The vertical height in which the runner’s center of mass is raised during the jump is 0.43 m.
What is the vertical height reached by the runner?
The vertical height reached by the runner is calculated by applying the third kinematic equation as shown below.
Mathematically, the formula is given as;
v² = u² - 2gh
where;
v is the final velocity of the runner at the maximum heightu is the initial velocity of the runnerg is acceleration due to gravityh is the height reached by the runnerat maximum height, the final velocity, v = 0
The vertical height reached by the runner is calculated as;
0 = u² - 2gh
2gh = u²
h = u² / 2g
h = ( 2.9² ) / ( 2 x 9.8 )
h = 0.43 m
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which objective lens(es) should immersion oil never be in contact with to prevent damaging it(them)?
Only objectives labelled as "Oil" objectives should be used with immersion oil; if you attempt to use immersion oil on a dry objective lens, the objective is likely to break.
In order to keep immersion oil from penetrating dry targets, their structure is not properly sealed. When handled carefully—and preferably on a tripod—mirror lens can be utilized to capture beautiful images of landscapes, seascapes, cities, or any other subject that requires longer focal length lenses. A personal target is a goal that you have established. A military aim is the term used to describe the overall plan for an operation. Money-raising is the main objective of a bake sale. If your objective was to pick up, you have succeeded.
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a store owner plans to hang a sign weighing 750 n so that cable a, attached to the store, makes a 30.0 degree angle to the vertical side of the building. cable b is horizontal and attached to an adjoining building. what is the tension in cable b?
A remains constant, the tension in cable B can be calculated using the formula T = W/sin(θ), where T is the tension, W is the weight of the sign, and θ is the angle formed by cable A. the tension in cable B is 750N/sin(30°) = 1333.38N.
what is cable ?
Cable is a type of wiring system used to transmit electrical signals. It consists of insulated conductors, usually copper, twisted together in a pattern that reduces interference from external sources. Cables are often used to connect components within a system, such as computers, televisions, and audio systems.
They can also be used to connect systems to each other, such as connecting a laptop to a router or connecting a router to a modem. Cables can be used to carry data as well as power. Depending on the type of cable, it can support various types of data transfer speeds and resolutions. For example, HDMI cables are used to transmit audio and video signals in high-definition.
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b) if the teacher wants to have the bungee stop his motion when he is 2 meters above the gym floor, how much energy will the bungee need to absorb?
The amount of energy will the bungee need to absorb for a motion is marked as 19.6xmass J potential energy.
Where does potential energy reach its peak?When the most energy is absorbed, potential energy is at its maximum. This might occur when something rises to the highest point in the air before dropping, when a roller coaster is about to plunge, or when a rubber band is stretched as far back as it can go before it breaks. After then, potential energy is changed into kinetic energy.
P.E. = mgh,
where m = mass - kilograms,
g = acceleration due to gravity = 9.8 m / s2
h = height = meters.
Potential energy = m x 9.8 x 2
=> 19.6xmass J
Why does potential energy fall off as height increases?Because kinetic energy gradually increases and potential energy gradually diminishes as a body descends from a height. Throughout this, all mechanical energy is kept in reserve.
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A highway curves to the left with radius of curvature of 44 m and is banked at 16 ◦ so that cars can take this curve at higher speeds. Consider a car of mass 1563 kg whose tires have a static friction coefficient 0.72 against the pavement.How fast can the car take this curve without skidding to the outside of the curve?
The car can take the curve without skidding at speeds up to 15.3 m/s.
What is speeds?Speeds refer to the rate of motion or operation of a machine, vehicle, or process. It can also refer to the rate of change of a variable. Speeds are often expressed in terms of the time it takes to travel a certain distance, the distance traveled in a certain amount of time, or the rate of rotation or revolution. Speeds can be measured in linear units such as meters per second or miles per hour, or in angular units such as revolutions per minute. Speed is an important factor in many activities, including transportation, sports, and manufacturing.
The maximum speed at which the car can take the curve without skidding to the outside of the curve is determined by the maximum static frictional force between the tires and the pavement, which is equal to the product of the normal force on the tires and the coefficient of static friction.
The normal force on the tires is equal to the weight of the car and can be calculated as follows:
Normal force = 1563 kg * 9.8 m/s2 = 15,319 N
The maximum static frictional force is then calculated as follows:
Maximum static frictional force = Normal force * coefficient of static friction = 15,319 N * 0.72 = 11,036 N
The maximum speed at which the car can take the curve without skidding is determined by the centripetal force of the car, which is equal to the product of the mass of the car, the speed of the car, and the radius of curvature of the road.
Therefore, the maximum speed of the car can be calculated as follows:
Maximum speed = sqrt(Maximum static frictional force/ Mass of car * Radius of curvature)
= sqrt(11,036 N / 1563 kg * 44 m)
= 15.3 m/s
Therefore, the car can take the curve without skidding at speeds up to 15.3 m/s.
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determine the reactions at the supports A and B for equilibrium of the beama. 200 N/m 4mb. 400N/m 3m
According to the question, 50 kN reactions at the supports A and B for equilibrium of the beama.
What is a physical example of equilibrium?When we move a body a tiny distance, the state creates forces that usually oppose the movement and bring the body back to its equilibrium, we say that the body is in stable equilibrium. Think of a stone at the base of a bowl as an illustration.
Since the laden beam is stationary, we should equalize each other out by moving upward and downward.
Thus,
= R+R
=40+60=100 kN - (1)
Now that the beam's force has been evenly distributed across the two supports, the reaction force exerted by the two supports will also be equally, or R=R.
2R=100 kN
R=50 kN
As a result, the reaction at supports A and B will each be 50 kN.
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find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 3.0 m from the center of the circle.
A helicopter's huge blade is turning in a horizontal arc. From the blade's tip to the middle of the circle, it is 6.7 meters long. find the centripetal acceleration ratio
How does acceleration function? What is it?
Any procedure where the velocity varies is referred to as acceleration. There are just two ways to accelerate: changing your speed or changing your direction, or changing both. This is because velocity is both a speed as well as a direction.
What does typical acceleration mean?
typical acceleration The overall change in velocity during the specified interval multiplied by the total amount of time required for the change is the definition of mean acceleration over a particular period of time. It lasts for a specific amount of time.
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Part C What is the value of the change in potential energy AU = U; Ui , of the alpha particle? Express your answcr in joules using thrcc significant figurcs_ View Available Hint(s) AU -1.1Ox10-21 J Sun Prevlous Answers Correct Correct answer shown: Your answer 11.04.10-2 1.104*10- was cither rounded dificrently or used different number significant figures than required for this part Important: If yOu use this answer in later parts use tne full unrounded value in your calculations
The value of the change in potential energy, AU, of the alpha particle is 1.104*10^-21 Joules. This value represents the energy gained or lost by the particle as it moves through a potential difference
The change in potential energy, AU, of the alpha particle is a measure of the energy gained or lost by the particle as it moves through a potential difference. It is calculated by subtracting the initial potential energy, Ui, from the final potential energy, U. The unit of potential energy is Joules. In this case, the change in potential energy of the alpha particle is given as 1.104*10^-21 Joules. This value represents the energy gained or lost by the particle as it moves through a potential difference. It is important to note that this value is given to three significant figures, and should be used with the same precision in any further calculations.
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Does the displacement of an object depend on the specific location of the origin of the coordinate system
Nope, your reference point can be anywhere because displacement is simply the change in position. So regardless of where your origin is, the change in position (displacement) is independent.
What is an example of a displacement?Alteration in an object's location in relation to a reference frame is known as displacement. For instance, a billiards ball travels from one spot to another as a player strikes it. It is alleged to have moved. A vector quantity with the both magnitude and direction is displacement.
Are displacement and distance the same thing?Sometimes people mistakenly believe that length and displacement are simply two different labels for the same thing. Displacement and distance, however, are two distinct ideas. The total distance covered is larger than movement between those two places if an item changes direction while traveling.
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a body collides with an identical body that is initially at rest. after the collision, they stick together. what is the percentage of kinetic energy that has been transferred to other forms of energy in the collision?
In a perfectly inelastic collision, where the two bodies stick together after the collision, the percentage of kinetic energy transferred to other forms of energy is 100%.
How does the mass and velocity of the colliding bodies affect the amount of kinetic energy transferred to other forms of energy?The mass and velocity of the colliding bodies have a direct relationship with the amount of kinetic energy transferred to other forms of energy. A higher mass will result in a larger amount of kinetic energy being transferred, as more force is required to bring the two bodies to a stop. Similarly, a higher velocity will result in a greater amount of kinetic energy being transferred, as the bodies have more kinetic energy to lose during the collision. Both mass and velocity contribute to the total kinetic energy of the colliding bodies and therefore the amount of kinetic energy that will be transferred to other forms of energy in the collision.
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a force of 100 n is required to move the smae object of 20 m/s find the coefeicent of kentixc friction
The coefficient of kinetic friction, also known as the "friction coefficient", is a dimensionless value that represents the amount of friction present between two surfaces in motion relative to one another.
To find the coefficient of kinetic friction for an object, one would need to measure the force required to keep the object moving at a constant velocity, and divide that force by the object's weight. The coefficient of kinetic friction (μk) can be calculated using the following equation:
μk = force of friction / normal forceTo find the normal force, we need to know the weight of the object which can be calculated by multiplying the mass of the object (m) by the acceleration due to gravity (g).
Weight = m * gIn this case, the force required to move the object at a constant velocity of 20 m/s is 100 N, and therefore the coefficient of kinetic friction can be calculated by dividing that value by the object's weight.
If the weight of the object is not provided and we only know the force required to move it, we can't calculate the coefficient of kinetic friction.
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A resistor with resistance R and a capacitor with capacitance C are connected in series to an AC voltage source. The time-dependent voltage across the capacitor is given by VC(t)=VC0sin?t.What is the amplitude I0 of the total current I(t) in the circuit?Express your answer in terms of any or all of R, C, VC0, and ?.Expert Answer
The time-dependent voltage across the capacitor is give below in the expression.
What is voltage in plain English?Voltage is the term used to describe the "pressure" that drives electricity. A voltage is measured in volts (V), and greater voltages result in more electricity flowing to electronic equipment.
What is a voltage in amps?A "volt," a unit of electric potential, also known as electromotive force, is defined as "the potential difference between two points of a conducting wire carrying a continuous current of 1 ampere, where the power expended between these locations is equal to 1 watt." It appears that there is a one-volt potential, to put it another way.
The time-dependent voltage across the capacitor V(t)=V0 sin(wt)
The amplitude of total current is I0=V0/x
here x is th inductive capacitance =1/(wc)
so, I0=V0 *c*w
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An electron is in a vacuum near the surface of the Earth. Where should a second electron be placed so that the electrostatic force it exerts on the first electron balances the gravitational force on the first electron due to Earth?
For the electrostatic force the second electron exerts on the first electron to counteract the gravitational force the first electron experiences from the Earth, the second electron must be placed below the first one.
In order for the repulsive force (working on the first) to be in the direction opposed to the pull of Earth's gravity, the second electron must be below the first one.
Repulsive force on electron=Weight of electron.
[tex]\frac{K*q*q}{D^{2} }[/tex] = m*g
K(In air)=9 x 10^9 Nm^2/C^2
q=-1.602 x 10^-19 C
Replacing values
D=5.08 m
Therefore, the second electron needs to be 5.08 m below the first electron in question.
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If two types of cations are moving in opposite directions and they are the only ions moving, and the membrane potential is positive, the ion moving faster has
A greater concentration gradient.
The movement of ions across a membrane is driven by their concentration gradient, which is the difference in concentration of the ion on one side of the membrane compared to the other side.
If the membrane potential is positive, it means that there is a higher concentration of one type of ion on one side of the membrane compared to the other side.
If two types of cations are moving in opposite directions, the one moving faster is the one that has a greater concentration gradient, meaning that it has a higher concentration on one side of the membrane compared to the other side.
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a space shuttle changes its circular orbit to a lower altitude. what is the work done on the shuttle?
The work done on the shuttle will be negative, if its changes its circular orbit to a lower altitude.
The gravitational force between the object and the earth is balanced by the centrifugal force acting on the object during the circular motion. If a satellite of mass m, orbits around the earth in a circular path of radius R, then centrifugal force will be, mv²/R.
if the mass of the earth is M, and universal gravitational constant is G, then gravitational force between the earth and the satellite would be GMm/R².
mv²/R = GMm/R²
mv² = GMm/R
0.5mv² = 0.5GMm/R
But 0.5mv² = K = Kinetic energy of the satellite
K = 0.5GMm/R
So lesser the radius of the orbit, more the kinetic energy will be required for the satellite to orbit around the earth. So the work will be done by the orbit, in other words the work done on the satellite will be negative because it is done by the satellite.
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studies show that in collisions where vehicle occupants who were totally ejected from the vehicle they were less likely to be killed. true false
False. According to studies, those who are completely ejected from a car during an accident are more likely to die than people who stay within the car.
What does a collision mean?When two or more things come into touch with one another and are impacted by one another, a collision occurs. This can happen in a multitude of contexts, such as on the roads when cars meet, in space when objects collide, or even during sports like soccer or hockey. The physical act of two particles coming into contact and reacting with one another, for instance in physics or chemistry, is sometimes referred to as a collision. Car crashes may cause damage to the vehicles as well as injuries or fatalities to the people. To reduce the incidence of accidents on the road, it is essential to prevent collisions through safe driving habits and traffic laws.
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Immediately after time t=0, what happens to the charge on the capacitor plates?Check all that apply.Individualcharges flow through the circuit from the positive to the negativeplate of the capacitor.Individualcharges flow through the circuit from the negative to the positiveplate of the capacitor.The positiveand negative charges attract each other, so they stay in thecapacitor.Currentflows clockwise through the circuit.Currentflows counterclockwise through the circuit.
Immediately after time t = 0, the positive and negative charges attract each other, so they stay in the capacitor. Current flows clockwise through the circuit.
The capacitor plates' charges have been divided after time t=0, leaving one plate with a positive charge and the other with a negative charge. The attractive force between the positive and negative charges will now cause the charges on the plates to remain in place. In the circuit, current also moves in a clockwise direction. This is due to the fact that the positive charges will travel toward the positive plate, and the negative charges will move toward the negative plate, causing a current to flow clockwise through the circuit.
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The number of cycles of a wave that passes a stationary point in one second is called its Select one: a. crest b. trough c. frequency d. wavelength
The speed of a waveform can be calculated by the number the crests who pass through a given location in a given period of time. A is the proper answer.
What is the sound's frequency?The frequency with which a sound level wave repeats itself all the second is its frequency, which is often referred to as pitch.The sound's frequency is the opposite of its period. if a wave has a short wavelength. Undoubtedly, the wave will have a lower number. Lower frequency is indicated by a longer wavelength.
What is the musical frequency?The speed of something like the vibration, or frequency, determines the sound's pitch. It is only applicable or relevant for musical when the waveform is extremely regular. Frequency
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A 60-cm-long heating wire is connected to a 120 V outlet. If the wire dissipates 45 W, what are (a) the current in and (b) the resistance of the wire?
There is a 240-volt outlet attached to a heating wire that is 60 cm long. What are the effects if the cable emits 45 W We calculate the voltage with in line I =U n = 45W/120V = 0.38A using P=45 W as well as V=120 V.
What does the word disperse mean?Verb intransitive: to disperse and disappear. The sun emerged as the clouds disappeared. The team's initial momentum has faded. : to indulgently or dissolutely pursue pleasure
Calculation
The power dissipated in the wire is
P = I2R = IV
where I is the current and V the voltage.
Using P=45 W and V=120 V, we find the value of the current in the wire:
I =P/V = 45W/120V = 0.38A
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an airplane travels 2750 km against the wind in 5 hrs and 3250 km with the wind in the same amount of time what is the rate of the plane in still in air and what is the rate of the wind?
We may utilize to determine the required wind speed to move persons and stuff. The formula is wind = 195 times the real number of the weight over the object's area in square feet.
What is speed and what is its unit in physics?The pace at which a distance changes over time is referred to as speed. It has a dimension of time-distance. As a result, the fundamental unit of time and all basic unit of travel are combined to form the Rectangular cross - section of speed. Thus, the metre per second (m/s) is the Input to the system of speed.
What does physics' law of speed entail?We can define our concepts first. Speed (s) is defined as the difference traveled per unit of time (d/t). Speed and furthermore a direction equals velocity.
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DJ wants to install a zipline between two trees. The zipline will be strung between the trees at points 32 feet and 4 feet high. Suppose the trees are 52 feet apart. Which sketch models this situation to find the length of the zipline if the zipline is x feet
The zipline is 59.06 feet long; it would be x feet long if it were a different length. DJ wants to set up a zipline in the space between two trees.
How are lengths determined?Length can be measured in a variety of ways, including handspan, foot span, meters, inches, and millimeters. Standard units of measuring length and non-standard units of measuring length are the two categories into which the units of measuring length can be divided. Look at the table below that displays length units.
What length is there?A segment's or a room's dimensions are examples of things that can be measured in terms of length. Distance is the separation between two things, like two cities or two points.
Length=√a²+b²
Length=√28²+52²
Length=√784+2,704
Length=√3,488
Length=59.06ft
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honeybees can see light in the ________ range of the electromagnetic spectrum.
A. beta
B. infrared
C. ultraviolet
D. gamma
The ultraviolet portion of the electromagnetic spectrum is visible to honeybees.
Ultraviolet (UV) light has shorter wavelengths than visible light. Some insects, like bumblebees, can perceive UV light even though it is invisible to the human eye. This is akin to how a dog's hearing extends just beyond the range of human hearing. The Sun emits the entire spectrum of ultraviolet radiation, which is commonly divided into UV-A, UV-B, and UV-C. These are the categories that are used in earth sciences the most frequently. Our atmosphere almost completely absorbs the most harmful UV-C rays. The sunburn is brought on by the harmful UV-B rays. When exposed to UV-B light, living things are more vulnerable to DNA and other cellular damage.
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a 800 n man is standing on a 4 m long plank of wood that is supported at each end by vertical ropes. the plank has a weight of 500 n and the man is standing 1 m from the left end. find the force of tension in the rope at the left end of the plank.
On the a 4 m long board of wood with vertical rope supports at either end, an 800 n man stands. Mass of work and scaffold = 800 N + 500 N = 1300 N, as well as the man stands 1 m from of the left end of the board.
What does tension force mean?The force transferred through a rope, string, or wire when pushed by forces acting from different sides is referred to as tension. Its tension force is applied along the entire length of the cable and exerts an equal amount of strain on the bodies at each end.
What is tension force measured in?In the International Systems of Units, tension is measured in newtons or pounds-force as a transmitted force, an action-reaction combination of forces, or a restoring force.
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a 65 kg trampoline artist jumps vertically upward from the top of a platform with a speed of 3.0 m/s. (ignore small changes in gravitational potential energy.) how fast is he going as he lands on the trampoline, 3.0 m below?
An 65 kg trampoline performer jumps vertically and at a rate of 3.0 m/s from the top of such a platform. Take into account only huge changes in the gravitational potential energy. 0.31 meters is how long depress is.
How is potential energy defined?Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases. The potential energy of a steel ball is greater when it is raised above the earth than when it is brought to Earth.
How is GPE determined?If the masses of the items and the separation between them are known, it is possible to compute the gravitational potential energies in relation to two objects in space. You can determine the GPE by multiplying each object's.
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If you are having trouble making auto loan payments and are really following a tight budget, w
hich recommendation below represents the WORST advice?
(2 Points)
O
Find an extra source of income by taking a second job, working longer hours, or borrowing from family
if they can afford to help
Stop making payments on some of your debts so you can focus on getting the most expensive or
largest debts under control
Continue making all payments and call your lenders and see if you can negotiate lower monthly pay-
ments, lower interest rates, or longer terms
O Explore whether a free or non-profit credit counseling service could help
Worst Advice : Stop making payments on some of your debts so you can focus on getting the most expensive or largest debts under control.
What is a Loan ?A loan occurs when one or more people, businesses, or other entities lend money to other people, businesses, or other entities. The receiver incurs a debt and is often responsible for both the main amount borrowed as well as interest payments until the loan is repaid.
A loan is when money is lent to another person with the understanding that it would be repaid, along with interest. Before agreeing to provide a borrower a loan, lenders will take into account the borrower's income, credit score, and degree of debt.
The sum of money that must be paid each week or month to fulfill the loan's requirements. An amortization table may be used to calculate this based on the principal, loan period, and interest rate.
The worst recommendation that one can make about loan payment if he or she is facing trouble in doing the same is Stop making payments on some of your debts so you can focus on getting the most expensive or largest debts under control.
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NASA's space shuttle program in Florida will end in 2011. Which of these would be the most likely outcome of this event on the locations near the space center?
increase in number of restaurants and decrease in unemployment
increase in tourism and decrease in use of space technologies in homes
increase in unemployment and decrease in profit made by local businesses
increase in profit made by construction companies and decrease in use of space technologies in homes
NASA's space shuttle program in Florida will end in 2011. Increase in tourism and decrease in use of space technologies in homes would be the most likely outcome of this event on the locations near the space center.
What is NASA?
The U.S. federal government's autonomous National Aeronautics and Space Administration (NASA) is in charge of the civil space programme, as well as space and aeronautics research.
NASA was created in 1958 to provide the American space development effort a distinctly civilian orientation, stressing peaceful applications in space science. It succeeded the National Advisory Committee for Aeronautics (NACA).
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Curling is a sport played with 20kg stones that slide across an ice surface. Suppose a curling stone sliding at 1m/s strikes another stone and comes to rest in 2.5 m/s.Approximately how much force is on the stone during impact. 160N 800N 1600N or 8000N160N
The stone exerts an impact force of 8000 N.
In the ice-based team sport of curling, two teams alternate sliding granite stones in the direction of a goal known as a House.
It is a winter Olympic and Paralympic sport that features medal divisions for mixed wheelchair teams, men's, women's, and mixed doubles teams. The goal of a game is to accumulate points by moving your stones closer than your opponent's stones to the center of the house, or the "button."
The calculation can be done as follows
mass= 20 kg
velocity= 1 m/s
t= 1ms to secs
= 1× 10⁻³
Force= 20 × 1/2.5 × 10⁻3
= 20/2.5 ×10⁻³
= 8000
Consequently, 8000 N of force is exerted on the stone during impact.
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Oil with a density of 842kg/m3842kg/m3 is flowing smoothly through a pipe, as shown. In the lower portion, the oil is flowing at v1=2.04m/sv1=2.04m/s, and the pressure gauge indicates P1=232kPaP1=232kPa. In the upper portion of the pipe, oil is flowing at v2=3.26m/sv2=3.26m/s at a height that is 12.28m12.28m above the lower portion.
What is the pressure reading, in kilopascals, on the gauge on the upper portion of the pipe?
The pressure reading on the upper portion of the pipe can be determined by using Bernoulli's equation. Bernoulli's equation relates the pressure, velocity, and height of a fluid in a steady state and incompressible flow.
The Bernoulli's equation states that:
P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2
Where:
P1 = pressure at point 1 (232 kPa)
v1 = velocity at point 1 (2.04 m/s)
h1 = height at point 1 (0 m)
P2 = pressure at point 2 (unknown)
v2 = velocity at point 2 (3.26 m/s)
h2 = height at point 2 (12.28 m)
ρ = density of the fluid (842 kg/m3)
g = acceleration due to gravity (9.81 m/s^2)
We can plug in the given values and solve for P2:
P2 = P1 + 1/2ρv1^2 + ρgh1 - 1/2ρv2^2 - ρgh2
P2 = 232 + 1/28422.04^2 + 8429.810 - 1/28423.26^2 - 8429.8112.28
P2 = 232 + 8424.16 + 0 - 84210.66 - 10,205.9
P2 = -9,973.7 Pa
Therefore, the pressure reading on the upper portion of the pipe is -9,973.7 Pa which is approximately -99.74 kPa.
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Describe the changes occur while mixing of two ideal gases Match the words in to the appropriate blanks in the sentence. Ideal gases mix because whilemong the ____ of Ideal gases ____
Entropy, Increases, enthalpy, decreases, potential energy
Ideal gases mix because while mixing the entropy of the system increases and the enthalpy decreases.
Entropy is a measure of the disorder of a system, the more disorder a system has the higher its entropy. Ideal gases have high entropy because their molecules are in constant random motion and have a large number of possible microstates. When two ideal gases mix, the number of microstates increases, leading to an increase in entropy.
Enthalpy is a measure of the total energy of a system, including both internal energy and potential energy. Ideal gases have low enthalpy because they have low internal energy and low potential energy. Mixing two ideal gases reduces the potential energy between the molecules, leading to a decrease in enthalpy.
In summary, the mixing of two ideal gases results in an increase in entropy, and a decrease in enthalpy and potential energy. This is an example of how the mixing of gases leads to an increase in disorder in the system.
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8. A bullet (mass=m) is fired at speed v into a block of mass M (with M> m) which is hanging
vertically from a light string of length L. The bullet is embedded in the block. If the recoiling
block-bullet system reaches a height of 2/3L, then the initial speed of the bullet is most nearly
a
Mx (1gL/3)1/2/m
b Mx (2gL/3)¹/2/m
C. Mx (3gL/4)¹/2/m
d. Mx (4gL/3)¹/2/m
Answer: A bullet (mass=m) is fired at speed v into a block of mass M (with M> m) which is hanging vertically from a light string of length L. The bullet is embedded in the block. If the recoiling block-bullet system reaches a height of 2/3L, then the initial speed of the bullet is most nearly
B. Mx (2gL/3)¹/2/m
Explanation:
When a bullet (mass=m) is fired at speed v into a block of mass M (with M> m) which is hanging vertically from a light string of length L, the bullet is embedded in the block. The bullet and block form a new system with a total mass of M+m and the system moves upward due to the kinetic energy imparted by the bullet.
Conservation of energy principle states that the initial kinetic energy of the bullet is equal to the final potential energy of the bullet-block system. The potential energy of the system is given by mgh, where h is the height to which the system rises.
Therefore, the initial kinetic energy of the bullet is given by:
1/2mv² = mgh
We know that h = 2/3L and g is the acceleration due to gravity. We can substitute these values into the above equation and solve for the initial speed of the bullet
v² = 2gmh/m = 2gh/m = 2g(2/3L) / m = 4gL/3m
v = (2gL/3m)^1/2 * m
v = M * (2gL/3)^1/2 / m
Therefore the initial speed of the bullet is most nearly Mx (2gL/3)¹/2/m
Summary, when a bullet (mass=m) is fired at speed v into a block of mass M (with M> m) which is hanging vertically from a light string of length L, the bullet is embedded in the block and the block and bullet form a new system. The initial kinetic energy of the bullet is equal to the final potential energy of the bullet-block system. The potential energy is given by mgh, where h is the height to which the system rises, h = 2/3L. Solving the equation gives the initial speed of the bullet is most nearly Mx (2gL/3)¹/2/m.
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Calculate the magnitude of gravitational force between two 1-kilogram masses separated center to center by 1 meter.
When two objects of equal mass are maintained at a distance of one meter apart, their gravitational pull is equal to 6.67*10^(-11).
The gravitational force (F) must be calculated using the equation shown below. All objects with mass are drawn toward one another by the gravitational attraction, whose strength is directly proportional to the masses of the two objects and inversely proportional to the square of their separation from one another.
As a result, the only remaining unit is newtons, or meters kilograms per second squared. Therefore, there is a 1.98 x 10^(-20) newton gravitational force between the Earth and the Moon.
Here r= 1, both masses m1=m2= 1
Magnitude F= 6.67*10^(-11)
[tex]F= Gmm/r^{2} \\G= 6.67*10^{-11}[/tex]
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