The buoyant force always pushes objects up toward the surface of the fluid because it is the upward force that acts on an object submerged in a fluid, such as water or air.
This upward force is known as the buoyant force and is equal to the weight of the fluid displaced by the object which means that the buoyant force is always pushing the object up toward the surface of the fluid. In general, the buoyant force is stronger than gravity when the object is less dense than the fluid and weaker when the object is more dense than the fluid. Thus, the force of gravity is always pulling objects down, but the buoyant force can be stronger or weaker than gravity depending on the object’s density and the density of the fluid. Hence, the buoyant force always pushes objects up toward the surface of the fluid, regardless of whether the fluid is water, air, or some other fluid.
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Derive from first principle the equation of motion of a one dimensional standing wave
The equation of motion of a one dimensional standing wave can be derived from first principles using the wave equation.
The wave equation states that the propagation speed of a wave, c, is equal to the square root of the ratio of the wave's tension (T) to its linear mass density (μ). In other words,
[tex]c = \sqrt{ \frac{T}{\mu}[/tex]
For a one dimensional standing wave, the equation of motion can be derived by taking the second derivative of the wave equation with respect to time. This is the equation of motion that results:
[tex]F = \mu (\frac{d2y}{dt2})[/tex]
where F is the total force applied to the wave, and [tex]\frac{dy}{dt}[/tex] is the wave velocity. The equation of motion can be further simplified by substituting the wave equation for c, resulting in the following equation of motion for a one dimensional standing wave:
[tex]F = (\frac{T}{\mu }) (\frac{d2y}{dt2})[/tex]
This equation of motion describes how the total force applied to a one dimensional standing wave affects the wave's velocity.
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complete question:What is the equation of motion for a one-dimensional standing wave?
A large 2.00×104 L aquarium is supported by four wood posts (Douglas fir) at the corners. Each post has a square 5.60 cm x 5.60 cm cross section and is 80.0 cm tall.
By how much is each post compressed by the weight of the aquarium?
The kinematic equations can describe phenomena other than motion through space and time. Suppose x represents a person’s bank account balance. The units of x would be dollars ($), and velocity v would give the rate at which the balance changes (in units of, for example, $/month). Acceleration would give the rate at which v changes. Suppose a person begins with ten thousand dollars in the bank. Initial money management leads to no net change in the account balance so that v0 5 0. Unfortunately, management worsens over time so that a 5 22.5 3 102 $/month2 . Assuming a is constant, find the amount of time in months until the bank account is empty.
We can use the kinetic equation that combines velocity, acceleration, and time to calculate the number of months until the bank account is empty:
[tex]v = v_0 + at[/tex]
Since initially there is no net change in the account balance, the initial velocity [tex](v_0)[/tex]in this case is 0. 22.5 * $102 per month expressed as Acceleration (a). The moment (t) at which the account balance reaches zero must be determined.
We can arrange the equation to solve for time as follows:
[tex]0 = 0 + (22.5 * 10^2) * t[/tex]
When we simplify the equation, we get:
2250t = 0
After 0 months the account balance will be zero as the result of the calculation will be 0. This shows that the bank account is currently empty or will be empty soon.
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What types of atoms are radioactive?
small atoms
atoms with many electrons
atoms with unstable nuclei
atoms with unbalanced charges
Answer:
An atom with an "unstable" nucleus is likely to split into two different atoms (elements) with emission of gamma, alpha, etc. which is radioactive radiation.
If the foot kicks the ball with an action force of 40 N, the force which the
ball exerts on the foot will:
O a. depend on the mass of the foot and the ball.
O b. depend on whether or not the ball is moving.
O c. depend on whether or not the player was running.
O d. be 40 N of reaction force.
Answer:
the answer is (d) the force which the ball exerts on the foot will be 40 N of reaction force.
Explanation:
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, the force exerted by the ball on the foot will be equal and opposite to the action force exerted by the foot on the ball.
When a social position is accompanied by accepted patterns of behavior it becomes
Answer:
When a social position is accompanied by accepted patterns of behavior, it becomes a role. A role is a set of expectations and behaviors that are associated with a particular social position. For example, a doctor's role includes expectations such as providing medical care to patients, making diagnoses, and prescribing treatments. Similarly, a teacher's role includes expectations such as instructing students, grading assignments, and providing feedback on student progress. Roles are important in society because they help to create order and stability, and they allow individuals to understand their place in society and how they are expected to behave.
Ionic bonds bond ions together(1 point) Responses because they connect in order for one to transfer their electrons to the other. because they connect in order for one to transfer their electrons to the other. through their electric attraction to each other due to their equal electrical charges. through their electric attraction to each other due to their equal electrical charges. through their electric attraction to each other due to their opposite electrical charges. through their electric attraction to each other due to their opposite electrical charges. because they share electrons with each other, pulling them together.
Ionic bonds bond ions together through their electric attraction to each other due to their opposite electrical charges.
In an ionic bond, one ion (typically a metal) loses one or more electrons and becomes a positively charged cation, while another ion (typically a nonmetal) gains one or more electrons and becomes a negatively charged anion. The opposite charges of the ions then attract each other, creating an ionic bond between them.
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EARTH AND SPACE SCIENCE! PLEASE HELP! Question: Tree with unknown height has a shadow that is 4200 centimeters long while a meter stick has a shadow when held vertical that 325 centimeters long. Identify below, the height of the tree in centimeters. The height of the meter stick is 100 centimeters(cm).
Potential answers:
a.) 1292 cm
b.) 1520 cm
Therefore, the answer is (a) 1292 cm is stick has a shadow when held vertical.
What causes the shadow's location to change?Additionally, since light moves in a straight path from its source to an object, the shadow of the object moves with the light source.
Let's use h centimetres to represent the tree's height. We have the following percentage in the problem:
height of tree/length of its shadow = height of meter stick/length of its shadow
or
h / 4200 = 100 / 325
We can solve this proportion for h:
h = 4200 * 100 / 325 = 1292.31 cm
Rounding to the nearest centimeter, we get:
h ≈ 1292 cm
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In a tractor pull, a tractor put 250,000 J of work into pulling a large mass.
The tractor pulls the mass using 98,000N of force. How far did the
tractor pull the mass?
In a tractor pull, a tractor put 250,000 J of work into pulling a large mass. The tractor pulls the mass using 98,000N of force. The tractor pulled the mass to a distance of 2.55 meters
We may use the work done formula to solve this problem:
Work = Force x Distance x Cosine (angle between force and displacement)
Yet, because the force and displacement are applied in the same direction, the angle between them is zero, and the cosine of zero is one. As a result, we may reduce the formula to:
Work = Force x Distance
Because we know the work done is 250,000 J and the force exerted is 98,000 N, we can rewrite the formula to solve for distance:
Distance = Work / Force
Distance = 250,000 J / 98,000 N
Distance = 2.55 meters
As a result, The tractor pulled the mass to a distance of 2.55 meters
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When light enters a new medium it changes speeds and bends; creating optical illusions like this. Which type of wave interaction is this?
A. Refraction
B. Reflection
C.absorption
D.diffraction
The type of wave interaction that occurs when light enters a new medium, changes speeds, and bends, creating optical illusions like the one shown, is called refraction.
What is refraction?Refraction is the bending of light as it passes through a medium with a different refractive index. The refractive index is a measure of how much a material can slow down the speed of light passing through it. When light travels from one medium to another, such as from air to water or from water to glass, its speed changes and it bends as a result of the change in the refractive index.
This bending of light is what causes objects to appear shifted or distorted when viewed through lenses or other transparent materials. Refraction is also responsible for many optical phenomena, such as mirages, rainbows, and the dispersion of white light into its component colors.
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Which is the correct resultant wave? *
The resultant wave is the combination of the two waves as we see in option A
What is the resultant wave?A resultant wave is a wave that is formed when two or more waves interact with each other. When waves meet, they can interfere constructively, destructively, or somewhere in between, depending on their amplitude, phase, frequency, and direction. The resulting wave that emerges from this interaction is called the resultant wave.
The nature of the resultant wave depends on the type of interference that occurs between the waves. If the waves are in phase and have the same amplitude, they will interfere constructively, resulting in a wave with a larger amplitude.
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A geographer wants to organize data on the changing economies of two
countries. The data show that one country's economy grew rapidly over 10
years, while the other country's economy declined slightly over the same
period.
The best way for the geographer to organize these data would be a
Answer:
line graph. A line graph is the best way to show changes in data over time. The geographer can plot the economic growth of one country as a line going up over the 10 years, and the economic decline of the other country as a line going down slightly over the same period. This will allow for a clear visual comparison of the changes in the economies of the two countries over time.
A jar of tea is placed in sunlight until it
reaches an equilibrium temperature of 33.3
◦C .
In an attempt to cool the liquid, which has a
mass of 187 g , 133 g of ice at 0.0
◦C is added.
At the time at which the temperature of the
tea is 31.8
◦C , find the mass of the remaining
ice in the jar. The specific heat of water
is 4186 J/kg ·
◦ C . Assume the specific heat
capacity of the tea to be that of pure liquid
water.
Answer in units of g.
(2 significant digits)
Answer:
To solve this problem, we need to use the following formula:
Q = m_tea * c_tea * (T_f - T_i) + m_ice * L_f + m_ice * c_ice * (T_f - 0)
where Q is the amount of heat transferred, m_tea is the mass of the tea, c_tea is the specific heat capacity of the tea, T_i is the initial temperature of the tea, T_f is the final temperature of the tea and ice mixture, m_ice is the mass of the ice, L_f is the latent heat of fusion of ice (334 J/g), and c_ice is the specific heat capacity of ice (2.108 J/g·°C).
First, we need to calculate the initial temperature of the tea. Since it has reached an equilibrium temperature of 33.3°C in sunlight, we can assume that its initial temperature was also 33.3°C.
So, the equation becomes:
Q = (187 g) * (4186 J/kg·°C) * (31.8°C - 33.3°C) + (133 g) * (334 J/g) + (m_ice) * (2.108 J/g·°C) * (31.8°C - 0°C)
Simplifying this equation, we get:
Q = -121732.8 J + 44422 J + 67.032 m_ice
Setting Q to zero, since we want to find the mass of the remaining ice when the temperature is 31.8°C, we get:
67.032 m_ice = 121732.8 J - 44422 J
m_ice = 114.9 g
Therefore, the mass of the remaining ice in the jar when the temperature is 31.8°C is 114.9 g (to 2 significant digits).
How does the heat from the Sun reach us on Earth?
Answer:
through space and through the earth's atmosphere to the earth's surface.
Explanation:
The heat source for our planet is the sun. Energy from the sun is transferred through space and through the earth's atmosphere to the earth's surface. Since this energy warms the earth's surface and atmosphere, some of it is or becomes heat energy.
energy is transferred from the sun thru radiation. the atmosphere keeps a large amount of the heat and UV rays from burning us into crisps
consider two vector A(18m) Along horizontal and B(8m) at angle of 60° above the horizontal find R and the angle between R and A,A and B
Answer:
angle between A and B is approximately 76.8°
Explanation:
Using the cosine law, we can find the magnitude of the resultant vector R:
R^2 = A^2 + B^2 - 2ABcosθ
where θ is the angle between A and B, which can be found using the sine law:
sinθ/8m = sin60°/18m
θ ≈ 43.2°
Substituting the given values into the cosine law:
R^2 = (18m)^2 + (8m)^2 - 2(18m)(8m)cos(43.2°)
R ≈ 19.4m
The angle between R and A can be found using trigonometry:
tanθ = 8m/18m
θ ≈ 24.4°
Therefore, the angle between R and A is approximately 24.4°, and the angles between A and B and between B and R can be found using the fact that they form a triangle:
180° - 60° - 43.2° = 76.8°
Therefore, the angle between A and B is approximately 76.8°, and the angle between B and R is approximately 60° - 76.8° = -16.8° (because B is above the horizontal).
If a 2.6 kilograms can of cranberry sauce with the radius of one point five meters is released from rest at the top of 15 mile high hill. if the hill is frictionless what is the velocity of the can's center of mass at the bottom of the hill?
To solve this problem, we can use conservation of energy. At the top of the hill, the can of cranberry sauce has gravitational potential energy given by:
U = mgh
where m is the mass of the can, g is the acceleration due to gravity, and h is the height of the hill. We can plug in the given values to get:
U = (2.6 kg)(9.81 m/s^2)(15 miles x 1609.34 m/mile) = 601266.8 J
At the bottom of the hill, all of this potential energy will be converted into kinetic energy:
K = (1/2)mv^2
where v is the velocity of the can's center of mass at the bottom of the hill. We can solve for v by equating K and U:
(1/2)mv^2 = mgh
Simplifying and solving for v, we get:
v = sqrt(2gh)
Plugging in the given values, we get:
v = sqrt(2 x 9.81 m/s^2 x 15 miles x 1609.34 m/mile) = 423.6 m/s
Therefore, the velocity of the can's center of mass at the bottom of the hill is 423.6 m/s.
Griffin throws a 0.25 kg football with a force of 10 N. The ball that started from rest took 3 second to reach a final velocity. What is the momentum of the ball?
Answer:
The momentum of the ball is 0.6225 kg/ms^-1
We are given that mass = 0.25 kg
force = 10 N
Time = 3 seconds
Momentum(p) = mv, where m is mass and v is velocity
First we need to find the final velocity, using the formula:-
v = u+at, where v is final velocity, u is initial velocity, a is acceleration and t is time.
rearranging the formula, we first find acceleration:-
a = (v-u)/t
substituting the values,
a = v/t
a = (0.25kg*10N)/3 seconds
a = 0.83 m/s^2
Finding final velocity using the formula v = u+at
v = 0 + (0.83m/s^2*3 seconds)
v = 2.49 m/s
Finally, using the formula p=mv to find the momentum:-
p = 0.25kg*2.49m/s
p = 0.6225 kg m/s^-1
Thus the momentum is 0.6225 kg m/s^-1.
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Of the following statements about the ChemBank at the Broad Institute, identify those that are correct.
ChemBank plans to sell the results of its research to various companies.
ChemBank is an open-source application.
ChemBank matches small molecules to various biological targets.
ChemBank performs pure research.
ChemBank uses known chemical compounds in new therapeutic applications.
ChemBank applies its research to therapeutic goals.
ChemBank matches small molecules to various biological targets and ChemBank uses known chemical compounds in new therapeutic applications are correct statements.
What is ChemBank?
ChemBank performs pure research and ChemBank applies its research to therapeutic goals could both be considered correct depending on the interpretation. ChemBank does perform pure research in the sense that it conducts basic scientific investigations to understand the properties and behavior of small molecules and their interactions with biological targets. However, ChemBank also applies its research to therapeutic goals by using this knowledge to develop new drugs and drug candidates.
ChemBank does not plan to sell the results of its research to various companies, so the statement "ChemBank plans to sell the results of its research to various companies" is incorrect.
ChemBank is not an open-source application, so the statement "ChemBank is an open-source application" is also incorrect.
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Complete question is: ChemBank matches small molecules to various biological targets and ChemBank uses known chemical compounds in new therapeutic applications are correct statements.
51 An electrician has to make eight connections from a switchboard to several outlets. Each
connection requires 50 centimeters of wire. How many meters of wire does the electrician need?
A.4,000 m
B.400 m
C.40 m
D.4 m
Answer:
Each connection requires 50 centimeters of wire, which is equal to 0.5 meters of wire. Therefore, for eight connections, the electrician would need:
8 * 0.5 = 4 meters of wire
Therefore, the correct answer is option D, 4 m.
:
Cheyenne wants to show her class a model that demonstrates sound reflection. Which model best represents what happens when sound waves are reflected?
The simulation of sound waves bouncing off a flat surface is one model that most accurately depicts what happens when sound waves are reflected.
Who or what names the sound wave reflection?The term "echo" refers to a sound reflection that follows a direct sound in reaching the listener. The delay increases with the distance between the source and the listener travelled by the reflecting surface.
A sound wave belongs to what kind of wave?Longitudinal waves are those produced by sound. Compressions and rarefactions occur during the propagation of longitudinal waves through any given medium. When particles are compressed, high pressure zones are created as a result of their near proximity.
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water pressurized to 450000 pa is flowing at 5.0m/s in a horizontal pipe which contracts to 1/3 its former area. what are the pressure and velocity of the water after the contraction?
the pressure of the water after the contraction is -50000 Pa (or 50 kPa below atmospheric pressure), and the velocity of the water after the contraction is 15.0 m/s.
The continuity equation states that the product of the cross-sectional area and the velocity of an incompressible fluid is constant along a pipe, so we can use it to relate the pressure and velocity before and after the contraction:
A₁v₁ = A₂v₂
where A₁ and v₁ are the area and velocity of the pipe before the contraction, and A₂ and v₂ are the area and velocity of the pipe after the contraction.
We can also use the Bernoulli equation, which relates the pressure and velocity of a fluid along a streamline:
P₁ + 1/2 ρv₁² = P₂ + 1/2 ρv₂²
where P₁ and v₁ are the pressure and velocity of the fluid before the contraction, and P₂ and v₂ are the pressure and velocity of the fluid after the contraction, and ρ is the density of the fluid, which we assume to be constant.
Solving for the pressure and velocity after the contraction, we can use the continuity equation to express v₁ in terms of v₂ and substitute it into the Bernoulli equation:
A₁v₁ = A₂v₂
v₁ = (A₂/A₁) v₂
P₁ + 1/2 ρ((A₂/A₁) v₂)² = P₂ + 1/2 ρv₂²
Simplifying and solving for P₂, we get:
P₂ = P₁ + 1/2 ρ(v₁² - v₂²)
Substituting the given values, we get:
A₂ = (1/3) A₁
v₁ = 5.0 m/s
P₁ = 450000 Pa
ρ = 1000 kg/m³
Using the continuity equation, we can find the value of v₂:
A₁v₁ = A₂v₂
v₂ = (A₁/A₂) v₁
v₂ = 3 × 5.0 m/s
v₂ = 15.0 m/s
Substituting this value into the Bernoulli equation, we can find the pressure P₂:
P₂ = P₁ + 1/2 ρ(v₁² - v₂²)
P₂ = 450000 Pa + 1/2 × 1000 kg/m³ × (5.0 m/s)² - (15.0 m/s)²
P₂ = 450000 Pa - 500000 Pa
P₂ = -50000 Pa
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If the atmospheric pressure is 15 lb/in^2, what is the corresponding downward force on the top of a horizontal square area 5 inches on each side?
Answer:
The downward force on the top of the horizontal square area can be found using the formula:
force = pressure x area
Given that the atmospheric pressure is 15 lb/in^2 and the square area is 5 inches on each side, the area can be calculated as:
area = length x width
= 5 inches x 5 inches
= 25 square inches
Substituting the values in the formula, we get:
force = 15 lb/in^2 x 25 square inches
= 375 lb
Therefore, the corresponding downward force on the top of the horizontal square area is 375 pounds.
Which of the following quantitative research methods should a researcher use when trying to understand the political views held by the young population of a specific area? a.) Participant observation b.) Written surveys c.) Secondary data analysis d.) Laboratory experiments
Answer:
Options B
Explanation:
The appropriate quantitative research method for understanding political views held by the young population of a specific area is written surveys (option b). Surveys allow for the collection of data from a large number of participants, and specific questions can be asked to gather data on political views.
Participant observation (option a) involves direct observation of individuals in a natural setting, which may not be practical for studying political views.
Secondary data analysis (option c) involves analyzing data that has already been collected, and may not be specific to the young population or the area of interest.
Laboratory experiments (option d) are typically used to study cause-and-effect relationships between variables, which may not be applicable to studying political views.
Therefore, the best option for understanding the political views held by the young population of a specific area is written surveys.
To understand the political views of the young population of a specific area, a researcher can use written surveys, participant observation, and secondary data analysis as quantitative research methods.
Explanation:If a researcher is trying to understand the political views held by the young population of a specific area, they should use written surveys, participant observation, and secondary data analysis as quantitative research methods.
Written surveys: This method involves distributing survey questionnaires to gather data on political opinions from a sample of the young population in the area. Participant observation: This method involves the researcher immersing themselves in the community and directly observing and interacting with individuals to understand their political views.Secondary data analysis: This method involves analyzing existing data sources, such as census records or previous surveys, to gain insights into the political views of the young population in the area.Learn more about Quantitative Research Methods here:https://brainly.com/question/33505242
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it 3 Review
tors and 2-D Kinematics
Find the direction of the sum
of these two vectors:
16.3 m
BV
7.70 m
A
27.8°
20.0°
When two vectors of magnitudes 16.3 m and 7.7 m are combined at an angle of 137.8 degrees, the resultant is equivalent to 23.87 metres.
What is the parallelograms law of vector addition?
The adjacent sides drawn from a point can be used to indicate the magnitude and direction of two vectors acting concurrently at a point.
7.7 m in size, with vector 1 pointing at the x-axis at a 27.8 degree angle.
vector 2 of magnitude 16.3 m, 20 degrees off the negative y plane.
Using the law of parallelogram vector addition
i.e.
resultant vector = √((v₁) ² + (v₂) ² + 2 × v₁ × v₂ × cos (angle between two vectors))
substituting given value in parallelogram vector addition we get,
resultant vector = √ (570)
resultant vector = 23.87 meters
As a consequence, the product of the two vectors, which have magnitudes of 16.3 metres and 7.7 metres and an angle of 137.8 degrees, is equal to 23.87 metres.
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Question:
Find the direction of the sum
of these two vectors:
16.3 m
7.70 m
20.0°
magnitude (m)
A 27.8°
Psi(x) = (alpha/pi) ^ (1/4) * e ^ (- (alpha * x ^ 2)/2)
Find wave function of
(Px)*2
(Pls if you know the answer writ it on the paper to be clear )
Note that the wave function of (Px)^2 is given by: (Px)^2 Psi(x) = (h^2/4π^2) [(3α^2 x^2 - α) (α/π)^(1/4) e^(-αx^2/2)]
What is the explanation for the above response?To find the wave function of (Px)^2, we need to use the momentum operator, which is represented by Px = -i(h/2π) d/dx.
First, let's find the wave function of Px, which is given by:
Px Psi(x) = -i(h/2π) d/dx [Psi(x)]
= -i(h/2π) [-αx Psi(x) + (α^2 x) Psi(x)]
Now, we can find the wave function of (Px)^2 by squaring the wave function of Px:
(Px)^2 Psi(x) = (-i(h/2π) d/dx) (-i(h/2π) d/dx) Psi(x)
= (h^2/4π^2) [α^2 x^2 Psi(x) - 2α x d/dx(Psi(x)) + (d^2/dx^2)(Psi(x))]
Substituting Psi(x) = (α/π)^(1/4) e^(-αx^2/2) into the above expression, we get:
(Px)^2 Psi(x) = (h^2/4π^2) [(3α^2 x^2 - α) (α/π)^(1/4) e^(-αx^2/2)]
Therefore, the wave function of (Px)^2 is given by:
(Px)^2 Psi(x) = (h^2/4π^2) [(3α^2 x^2 - α) (α/π)^(1/4) e^(-αx^2/2)]
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How do I draw a schematic of this circuit?
A schematic diagram is a graphical representation of an electrical circuit, showing the arrangement of components and their connections.
What is the schematic diagram of a circuit?The lines connecting the components in the schematic diagram represent wires or conductive paths.
The direction of the arrows and the polarity of the symbols indicate the direction of the flow of electrical current. The schematic diagram helps engineers and technicians understand the circuit and troubleshoot problems.
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In an electric circuit, what is one material that the connector can be made of?
A man walking at 3.56 m/s accelerates at 2.50 m/s2 for 9.28 s. How far does he get?
The man who walks at 3.56 m/s and accelerates at 2.50 m/s2 for 9.28 s would walk a distance of 135.245 meters.
Kinematic motionWe can use the kinematic equation:
distance = initial velocity x time + (1/2) x acceleration x time^2
To use this equation, we need to find the initial velocity of the man before he started accelerating. We can do this using the formula:
final velocity = initial velocity + acceleration x time
At the start, the man's velocity was 3.56 m/s, and he accelerates at 2.50 m/s^2 for 9.28 s. Therefore, his final velocity can be calculated as:
final velocity = 3.56 + 2.50 x 9.28
final velocity = 26.08 m/s
Now we can use the distance formula:
distance = initial velocity x time + (1/2) x acceleration x time^2
with initial velocity being 3.56 m/s, time being 9.28 s, acceleration being 2.50 m/s^2, and final velocity being 26.08 m/s:
distance = 3.56 x 9.28 + (1/2) x 2.50 x (9.28)^2
distance = 32.968 + 102.277
distance = 135.245 m
Therefore, the man traveled a distance of approximately 135.245 meters.
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answer and solution to this question
Frequency= 30 Hz, Period= 0.0333 s, Wave Number=15.708 rad/m, Wave Function= y(x, t) = 0.05 sin(15.708x - 94.248t), Transverse displacement= -0.013 m, Time= 0.297 s.
How to calculate the frequency?(a) To find the frequency (f), we can use the equation: wave speed = frequency x wavelength. Rearranging this equation, we get:
frequency = wave speed / wavelength
Substituting the given values, we get:
frequency = 12 m/s / 0.4 m = 30 Hz
Therefore, the frequency of the wave is 30 Hz.
To find the period (T), we can use the equation:
period = 1 / frequency
Substituting the frequency value we just calculated, we get:
period = 1 / 30 Hz = 0.0333... s (rounded to four decimal places)
Therefore, the period of the wave is approximately 0.0333 s.
To find the wave number (k), we can use the equation:
wave number = 2π / wavelength
Substituting the given values, we get:
wave number = 2π / 0.4 m = 15.708 rad/m (rounded to three decimal places)
Therefore, the wave number of the wave is approximately 15.708 rad/m.
(b) The wave function for a transverse wave on a string is given by:
y(x, t) = A sin(kx - ωt + φ)
where A is the amplitude, k is the wave number, x is the position of the point on the string, t is the time, ω is the angular frequency, and φ is the phase constant.
We already know the values of A, k, and ω from the previous calculations. To find φ, we can use the given initial condition: "at t = 0 end of the string has zero displacement and is moving upward". This means that y(0,0) = 0 and ∂y/∂t(0,0) > 0. Substituting these conditions into the wave function, we get:
0 = A sin(0 + φ)
∂y/∂t = -Aω cos(0 + φ)
Since sin(0 + φ) = sin(φ) = 0 (because sin(0) = 0), we get:
φ = nπ, where n is an integer
Since cos(0 + φ) = cos(φ) = 1 (because cos(0) = 1) and ∂y/∂t(0,0) > 0, we get:
n = 0 or 2
Therefore, the possible values of φ are 0 or 2π.
Substituting the values of A, k, ω, and φ, we get:
y(x, t) = 0.05 sin(15.708x - 94.248t)
Therefore, the wave function describing the wave is:
y(x, t) = 0.05 sin(15.708x - 94.248t)
(c) To find the transverse displacement of a wave at x = 0.25 m and t = 0.15 s, we can use the wave function we just found:
y(0.25, 0.15) = 0.05 sin(15.708(0.25) - 94.248(0.15))
y(0.25, 0.15) ≈ -0.013 m (rounded to three decimal places)
Therefore, the transverse displacement of the wave at x = 0.25 m and t = 0.15 s is approximately -0.013 m.
(d) To find how much time must elapse from the instant in part (c) until the point at x = 0.25 m has zero displacement,
From part (c), we know that the transverse displacement of the wave at x = 0.25 m and t = 0.15 s is approximately -0.013 m. We need to find the time it takes for this point to return to zero displacement.
We can use the wave function we found in part (b) and set y(0.25, t) = 0:
0 = 0.05 sin(15.708(0.25) - 94.248t)
Since sin(θ) = 0 when θ = nπ (where n is an integer), we get:
15.708(0.25) - 94.248t = nπ
Solving for t, we get:
t = (15.708(0.25) - nπ) / 94.248
To find the smallest positive value of t that satisfies this equation, we need to use the smallest positive value of n that makes the right-hand side of the equation positive (because we want to find the time it takes for the point at x = 0.25 m to return to zero displacement, which happens after the point has completed a full cycle). We can see from the equation that n must be an even integer to make the right-hand side positive. The smallest even integer greater than zero is 2. Substituting n = 2, we get:
t = (15.708(0.25) - 2π) / 94.248
t ≈ 0.297 s (rounded to three decimal places)
Therefore, the time it takes for the point at x = 0.25 m to return to zero displacement is approximately 0.297 s.
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You are investigating an accident that occurred early on a foggy morning in Oxfordshire. A 2015 Prius Hatchback traveling due north collided in a highway intersection with a 2012 Nissan Pathfinder that was traveling due east. After the collision, the wreckage of the two vehicles was locked together and skidded across the level ground until it struck a tree. You measure that the tree is 11 m from the point of impact. The line from the point of impact to the tree is in a direction 39∘ north of east. From experience, you estimate that the coefficient of kinetic friction between the ground and the wreckage is 0.45. Shortly before the collision, a police officer with a laser speed gun measured the speed of the Prius to be 80 km/h and, according to a witness, the Prius driver made no attempt to slow down. Four people with a total mass of 230 kg were in the Nissan. The only person in the Prius was the 80 kg driver. The Nissan with its passengers had a mass of 2362 kg , and the Prius with its driver had a mass of 1460 kg .
The given and calculated values: force_impact = (0 - 32,488.4 kg*m/s) / 1.34 s = -24,277.6 N The negative sign indicates that the force is in the opposite direction to the motion, which is consistent with the wreckage coming to a stop.
What does the restoring force's negative value mean?The negative sign informs us that the restoring force is acting in the direction that is opposed to the distortion. For instance, when a spring is stretched, the restoring force pulls in the opposite way. When a spring is compressed, the restoring force pulls against the compression's direction.
We employ the following formula to determine the power of friction:
f_friction = friction coefficient * normal force
normal force = (1460 kg + 2362 kg + 230 kg) * 9.8 m/s^2 = 38,496.4 N
So the force of friction is:
f_friction = 0.45 * 38,496.4 N = 17,323.4 N
momentum_before = (mass_Prius * velocity_Prius) + (mass_Nissan * velocity_Nissan)
Substituting the given values:
momentum_before = (1460 kg * 22.22 m/s) + (2362 kg * 0 m/s) = 32,488.4 kg*m/s
momentum_after = (mass_Prius + mass_Nissan + 230 kg) * velocity_final
Substituting the given values:
32,488.4 kg*m/s = (1460 kg + 2362 kg + 230 kg) * velocity_final
velocity_final = 11.06 m/s
To calculate the force of the impact, we use the formula:
force_impact = (momentum_after - momentum_before) / time
distance = √((11 m)² + (11 m / tan(39°))) = 14.86 m
Assuming the wreckage was traveling at a constant speed during the skid, we can estimate the time as:
time = distance / velocity_final = 1.34 s
Substituting the given and calculated values:
force_impact = (0 - 32,488.4 kg*m/s) / 1.34 s = -24,277.6 N
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