Answer:
Hyperbole
Explanation:
this is an extreme exaggeration or overstatement/ magnification
An RL circuit has L=5 H and R = 22.
a) How long would it take, following the removal of the battery, for the magnetic energy to decay to 13% of its maximum value?
b) What is the voltage across the inductor at that instant?
a) , it would take approximately 0.4638 seconds for the magnetic energy to decay to 13% of its maximum value.. b) the voltage across the inductor at the instant when the magnetic energy has decayed to 13% of its maximum value is 6.4 times the initial current in the circuit.
An RL circuit consists of a resistor (R) and an inductor (L) connected in series. When a battery is connected to the circuit, the inductor stores magnetic energy, which creates a magnetic field. When the battery is removed, the magnetic energy in the inductor begins to decay, and the magnetic field collapses, inducing a voltage across the inductor.
a) The time constant (τ) of an RL circuit is given by the formula:
τ = L/R
where L is the inductance in henries, and R is the resistance in ohms. The time constant represents the time required for the magnetic energy to decay to approximately 36.8% of its maximum value.
In this case, L = 5 H and R = 22 ohms. Therefore, the time constant of the circuit is:
τ = L/R = 5 H / 22 ohms = 0.2273 seconds
To calculate the time required for the magnetic energy to decay to 13% of its maximum value, we can use the formula:
t = -ln(0.13) * τ
where ln is the natural logarithm. Plugging in the values, we get:
t = -ln(0.13) * 0.2273 seconds
t = 0.533 seconds
Therefore, it would take approximately 0.533 seconds for the magnetic energy in the inductor to decay to 13% of its maximum value.
b) To find the voltage across the inductor at that instant, we can use the formula:
V = L * di/dt
where V is the voltage across the inductor, L is the inductance, and di/dt is the rate of change of the current in the circuit.
At the instant when the magnetic energy in the inductor has decayed to 13% of its maximum value, the current in the circuit is given by:
I = I0 * e^(-t/τ)
where I0 is the initial current, and e is the mathematical constant approximately equal to 2.71828. Plugging in the values, we get:
I = I0 * e^(-0.533/0.2273)
I = 0.292 * I0
Therefore, the rate of change of current (di/dt) at that instant is given by:
di/dt = I / τ = (0.292 * I0) / 0.2273
Now, we can calculate the voltage across the inductor:
V = L * di/dt = 5 H * (0.292 * I0 / 0.2273)
V = 6.4 * I0 volts
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You lift a 10-N physics book up in the air a distance of 1.0 m, at a constant velocity
of 0.50 m/s. What is the work done by gravity on the book?
1) +10 J
2) -10
3) +5.0
4) -5.0
The book is lifted upward, but gravity points down, so the work done by gravity must be negative (so you can eliminate options 1 and 3).
The force exerted on the book by gravity has magnitude
F = mg = (10 N) (9.80 m/s^2) = 9.8 N ≈ 10 N
You raise the book 1.0 m in the opposite direction, so the work done is
W = (10 N) (-1.0 m) = -10 J
The work done by gravity on the book is -10 Joules. The correct option is 2.
What is gravity?The force of attraction felt by a person at the center of a planet or Earth is called as the gravity.
Given are the three positions. The Earth has the acceleration due to gravity, g = 9.81 m/s²,
The book is lifted upward, but gravity points down, so the work done by gravity must be negative (so you can eliminate options 1 and 3).
The force exerted on the book by gravity has magnitude
F = mg = 10 N x( -9.80 m/s² )= -9.8 N
F ≈ -10 N
The book is raised by 1.0 m in the opposite direction, so the work done is
W =- 10 N x 1.0 m = -10 J
Thus, the correct option is 2.
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predict the order of increasing electronegativity in each of the following groups of elements. (use < symbol to separate substances in the list.)
Electronegativity is a tendency of a atom/element to attract the pair of electrons.
B,O,Gaelectronegativity order = O>B>Ga
Mg,Ba,Caelectronegativity order = Mg>Ba>Ca
Ga,Al,Pelectronegativity order =P>Ga>Al
Al,O,Celectronegativity order =O>C>Al
When an atom of a certain chemical element forms a chemical bond, it has a propensity to draw shared electrons (or electron density). The atomic number and the separation of the valence electrons from the charged nucleus have an impact on an atom's electronegativity. An atom or a substituent group will draw electrons in greater amounts the higher the associated electronegativity. The sign and amplitude of a bond's chemical polarity, which characterizes a bond along the continuous scale from covalent to ionic bonding, can be quantitatively estimated using electronegativity. The inverse of electronegativity is electropositivity, which describes an element's propensity to accept valence electrons.
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why is it easy to pull downwards
Answer:Because you just really need help on your work!
Explanation:
Answer:
Gravity is on our side. On top of that, the optimal body position allows us to do it.
If the range of a projectile is and 256√3 m in the maximum height reached is 64 m. calculate the angle of projection
The angle of projection given that the range is 256√3 m and the maximum height reached is 64 m is 30°
Data obtained from the questionRange (R) = 256√3 mMaximum height (H) = 64 mAcceleration due to gravity (g) = 9.8 m/s²Angle of projection (θ) = ?How to determine the angle of projectionR = u²Sine(2θ) / g
256√3 = u²Sine(2θ) / 9.8
Cross multiply
256√3 × 9.8 = u²Sine(2θ)
Divide both sides by Sine(2θ)
u² = 256√3 × 9.8 / Sine(2θ)
H = u²Sine²θ / 2g
64 = [256√3 × 9.8 / Sine(2θ)] × [Sine²θ / 2 × 9.8]
64 = [256√3 / Sine(2θ)] × [Sine²θ / 2]
Recall
Sine²θ = SineθSineθ
Sine2θ = 2SineθCosθ
Thus,
64 = [256√3 / 2SineθCosθ] × [SineθSineθ / 2]
64 = 256√3 × Sineθ / 4Cosθ
Recall
Sineθ / Cosθ = Tanθ
Thus,
64 = 256√3 / 4 × Tanθ
Divide both side by 256√3 / 4
Tanθ = 64 ÷ 256√3 / 4
Tanθ = 0.5774
Take the inverse of Tan
θ = Tan⁻¹ 0.5774
θ = 30°
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Need answer asap. A spider spots a female on a branch 2.11m directly above. How fast mist the spider jump to reach that branch?
On a still water, a speedboat decreases its speed uniformly from 30 m/s to 20 m/s. How long does it take the boat to travel a distance of 200m?
a. -8 s
b. 8 s
c. -200 s
d. 200 s
Answer:
t=8
Explanation:
u have solution I give solution also
don't mark plzz follow y
What is audience going to be in the nine grade physic MCAS 
The audience for the 9th grade physics MCAS is students in the 9th grade who are taking the Massachusetts Comprehensive Assessment System (MCAS) physics exam.
How to explain the informationThe exam is designed to assess students' knowledge and skills in physics, and it is used to make decisions about students' placement in courses, graduation requirements, and eligibility for college and career programs.
The 9th grade physics MCAS is a multiple-choice exam that consists of 50 questions. The questions are based on the Massachusetts Curriculum Framework for Science, which outlines the standards that students are expected to meet in physics.
Students who take the 9th grade physics MCAS must score at least proficient in order to meet the state's graduation requirements. Students who score below proficient may be required to take additional courses or remediation.
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a rectangular container measuring 20cmX20cmX30cm is filled withn water.What is the mass of the voulme of water in kilogram and in grams?
Answer:
12,000 grams = 12 kg
Explanation:
Volume V = 20 x 20 x 30 cm³ = 12,000 cm³
density of water d = 1 g/cm³
so the mass is 12,000 grams = 12 kg
Which formula is used to find an object’s acceleration?
Its not A. btw
Can someone plz respond with an answer.
Answer:
Δv/Δt
Explanation:
I beat your game SAW.
Which atoms were cations?
Alkali and alkaline earth metals invariably produce cations.
What kind of compounds are cations?Calcium (Ca2+), potassium (K+), and hydrogen (H+) are a few examples of cations.
What does common cation mean?Positively charged ions are referred to as cations. Less electrons than protons make up cations. An ion can be made up of a single atom of an element (a monatomic ion, monatomic cation, or monatomic anion) or many atoms that are chemically connected to one another (a polyatomic ion or polyatomic cation or anion)
Alkali and alkaline earth metals always create cations, whereas halogens always produce anions. Most nonmetals normally create anions, while the majority of other metals typically produce cations (such as iron, silver, and nickel) (e.g. oxygen, carbon, sulfur)
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Smita is experimenting with how a paper airplane's shape affects the distance it will fly. Which action is the result of her logical reasoning? A. She records only the data that support her favorite hypothesis. B. She follows her procedure carefully. C. She decides to perform the experiment outside on a windy day. D. She decides to use the same type of paper for each airplane.
Answer:
So, the answer is eather B or D.
Explanation:
It could be b because she needs to make sure everything is good but it could be d because yopu need to keep everything the same. I personally would go d
in the figure a crate of mass m = 75 kg is pushed at a constant speed up a frictionless ramp (θ=34) by a horizontal force F. The positive direction of an X-axis is up the ramp, and the positive direction of a y-axis is perpendicular to the ramp. (a) What is the magnitude of F? (b) What is the magnitude of the normal force on the crate?
Explanation:
Thanx for the figure;
The force component of F UP the ramp that moves the crate must equal the force of the crate DOWN the ramp
75 kg = mg Newtons = 735.8 Newtons
Downplane force is 735.8 sin 34° = 411.4 Newtons
Fn =The horizontal force will be found by cos 34 = 411.4/ F F = 411.4/cos (34) = 496 N
Normal Force = 735.8 cos 34° = 610 N This part is due to the mass of the crate....there is additional normal force from the force pushing the crate up the hill (from below)
= F sin34 = 496 sin 34 = 277.4 N
SUM of normal forces = 610 + 277.4 = 887.4 N
Answer:
a. |F| ≈ 496 N
b. normal force ≈ 887 N
Explanation:
You want the magnitude of the horizontal force F that moves a crate up a 34° ramp at constant speed, and you want the magnitude of the normal force on the crate.
a) Force FThe constant speed of the crate tells you the net force up the ramp is zero. This is the sum of the component of force F in that direction and the force due to gravity in the opposite direction:
F·cos(34°) - m·g·sin(34°) = 0
F = mg·tan(34°) = (75 kg)(9.8 m/s²)tan(34°) ≈ 496 N
The magnitude of force F is about 496 N.
b) Normal forceThe normal force on the crate will be the sum of the component of F in that direction and the force due to gravity in the same direction:
F·sin(34°) +m·g·cos(34°) ≈ 887 N
The magnitude of the normal force is about 887 N.
Martin has hypothesized that the size and types of trees differ between valleys and higher elevations. He sets up a transect line in a wooded valley and randomly creates three 10 x 10 meter plots along the transect line, recording GPS coordinates for the northwest corner of each plot. He identifies and measures (diameter at breast height) every tree within the plots. He repeats this procedure in a wooded area on the ridge above the valley.
Using the scenario above, state the independent and dependent variables.
Answer: The dependent Variables include: Size and Types of trees.
The independent Variables include:
geographic elevations that is, valleys and the higher elevations.
Explanation:
The dependent variable simply refers to the variable a researcher tests or measures during an experiment. On the other hand, the independent variable simply refers to the variable that's controlled during an experiment.
Based on the definition above, the dependent variables include the size and the types of trees while the independent variables include the
geographic elevations that is, the valleys and the higher elevations.
The idea that John Marshall, the first Chief Justice of the Supreme Court, singularly established the principle of judicial review in Marbury v. Madison(1803)
a. Was an idea created and supported by James Madison and his friend Marbury.b. Is ridiculous because the US Supreme Court had made constitutional rulings well before Marbury v. Madison.c. Was an idea created and supported by Congress.d. Is a well established in the historical record and the papers of John Marshall
Answer:
c. Was an idea created and supported by Congress.
Explanation:
The idea that John Marshall, the first Chief Justice of the Supreme Court, singularly established the principle of judicial review in Marbury v. Madison(1803) was an idea created and supported by Congress.
Problem B.2: Escaping a Star (6 Points) It takes many years for a photon produced in a star's centre to reach its surface and escape into space. This is due to its constant interaction with other particles. To estimate the time it takes for a photon to escape a star's interior, we assume that the photon is deflected in equal time intervals into a random direction in a two-dimensional space (i.e., a random walk): At each step i, the photon moves a constant distance in an angle, thus changing its position: cos(4) sin(y) Ai, - c (a) Determine the distance R(n) from the centre (0,0) after n steps.
Answer:
This problem involves the concept of a random walk, which is a mathematical model of a path consisting of a succession of random steps.
The question asks for the distance, R(n), from the center of a star after n steps of a photon, assuming a 2D random walk.
The random walk in two dimensions has a step length of A_i and the direction of the steps is uniformly distributed in [0, 2π). The change in position after each step can be written in Cartesian coordinates (Δx, Δy), where Δx = A_i cos(θ_i) and Δy = A_i sin(θ_i).
The displacement from the center after n steps is given by the vector sum of all the individual steps. This vector sum can be written in terms of its Cartesian coordinates, (X, Y), where X = Σ Δx and Y = Σ Δy. This sum over n random vectors is itself a random variable. The net displacement R(n) from the center of the star after n steps is given by the magnitude of the net displacement vector:
R(n) = √(X² + Y²)
Because each step is independent and has a random direction, the expected value of the cosine and sine for any step is zero. This means that the expected values of X and Y are both zero.
However, the mean square displacement is not zero. Because the steps are independent, the mean square displacement in each direction is additive. For a 2D random walk:
<X²> = Σ <(Δx)²> = n <(A cos θ)²> = n A²/2
<Y²> = Σ <(Δy)²> = n <(A sin θ)²> = n A²/2
Because <X²> = <Y²>, we can write:
<R²> = <X²> + <Y²> = n A²
So, the root mean square distance (the square root of the mean square displacement) after n steps is:
R(n) = √(<R²>) = √(n) * A
Therefore, the distance R(n) that the photon is expected to be from the center of the star after n steps grows as the square root of the number of steps, with each step having a length A. Please note that this result holds for a 2D random walk. A real photon in a star would be performing a 3D random walk, which would have slightly different characteristics.
two point charge of 20nc and -20nc are situated at (1,0,0) and (0,1,0) in free. Determine the electric field intensity at (0,0,1)
The vector characteristics of the electric field allow to find the result for the electric field at the point of interest is;
The total electric field is \(E= 14.1 ( - \hat i + \hat j) \frac{N}{C}\)
Given parameters.
1) Electric charges:
q₁ = 20 nC = 20 10⁻⁹ C q₂ = -20 nC = -20 10⁻⁹ C2)Charge positions
r₁ = (1,0,0) = 1 \(\hat i\) m r₂ = (0,1,0) = 1 \(\hat j\) m3) Points of interest r = (0,0,1) = 1 \(\hat k\)
To find.
the electric field at point r.
The intensity of the electric field is given by the ratio of the electric force to the positive test charge at the point of interest.
\(E= k \frac{q}{r^2 }\)
where E is the electric field, k the constant of Coulomb, q the charge and r the distance.
In the attached we see a diagram of the test charges and the distance to the point of interest on the z axis.
Vector addition electric field
The total field is the vector addition of the fields created by each charge
\(E_{total} = E_1 +E_2\)
Let's look for the components of each electric field.
Field created by charge q₁
tan θ = \(\frac{z}{x}\)
tan θ = 1/1 = 1
tea = 45º
x-axis
cos 45 = \(\frac{E_{1x}}{E_1}\)
z axis
sin 45= \(\frac{E_{1z}}{E_1}\)
E₁ₓ = E₁ cos 45
\(E_{1z}\) = E₁ sin 45
Field created by load 2
y-axis
cos 45 = \(\frac{E_{2y}}{E_2}\)
z- axis
sin 45 = \(\frac{E_{2z}}{E_2}\)
\(E_{2y}\) = E2 cos 45
\(E_{2z}\) = E2 sin 45
We look for the components of the total electric field, where the signs are taken from the direction of the vectors in the attached.
\(E_{total} = - E_{1x} \hat i + E_{2y} \hat j + ( E_{1z} - E_{2z} ) \hat k\)
Let's substitute.
\(E_{total } = - E_1 cos 45 \hat i + E_2 cos 45 \hat j + (E_1 sin 45 - E_2 sin 45) \hat k\)
Calculate the distance and each electric field.
Let's find the distance for each charge to the test point using the Pythagorean Theorem.
r₁₃² = x² + z²
r₁₃² = 1 + 1
r₁₃² = 2
r₂₃² = y² + z²
r₂₃² = 1² + 1²
r₂₃² = 2
Let's look for the magnitud of the electric fields.
Charge q₁
\(E_1 = k \frac{q_1}{r_{13}^2}\)
E₁ = \(9 \ 10^9 \frac{20 \ 10^{-9}}{2}\)
E₁ = 20 N / m
Charge q₂
\(E_2 = k \frac{q_2}{r_{23}^2}\)
E₂ = \(9 \ 10^9 \frac{20 \ 10^{-9}}{2}\)
E₂ = 20 C / N
Let's substitute in the expression of the total eletric field.
\(E_{total} = -20 \ cos45 \ \hat i + 20 \ cos 45\ \hat j + ( 20 -20) sin 45 \ \hat k\)
\(E_{total} = 14.1 ( - \hat i + \hat j) \ \frac{N}{C}\)
In conclusion using the vector characteristics of the electric field we can find the result for the electric field at the point of interest is;
The total electric field is \(E = 14.1 ( - \hat i + \hat j ) \frac{N}{C}\)Learn more about the electric field here: brainly.com/question/14372859
A(n) ____ is an example of a mechanical wave.
Answer:
like fixing are car engine would be an example of a mechanical wave
What’s the meaning of physics??
Answer:the branch of science concerned with the nature and properties of matter and energy. The subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms.
Explanation:
A child at the beach digs a hole in the sand and, using a
pail, fills it with water having a mass of 1.20 kg. The mo-
lar mass of water is 18.0 g/mol. (a) Find the number of
water molecules in this pail of water. (b) Suppose the
quantity of water on the Earth is 1.32 1021 kg and re-
mains constant. How many of the water molecules in
this pail of water were likely to have been in an equal
quantity of water that once filled a particular claw print
left by a dinosaur?
Answer:
suppose the
quantity of water on the earth is 1.32 1021 kg and remains constant
the
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
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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Explain why refraction of light waves occurs
Answer:
As light waves transmit from one medium to another medium ( of different optical densities ), the speed of the light wave changes. When speed changes the direction of the wave changes hence refracted.
\(.\)
A ball is tossed up into the air with an initial speed of 5.0. How long does it take to return to the person's hand
Answer:
Explanation:
\(y(t) = 5t-5t^2\)
When y(t) = 0, the ball is on the hand.
\(0=5t-5t^2\\0=5t(1-t)\\t=0,1\)
It takes 1 second.
There are several different possibilities.
==> If the 5.0 means 5 miles per hour, that's 2.24 meters per second, up.
The acceleration of gravity is 9.8 m/s down, so the ball stops, turns around, and starts falling in (2.24/9.8) = 0.229 second. Then, after is starts to fall, it takes the same amount of time to the person's hand.
Total time = 0.457 second.
==> If the 5.0 means 5 meters per second, up . . .
The acceleration of gravity is 9.8 m/s down, so the ball stops, turns around, and starts falling in (5.0/9.8) = 0.51 second. Then, after is starts to fall, it takes the same amount of time to the person's hand.
Total time = 1.02 second.
==> If the 5.0 means 5 km/minute, that's about 83.33 meters per second, up.
The acceleration of gravity is 9.8 m/s down, so the ball stops, turns around, and starts falling in (83.33/9.8) = 8.503 seconds. Then, after is starts to fall, it takes the same amount of time to the person's hand.
Total time = 17.01 seconds.
==> If the 5.0 means 5 furlongs per fortnight, that's about 0.00083 meters per second, up.
The acceleration of gravity is 9.8 m/s down, so the ball stops, turns around, and starts falling in (0.00083/9.8) = 0.000085 second. Then, after is starts to fall, it takes the same amount of time to the person's hand.
Total time = 0.00017 second.
This is why all of your numbers always need their units.
I need help on this question, i might need an explanation.
In order to calculate the value of the sine of 40°, let's use a calculator with the value 40 and use the sine function.
We need to check if the calculator is in the "degree" mode, instead of the "radians" mode.
Then, calculating the sine of 40°, the result rounded to two decimal places is:
\(\sin40°=0.64\)Therefore the correct option is B.
Suppose, that you are measuring the length of a wood block and the edge of your block appears to be lined up exactly with a millimeter mark. How would you express the estimate part of a millimeter when you record the block’s length?
When taking the measurement, the estimate part of a millimeter when recording the block’s length can be expressed as ± 0.5 mm.
What are measurements?Measurements are the processes by which the attributes and properties of a given object or substance is quantified.
There are two types of measurements that can be obtained from any given object and they are:
quantitative measurementsqualitative measurementsQuantitative measurements measures the properties of objects in terms of numbers. Some examples of quantitative measurements are length, temperature, time, mass, etc.
Qualitative measurements describe the non-numerical features of objects such as color, texture, etc.
The measurement of length of a block of wood is a quantitative measurement.
The uncertainty or estimate of a measurement is half plus or minus the smallest division in the measurement.
The uncertainty or estimate of the millimeter block = ¹/₂ * 1 mm
The uncertainty or estimate of the millimeter block = ±0.5 mm
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Which one is the answer
The graph that shows the relationship between the speed and the kinetic energy is option B.
What is the relationship between kinetic energy and speed?Recall that the kinetic energy is referred to as the speed that a body possess by virtue of its motion. Thus an object that is in motion is said to posses the kinetic energy. The kinetic energy is the energy of an object that has a velocity
The kinetic energy is linearly related to the speed of the object. This implies that the speed is directly proportional to the kinetic energy of the object. If there is a direct relationship, it the follows that the graph of the speed against the kinetic energy of the object ought to be a straight line graph.
As such, the relationship between the kinetic energy and the speed of the object can be seen from the image in option B.
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A few years ago, the legal speed limit on the Turner Turnpike was changed from 55.0 mi/h to 75.0 mi/h.
How much time (in hours) was saved on the 86.0 mile trip from the Tulsa entrance to the Oklahoma City
exit for someone traveling at the legal speed limit?
The amount of time saved on the 86.0 mile trip from Tulsa entrance to Oklahoma City is 0.42 hours
What is time?
Time is the measurement of a past, present, or future event. The S.I unit of time is seconds (s)
To get the time that was saved on the 8.6-mile trip, we use the formula below.
Formula:
Ts = (d/v₁)-(d/v₂)................. Equation 1.Where:
Ts = Time saved on the tripd = distance covered during the tripv₁ = Initial legal speed limitv₂ = final/current legal speed limit.From the question,
Given:
d = 86.0 milev₁ = 55.0 mi/hv₂ = 75.0 mi/hSubstitute these values into equation 1
Ts = (86/55)-(86/75)Ts = 1.564-1.147Ts = 0.42 h.Hence, The amount of time saved on the 86.0 mile trip from Tulsa entrance to Oklahoma City is 0.42 hours.
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What average net force is required to stop a 3.5 kg bowling ball initially travelling at a speed of 1.5 m/s over a distance of 0.4 m?
First the aceleration:
Vf² = Vo² - 2ad
a = (Vf² - Vo²) / 2d
a = (0 m/s)² - (1,5 m/s)²) / 2 * 0,4 m
a = -2,25 m²/s² / 0,8 m
a = -2,81 m/s²
Now, for the net force, use 2nd law of Newton:
F = ma
F = 3,5 kg * (-2,81 m/s²)
F = -9,835 N
The force for stop the bowling ball is -9,835 Newtons.
How long does it take for the total energy stored in the circuit to drop to 10% of that value?
Express your answer with the appropriate units.A cylindrical solenoid with radius 1.00 cm
and length 10.0 cm
consists of 150 windings of AWG 20 copper wire, which has a resistance per length of 0.0333 Ω/m
. This solenoid is connected in series with a 10.0 μF
capacitor, which is initially uncharged. A magnetic field directed along the axis of the solenoid with strength 0.160 T
is switched on abruptly.
How long does it take for the total energy stored in the circuit to drop to 10% of that value?
Express your answer with the appropriate units.
The energy stored in the circuit at any time t is given by \(U = (1/2)L*I^{2} + (1/2)Q^{2} /C = (1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C))} + (1/2)C*V_{0} ^{2} *(1 - e^{(-2t/(R*C)})).\)The units are in seconds.
The total energy stored in the circuit can be calculated using the formula: U = (1/2)L*I² + (1/2)Q²/C, where L is the inductance, I is the current, Q is the charge on the capacitor, and C is the capacitance.
Initially, the capacitor is uncharged, so the second term is zero.
Therefore, the initial energy stored in the circuit is U₀ = (1/2)L*I₀², where I₀ is the initial current, which is zero.
When the magnetic field is switched on, a current begins to flow in the solenoid.
This current increases until it reaches its maximum value, given by I = V/R, where V is the voltage across the solenoid and R is its resistance.
Since the solenoid is connected in series with the capacitor, the voltage across the solenoid is equal to the voltage across the capacitor, which is given by V = Q/C, where Q is the charge on the capacitor.
The charge on the capacitor is given by Q = C*V, where V is the voltage across the capacitor at any time t.
Therefore, we have I = V/R = Q/(R*C) = dQ/dt*(1/R*C), where dQ/dt is the rate of change of charge on the capacitor.
This is a first-order linear differential equation, which can be solved to give \(Q(t) = Q_{0} *(1 - e^{(-t/(R*C)}))\), where Q₀ is the maximum charge on the capacitor, given by Q₀ = C*V₀, where V₀ is the voltage across the capacitor at t=0.
The current in the solenoid is given by I(t) = \(dQ/dt*(1/R*C) = (V_{0} /R)*e^{(-t/(R*C)}).\)
The energy stored in the circuit at any time t is given by\(U = (1/2)L*I^{2} + (1/2)Q^{2} /C = (1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C))} + (1/2)C*V_{0} ^{2} *(1 - e^{(-2t/(R*C)})).\)
The time t at which the energy stored in the circuit drops to 10% of its initial value can be found by solving the equation U(t) = U₀/10, or equivalently, \((1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C)}) + (1/2)C*V_{0} /R)^{2}*(1 - e^{(-2t/(R*C)})) = (1/20)L*I_{0} /R)^{2}.\)
This equation can be solved numerically using a computer program, or graphically by plotting U(t) and U₀/10 versus t on the same axes and finding their intersection point.
The solution is t = 1.74 ms.
The units are in seconds.
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The input and output forces for four machines are shown in the table. Machine Forces Machine Input Force (N) Output Force (N) 1 5 50 2 10 50 3 25 50 4 50 50 Which machine would have the greatest mechanical advantage? Responses 1 1 2 2 3 3 4
Machine 1 has the greatest mechanical advantage among the given machines. To determine the machine with the greatest mechanical advantage, we need to calculate the mechanical advantage for each machine.
Machine 1: Mechanical Advantage = Output Force / Input Force = 50 N / 5 N = 10
Machine 2: Mechanical Advantage = Output Force / Input Force = 50 N / 10 N = 5
Machine 3: Mechanical Advantage = Output Force / Input Force = 50 N / 25 N = 2
Machine 4: Mechanical Advantage = Output Force / Input Force = 50 N / 50 N = 1
Comparing the mechanical advantages, we can see that Machine 1 has the highest mechanical advantage of 10. This means that Machine 1 can multiply the input force by 10 to produce the output force. It provides the greatest amplification of force among the four machines.
Machine 2 has a mechanical advantage of 5, Machine 3 has a mechanical advantage of 2, and Machine 4 has a mechanical advantage of 1. Therefore, Machine 1 has the greatest mechanical advantage among the given machines.
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