Answers
Answer:
The speed is \(v = 9.8 \ m/s\)
Explanation:
From the question w are told that
The angle made is \(\theta = 30^o\)
The distance above the surface of the water is \(h_{max} = 1.2 \ m\)
The value of \(g = 10 \ m/s^2\)
The maximum height attained by the fish is mathematically evaluate as
\(h_{max} = \frac{v^2 sin ^2 \theta }{2g }\)
Making v which is the speed of the fish the subject of the formula
\(v = \sqrt{ \frac{2gh_{max}}{ sin^2 \theta } }\)
substituting values
\(v = \sqrt{ \frac{2*10 *1.2 }{ [sin (30)]^2 } }\)
\(v = 9.8 \ m/s\)
Related Questions
Kevin takes his dog out for a walk every day after work. He parks his car behind his home and uses the back door to get in. His dog waits for him every afternoon by the back door, knowing that Kevin will take him for a walk when he returns from work. Kevin's wife usually uses the front door to get in and out of the house. However, one afternoon, Kevin's wife arrives from work early and decides to home into the house using the back door. As she starts opening the back door, the dog starts running around like crazy, thinking its time for his walk. In this scenario, the CR is
Answers
Answer:
In this scenario, the CR (conditioned response) is the dog's behavior of running around like crazy upon hearing the sound of the back door opening. This behavior has been conditioned by the repeated pairing of the back door opening with Kevin taking the dog for a walk. The dog has learned to associate the sound of the back door opening with the upcoming walk, which causes the conditioned response of excitement and anticipation.
Explanation:
The conditioned response (CR) in this scenario is the dog running around like crazy when Kevin's wife starts opening the back door. The dog has learned to associate Kevin's return from work with going for a walk, and the sound of the back door opening has become a conditioned stimulus (CS) that elicits the CR of excitement and anticipation for the walk. When Kevin's wife opens the back door, the dog responds with the same CR, even though it's not Kevin returning from work.
Select ALL the
correct answers.
Which two examples describe ways that corporations can give large donations to presidential candidates?
A corporation leader makes
direct payment to the candidate.
A corporation creates another company to accept candidate contributions
A corporation collects moneys from its employees to contribute to
A corporation contributes to a Super PAC that
a PAC
accepts contributions
for a candidate,
Reset
Next
Answers
Answer: Hope this helps ;) don't forget to rate this answer !
Explanation:
There are two correct answers:
A) A corporation leader makes direct payment to the candidate.
D) A corporation contributes to a Super PAC that a PAC accepts contributions for a candidate.
Option A describes a scenario where a corporation directly donates money to a presidential candidate, which is allowed as long as it is done within the limits set by campaign finance laws.
Option D describes a scenario where a corporation donates money to a Super PAC, which is a type of political action committee that can accept unlimited donations from individuals, corporations, and other organizations. The Super PAC can then use the money to support or oppose a particular candidate, but it is not allowed to coordinate directly with the candidate or the candidate's campaign.
I hope this helps! Let me know if you have any other questions.
11. How can you determine if there is net force acting
on an
object?
Answers
Answer:
Explanation:
Sum all the forces that are acting on the object and what ever the sum is, is what the net force is.
For example if there is a piece of wood sitting on a table the net force would be the sum of the forces that are acting on it, so the force of gravity (which is negative) + the normal force which would equal zero because they are the same value.
The force of gravity on a person or object on the surface of a planet is called
A. gravity
ОВ.
B. free fall
OC
c. terminal velocity
D. weight
Answers
Answer:
D. Weight
Explanation:
Hope that helps:)
HOPE IT HELPS U!!!!!!
A baseball accelerates at 15m/s2, changing its velocity from 0m/s to 50 m/s down the way. How long did it take the baseball to accelerate?
Answers
Answer:
3.33s
Explanation:
Given parameters:
Acceleration = 15m/s²
Initial velocity = 0m/s
Final velocity = 50m/s
Unknown:
Time taken for the acceleration = ?
Solution:
To solve this problem, we must understand that acceleration is the rate of change of velocity with time.
Mathematically;
a = \(\frac{v - u}{t}\)
a is the acceleration
v is the final velocity
u is the initial velocity
t is the time taken
So;
15 = \(\frac{50 - 0}{t}\)
15t = 50
t = 3.33s
A puffin accidentally drops a 0.3 kg fish from a height of 9 meters. What is the fish's GPE (in J) from this height?
Answers
Answer:
Therefore, the GPE of the fish from the given height is 26.19 J.
Explanation:
The gravitational potential energy (GPE) of an object at a height h is given by the formula:
GPE = mgh
where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.
In this case, the mass of the fish is 0.3 kg, the height from which it was dropped is 9 meters, and the acceleration due to gravity on Earth is approximately 9.81 m/s². Thus, the GPE of the fish can be calculated as:
GPE = (0.3 kg) × (9.81 m/s²) × (9 m) = 26.19 J
Therefore, the GPE of the fish from the given height is 26.19 J.
I like puffins
1) Which of the following is considered an effective treatment for someone with hearing loss based on nerve damage?
TAD
Cochlear implant
Hearing aid
OBI
No treatment available
2) Sylvester is dealing with hearing loss. The doctor informs him that his basilar membrane is damaged. What type of hearing loss is Sylvester experiencing?
Nerve deafness
Conduction hearing loss
Cochlear hearing loss
Conduction deafness
Sensory hearing loss
Answers
Answer:
For number 1 no treatment available , number 2 cochlear hearing loss
Explanation:
nerve damage is permanent
A crate with a mass of 35.0 kg is pushed with a horizontal force of 150 N. The crate moves at a constant speed across a level, rough surface a distance of 5.85 m
Answers
(a) The work done by the 150 N force is 877.5 Joules.
(b) The coefficient of kinetic friction between the crate and the surface is approximately 0.437.
To answer this problem, we must take into account the work done by the applied force as well as the work done by friction.
(a) The applied force's work may be estimated using the following formula:
Work = Force * Distance * cos(theta)
where the force is 150 N and the distance is 5.85 m. Since the force is applied horizontally and the displacement is also horizontal, the angle theta between them is 0 degrees, and the cosine of 0 degrees is 1.
As a result, the applied force's work is:
Work = 150 N * 5.85 m * cos(0) = 877.5 J
So, the work done by the 150 N force is 877.5 Joules.
(b) Frictional work is equal to the force of friction multiplied by the distance. The work done by friction is identical in amount but opposite in direction to the work done by the applied force since the crate travels at a constant speed.
The frictional work may be estimated using the following formula:
Work = Force of Friction * Distance * cos(theta)
The net force applied on the crate is zero since it is travelling at a constant pace. As a result, the friction force must be equal to the applied force, which is 150 N.
Thus, the work done by friction is:
Work = 150 N * 5.85 m * cos(180) = -877.5 J
Since the work done by friction is negative, it indicates that the direction of the frictional force is opposite to the direction of motion.
The coefficient of kinetic friction may be calculated using the following equation:
Friction Force = Kinetic Friction Coefficient * Normal Force
The normal force equals the crate's weight, which may be computed as:
Normal Force = mass * gravity
where the mass is 35.0 kg and the acceleration due to gravity is approximately 9.8 m/s^2.
Normal Force = 35.0 kg * 9.8 m/s^2 = 343 N
Now, we can rearrange the equation for the force of friction to solve for the coefficient of kinetic friction:
Force of Friction = coefficient of kinetic friction * Normal Force
150 N = coefficient of kinetic friction * 343 N
coefficient of kinetic friction = 150 N / 343 N ≈ 0.437
As a result, the kinetic friction coefficient between the container and the surface is roughly 0.437.
In summary, the work done by the 150 N force is 877.5 Joules, and the coefficient of kinetic friction between the crate and the surface is approximately 0.437.
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A car is moving at a constant speed along a straight line. Which statement is true about the forces acting on the car?
Answers
The statement that is true about the forces acting on the car is that the net force acting on the car from all directions is zero. Option A is correct.
What is force?Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body.
The complete question is
"A car is moving at a constant speed along a straight line. Which statement is true about the forces acting on the car?
A.
The net force acting on the car from all directions is zero.
B.
The net force acting on the car is greater than the car's weight.
C.
The net force acting on the car is in the direction of the car's motion.
D.
The net force acting on the car is in the opposite direction of the car's motion."
The net force operating on the automobile in all directions is zero,
The statement that is true about the forces acting on the car is that the net force acting on the car from all directions is zero. Option A is correct.
Hence option A is correct.
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When is the kinetic energy of an electron transformed into potential energy?
when it interacts with other electrons, decreasing its speed
when it interacts with neutrons without changing its speed
when it interacts with other electrons without changing its speed
when it interacts with neutrons, increasing its speed
Answers
The kinetic energy of an electron transformed into potential energy when it interacts with other electrons without changing its speed.
What is kinetic energy?The average kinetic energy (KE) is defined as the one-half of the mass of each gas molecule times multiplied by the square of RMS velocity.
\(\rm {KE = \frac{1}{2} mv^2}\)
where,
KE is the kinetic energy
m is the mass of each molecule
(V)rms is the RMS velocity
According to the law of conservation of energy, kinetic energy gets converted into potential energy. In that case, speed does not play a major role.
When an electron collides with the other electron Its energy gets transferred to the other electrons. The moving electrons get stuck and come to rest.
Hence the kinetic energy of an electron transformed into potential energy when it interacts with other electrons without changing its speed.
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As a person pushes a box across a floor, the energy from the person's moving arm is transferred to the box, and the box and the floor become warm. During this process, what happens to energy? It is increased. It is conserved. It is decreased. It is created.
Answers
Answer:
It is conserved
Explanation:
Converted to heat energy due to the friction caused by the box rubbing on the floor
Answer:
it is conserved
Explanation:
A golfer is attempting to reach the elevated green by hitting his ball under a low-hanging branch in one tree A, but over the top of a second tree B. If the launch speed of the golf ball is v0 = 115 mi/hr, what launch angle will put the first impact point of the ball closest to the pin? How far from the pin (distance d) is this impact point?
Answers
A golfer is attempting to reach the elevated green by hitting his ball under a low-hanging branch in one tree A, but over the top of a second tree B. If the launch speed of the golf ball is vo = 115 mi/hr, what launch angle 0 will put the first impact point of the ball closest to the pin. The first impact point of the ball closest to the pin will be approximately 407.5 ft from the launch point.
The equation for the range of a projectile is R = (V0² / g) * sin(2θ)The golfer has to hit the ball under a low-hanging branch in tree A and over the top of tree B to reach the elevated green.
Let's denote the distance between the golfer and the green as d. The range (R) of the projectile will equal the distance to the pin (d) if the ball lands at the same level as it was launched. If the ball has to land at a higher elevation than the launch point, the launch angle must be greater than the optimal angle that maximizes range.
Assuming the golfer is hitting from a horizontal surface (i.e. the ball is launched from the same level as the pin), the launch angle that will give the first impact point of the ball closest to the pin is 60°.At the launch angle of 60°, the distance to the pin (d) will be the range of the projectile (R).The velocity of the golf ball at launch is vo = 115 mi/hr.
The horizontal distance to the pin, which is the range of the projectile, is given by the equation;
R = (V0² / g) * sin(2θ)
where g = acceleration due to gravity = 32.2 ft/s² (let's convert the velocity to ft/s first)
vo = 115 mi/hr = 115 x 5280 ft/hr = 607200 ft/hr ≈ 168666.7 ft/hr
The initial velocity of the projectile, V0 = 168666.7 ft/hr. The optimal angle of launch is given by the equation:θ = 45° (for maximum range)The angle of launch required to achieve the shortest distance to the pin is 60°Let's substitute the values of V0 and θ into the range equation.
To calculate the range of the projectile R = (V0² / g) * sin(2θ)R = (168666.7² / 32.2) * sin(2(60))R ≈ 407.5 ft
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The magnitude of the force of gravity between two identical objects is given to be F0. Calculate the new force of gravity between the objects if the mass of each object and the distance between them is doubled.
Answers
The force of gravity between two objects is given by:
\(F=G\frac{m_1m_2}{r^2}\)where G is the gravitational constant, m1 and m2 are the masses of the objects and r is the distance between them.
In this case we know that the objects are identical, this means that the masses are the same:
\(\begin{gathered} m_1=m_2 \\ \text{for simplicity let's call them }m \end{gathered}\)Then we have that:
\(F_0=G\frac{m^2}{r^2}\)Now, if we double the mass of each object and the distance between them we have that:
\(\begin{gathered} F=G\frac{(2m)^2}{(2r)^2} \\ F=G\frac{4m^2}{4r^2} \\ F=G\frac{m^2}{r^2} \\ F=F_0_{} \end{gathered}\)Therefore the new force is the same if doubled both the mass of each object and the distance between them.
# 5 what will most likely happen when an air mas of low temperature exists above a water body at a higher temperature?
Heat will transfer from the wetter to the air
Answers
Answer:
yes u are correct
Explanation:
India's employment situation is bad. While structural factors are responsible for the high unemployment rate, the current slowdown has made things worse. In order to improve the employment situation in India, there is a need to recast the present educational system towards implementation of scientific discoveries in daily life.
India's employment situation can improve with efforts in the field
Answers
India's employment situation can be improved by recasting the present educational system towards the implementation of scientific discoveries in daily life.
India's employment situation has been a concern for a long time now, and it is true that structural factors are responsible for the high unemployment rate.
However, the current slowdown has made things worse, and there is a need for urgent action to address the situation. One way to improve the employment situation in India is to recast the present educational system towards the implementation of scientific discoveries in daily life.
The implementation of scientific discoveries in daily life can help in the development of new industries and the growth of existing ones. This can create new jobs and lead to economic growth.
For example, the implementation of renewable energy technologies can create jobs in the manufacturing, installation, and maintenance of solar panels and wind turbines. Similarly, the implementation of biotechnology in agriculture can lead to the development of new crop varieties and the creation of jobs in the agricultural sector.
Furthermore, the implementation of scientific discoveries can also lead to the development of new products and services that can be exported. This can help in the growth of the economy and create new jobs in the process. For example, the development of new software products and services can create jobs in the IT sector.
In order to achieve this, there is a need to recast the present educational system in India. This can be done by emphasizing the teaching of science, technology, engineering, and mathematics (STEM) subjects.
Furthermore, there is a need to improve the quality of education in India by investing in research and development, and by promoting entrepreneurship and innovation. This can help in the creation of a knowledge-based economy that can create new jobs and lead to economic growth.
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During which type of change should you expect to see different chemical
symbols before and after the change?
A. Chemical
B. Phase
C. Nuclear
D. Physical
Answers
During the nuclear change we can expect to see different chemical symbols before and after the change
Chemical and nuclear reactions are quite different from one another. Atoms can share electrons with other atoms or participate in an electron transfer to increase their stability in chemical reactions. In nuclear reactions, the atom's nucleus stabilizes itself by going through some sort of alteration. Compared to the energies involved in chemical reactions, the energies produced in nuclear reactions are many orders of magnitude higher. Environmental factors like temperature or pressure do not significantly affect nuclear reactions like they do with chemical ones.
Nuclear reactions involve a change in an atom's nucleus, usually producing a different element. Chemical reactions, on the other hand, involve only a rearrangement of electrons and do not involve changes in the nuclei
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Two forces 100n and 42.5n are acting on an object what is the resultant force if the first acts upward and the second acts downward
Answers
The resultant force if the first acts upward and the second acts downward will be 57.5 N
Force is defined as an external cause that changes or tends to change the state of the body once applied; if the body is in motion, it comes to rest and if at rest, then it will come to motion.
since , both the forces are in different direction , have to work according sign convention .
let upward forces = + ve
downward forces = - ve
f1 = + 100 N
f2 = - 42.5 N
f1 + f2 = F net
F net = + 100 + (- 42.5 )
= + 57.5 N
hence , net force will be 57.5 N in upward direction
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A car accelerates uniformly from rest to a speed of 10 meters per second in 2 seconds.
The acceleration of the car is?
Answers
The acceleration with which the car uniformly increases its speed from zero to the given speed is 5m/s².
Given the data in the question
Since the car was initially at rest
Initial velocity; \(u = 0m/s\)Final velocity; \(v = 10m/s\)Time taken; \(t = 2s\)Acceleration of the car; \(a = \ ?\)
Using the First Equation of Motion:
\(v = u + at\)
Where u is the initial velocity, v is the final velocity, a is the acceleration and t is the time taken.
We substitute our given values into the equation and solve for "a"
\(10m/s = 0m/s\ +\ ( a * 2s ) \\\\10m/s = a * 2s\\\\a = \frac{10m/s}{2s}\\\\a = 5m/s^2\)
Therefore, the acceleration with which the car uniformly increases its speed from zero to the given speed is 5m/s².
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A uniform line of charge with length 20.0 cm
is along the x
-axis, with its midpoint at x
= 0. Its charge per length is +6.30 nC/m
. A small sphere with charge -4.00 μC
is located at x
= 0, y
= 5.00 cm
What is the magnitude of the force that the charged sphere exerts on the line of charge?
Answers
The force is pointed towards the line of charge, which is the direction opposite to the electric field, as indicated by the force's negative sign. Hence, the charged sphere's force on the line of charge is 1.10 N in size.
What does an electrostatic force with a negative sign mean?Coulomb's law has an undesirable effect if the two charges have opposing signs. This indicates that there is an attractive force acting on the particles. Coulomb's law produces a favourable outcome if the signs of the two charges are same. This indicates that there is a repelling force acting between the particles.
E = kλ/r
\(d = sqrt((0.2/2)^2 + 0.05^2) = 0.206 m\)
\(E = kλ/d = (9 × 10^9 N·m^2/C^2) × (6.30 × 10^-9 C/m) / 0.206 m = 2.75 × 10^5 N/C\)
F = qE
where q represents the sphere's charge.
Substituting q = \(-4.00 μC and E = 2.75 × 10^5 N/C,\)we get:
\(F = (-4.00 × 10^-6 C) × (2.75 × 10^5 N/C) = -1.10 N\)
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Scientists can help us understand the impact of human activities on the environment. True or false?
Answers
Answer:
True
Explanation:
hope it will help you
When three people with a total mass of 2.00 x 102 kg step into their 1.200 x 103 kg car, the car’s
springs are compressed by 3.0 cm.
1.2.a. What is the spring constant of the car’s springs assuming they act as a single spring?
1.2.b. How far will the car lower if loaded with 3.00 x 102 kg rather than 2.00 x 102 kg
Answers
Answer:
a
\(k = 457333.3 N/m\)
b
\(x_a =0.09\ m\)
Explanation:
From the question we are told that
The total mass of three people is \(M = 2.00*10^{2} \ kg\)
The mass of the car is \(m_c = 1.200 *10^{3} \ kg\)
The compression of the car spring is \(x = 3 \ cm = 0.03 \ m\)
Generally the spring constant is mathematically represented as
\(k = \frac{F}{x}\)
Here F is the force exerted by the mass of three people and that of the car , this is mathematically represented as
=> \(F = (M +m_c) *g\)
=> \(F = ([2.0*10^{2} ]+[ 1.200*10^{3}]) * 9.8\)
=> \(F = 13720 \ N\)
So
\(k = \frac{13720}{0.03}\)
=> \(k = 457333.3 N/m\)
Generally if the mass which the car is loaded with is \(m = 3.00*10^{2} \ kg\)
Then the force experienced by the spring is
=> \(F_a = (m +m_c) *g\)
=> \(F_a = (3.00*10^{3} + 1.200 *10^{3}) * 9.8\)
=> \(F_a = 41160 \ N\)
Generally from the above formula the compression is
\(x_a = \frac{F_a}{k}\)
=> \(x_a = \frac{41160}{457333.3}\)
=> \(x_a =0.09\ m\)
Identify the characteristic of the transverse wave that halved from wave A (black) to wave B (green).
a) amplitude
b) crest
c) trough
d) wavelength
Answers
Answer:
D
Explanation:
The wavelength of wave B (green) is half of the wavelength of wave A (black). Therefore, option (d) is correct.
What is wavelength?The wavelength of a wave can be defined as the distance between the two adjacent points which are in phase with respect to each other. The separation between the two adjacent crests or adjacent troughs on a wave is also known as wavelength.
The relationship between the wavelength (λ) of the wave, frequency (ν), and speed of the wave (V) is:
V = νλ
Transverse waves oscillate along routes that are perpendicular to the direction in which the wave is propagating forward. In a transverse wave, particles of matter are oscillated up and down about their mean position instead of following the path of the wave.
Therefore, the wavelength of the transverse wave halved from black wave A to green wave B.
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If an elevator accelerates upward at 10 ms−2 , what is the average blood pressure in the brain? What is the average blood pressure in the feet? If the elevator accelerates downward with the same acceleration, what is the average blood pressure in the brain and feet? take g = 10
Answers
The average blood pressure in the brain will be higher than the average blood pressure in the feet. the average blood pressure in the brain will be lower than the average blood pressure in the feet.
When the elevator accelerates upward at \(10 ms^{-2}\), the blood pressure in the brain and feet of a person changes.
Similarly, when the elevator accelerates downward with the same acceleration, the blood pressure in the brain and feet of a person changes.
Let's discuss them one by one:Blood Pressure When Elevator Accelerates Upward at \(10 ms^{-2}\)
When the elevator accelerates upward at \(10 ms^{-2}\), the blood pressure in the brain of a person increases, while the blood pressure in the feet of a person decreases.
This happens due to the gravitational force acting on the body.
Since the gravitational force on the head is greater than the gravitational force on the feet, the blood pressure in the brain increases while the blood pressure in the feet decreases.
Therefore, the average blood pressure in the brain will be higher than the average blood pressure in the feet.
Blood Pressure When Elevator Accelerates Downward at \(10 ms^{-2}\) When the elevator accelerates downward at \(10 ms^{-2}\), the blood pressure in the brain of a person decreases, while the blood pressure in the feet of a person increases.
This also happens due to the gravitational force acting on the body. Since the gravitational force on the head is less than the gravitational force on the feet, the blood pressure in the brain decreases while the blood pressure in the feet increases.
Therefore, the average blood pressure in the brain will be lower than the average blood pressure in the feet.
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Fill in the graph for 50 points
Answers
Answer:
Speed: 3, 4, 5, 6. Distance: 1, 2, 3, 4, 5
Answer:
Speed: 3, 4, 5, 6. Distance: 1, 2, 3, 4, 5
Explanation:
Potassium-40 has a half-life of approximately 1.25 billion years. Approximately how many years will pass before a sample of potassium-40 contains one-eighth the original amount of parent isotope?
Answers
Answer:
3.75 billion years
Explanation:
From the question given above, the following data were obtained:
Half-life (t½) = 1.25 billion years
Number of half-lives (n) = 3
Time (t) =?
The time taken for the sample of potassium-40 to contains one-eighth the original amount of parent isotope can be obtained as:
n = t / t½
3 = t / 1.25
Cross multiply
t = 3 × 1.25
t = 3.75 billion years.
Therefore, it will take 3.75 billion years for the sample of potassium-40 to contains one-eighth the original amount of parent isotope
The figure shows the cross section of a long cylindrical wire of
radius aa, which carries a uniform current ii0. Determine the module of the field
magnetic produced by the current at a distance from the axis of the wire equal to (a)
0, (b) a/2, (c) a (wire surface) and (d) 2a.
Answers
Hi there!
Recall Ampere's Law:
\(\oint B \cdot dl = \mu_0 i_{encl}\)
B = Magnetic Field Strength (T)
μ₀ = Permeability of Free Space (Tm/A)
i = Enclosed Current (A)
dL = differential path length
To begin, we must derive an expression for the magnetic field strength inside a wire that contains a uniformly-distributed current.
Using the expression:
\(i = \int J \cdot dA\)
Where 'J' is the density of current, and A is the cross-sectional area:
\(A = \pi r^2\\\\dA = 2\pi r dr\)
We know that:
\(J = \frac{i_0 }{A}\\\\J = \frac{i_0}{\pi a^2}\)
This is the current density. We can now integrate:
\(i = \int\limits^r_0 {\frac{i_0}{\pi a^2} \cdot 2\pi r} \, dr\\ \\i =\frac{i_0}{a^2}\int\limits^r_0 {2r } \, dr\\\\i = \frac{i_0}{a^2} \cdot r^2 = \frac{i_0 r^2}{a^2}\)
Now, substitute this expression back into the above equation for the magnetic field:
\(\oint B \cdot dl = \mu _0 \frac{i_0r^2}{a^2}\)
The path of integration is a closed loop of length 2πr, so:
\(B \cdot 2\pi r = \mu_0 \frac{i_0r^2}{a^2}\\\\B = \frac{\mu_0 i_0r}{2\pi a^2}\)
We can now use this equation for the first 2 parts.
a)
If 'r' equals 0:
\(B = \frac{\mu _0 i_0 (0)}{2\pi a^2} = \boxed{0 T}\)
b)
If 'r' equals a/2:
\(B = \frac{\mu _0 i_0 (\frac{a}{2})}{2\pi a^2} =B =\boxed{ \frac{\mu _0 i_0 }{4\pi a} T}\)
c)
At the wire's surface, 'r' = a:
\(B = \frac{\mu _0 i_0 (a)}{2\pi a^2} =B =\boxed{ \frac{\mu _0 i_0 }{2\pi a} T}\)
d)
At 'r' = 2a, since this is outside of the wire, the relationship between magnetic field and distance from the wire becomes a 1/r (inverse) relationship. This is found using Ampere's Law:
\(B = \frac{\mu_0 i_0}{2\pi r}\\\)
\(B = \frac{\mu_0 i_0}{2\pi (2a)} \\\\\boxed{B = \frac{\mu_0 i_0}{4\pi a}\\}\)
2) Which of the following is not a quality of a healthy relationship?
A) respect
B) trust
C) closed communication
D) honesty
Answers
Can someone explain how to do the algebra for this question? I know everything else, I just don’t know how to rearrange the question to solve for v.
Answers
Answer:
Refer to the step-by-step Explanation.
Step-by-step Explanation:
Simplify the equation with given substitutions,
Given Equation:
\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)
Given Substitutions:
\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)
Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)
Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the left-hand side of the equation:
\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
Simplifying the third term.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)
"R²'s" cancel, we are left with:
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)
We have like terms, combine them.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)
Each term has an "m" in common, factor it out.
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)
Now we have the following equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the right-hand side of the equation:
\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)
\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)
Now we have the equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
\(\hrulefill\)
Now solving the equation for the variable "v":
\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
Dividing each side by "m," this will cancel the "m" variable on each side.
\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)
Subtract the term "gh" from either side of the equation.
\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)
Multiply each side of the equation by "10/7."
\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)
Now squaring both sides.
\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)
Thus, the simplified equation above matches the simplified equation that was given.
A street bridge is 5.5m long if the linear expansion of steel is 0.00001 oc How much will it expand when temperatures is by 10oc? Give answer in Cm
Answers
Answer:
\(l_o=550.055\ cm\)
Explanation:
Given that,
Length of a street bridge, l = 5.5 m
The coefficient of bridge, \(\alpha =0.00001 ^0 C\)
We need to find how much will it expand when temperatures is by 10°C.
The change in length per unit original length is given by :
\(\dfrac{\Delta l}{l}=\alpha \Delta T\\\\\Delta l = l\alpha \Delta T\\\\=5.5\times 0.00001 \times 10\\\\\Delta l=0.00055\\\\(l_o-l)=0.00055\\\\l_o=0.00055+5.5\\\\=5.50055\ m\\\\l_o=550.055\ cm\)
Hence, the length will expanded 550.055 cm.
A roller coaster is at a peak of 20m and has a mass of 900kg. What is the potential energy of the roller coaster?
O 100000 J
10000 J
O 9.8 J
O 176400 J
Answers
The potential energy of the roller coaster is 176,400 J (joules).
The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.
In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).
Using the formula, we can calculate the potential energy:
PE = mgh
= (900 kg)(9.8 \(m/s^2\))(20 m)
= 176,400 J
Therefore, the potential energy of the roller coaster is 176,400 J (joules).
Know more about potential energy here:
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