To derive an approximate formula for the induced emf in the large loop due to the time-varying current i(t) in the small loop, we can use Faraday's Law of Electromagnetic Induction:
What is Faraday's law ?emf = - dΦ/dt
where emf is the induced electromotive force, Φ is the magnetic flux, and t is time. In this case, we want to find the emf induced in the large loop due to the current in the small loop. To do this, we need to calculate the magnetic flux Φ through the large loop due to the current in the small loop.Assuming that the radius of the small loop is much smaller than the radius of the large loop (i.e., a << b), we can make the approximation that the magnetic field due to the small loop is uniform over the area of the large loop. This is because the distance between the small loop and any point on the large loop is approximately the same, and therefore the magnetic field strength at any point on the large loop is approximately the same.To know more about faraday's law , check out :
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If 2 J of wok is done in raising a 180 g red delicious apple to bring it to your mouth to take a bite of the apple, how far is it lifted?
Answer:1.13m
Explanation:
Potential Energy= mgh
m= mass(kg)
g= gravitational field strength(9.81m/s^2)
h= height
PE=mgh
PE= 2J
therefore: 2J= 0.180kg x 9.81 m/s^2 x h
h= 2/(1.764)
h= 1.13m
the large positive charge inside the shell causes equal in magnitude charges distributed on the inner and outer surfaces of the spherical shell. which of the pictures best represents the charge distribution on the inner and outer walls of the shell? (figure 1)
The picture that best represents the charge distribution on the inner and outer walls of the shell is picture 4
How does charge distribution affect a conducting shell?Charge distribution on a conducting shell can affect the electric field both inside and outside the shell. If the charge is distributed uniformly on the surface of the shell, the electric field inside the shell will be zero, while the electric field outside the shell will be the same as that of a point charge located at the center of the shell.
If the charge is distributed non-uniformly, then the electric field inside and outside the shell will be affected accordingly. In general, the charge distribution will determine the potential difference between the inside and outside of the shell, which can have important implications for the behavior of charged particles both inside and outside the shell.
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Two children, who are 224 meters apart, start walking toward each other at the same instant at rates of 1.5 m/sec and 2 m/sec, respectively when will they meet? How far will each have walked?
Both the children meet at t = 64 s and the distance travelled by first child is 96 m, distance travelled by second child is 128 m.
Two children are said to be 224 m apart.
First child walks towards the second with 1.5 m/s.
Second child walks towards the first with 2 m/s.
Let V = V₁ + V₂ = 1.5 + 2 = 3.5 m/s
We know the expression for, distance, velocity and time as,
s = v t
where,
v is velocity
t is time
s is distance
Let us find out the time at which they meet.
t = s/v = 224/3.5 = 64 s.
They meet at t = 64 s.
The distance travelled by first child s₁ = V₁ t = 1.5 × 64 = 96 m.
The distance travelled by first child s₂ = V₂ t = 2 × 64 = 128 m.
Thus, the first child walked 96 m and the second child walked 128 m.
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Lake Erie is prone to remarkable seiches-standing waves that slosh water back and forth in the lake basin from the west end at Toledo to the east end at Buffalo. The figure shows smoothed data for the displacement from normal water levels along the lake at the high point of one particular seiche. 3 hours later the water was at normal levels throughout the basin; 6 hours later the water was high in Toledo and low in Buffalo.
the Wavelength is 800 km
What is the frequency and wave speed?
The frequency and wave speed after the water was high in Toledo and low in Buffalo is 2.3 * 10^-5 Hz and 18 m/s
Period = 12 hours
= 43,200 seconds.
The number of cycles or vibrations that a body in periodic motion experiences during one unit of time, as well as the number of waves that pass a fixed point in a unit of time. After moving through a series of situations or positions and then returning to its initial position, a body in periodic motion is said to have experienced one cycle or one vibration.
Frequency= 1/T
= 1/43200
= 2.3 * 10^-5 Hz
The amount of space a wave covers in a certain amount of time, such as the number of metres it covers in a second, is known as its wave speed. Speed = Wavelength x Frequency is an equation that describes how wave speed relates to wave wavelength and wave frequency. When the wavelength and frequency are known, this equation can be used to determine the wave speed.
Wave speed
= wavelength*(1/period)
= wavelength*frequency
= 800,000 m * 2.3 * 10^-5 Hz
= 18 m/s
Therefore, wave speed of the water be 18 m/s.
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to determine the effect of the temperature dependence of the thermal conductivity on the temperature distribution in a solid, consider a material for which this dependence may be represented as k
To determine the effect of the temperature dependence of the thermal conductivity on the temperature distribution in a solid, consider a material for which this dependence may be represented as K=K1+aT.
Temperature and conductivity is inversely related as temeprature increases ,thermal diffusivity and thermal conductivity decrease. Thermal conductivity is related linearly so it decrease with increasing temperature. At high temperature, thermal diffusivity and conductivity approach constant.
Given that
k = ko + aT
From Fourier law
Heat transfer per unit volume given as
x measured from left hand side of wall.
By integrating
qdx=-(ko + aT)dT
When a = 0 :
qx=-koT+C
This is become straight line.
When a > 0 :
dT/dX= increase
K decrease when x is increases.
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Two negatively-charged objects are located on the x axis, equally distant from the origin as shown. Consider the electric field at the point P1. How will that electric field change if a third object with a charge +q is placed at point P2? Note: the point P2 is the same distance from the origin as the point P1 and the magnitude of each of the charges is the same.a) The magnitude of the electric field will decrease by 25%.b) The magnitude of the electric field will increase by 25%.c) The magnitude of the electric field will decrease by 50%.d) The magnitude of the electric field will increase by 50%. e) The magnitude of the electric field will increase by 100%.
Electric field change if a third object with a charge +q is placed at point P2 is the magnitude of the electric field will decrease by 25%.
Electric field is a vector quantity. It has a direction towards the negative charge and away from a positive charge.
Due to the 2 negatice charges, electric field E's verticle component will add up and horizontal component will cancel each other.
Electric field due to a charge particle = K q / r^2
K = constant
q = charge
r = distance of the point from the charge
Angle made by electric field = 45 degrees
Verticle component of the electric field due to two -q = E =2 * K(-q) cos 45 / (V2 R)^2 \
= -V2 Kq/2R^2 = -0.71 Kq/R^2
New electric field after a charge +q is introduced = initial E + E due to +q
E due to +q = Kq / (2R)^2 = 0.25 Kq/R^2
Percentage Change in electric field = (Change in electric field / Initial electric field) * 100 = 0.25 *100 / -0.71 = -25%.
Therefore, the magnitude of the electric field will decrease by 25%.
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(6%) problem 12: a stone is tossed horizontally from the highest point of a 85 m building and lands 105 m from the base of the building. ignore air resistance, and use a coordinate system whose origin is at the highest point of the building, with positive y upwards and positive x in the direction of the throw.A. How long is the stone in the air in s?
B. What must have been the initial horizontal component of the velocity, in m/s?
C. What is the vertical component of the velocity just before the stone hits the ground, in m/s?
D. What is the magnitude of the velocity of the stone just before it hits the ground, in m/s?
A ball is thrown horizontally from a 95 m-high building's highest point and landing 125 m from the building's base. Use a coordinate and disregard air resistance.
What does the word "resistance" mean?
Describe resistance. Electrical | January 12, 2021 The obstruction to part of the electrical circuit is measured by resistance. The Greek letter beta () represents the unit of measurement for resistance, known as ohms. Georg Simon Ohm (1784–1854), a German physicist that investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance.
What is a circuit's electrical resistance?
The relationship between the induced voltage and the current that flows through a circuit determines its electrical resistance. Ohms is the symbol for electrical resistance. Some materials permit the flow of electric charge more easily than others. The electrical resistance gauges how much the circuit restricts the flow of the this electric charge.
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Two parallel conducting plates are charged with an equal and opposite charges. Which statement is true about the magnitude of the electric potential? A Greater at point A (B) Greater at point B (C) Greater at point (D) Greater at point D (E) The same at points B, C, D and zero at point A Moving to another question will save this response.
Two parallel conducting plates are charged with equal and opposite charges. Then the correct statement about the magnitude of the electric potential is greater at point B.
Here electric field exists between the positive and negative plates. Its direction will be from the positive plate to the negative plate. The electrostatic potential is the work done in moving a unit charge in the electric field. The relationship between the electric field and electric potential is electric field is the negative gradient of electric potential.
E = -dV/dr
V = -∫E.dr
E.dr = E×dr×cos(theta)
Here on moving from the positive plate to the negative plate Electric field and distance are in the same direction.
Hence the value of the angle theta between them will be 0 degrees. Then we will potential as negative. That is on moving from the positive plate to the negative plate potential decreases. So, point B near the positive plate is having higher potential compared to others.
Point A is outside the plates where the electric field and hence potential is zero.
This question is accompanied by an image and Option B is the correct one.
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A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms
a)his moment of inertia decreases.
b)his angular momentum decreases.
c)his angular momentum remains the same.
d)his angular velocity increases.
e)his angular velocity remains the same.
A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms his angular velocity remains the same. Option e is the correct choice.
When the arms are folded the rotational inertia is lower. When the man extends his arm he is basically increasing his rotational inertia thereby loosing angular velocity using the principle of conservation of angular momentum. This implies less angular distance is covered in the same time giving us negative work.
After pulling arms, the angular velocity increases but moment of inertia of decreases in, such a way that angular momentum remains constant.
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in terms of mass and diameter, _____ is by far the largest of the there, followed by _____ and then _____. the earth and ____ are very similar in terms of density, indicating a composition of about equal measures of rock and metal. _____, however, has a density almost half that of the earth and _____, indicating a composition of mostly rock.
____ has has the most powerful gravitational field of the three, one of the reasons it is the only one of the three to have an atmosphere. Because it has an atmosphere, ______'s temperature _____ by much from day to night, but _____ and the moon experience ______ temperature extremes.
- small
- the moon
- great
- do not vary
- varies
- the earth
- mercury
What is the velocity resulting from gravity here on surface of a star with a mass and diameter that are three times those of the earth (assuming that the earth's surface gravity is 9.8 m/s-2)
What is the ultimate speed?
The final velocity, on the other hand, is a vector number that gauges a moving body's speed and direction once it's reached maximum acceleration. How is the final velocity determined? It is easy to determine the final velocity with a few computations and little conceptual understanding.
What makes speed and velocity different from one another?
Most people mix the terms velocity and velocity in regular speech. These are different concepts that don't share the same significance in physics. Speed has no direction, which is one critical difference. Speed is therefore a scalar.
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How do you find the VM the muzzle velocity of the ball?
The muzzle velocity (VM) of a ball can be found by using a ballistic pendulum.
The basic principle of a ballistic pendulum is that the momentum of the ball before it hits the pendulum equals the momentum of the pendulum and the ball immediately after the collision.
The equation for this is
[tex]m_1v_1 = (m_1 + m_2) v_2[/tex]
, where m₁ is the mass of the ball, v₁ is the initial velocity of the ball, m₂ is the mass of the pendulum, and v₂ is the velocity of the pendulum and the ball immediately after the collision.
Solving for v₁, we get
[tex]VM = v_1 = (m_1 + m_2) \dfrac{v_2}{m_1}[/tex]
By measuring the height to which the pendulum rises and the mass of the pendulum, we can determine the velocity of the ball.
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A 6N force pushes to gliders along an air track. The 200 g spring between the gliders is compressed. How much force does the spring exert on (a) glider A and (b) glider B? Mass of Glider A = 400 g Mass of Glider B = 600 g
The spring exerts the same force on both glider A and glider B, equal to (Fa - (-6N))/2 = (Fb - (6N))/2.
How much force does the spring exert on each other?The force of the spring can be calculated using Hooke's law, which states that the force exerted by a spring is proportional to the displacement of the spring from its rest position.
Let's call the spring force "Fspring". Since the spring is compressed, it is exerting a force on both gliders, which we can call "Fa" for glider A and "Fb" for glider B.
The total force on each glider is equal to the spring force plus the force of the 6N external force:
Fa = Fspring + (-6N)
Fb = Fspring + (6N)
Since the forces on both gliders are equal in magnitude and opposite in direction, we can write the following equation:
Fspring = (Fa - (-6N))/2 = (Fb - (6N))/2
To calculate the spring force, we need to find the displacement of the spring from its rest position. This can be done using the following equation:
Fspring = kx
Where;
k is the spring constant
Since the spring is compressed, the displacement "x" is negative. We can find the spring constant "k" using the equation:
k = Fspring / x
We can substitute the equation for Fspring from above into this equation:
k = (Fa - (-6N))/2x / x
We can rearrange this equation to solve for "x":
x = (Fa - (-6N))/(2k)
We can then substitute this value of "x" back into the equation for Fspring to find the force exerted by the spring:
Fspring = (Fa - (-6N))/2 = (Fb - (6N))/2
Since the masses of glider A and glider B are known, we can use the following equation to find the acceleration of each glider:
Fa = ma
Fb = mb
Where "m" is the mass of each glider and "a" is the acceleration of each glider.
We can rearrange these equations to solve for the acceleration of each glider:
a = Fa / m
b = Fb / m
Now that we have the acceleration of each glider, we can use Newton's second law to find the force exerted by the spring on each glider:
Fa = ma = 400 g * a
Fb = mb = 600 g * b
Finally, we can substitute the value of Fspring from above into these equations to find the force exerted by the spring on each glider:
Fa = Fspring + (-6N) = (Fa - (-6N))/2 + (-6N)
Fb = Fspring + (6N) = (Fb - (6N))/2 + (6N)
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What is the average force of gravitation between Venus and the sun?
The average force of gravitation between Venus and the Sun is3.24 x 10²² N.
What is average gravitational force?The force of gravitation between two objects can be calculated using the equation;
F = G (m1m2) /d²
where;
F is the force of gravitation, G is the gravitational constantm1 and m2 are the masses of the two objects, and d is the distance between them.To find the average force of gravitation between Venus and the Sun, we need to know their masses and the average distance between them.
Venus has a mass of approximately 4.87 x 10²⁴ kg, and the average distance between Jupiter and the Sun is about 108 million kilometers.
Plugging these values into the equation, we get:
F = 6.67 x 10⁻¹¹ (4.87 x 10²⁴) x (1.989 x 10³⁰ kg) / (108 x 10⁶)²
F = 3.24 x 10²² N.
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What two processes are part of electromagnetism?
A. The attraction of electric charges for each other
B. The production of a magnetic field by an electric current
C. The production of an electric current by a moving magnet
D. The production of a magnetic field by permanent magnets
Answer:
C. The production of an electric current by a moving magnet
B. The production of a magnetic field by an electric current
What is electromagnetism?
The " real definition " of electromagnetism is the following:
Electromagnetism is the physical interaction among electric charges, magnetic moments, and the electromagnetic field.
There are different " types " of electromagnetic fields
StaticSlowly changingWavesThe last thing that YOU should know is that electromagnetic waves are generally known as light and obey the laws of optics. Which means in similar terms they just obey the laws of optics.
Thus, the answers to your question is, C & B
compute the initial upward acceleration of a rocket of mass 1.80 x 104 kg if the initial upward force produced by its engine (the thrust) is 4.60 x 105 n. do not neglect the gravitational force on the rocket.
The initial upward acceleration of the rocket is 15.75 m/s. The result is obtained using Newton's second law.
How to find the acceleration of a rocket?A rocket with a mass of 1.80 × 10⁴ kg is moving upward. The initial upward force produced by its engine (the thrust) is 4.60 × 10 N.
Find the initial upward acceleration without neglecting the gravitational force on the rocket!
We have
m = 1.80 × 10⁴ kgF = 4.60 × 10⁵ NWhen the rocket moves upward, the acceleration can be found by Newton's second law equation.
F = ma
Without neglecting the gravitational force in the opposite direction, it will be
F - W = ma
F - mg = ma
With g = 9.8 m/s², the initial upward acceleration is
ma = F - mg
1.80 × 10⁴a = 4.60 × 10⁵ - 1.80 × 10⁴ × 9.8
1.80 × 10⁴a = 4.60 × 10⁵ - 1.764 × 10⁵
1.80 × 10⁴a = 2.836 × 10⁵
a = 1.575 × 10¹
a = 15.75 m/s
Hence, the rocket's initial upward acceleration is 15.75 m/s.
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A parallel-plate capacitor has plate area A. A battery is used to charge the capacitor so that the magnitude of charge on each plate is Q, and then is disconnected. Initially, the capacitor has a plate separation of d. At this separation the capacitor contains energy U. The plates are then moved to a separation of 2d without disturbing the charge. What is the energy of the capacitor at this larger plate separation? Show work and steps.
(a) U
(b) U/2
(c) 2U
(d) U/4
(e) 4U
The energy of the capacitor at this larger plate separation will be= D) U/4
The energy stored in a parallel-plate capacitor with plate area A, plate separation d, and charge Q is given by the formula:
U = (1/2) * (Q^2 / (ε_0 * A * d))
where ε_0 is the permittivity of free space.
If the separation between the plates is increased from d to 2d without changing the charge on the plates, the capacitance of the capacitor will be reduced by a factor of 2. This is because the capacitance of a parallel-plate capacitor is given by the formula:
C = ε_0 * A / d
So, when the separation is doubled, the capacitance is halved.
Since the charge on the plates remains constant, the energy stored in the capacitor is proportional to the square of the charge and inversely proportional to the capacitance. Thus, the new energy of the capacitor when the plates are separated by 2d is given by:
U' = (1/2) * (Q^2 / (ε_0 * A * (2d))) * (1/2)
where the factor of 1/2 is included because the capacitance is halved.
Simplifying this expression, we get:
U' = U / 4
Therefore, the energy of the capacitor at the larger plate separation is (d) U/4.
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An electron is moving at a constant speed of 83 m/s on a circle of radius 3.7 m. Part (a) Express the circumference of the circle C in terms of its radius R. Expression C= Select from the variables below to write your expression. Note that all variables may not be required. a. B. At, 2. 0. C. d. g, h, m, P. Q, R, t. Part (b) Express the time interval At for the electron to finish one circle in terms of the circumference and speed v. Expression 41 = Select from the variables below to write your expression. Note that all variables may not be required. a,B,A,2, 0. C. d.g,h,m, P, Q, R, L, V Part (e) Express the current on the circle through the charge e and time interval 41. Expression: Select from the variables below to write your expression. Note that all variables may not be required. a, b, At,, 0,C,d,e, g, h, k, m, n, P. Part (d) Calculate the numerical value of 7 in A. Numeric : A numeric value is expected and not an expression. I=
(a) Circumference is, C = 7.4π. (b) Time interval is, [tex]A_t = 0.089 s[/tex]. (c) Current value is, [tex]I = -1.80 \times 10^{-18} A[/tex]
Part (a): The circumference of a circle with radius R is given by C = 2πR. Therefore, for a circle of radius 3.7 m, we have:
[tex]C = 2\pi(3.7) = 7.4\pi[/tex]
[tex]Expression: C = 7.4\pi[/tex]
Part (b): The time interval At for electron to finish one circle is given by the distance traveled divided by the speed. In this case, the distance traveled is equal to the circumference of the circle, so we have:
[tex]At = C/v[/tex]
[tex]At = 7.4\pi/83[/tex]
[tex]A_t = 0.089 s[/tex]
Part (c): The current on the circle can be found using the formula [tex]I = Q/t,[/tex]where Q is the charge and t is the time interval. Since the electron has a charge of -e,
[tex]I = (-e)/At[/tex]
Substituting the value of At from above,
[tex]I = (-1.602 * 10^-19 C)/0.089 s[/tex]
[tex]I = -1.80 * 10^{-18} A[/tex]
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Read the following paragraph and answer the question. "Ernest Cline is an American Screenwriter and author. Ernest was born in 1972. He started his writing career in 1992
doing spoken word poetry. His best known works include 'Dance Monkey Dance' and 'When I Was a Kid. He then moved to film, as the screenwriter of the film Fanboys. He then released one of the most entertaining novels of all time, Ready Player One. Today Cline is still working, writing for many projects." What is the structure of this paragraph?
A. Causeleffect
B. Sequence
C. Problem/solution
D. Comparison
The structure of the given paragraph about Ernest Cline is sequence writing.
The correct option is B.
What is sequence writing?Writing that organizes information or events in a certain order is known as sequence writing. In order for the reader to understand and follow the flow of events, sequence writing aims to convey information or events in a straightforward and logical manner.
For instance, the phases in a procedure are described sequentially in instructional writing to aid the reader in comprehending how to carry out a task. Events in narratives are presented chronologically to make it easier for the reader to follow the plot.
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in terms of known quantities, write an expression for the time the arrow is in the air until it returns to launch height.
Assuming that the arrow is launched vertically upward with an initial velocity v and air resistance is negligible, the time the arrow is in the air until it returns to launch height can be expressed as:
What is air resistance ?When air resistance is minimal and an arrow is shot vertically upward with an initial velocity of v, the time it spends in the air before returning to launch height can be represented as:t = 2v/g
where g is the acceleration brought on by gravity (about 9.81 m/s2), t is the passage of time, v is the arrow's starting speed.To know more about air resistance , check out :
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A positive test charge is brought near to, but not touching a conducting sphere that is connected to the ground. Both objects remain at rest in the positions shown above. Charge begins to flow from the ground to the sphere. Which of the following statements best describes when charge stops flowing and provides justification for the claim? A. Charge will flow until the electric field at the surface of the sphere is equivalent to the electric field of the test charge, because then the excess charge on the surface of the sphere will be equal to the charge of the test charge B. Charge will flow until the electric field at the surface of the sphere is equivalent to the electric field of the test charge, because then the net force on all charges on the surface of the sphere will be zero C. Charge will flow until the potential at the surface of the sphere is the same as the potential of the test charge, because then the net force on all charges on the surface of the sphere will be zero. D. Charge will flow from the ground to the sphere until the potential is the same everywhere within the sphere, because then the excess charge on the surface of the sphere will be equal to the charge of the test charge.
E. Charge will flow from the ground to the sphere until the potential is the same everywhere within the sphere, because then the net force on all charges on the surface of the sphere will be zero
A charge will flow until the electric field at the surface of the sphere is equivalent to the electric field of the test charge, because then the net force on all charges on the surface of the sphere will be zero. Here option B is the correct answer.
When the positive test charge is brought near the conducting sphere, the excess negative charge from the ground flows onto the surface of the sphere until equilibrium is reached. At this point, the electric field at the surface of the sphere becomes equal and opposite to the electric field of the test charge, thus canceling out the electric field of the test charge within the sphere.
Since the electric field inside the conductor is zero, the excess charges on the surface of the conductor are uniformly distributed and the net force on them is zero. Therefore, option B is the correct answer. Option A is incorrect because the excess charge on the surface of the sphere will be opposite in sign and not equal in magnitude to the test charge.
Option C is incorrect because the potential at the surface of the sphere is not necessarily the same as that of the test charge. Option D is incorrect because the excess charge on the surface of the sphere will be opposite in sign and not equal in magnitude to the test charge. Option E is incorrect because the net force on charges on the surface of the sphere is zero when the electric field at the surface of the sphere is equivalent to the electric field of the test charge.
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Question 1 of 10
Which answer best describes the scientific method?
A. The exact order of steps used in every experiment
B. Ten steps that are followed in a certain order
C. The basic categories for five processes that scientists use
D. An experiment that has no independent variables
The exact order of steps used in every experiment of the scientific method.
What is the scientific method?The scientific method is defined as the process of making facts through testing and experimentation. The basic process includes making an observation, forming a hypothesis, making a prediction, carrying out an experiment, and then analyzing the results.
The six steps of the scientific method include asking a question about something doing background research about the topic, constructing a hypothesis, doing experiments to test the hypothesis, analyzing the data from the experiment, and making conclusions.
So we can conclude that option A is the correct answer.
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If the mass between two objects remains the same but the distance from their centers decreases, the force of gravity between them increases
A.True
B.False
The gravitational force between the objects depends on their mass as well as distance between them. If the distance increases, the gravitational force decreases. Hence, the statement is false.
What is gravitational force?The gravitational force is the force by which an object attracts other object into its center of mass. The gravitational force depends on the masses of the objects and distance between them by the equation written below:
Fg = G m1 m2/r²
where G is the universal gravitational constant equal to 6.67 × 10⁻¹¹ N/kg²m²
As per this universal equation for gravitation, as the mass increases, gravitational force between the objects increases. If the force between the two masses decreases 2 times with an increase in distance.
Therefore, the statement is false.
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A cat is being chased by a dog. both are running in a straight line at constant speeds. the cat has a head start of 4.2 m. the dog is running with a speed of 9 m/s and catches the cat after 5.6 s. How fast did the cat run?
The required speed of the cat when the relative speed and the speed of the dog are given is calculated to be 8.25 m/s.
Distance by which the dog lags behind the cat is given as d = 4.2 m
Speed of the dog v₂ = 9 m/s
The dog catches the cat in time t = 5.6 s
Relative speed of the dog with respect to the cat is given by,
vr = v₂ - v₁ = 9 - v₁
where,
v₁ is the speed of the cat
Therefore, we can write,
t = d/(9 - v₁)
Making v₁ as subject, we have,
v₁ = v₂ - d/t = 9 - 4.2/5.6 = 9 - 0.75 = 8.25 m/s
Thus, the speed of the cat is calculated to be 8.25 m/s.
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suppose that the force applied to the object were twice as large. sketch with dashed lines on the same axes above the force, acceleration, and velocity vs. time
Force is a physical quantity that describes the interaction between two objects, which can cause a change in the motion of an object. When a force is applied to an object, it can either cause the object to start moving, speed up, slow down, or change direction.
Force is typically measured in units of Newtons (N) and is represented by a vector, which has both magnitude (strength) and direction.
For example, pushing a book across a table requires a force that is applied in the direction of the push. If the force is strong enough to overcome the book's friction with the table, the book will begin to move in the direction of the force.
The amount of force required to produce a given effect on an object depends on several factors, including the mass of the object, the nature of the force, and the length of time the force is applied. In general, the greater the force applied to an object, the greater the acceleration (or deceleration) of the object.
Assuming that the force applied to an object is directly proportional to the acceleration it experiences, if the force were doubled, the acceleration would also double. This would result in a steeper slope on the acceleration vs. time graph.
As velocity is the integral of acceleration over time, if the acceleration were doubled, the velocity would increase at a faster rate than before. This would result in a steeper slope on the velocity vs. time graph.
Lastly, if the force applied to an object were doubled, the object would reach a higher velocity than before in the same amount of time. This would result in a higher maximum velocity and a longer time to come to a stop (assuming a constant force is applied). The velocity vs. time graph would shift upward and to the right, indicating a higher maximum velocity and a longer time to reach that maximum velocity.
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A bolt is dropped from a bridge under construction, falling 95 m to the valley below the bridge. (a) How much time does it take to pass
through the last 30 % of its fall? What is its speed (b) when it begins that last 30 % of its fall and (c) just before it reaches the ground?
(a) 0.72
(b) ?
(c) ?
The bolt's initial velocity, V, is zero when it is released from the container at a height of 94 meters.
A height of 0.26*94 = 24.4 m marks the final 26% of its descent.
By then, the bolt had dropped 94 - 24.4 = 69.56 m.
The last 26% of the bolt's fall takes 0.6122 seconds to complete.
(b) The bolt travels at a speed of 36.92 m/s for the final 26% of its descent (nearest hundredth).
(c) The bolt's speed is 42.94 m/s just before it touches the earth (nearest hundredth).
When does acceleration differ from velocity?The change in displacement is measured in terms of velocity. The rate of velocity that changes is known termed accelerated. Due to the magnitude it contains, velocity is a vector quantity.
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Three ice skaters, numbered 1, 2, and 3, stand in a line, each with her hands on the shoulders of the skater in front. Skater 3, at the rear, pushes forward on skater 2. Assume the ice is frictionless. Draw a free body diagram for skater 2 in the middle.Â
Since skater 2 is in the middle, force acting on her from both skater 1 in front and skater 3 behind. The free body diagram for skater 2 would include two arrows pointing towards her, representing the forces from skater 1 and skater 3. Since there is no friction, there are no other forces to consider.
The diagram would look something like this:
∧
|
F3 ← I → F1
|
v
where F1 is the force from skater 1 and F3 is the force from skater 3.
What is friction?A force called friction works against the relative velocity of two surfaces coming into contact. The minute imperfections on the surfaces that interlock with one another when they come into touch are what cause it. We experience friction as a result of this interlocking as resistance to motion. The type of surfaces in contact, the force forcing the surfaces together, and the rate of motion can all have an impact on the frictional force. As some of the kinetic energy is transformed into heat energy during friction, this can also result in energy loss. Designing machinery, vehicles, and structures to reduce wear and tear and maximize performance requires an understanding of friction.
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7. A 1,2 kg hammer is used to hit a nail horizontally into a block of wood. The hammer is moving at 15 m.s¹ immediately before it collides with the nail and rebounds at 60% of that speed. The nail's resisting force is 9 000 N. Calculate how long the hammer is in contact with the nail.
Answer:
ETo calculate the duration of the hammer's collision with the nail, we need to find the time it takes for the hammer to come to a stop and then reverse direction.
The hammer's initial momentum before the collision is given by its mass and velocity:
p_i = m * v_i = 1.2 kg * 15 m/s = 18 kg m/s
The hammer's final velocity after the collision can be found using the law of conservation of momentum, which states that the total momentum of an isolated system remains constant. We can write this as:
p_f = m * v_f = m * (-v_i * 0.6) = m * (-15 m/s * 0.6) = 9 kg m/s
The force experienced by the nail during the collision can be calculated as:
F = ma = (m * (v_f - v_i)) / t = (m * (9 kg m/s - 18 kg m/s)) / t
Since we know the force experienced by the nail is 9 000 N, we can use this to solve for t:
9 000 N = (1.2 kg * (9 kg m/s - 18 kg m/s)) / t
t = (1.2 kg * (9 kg m/s - 18 kg m/s)) / 9000 N
t = 0.00133 seconds
So the hammer is in contact with the nail for approximately 0.00133 seconds.
variable:
m: mass of the hammer, 1.2 kg
v_i: initial velocity of the hammer before the collision, 15 m/s
v_f: final velocity of the hammer after the collision, -9 m/s (negative sign indicates the direction of motion is opposite to the initial velocity)
t: duration of the hammer's collision with the nail, approximately 0
We are given 5 (independent) equations and 6 unknowns. Currents (the I variables) are given in amps and voltage (the V variables) in volts. I = I_1 + I_2 V_1 = 2l_1 V_2 = 5l_2 V_1 - V_2 = 0 V - 5 = V_1 Solve (using multiple substitutions) to find I in terms of V and no other variables. I = V+ (within three significant digits) If we are giving one more fact (a 6^th equation) V = 3 volts what will be the value of 1? I = amps (within three significant digits)
An independent equation is an equation in a system of simultaneous equations which cannot be derived algebraically from the other equations. The concept typically arises in the context of linear equations.
I = [tex]I_{1} + I_{2}[/tex]
[tex]V_{1} = 2I_{1}[/tex]
[tex]V_{2} = 5I_{2}\\V_{1} - V_{2} = 0 \\V_{1} = V_{2}\\V-5= V_{1}\\V = V_{1} + 5[/tex]
put equation 2 and 3 in 1
[tex]I =V_{1}/2 + V_{2} /5\\= V_{1} [1/2 + 1/5]\\= 7V_{1}/ 10\\I = 7V_{1} / 10[/tex]
put 5 in 6
[tex]I = 7/10 (v-5) [ I = 0.7V- 3.5][/tex]
given V= 3
I = 0.7 V - 3.5
I = 0.7 (3) - 3.5
[ I = -1.4 A]
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a parallel-plate vacuum capacitor is connected to a battery and charged until the stored electric energy is u. the battery is removed, and then a dielectric material with dielectric constant k is inserted into the capacitor, filling the space between the plates. finally, the capacitor is fully discharged through a resistor (which is connected across the capacitor terminals).
All of the electrical energy held in the capacitor is released as heat when it is fully discharged through the resistor.
What purpose does a capacitor serve?Two conductors that are separated from one another and positioned close to one another make up a capacitor, an electrical energy storage device.A straightforward illustration of one such storage device is a parallel-plate capacitor.
The following formula can be used to determine how much energy was lost inside the resistor:
= ½ × ×
A parallel-plate capacitor's capacitance is determined by:
= × 0 × /,
Since the capacitor is charged until the stored electric energy is , we can write:
½ × × =
Solving for gives:
= 2 × /
Substituting this expression for into the formula for, we get:
½ × × ² × ( − 1)
(B) The potential difference across the capacitor will rise as long as the charging battery is still attached and the dielectric is inserted because of the higher capacitance. The following formula can be used to compute the new potential difference:
The capacitor's newly accumulated electrical energy is:
½ × × × ²
= ½ × × ² × ( − 1)
= ½ × × ² × ( − 1)
= ½ × × (² − ²)
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Question:
A parallel-plate vacuum capacitor is connected to a battery and charged until the stored electric energy is . The battery is removed, and then a dielectric material with dielectric constant is inserted into the capacitor, filling the space between the plates. Finally, the capacitor is fully discharged through a resistor (a resistor is connected across the capacitor terminals).
A) Find , the energy dissipated in the resistor.
Express your answer in terms of and other given quantities.
B)Consider the same situation as in the previous part, except that the charging battery remains connected while the dielectric is inserted. (Part B figure) The battery is then disconnected and the capacitor discharged. For this situation, what is , the energy dissipated in the resistor?
Express your answer in terms of and other given quantities.
A particle of charge + is at point A a distance from the center of a sphere of charge +Q.The particle is moved to point B, a distance expressions represents the electric potential difference between the two points due to the charge on the sphere? from the center of the sphere. Which of the following (1-4) % (4) (9) (-)
The expressions which represent the electric potential difference between the two points due to the charge on the sphere qQ/4πε0 (1/rb- 1/ra). (Option C)
The electric eventuality, also known as implicit drop or the electrostatic eventuality refers to the quantum of work energy needed to move a unit of electric charge from a reference point to the specific point in an electric field. The electric implicit generated from a point charge, Q, at a distance, r, from the position of Q is given by
V = 1/ 4πε0 Q/ r
When the electric eventuality is told by two point charge, Q and q, the formula is
V = 1/ 4πε0 qQ/ r
Electric implicit difference refers to the external work needed to bring a charge from one position to another position in an electric field. It's the change of implicit energy endured by a test charge that has a value of 1. The electric implicit difference is given as ΔV = Vb- Va
Hence, the expressions which represent the electric implicit difference between the two points due to the charge on the sphere qQ/ 4πε0( 1/ rb- 1/ ra).
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Complete question:
a particle of charge q is at point a , a distance ra from the center of a sphere of charge q . the particle is moved to point b , a distance rb from the center of the sphere. which of the following expressions represents the electric potential difference between the two points due to the charge on the sphere?
A) Q/4πε0 (1/rb- 1/ra) B) 1/4πε0 Q/rb C) qQ/4πε0 (1/rb- 1/ra) D) 1/4πε0 qQ/rb