m/s
Once the sound is send and reflects, the total distance covered by it is 2d such that,
[tex]t=\dfrac{2d}{v}\\\\t=\dfrac{2\times 80}{1530}\\\\t=0.104\ s[/tex]
So, the time elapses before the dolphin hears the echoes of the clicks is 0.104 seconds.
Use the following terms to write a short paragraph that describes what you learned from this lab: potential energy, kinetic energy, mass, velocity, collision and momentum. (underline or bold the terms in your paragraph, thank you!)
please help me~
due tomorrow at 12 pm
Answer:
Kinetic Energy is proportional to mass and velocity squared. Potential energy can be transferred to and from Kinetic Energy by doing work on a mass to raise it from the ground. Both momentum and kinetic energy are conserved during elastic collisions.
The lab illustrated energy transformation from potential to kinetic, the role of mass and velocity in kinetic energy and momentum, and the principles of elastic collision conserving total kinetic energy and momentum.
Explanation:Through this lab, I better understood the concepts of energy and its transformation. Initially, an object at rest on a height possesses potential energy, which depends on its mass and the height from the ground. As it falls, this potential energy converts into kinetic energy, which is directly proportional to the mass of the object and the square of its velocity. Moreover, when two objects collide, they exchange energy and momentum, where momentum is calculated as the product of an object's mass and velocity.
An elastic collision is a special scenario in which the total kinetic energy before and after the collision remains the same, demonstrating the law of conservation of momentum and kinetic energy.
Peter was holding a Human Physiology textbook that weighs about 4lbs with his non- writing arm for one minute. His elbow remained exactly at a 45° isometric position. He did not complain of any muscle fatigue or muscle weakness. a) i. Is the number of activated motor units stay the same while he was holding the book for two minutes? (0.5 pt) ii. Why? (0.5 pt) Increasing the period Peter is holding the texting will only cause the motor units to fire more frequently to keep the muscles from relaxing. b) i. Are the same motor units activated while he was holding the book for two minutes? (0.5 pt) ii. Why? (0.5 pt)
Answer:
a
When peter held the book for one minute the rate at which motor unites are fired increase steeply but as the duration increases the increese in the rate at which it is being fired becomes linear so the number of activated motors stay the same but are being activated at a more rapidly
b
The same motors are activated whilest he is hold the book for 2 minutes this is because for peter to hold the book in one fixed position one specific motor units need to be activated
Note changing the motor unites would change the positon of the hand
Explanation:
A conducting loop is lying flat on the ground. The north pole of a bar magnet is grought down toward the loop. As the magnet approaches the loop, will the magnetic field created by the induced current point up of down?
Answer:
The current in the loop will flow in anticlockwise direction , and the magnetic field created by the induced current point up.
Explanation:
If you were to separate all of the electrons and protons in 1.00 g (0.001 kg) of matter, you’d have about 96,000 C of positive charge and the same amount of negative charge. If you placed these charges 8.00 m apart, how strong would the attractive forces between them be?
Answer:
The attractive force between them is [tex]1.296 \times 10^{18}[/tex] N
Explanation:
Given:
Charge [tex]q = 96000[/tex] C
Distance between two charges [tex]r = 8[/tex] m
According to the coulomb's law,
[tex]F = \frac{kq^{2} }{r^{2} }[/tex]
Where [tex]k = 9 \times 10^{9}[/tex] = force constant.
[tex]F = \frac{9 \times 10^{9} \times (96000)^{2} }{8^{2} }[/tex]
[tex]F = 1.296 \times 10^{18}[/tex] N
Therefore, the attractive force between them is [tex]1.296 \times 10^{18}[/tex] N
Which category of materials allows electrons to travel through them freely
Does the air exert a buoyant force on all objects in air or only on objects such as balloons that are very light for their size? Does the air exert a buoyant force on all objects in air or only on objects such as balloons that are very light for their size? Air exerts a buoyant force on all objects. Air has too low a density to exert a buoyant force. Air exerts a buoyant force only on objects less dense than air. Air exerts a buoyant force only on objects more dense than air.
Answer:
See explanation
Explanation:
Solution:-
Buoyancy is the force that causes objects to float. It is the force exerted on an object that is partly or wholly immersed in a fluid. Buoyancy is caused by the differences in pressure acting on opposite sides of an object immersed in a static fluid. It is also known as the buoyant force. Buoyancy is the phenomena due to Buoyant Force.
It is as an upward force exerted by a fluid that opposes the weight of an object immersed in a fluid. As we know, the pressure in a fluid column increases with depth. Thus, the pressure at the bottom of an object submerged in the fluid is greater than that at the top. The difference in this pressure results in a net upward force on the object which we define as buoyancy.
- The formula for buoyant force (Fb) is given:
Fb = ρ*g*V
- The force acts on all objects. However, it depends on the fluid density and amount of volume displaced.
- The Buoyant force exerted by air with density = 1.225 kg/m^3 on an object with volume (V) is:
Fb = ρ*g*V = 1.225*9.81*V = 12.02*V
- For the similar object with mass (m), the downward weight would be:
W = m*g
- For the object to float the buoyant force (Fb) must be greater than weight of the object:
Fb > W
12.02*V > m*9.81
V / m > 0.816
- The ratio of V / m must be at-least = 0.816.
- Assuming the object is fully immersed in air, then the volume displaced V = ρ_material*V
ρ_material < 1 / 0.816
ρ_material < 1.225 or ( ρ_air )
- So the for an object to float in air its material density must always be less than that of air. That why in balloons lighter gas is used which have density less than that of air like Helium.
Final answer:
The air exerts a buoyant force on all objects due to Archimedes' principle, which states that the force on an object in a fluid is equal to the weight of the fluid it displaces. An object's ability to float is determined by its density relative to the surrounding air. All objects are subject to this force, whether they rise, sink, or remain suspended.
Explanation:
The air does indeed exert a buoyant force on all objects, not just on light objects like balloons. This buoyant force is a result of Archimedes' principle, which states that the force on an object in a fluid is equal to the weight of the fluid it displaces. Therefore, if an object's average density is less than that of the surrounding fluid, it will float. On the other hand, if an object's density is greater, it will sink. The key factor is the object's density relative to the air around it, determining if it will rise, fall, or remain suspended.
This principle extends to all objects in fluids, including gases such as air. It means that even objects that do not float, such as rocks or metal items, experience a buoyant force; however, this force is not enough to overcome their weight and make them float. Similarly, our bodies are buoyed by the atmosphere to some degree; it's just that the effect is not as noticeable as it is with helium balloons, which have a density much lower than that of air.
3 examples of mechanical force we use in daily life?
Answer:
Picking up a cup, throw or stop a ball, eating food.
Explanation:
A mechanical force can be defined as a force that features some direct contact between two objects (one applying the force and another which is in a state of rest or in a state of motion) and results in the production of a change in the state of the object (state of rest or state of motion).
So anything that moves an object to a different state of rest.
What is the energy difference between the h2 molecule and the separated atoms?
Answer:My answer its a little large so
Explanation:
i write in a paper for you i believe you can be able to read it good
The bond energy is the difference in energy between a molecule and its separated atoms. For the H2 molecule, the energy difference is 7.24 × 10-19 J at a bond distance of 74 pm.
Explanation:The energy difference between the H2 molecule and the separated hydrogen atoms is the bond energy, which is the difference between the energy minimum at the bond distance and the energy of the separated atoms. For the H2 molecule, at a bond distance of 74 pm, the system is lower in energy by 7.24 × 10-19 J compared to the separated atoms. This small energy difference is important for the stability of the H2 molecule.
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The five general principles from the APA are meant to __________. A. be enforceable rules B. be posted in every office C. guide and inspire good conduct D. stand up in court Please select the best answer from the choices provided A B C D
Answer: C
guide and inspire good conduct
Explanation:
APA are rules of proper source documentation to avert difficulty. This makes you feel that you are not alone. Having to follow detailed citation and formatting guidelines as well may seem like just one more task to add to an already-too-long list of requirements.
Final answer:
Correct answer is C. The five general principles of the APA are meant to guide and inspire good conduct among psychologists, offering a values framework rather than serving as enforceable rules.
Explanation:
The five general principles from the American Psychological Association (APA) are meant to guide and inspire good conduct. These principles serve as ethical guidelines for behaviors and decision-making in psychological practice.
In contrast to enforceable rules, which are mandatory and spell out specific prohibitions and mandates, principles and guidelines such as those provided by the APA are not meant to be enforceable or stand up in court but rather to provide a framework for ethical practice.
They offer a set of values that psychologists are encouraged to aspire to in their professional conduct. These principles cover important areas such as respect for people's rights, integrity, and social responsibility in practice.
An automobile tire having a temperature of 6.7 ◦C (a cold tire on a cold day) is filled to a gauge pressure of 25 lb/in2 . What would be the gauge pressure in the tire when its temperature rises to 33◦C? For simplicity, assume that the volume of the tire remains constant, that the air does not leak out and that the atmospheric pressure remains constant at 14.7 lb/in2 . Answer in units of lb/in2 .
Answer: The gauge pressure in the tire when its temperature rises to 33◦C will be 28.7 lb/in2
Explanation: Please see the attachments below
What is the force exerted on a moving charge of -2.0 C at a 20° angle through a magnetic field of 3.0 x 10-4T with a
velocity of 5.0 x 106 m/s?
Answer:
1026 N
Explanation:
Force on a moving charge in a magnetic field is given by
F= qvB Sinθ
F = 2 x 5 x 10^6 x 3 x 10-4 x Sin (20)
F = 1026 N
Answer:
1.0 x 10^-3 N
Explanation:
got it right on edge:3
Where is the image located in the case of an object placed at a distance to the left of a converging lens?
Answer:
the object is placed at 2f
Explanation:
Converging lens are convex lens, as the name emanates , they are light rays that converge at a point via a certain distance at the opposite side. Often times , any incident rays that is moving and is parallel to the principal axis is usually termed as Converging lens.
So when the object is placed at 2f , the image will be formed at 2f to the right for converging lens.
Sphere A with mass 80 kg is located at the origin of an xy coordinate system; sphere B with mass 60 kg is located at coordinates (0.25 m, 0); sphere C with mass 0.20 kg is located in the first quadrant 0.20 m from A and 0.15 m from B. In unit-vector notation, what is the gravitational force on C due to A and B?
Answer:
Fc = [ - 4.45 * 10^-8 j ] N
Explanation:
Given:-
- The masses and the position coordinates from ( 0 , 0 ) are:
Sphere A : ma = 80 kg , ( 0 , 0 )
Sphere B : ma = 60 kg , ( 0.25 , 0 )
Sphere C : ma = 0.2 kg , ra = 0.2 m , rb = 0.15
- The gravitational constant G = 6.674×10−11 m3⋅kg−1⋅s−2
Find:-
what is the gravitational force on C due to A and B?
Solution:-
- The gravitational force between spheres is given by:
F = G*m1*m2 / r^2
Where, r : The distance between two bodies (sphere).
- The vector (rac and rbc) denote the position of sphere C from spheres A and B:-
Determine the angle (α) between vectors rac and rab using cosine rule:
[tex]cos ( \alpha ) = \frac{rab^2 + rac^2 - rbc^2}{2*rab*rac} \\\\cos ( \alpha ) = \frac{0.25^2 + 0.2^2 - 0.15^2}{2*0.25*0.2}\\\\cos ( \alpha ) = 0.8\\\\\alpha = 36.87^{\circ \:}[/tex]
Determine the angle (β) between vectors rbc and rab using cosine rule:
[tex]cos ( \beta ) = \frac{rab^2 + rbc^2 - rac^2}{2*rab*rbc} \\\\cos ( \beta ) = \frac{0.25^2 + 0.15^2 - 0.2^2}{2*0.25*0.15}\\\\cos ( \beta ) = 0.6\\\\\beta = 53.13^{\circ \:}[/tex]
- Now determine the scalar gravitational forces due to sphere A and B on C:
Between sphere A and C:
Fac = G*ma*mc / rac^2
Fac = (6.674×10−11)*80*0.2 / 0.2^2
Fac = 2.67*10^-8 N
vector Fac = Fac* [ - cos (α) i + - sin (α) j ]
vector Fac = 2.67*10^-8* [ - cos (36.87°) i + -sin (36.87°) j ]
vector Fac = [ - 2.136 i - 1.602 j ]*10^-8 N
Between sphere B and C:
Fbc = G*mb*mc / rbc^2
Fbc = (6.674×10−11)*60*0.2 / 0.15^2
Fbc = 3.56*10^-8 N
vector Fbc = Fbc* [ cos (β) i - sin (β) j ]
vector Fbc = 3.56*10^-8* [ cos (53.13°) i - sin (53.13°) j ]
vector Fbc = [ 2.136 i - 2.848 j ]*10^-8 N
- The Net gravitational force can now be determined from vector additon of Fac and Fbc:
Fc = vector Fac + vector Fbc
Fc = [ - 2.136 i - 1.602 j ]*10^-8 + [ 2.136 i - 2.848 j ]*10^-8
Fc = [ - 4.45 * 10^-8 j ] N
The heat loss through a window (R-2) is 10 MMBTU/year. Calculate the payback period (in years) ifArgon is filled in the window to increase the effective R-value of the window to 7. Assume heating price to be $10/MMBTU and the cost for filling Argon is $20.Heat lost through new window per year = (10 x 2) / 7 = 2.84 MMBTUs/yrReduction in heat lost per year = 10 - 2.84 = 7.16 MMBTUs/yrSavings in energy cost per year = 7.16 x 10 = $71.6Payback period = 20 / 71.6 = 0.28 yrs
Answer:
0.28 year
Explanation:
Heat lost through new window per year = heat loss through a window / R- value = (10 MMBTU/year × 2) / 7 = 2.86 MMBTUs/yr
Reduction in heat lost per year = heat loss through a window - Heat lost through new window per year = 10 MMBTUs/yr - 2.86 MMBTUs/yr = 7.14 MMBTUs/yr
Savings in energy cost per year = Reduction in heat lost per year × heating price = 7.14 MMBTUs/yr × $10/MMBTU = $71.4 / yr
Payback period = cost for filling Argon / Savings in energy cost per year = $20 / $71.4 /yr = 0.28 yrs
Which statement best explains the relationship between current, voltage, and resistance?
A) If we increase the amount of voltage applied, and do not change the resistance, this will result in a decrease in current.
B) If we decrease the current applied, and do not change the resistance, we increase the voltage.
C) If we increase the amount of voltage applied, and do not change the resistance, we will also increase the current.
D) If we decrease the amount of current, this will not affect the amount of voltage, only the amount of resistance.
(FLVS Physical Science 03.09)
Answer:
c
Explanation:
big brain
Tire inflation is very important to the safe and economical operation of any vehicle. Technician A says that the tire pressure should never exceed the maximum pressure imprinted on the sidewall of the tire. Technician B says to inflate tires to the pressures recommended on the tire information decal or placard on the drivers door. Which technician is correct? Group of answer choices: a) Technician A only b) Tehnician B only c) Both tehnicians A and B d) Neither tehnicians A nor B.
Answer:
The correct option is;
c) Both technicians A and B
Explanation:
Normally the pressure required for a normally inflated tire is included on the side or sidewall of the tire along with the instruction as to the qualification and training required to inflate the vehicle tire. Other information on the sidewall includes the tire model, brand name and manufacturer.
The proper inflation pressure can also be located on the tire information manual or decal as well on the door on the driver's side.
Technician B is correct in recommending that tires should be inflated to the pressure specified on the vehicle's placard. It is more accurate than the maximum pressure imprinted on the tire sidewall.
When considering tire inflation for safe and economical operation of a vehicle, there seem to be conflicting recommendations from two technicians on the correct pressure. Technician A suggests that tire pressure should never exceed the maximum pressure imprinted on the sidewall of the tire. However, this is not necessarily the recommended operating pressure; it is simply the maximum pressure that the tire can safely handle. Technician B provides a more accurate recommendation by advising to inflate tires to the pressures recommended on the tire information decal or placard on the driver's door. This placard usually lists the optimal pressure for the vehicle's tires based on the manufacturer's specifications, and accounts for the best performance and safety.
Most vehicle manufacturers specify the optimal tire pressure for cold tires, which might differ from the maximum pressure on the tire sidewall. Maintaining the proper air pressure in the tires ensures smoother and safer rides, better gas mileage, and longer tire life. Therefore, the correct answer to the question is (b) Technician B only.
If deep-sea divers rise to the surface too quickly, nitrogen bubbles in their blood can expand and prove fatal. This phenomenon is known as the bends. If a scuba diver rises quickly from a depth of 25.0 m in Lake Michigan (which is fresh water), what will be the volume at the surface of an N2 bubble that occupied 1.00 mm3 in his blood at the lower depth?
Answer:
3.42 cubic mm
Explanation:
Let density of fresh water be [tex]\rho_w = 1000 kg/m^3[/tex]
And atmospheric pressure at the water surface be [tex]P_a = 101325 Pa[/tex]
Let g = 9.8 m/s2. The pressure at the dept of h = 25 m is
[tex]P = P_a + \rho_wgh = 101325 + 1000*9.8*25 = 346325 Pa[/tex]
Using ideal gas law and assume constant temperature, we have the following equation to calculate the volume at the water surface [tex]V_a[/tex], knowing that the volume at the lower depth V = 1 mm3:
[tex]P_aV_a = PV[/tex]
[tex]V_a = PV/P_a = 346325*1/101325 = 3.42 mm^3[/tex]
The volume of a nitrogen bubble in a diver's blood will expand when the pressure decreases as they rise to the surface. If the bubble was 1.00 mm3 at 25.0 m depth, it would expand to 2.5 mm3 at the surface. Rapid ascent can cause the bubbles to expand too quickly, leading to the condition known as Decompression Sickness, or The Bends.
Explanation:The volume expansion of nitrogen bubbles in a diver's blood due to rapid ascent from a certain depth is governed by Boyle's Law that states the volume of gas is inversely proportional to its pressure, assuming the temperature remains constant. When a diver rises quickly from a depth of 25.0 m (approximately 2.5 atm, as each 10m of water is approximately 1 atm) to the surface (1 atm), the pressure decreases. According to Boyle's Law, the volume would therefore increase, thus, if a nitrogen bubble occupied 1.00 mm3 at the depth, at the surface it would expand to 2.5 x 1.00 mm3, or 2.5 mm3. This is why divers must ascend slowly, to allow gases to dissipate gradually and avoid the dangerous condition known as Decompression Sickness or The Bends.
Learn more about Decompression Sickness here:https://brainly.com/question/36494413
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if an electron in an electron beam experiences a downward force of 2.0x10^-14N while traveling in a magnetic field of 8.3x10^-2T west, what are the direction and the magnitude of the velocity?
Answer:
[tex]1.51\cdot 10^6 m/s[/tex] north
Explanation:
When a charged particle moves in a magnetic field, the particle experiences a force given by the formula:
[tex]F=qvB sin \theta[/tex]
where
q is the magnitude of the charge
v is its velocity
B is the magnetic field
[tex]\theta[/tex] is the angle between the directions of v and B
In this problem,
[tex]q=1.6\cdot 10^{-19}C[/tex] (charge of the electron)
[tex]B=8.3\cdot 10^{-2} T[/tex] (strength of magnetic field)
[tex]F=2.0\cdot 10^{-14} N[/tex] (force)
[tex]\theta=90^{\circ}[/tex]
Therefore, the velocity is
[tex]v=\frac{F}{qB sin \theta}=\frac{2.0\cdot 10^{-14}}{(1.6\cdot 10^{-19})(8.3\cdot 10^{-2})(sin 90^{\circ})}=1.51\cdot 10^6 m/s[/tex]
The direction of the force is perpendicular to both the direction of the velocity and the magnetic field, and it can be found using the right-hand rule:
. Thumb: direction of the force (downward) --> however the charge is negative, so this direction must be reversed: upward
- Middle finger: direction of the field (west)
- Index finger: direction of velocity --> north
So, the electron is travelling north.
If an alloyed guitar B string (147 Hz resonance) has an average diameter of .6 mm over an effective oscillating length of 65 cm, what is the tension in Newtons if the alloy is 10% aluminum and 90% copper? (assume the specific gravities of the metals are 2.6 and 8.9 grams per cubic centimeter, respectively)
Answer:
73.8 N
Explanation:
The total volume is,
V = [tex]\frac{m_Al}{P_Al} = \frac{m_copper}{P_copper}[/tex]
= [tex]\frac{10m}{(100)(2.6)} = \frac{90m}{(100)(8.9)}[/tex]
= 0.1396 m
The average density is,
[tex]p = \frac{m}{V}[/tex]
= [tex]\frac{m}{0.1396}[/tex]
= 7.169 g/cm³
The linear mass density is,
μ = pπr²
= (7.169 x 10⁹) (π (0.3 x 10⁻³)²)
= 2.026 x 10⁻³ Kg/m
The fundamental mode of length is,
L = λ/2
λ=2L
= 2 x 0.65
= 1.3 m
The speed of the wave is,
v = λf
= 1.3 m x 147 Hz
= 1.91 m/s
The tension is,
v = √T/ц
T = ц v²
= 2.026 x 10⁻³)(1.91 m/s)²
= 73.769N
73.8N