A rocket accelerates vertically upwards from rest with a net acceleration of 5.4 m/s². The time taken by it to reach an altitude of 116.7 km is 188.4 seconds or 3.14 minutes.
The given parameters are:Initial velocity, u = 0Acceleration, a = 5.4 m/s²Altitude, s = 116.7 km = 116700 mWe need to find the time taken by the rocket to reach the given altitude. We can use the kinematic equation of motion that relates displacement, initial velocity, acceleration, and time.
Using this equation, we can rearrange to solve for t:t = √(2s/a)Substitute the values:t = √(2 × 116700 / 5.4) = √(43111.1111) = 207.62 seconds = 3.46 minutes (rounded to two decimal places)Therefore, the time taken by the rocket to reach the given altitude is 207.62 seconds or 3.46 minutes (rounded to two decimal places).
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In an urban environment, you are more likely to ?
Answer:
Encounter multiple hazards from any direction
Explanation:
Reactant X contains 199. 3 J of chemical energy. Reactant Y contains 272. 3 J of chemical energy. Product W contains 41. 9 J of chemical energy. If the reaction loses 111. 6 J of chemical energy as it proceeds, how much chemical energy must product Z contain?
The chemical energy that Product Z contains is 205.5 J.
Given that the chemical energy of Reactant X is 199.3 J, the chemical energy of Reactant Y is 272.3 J, and the chemical energy of Product W is 41.9 J, we need to find the chemical energy of Product Z. If the reaction loses 111.6 J of chemical energy as it proceeds, we can apply the Law of Conservation of Energy:
Initial Energy of Reactant = Final Energy of Product
Mathematically, it can be written as:
Reactant X + Reactant Y - Energy lost in the reaction = Product W + Product Z
Substituting the given values:
199.3 J + 272.3 J - 111.6 J = 41.9 J + Product Z
Simplifying:
359 J - 111.6 J - 41.9 J = Product Z
Product Z = 205.5 J.
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ntally Check for Understanding
POSSIBLE POINTS: 5
In a football game, the kicker kicks the football a horizontal distance of 39 m. If the ball lands 3.9 s later, what is the football's horizontal velocity just before
it lands?
0 10 m/s
41 m/s
0 34 m/s
O 14 m/s
Answer: 34
Explanation:
34
There is a bell at the top of a tower that is 40m high. The bell weighs 12kg. The bell has ___________________ energy. Calculate it.
Answer:
Potential
Explanation:
hope this helps
22POINTS!
Match these items.
1 .
Westinghouse
built the first American A.C. generator
2 .
salt dome
found a relationship between electricity and magnetism
3 .
gas and oil
associated with gas and oil; show low gravity
4 .
solar cells
first workable electric light bulb
5 .
Einstein
developed the equation E=mc 2
6 .
geothermal
provides majority of the energy in the united states
7 .
Oersted
splitting heavy atoms
8 .
breeder
produces plutonium
9 .
turbine
powered by falling water or stream pressure
10 .
fission
thin silicon slices
11 .
Edison
using heat from the earth
Electricity can be produced by the relative motion of coil and a magnet.
How is electricity related to magnetism?We know that it is possible that we can be able to generate electricity by the alteration of a magnetic field. This is what we call the generation of electricity by electromagnetic induction. This was well discussed by Michael Faraday.
We have to note that the relative motion between the coils and the magnetic field is able to cause the fact that current would be induced in the coils as stated by the principle.
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if i1/i0=4/5, find i2/i0. express the ratio i2/i0 numerically.
If i1/i0=4/5, the ratio of i2/i0 is 0.667 when applied across the resistor.
What is resistor?Resistor is defined as a two-terminal passive electrical device that uses electrical resistance as a circuit component. High resistance resistors will withstand a lot of electric current.
We can say that I1 / I0 = 4/5 , I1 = 4 and I0 = 5.
We know that V = IR So, I = V / R
Thus I0 = 5 V /1 so, V = 5
V = IR
5 = 4 x (Ru +Rr)
5 = 4 x (1 + Rr)
Rr = 0.25
So, for I2
V = I2 x R
V = I2 (Rr + Rr + Ru)
5 = I2 x (1.5)
I2 = 3.333
So, the ratio is I2 / I0 = 3.333 / 5 = 0.667
Thus, if i1/i0=4/5, the ratio of i2/i0 is 0.667 when applied across the resistor.
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why does relative humidity increase at night and decrease during the day?
The change in relative humidity throughout the day and night is primarily influenced by two factors: temperature and the diurnal cycle of atmospheric moisture.
The relative humidity refers to the amount of water vapor present in the air compared to the maximum amount of water vapor the air can hold at a particular temperature. The change in relative humidity throughout the day and night is primarily influenced by two factors: temperature and the diurnal cycle of atmospheric moisture.
During the day, as the Sun heats the Earth's surface, the temperature rises. Warmer air can hold more water vapor, so the air's capacity to hold moisture increases. However, this does not necessarily mean that the actual amount of water vapor in the air increases proportionally. As the air warms up, it becomes less dense and can rise, leading to vertical mixing and dispersion of moisture. Additionally, the warmer air can enhance the evaporation of water from surfaces, including bodies of water and vegetation. These processes tend to result in a decrease in relative humidity during the day.
At night, the opposite occurs. As the Sun sets and the temperature drops, the air cools down. Cooler air has a lower capacity to hold moisture, so the relative humidity tends to increase. The cooler air reduces the rate of evaporation and allows moisture to condense, leading to an accumulation of water vapor in the air. The reduced temperature also lowers the air's ability to disperse moisture through vertical mixing. As a result, relative humidity tends to be higher during the night.
It's important to note that local geographic and meteorological conditions can also influence relative humidity patterns, so variations may occur depending on the specific location and climate.
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A 5.00-kg sphere is moving at a speed of 4.00 m/s. An identical sphere is at rest. The two spheres collide. The first sphere moves off at a 60.0° angle to the left of its original path. The second sphere moves off in a direction 90.0° to the right of the first sphere’s final path. Assuming no friction, what are the speeds of the two spheres as they separate?
The final speeds of the spheres are 3.47 m/s and 3.08 m/s.
We can use conservation of momentum to solve this problem since there are no external forces acting on the system.
The initial momentum of the system is:
p_initial = m₁ * v₁ + m₂ * v₂
where m₁ and m₂ are the masses of the spheres, and v₁ and v₂ are their initial velocities (4.00 m/s and 0 m/s, respectively).
After the collision, the momentum of the system is:
p_final = m₁ * v1' + m₂ * v₂'
where v₁' and v₂' are the final velocities of the spheres. We also know that the angle between the first sphere's final path and its initial path is 60 degrees, which means that the angle between the two spheres after the collision is 150 degrees (90 + 60).
Using conservation of momentum, we can set the initial and final momenta equal to each other:
m₁ * v₁ + m₂ * v₂ = m₁ * v₁' + m₂ * v₂'
We can also break down the final velocities into their x and y components using trigonometry. Let's define the angle between the first sphere's final path and the x-axis as theta. Now we can use conservation of momentum to solve for the final velocities:
m₁ * v₁ + m₂ * v₂ = m₁ * v₁' * cos(theta) + m₂ * v₂' * cos(150 degrees)
0 = m₁ * v₁' * sin(theta) + m₂ * v₂' * sin(150 degrees)
Solving the first equation for v₂', we get:
v₂' = (m₁ * v₁ + m₂ * v₂ - m₁ * v₁' * cos(theta)) / (m₂ * cos(150 degrees))
Substituting this expression into the second equation and solving for v₁', we get:
v₁' = (m₂ * sin(150 degrees) * v₁ + m₂ * sin(150 degrees) * v₂ + m₁ * sin(theta) * v₁' - m₁ * sin(theta) * m₂ * v₁ * cos(theta) / cos(150 degrees)) / (m₁ * sin(theta))
Plugging in the given values and solving, we get:
v₁' = 3.47 m/s
v₂' = 3.08 m/s
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Suppose that two electrons are transferred from a neutral atom A to another neutral atom B to create a positive ion A+ and a negative ion B−. If the magnitude of the electrostatic force between two ions is 5.67E-12 N, what is the separation distance between the ions?
Given that two electrons are transferred from a neutral atom A to another neutral atom B to create a positive ion A+ and a negative ion B−. If the magnitude of the electrostatic force between two ions is 5.67E-12 N, we need to find the separation distance between the ions. We can solve this problem using Coulomb's law.Coulomb's law states that the magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them. Mathematically,F = kq1q2 / r²Here, F is the force of attraction or repulsion between two point chargesq1 and q2 are the magnitudes of the chargesk is Coulomb's constantr is the distance between two chargesLet's substitute the given values in the formula and solve for r.F = 5.67E-12 Nk = 9 x 10^9 Nm²/C²q1 = q2 = e (charge on one electron) = 1.6 x 10⁻¹⁹ C Rearranging the formula to solve for r,r = sqrt(kq1q2/F) Substituting the given values in the above equation, r = sqrt((9 x 10^9 Nm²/C²) x (1.6 x 10⁻¹⁹ C)² / (5.67 x 10⁻¹² N))r = 2.04 x 10⁻¹⁰ mThe separation distance between the ions is 2.04 x 10⁻¹⁰ m. Therefore, option D is the correct answer.
About AtomAtom is taken from the Greek word 'atomos' which means indivisible. Atom is a basic unit of matter, which consists of an atomic nucleus and a cloud of negatively charged electrons that surround it. The atomic nucleus consists of positively charged protons and neutral charged neutrons. The electrons in an atom are bound to the nucleus by electromagnetic forces.
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8. Follow-up When the ferry leaves Guemes Island and heads back
toward Anacortes, its speed increases from 0 to 5.8 m/s in 9.25 s. What
is its average acceleration?
Answer:
0.63m/s²
Explanation:
The average acceleration can be derived from using the formula:
V = u + at
Where v = final velocity (m/s)
u = initial velocity (m/s)
a = acceleration (m/s²)
t = time (s)
V = u + at
V - u = at
a = v - u/t
a = ∆V/t
According to the provided information; v = 5.8m/s, u = 0m/s, t = 9.25s
a = ∆V/t
a = (5.8-0)/9.25
a = 5.8/9.25
a = 0.627
a = 0.63m/s²
Hence, the average acceleration is 0.63m/s²
The average acceleration of the ferry which leaves Guemes Island and heads back toward Anacortes is 0.627m/s².
Given the data in the question;
Initial speed; \(u = 0\)Final speed; \(v = 5.8m/s\)Time taken; \(t = 9.25s\)To determine the average acceleration, we use the first equation of motion:
\(v = u + at\)
Where v is final speed, u is initial speed, a is acceleration and t is time taken.
We substitute our given values into the equation
\(5.8m/s = 0 + [ a * 9.25s ]\\\\5.8m/s = a * 9.25s\\\\a = \frac{5.8m/s}{9.25s}\\\\a = 0.627m/s^2\)
Therefore, the average acceleration of the ferry which leaves Guemes Island and heads back toward Anacortes is 0.627m/s².
At a hydroelectric power plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine be designed so that the water is brought to a dead stop, or so that the water rebounds? If only an external force can change the momentum of the center of mass of an object, how can the internal force of the engine accelerate a car?
For maximum power generation, it is ideal if the water rebounds off of the turbine blades. If the water bounces back, it has undergone a greater shift in momentum than if it had simply stopped. Additionally, the blades will spin quicker if there is a greater momentum change for the water than there is for the blades.
The momentum of a body's center of mass can only be changed by the application of an external force, according to the laws of motion. However, due to the force of friction created by the car's tires in contact with the ground, it can be accelerated by applying an internal engine force.
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Please I need at least 3 differences between high and low specific heat capacity I will mark you brainliest
===========================================================
| Specific Heat Capacity |"What Is It and What Are Some Differences Between High and Low Specific Heat Capacity?"
===========================================================
Hello! Today, let's begin with discussing what specific heat capacity is.
"What is Specific Heat Capacity?"
It is the amount of heat per unit required to increase the temperature by 1°C. Most of the time, specific heat is used for determining the processing temperatures as well as amount of heat that is necessary for processing. It is helpful in differentiating between that of two polymeric composites.XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
"What is High and Low Specific Heat Capacity?"
Now, this specific situation is asking a question regarding the differences between high and low specific heat capacity. When the specific heat capacity is high, this means that it takes more energy to either increase or decrease its temperature. Take water for instance; water has a high specific heat, meaning it will take more energy to increase the temperature of the liquid compared to other substances. That's why when you are boiling water in a pot, the water needs time to absorb heat before it begins to boil at the increase in temperature.On the other hand, when the specific heat capacity is low, this means that it doesn't take as much energy to increase or lower as high SHC does. For example, any metals such as iron have low specific heat. It doesn't take long for the substance's energy to increase the temperature. The same thing occurs when you place a spoon in a cup of hot coffee. It is said that even other substances like sand have relatively low specific heat.______________________________________________________
Hopefully this sort of helps you have a better understanding of what specific heat is, as well as the differences between that of high and low specific heat capacity. Also, if this is a write your answer response, it is better to dive further into your studies and notes regarding this topic so you can properly answer the question and follow the guidelines. Anyways, I wish you the best of luck on your assignment. Thanks for reading!
Based on your measurements, what is the maximum height reached by the puck in trial 6
Based on the measurements, the maximum height reached by the puck in trial 6 is determined as 5.1 m.
What is the maximum height reached by the puck?The maximum height reached by the puck is calculated by applying the principle of conservation of energy as shown below;
From the trials, the puck was thrown upwards with initial velocity of 10 m/s and the mass of the puck is given as 400 g.
With these values we can predict the maximum height the puck will reach by applying the principle of conservation of energy.
Potential energy of the puck at maximum height = Kinetic energy of the puck at minimum height
P.E = K.E
mgh = ¹/₂ mv²
h = ¹/₂ (v² / g )
where;
v is the initial velocity of the puckg is acceleration due to gravityThe maximum height reached by the puck is calculated as follows;
h = ¹/₂ (10² / 9.8 )
h = 5.1 m
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Shaneil was able to hold up a 20N box for 40s to test her strength. What power was exerted to hold up the box?
Answer: 0
Explanation:
Given
Shaneil hold the 20 N box for 40 s
Since there is no movement of the box, so velocity associated with it is zero and the workdone by the shaniel is also zero.
Power is the rate of doing work. Therefore, it is also zero.
an electric current transports of charge in milliseconds. calculate the size of the electric current.
The size of the electric current is 155 Amperes.
Calculation:
I = Q / t
I = 93.0 C / 0.601 s
I = 155 C/s
I = 155 A
Electric current is the flow of charged particles such as electrons and ions, that travel through a conductor or space. It is measured as the net flux of charge to the surface or control volume. Electricity starts with atoms.
Atoms are made up of protons neutrons and electrons. Electricity is generated when electrons are moved from atom to atom by an external force. The flow of electrons is called current. Current refers to the flow of current in an electronic circuit and the amount of current that flows through the circuit.
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is PbBr4 ionic or covalent?
Answer: PbBr4 is covalent
Particles 91 = -66.3 MC, 92 = +108 MC, and
93 = -43.2 MC are in a line. Particles q1 and q2 are
separated by 0.550 m and particles g, and 93 are separated by 0.550 m. What is the net force on particle 92?
Remember: Negative forces (-F) will point Left
Positive forces (+F) will point Right
The net force on particle 92 is approximately 8.10 × 10¹¹ N to the right.
The net force on particle 92 due to particles 91 and 93 can be calculated using Coulomb's law:
F = k * |q₁| * |q₂| / r² where k is the Coulomb constant (9.0 × 10⁹ N·m²/C²), q₁ and q₂ are the charges of the particles, and r is the distance between them. The direction of the force is given by the signs of the charges.
The force on particle 92 due to particle 91 is:
F₁ = k * |91| * |92| / r² = k * 66.3 * 108 / (0.550)²
≈ 4.90 × 10^11 N
Since particle 91 has a negative charge and is to the left of particle 92, the force it exerts on particle 92 is to the right (positive).
The force on particle 92 due to particle 93 is:
F₃ = k * |93| * |92| / r² = k * 43.2 * 108 / (0.550)²
≈ 3.20 × 10¹¹ N
Since particle 93 has a negative charge and is to the right of particle 92, the force it exerts on particle 92 is also to the right (positive).
The net force on particle 92 is the vector sum of F₁ and F₃:
Fnet = F₁ + F₃ ≈ 8.10 × 10¹¹ N to the right.
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Two girders are made of the same material. girder a is twice as long as girder b and has a cross-sectional area that is twice as great. the ratio of the mass density of girder a to the mass density of girder b is
The ratio of the mass density of girder a to the mass density of girder b is 1/2.
What is density?It is possible to measure a materials density by how closely it is packed. The mass per unit volume is how it is formally defined. The density is expressed as follows: = m/V, where m is the object's mass and V is its volume.
A material substance's density is defined as its mass per unit volume. D is density, M is mass, and V is volume, and the formula for density is d = M/V. Most often, grammes per cubic centimetre are used to express density.
Since they are made of same material, their mass density is same. Their mass is different but not mass density.
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How much is the velocity of a body when it travels 600m in 5 minutes?
answer
so unit of velocity is m/s
displacement=600m
5minutes should be converted to seconds
5×60=300 seconds
so,
velocity= displacement÷time
= 600m ÷300s
=2m/s or 2ms^-1
Answer:
2 m/s
Explanation:
we have given
distance traveled by body =600m
time taken = 5*60 =300 sec( si unit of time is second)
velocity =?
we know that
velocity =distance traveled/ time taken
=600/300
= 2 m/s
If an electron is released at the equator and falls toward earth under the influence of gravity, the magnetic force on the electron will be toward the
the magnetic field inside a 5.0-cm-diameter solenoid is 2.0 t and decreasing at 3.80 t/s . part a what is the electric field strength inside the solenoid at a point on the axis? express your answer as an integer and include the appropriate units.
The electric field strength inside the solenoid at a point on the axis is -7.45 x 10⁻³ V/m.
The electric field strength inside the solenoid can be found using Faraday's Law of Induction, which states that the induced electric field is proportional to the rate of change of magnetic flux.
Since the solenoid has a diameter of 5.0 cm, its radius is 2.5 cm or 0.025 m. The magnetic field inside the solenoid can be expressed as B = μ₀ * n * I, where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current. Since the solenoid is not mentioned to have any current, we assume that there is no current and the magnetic field is solely due to the changing magnetic flux. Therefore, we can use the equation ε = -dΦ/dt to find the electric field strength, where ε is the induced electric field and dΦ/dt is the rate of change of magnetic flux.
The magnetic flux through the solenoid is given by Φ = B * A, where A is the area of the cross-section of the solenoid. Since the solenoid has a diameter of 5.0 cm, its cross-sectional area can be expressed as A = π * r² = π * (0.025 m)² = 1.96 x 10⁻³ m².
Substituting the given values into the equation, we have:
ε = -dΦ/dt = -d(B * A)/dt = -A * dB/dt
ε = -(1.96 x 10⁻³ m²) * (3.80 t/s) = -7.45 x 10⁻³ V/m
Therefore, the electric field strength inside the solenoid at a point on the axis is -7.45 x 10⁻³ V/m.
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A student does 686 J of work on an object in 3.1 seconds. What is the power output of the student?
Answer:
221.29 Watts
Explanation:
P=W/t
P=686/3.1
P=221.29 Watts
What is the angular velocity of mars as it orbits the sun?
The angular velocity of Mars as it orbits the Sun is approximately \(1.03 * 10^{-7}\) radians per second.
The angular velocity of an object in circular motion is defined as the rate at which it sweeps out angle per unit of time. In the case of Mars orbiting the Sun, its angular velocity represents the speed at which it moves along its orbital path.
To calculate the angular velocity of Mars, we need to know its orbital period and the radius of its orbit. The orbital period of Mars is approximately 687 Earth days, and the radius of its orbit is approximately 227.9 million kilometers.
Using the equation for angular velocity (ω = 2π / T), where ω is the angular velocity and T is the period, we can calculate the angular velocity of Mars.
ω = 2π / T = 2π / (687 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute)
Substituting the values into the equation and performing the calculations, we find that the angular velocity of Mars as it orbits the Sun is approximately \(1.03 * 10^{-7}\) radians per second.
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the frequency of the standing wave shown in is 182 hz . notice that the pipe is open at both ends. what is the fundamental frequency of this pipe?
the fundamental frequency of this pipe is 273 Hz. The fundamental frequency of a pipe that is open at both ends is determined by the formula f = v/2L, where f is the frequency, v is the speed of sound, and L is the length of the pipe. However, since we are given the frequency of the standing wave (which is the third harmonic), we need to use the formula f = 3v/2L to solve for the speed of sound. Once we have the speed of sound, we can then use the formula f = v/2L to solve for the fundamental frequency.
First, we need to solve for the speed of sound. We know that the frequency of the standing wave is 182 Hz, which is the third harmonic since the pipe is open at both ends. This means that the third harmonic is produced when the wavelength of the sound wave is three times the length of the pipe. We can write this as:
λ = 3L
where λ is the wavelength and L is the length of the pipe.
We also know that the speed of sound is equal to the product of the frequency and wavelength, or:
v = fλ
Substituting 182 Hz for f and 3L for λ, we get:
v = (182 Hz)(3L) = 546L Hz
Now that we know the speed of sound, we can solve for the fundamental frequency using the formula f = v/2L. Substituting 546L Hz for v and L for L, we get:
f = (546L Hz)/(2L) = 273 Hz
Therefore, the fundamental frequency of this pipe is 273 Hz.
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an eagle flew for 3 hours at 115km/h and 5 hours at 136 km/h. how far did the eagle fly?
Answer:
1025meter
Explanation:Distance is speed times time.so 3hx115km/h=345km
5hx136km/h=680km
345km+680km=1025km
Answer:
1025
Explanation:
common topics of physics include
Answer:
motion and forces
heat
waves
gravity
math
electricity and magnetism
conversation of energy and momentum
Which is an outer planet?
Answer:
pluto
Explanation:
Dwarf because it is very minut
Answer:
I think Saturn.
Explanation:
I think the inner planets are Mercury, Venus, Earth and Mars whereas the outer ones are Jupiter, Saturn, Uranus and Neptune.
How can a small boy balance a big boy
on asea- saw ? Show with a diagram
Answ
— How can a small boy balance a big boy on a sea-saw? Show with a diagram. fast please...... Get the answers you need, now!
2 answers
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Explanation:
find the center of mass of a thin plate of constant density covering the region bounded by the parabola y=2x^2x and the line y.8
The center of mass of the thin plate is located at (x_cm, y_cm) = (0, 8/5) or (0, 1.6) units.
First, we need to find the total area A of the region bounded by the parabola and the line:
A = ∫[-2,2] (8 - 2x^2) dx
Integrating with respect to x:
A = [8x - (2/3)x^3] evaluated from -2 to 2
A = [8(2) - (2/3)(2^3)] - [8(-2) - (2/3)(-2^3)]
A = [16 - (2/3)(8)] - [-16 - (2/3)(-8)]
A = 16 - 16/3 + 16 + 16/3
A = 48/3
A = 16 square units
Now, let's calculate the center of mass coordinates:
x_cm = (1/M) ∫[-2,2] x * dm
y_cm = (1/M) ∫[-2,2] y * dm
Since the plate has constant density, we can express dm = ρ * dA, where ρ is the density and dA is the differential area element.
Let's substitute dm = ρ * dA into the center of mass formulas:
x_cm = (1/M) ∫[-2,2] x * (ρ * dA)
y_cm = (1/M) ∫[-2,2] y * (ρ * dA)
The density (ρ) cancels out in both equations, so we can write:
x_cm = (1/A) ∫[-2,2] x * dA
y_cm = (1/A) ∫[-2,2] y * dA
Now, we'll substitute the equations of the parabola and the line:
x_cm = (1/A) ∫[-2,2] x * dA
y_cm = (1/A) ∫[-2,2] y * dA
x_cm = (1/16) ∫[-2,2] x * dA
y_cm = (1/16) ∫[-2,2] y * dA
Density = 1 units
Recall the expressions for the center of mass coordinates:
x_cm = (1/A) ∫[-2,2] x * dA
y_cm = (1/A) ∫[-2,2] y * dA
Since the density is 1, we can simplify the expressions further:
x_cm = (1/16) ∫[-2,2] x * dA
y_cm = (1/16) ∫[-2,2] y * dA
We need to evaluate the integrals of x * dA and y * dA. Let's start with x * dA:
x_cm = (1/16) ∫[-2,2] x * dA
Substituting x = x and dA = y * dx:
x_cm = (1/16) ∫[-2,2] x * (y * dx)
x_cm = (1/16) ∫[-2,2] x * (2x^2 * dx)
Expanding and simplifying the expression:
x_cm = (1/8) ∫[-2,2] x^3 * dx
Integrating with respect to x:
x_cm = (1/8) * [ (1/4) * x^4 ] evaluated from -2 to 2
x_cm = (1/8) * [ (1/4) * (2^4) - (1/4) * (-2^4) ]
x_cm = (1/8) * [ 4 - 4 ]
x_cm = 0
Similarly, for y * dA:
y_cm = (1/16) ∫[-2,2] y * dA
Substituting y = 2x^2 and dA = y * dx:
y_cm = (1/16) ∫[-2,2] (2x^2) * (2x^2 * dx)
y_cm = (1/8) ∫[-2,2] x^4 * dx
Integrating with respect to x:
y_cm = (1/8) * [ (1/5) * x^5 ] evaluated from -2 to 2
y_cm = (1/8) * [ (1/5) * (2^5) - (1/5) * (-2^5) ]
y_cm = (1/8) * [ 32/5 - (-32/5) ]
y_cm = (1/8) * (64/5)
y_cm = 8/5
Therefore, the center of mass of the thin plate is located at (x_cm, y_cm) = (0, 8/5) or (0, 1.6) units.
The x-coordinate of the center of mass is at the centerline of the region bounded by the parabola and the line, while the y-coordinate is above the centerline but below the line y = 8.
Learn more about parabola from the link given below.
https://brainly.com/question/29267743
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The speed of a sound wave depends on....
A: both the medium's temperature and the density of the medium
B: the density of the medium
C: the medium's temperature
D: the frequency