Answer:
Explanation:
Use that:
[tex]F=-\vec{\nabla}U(x,y)=-\left(\hat{i} \frac{\partial U}{\partial x}+\hat{j}\frac{\partial U}{\partial y}\right)=-11.6x\hat{i}+10.8y^{2}\hat{j}[/tex]
Then use the 2nd Newton's Law of Motion:
[tex]\vec{a}=\frac{\vec{F}}{m}=\frac{-11.6x\hat{i}+10.8y^{2}\hat{j}}{0.04}=-290x\hat{i}+270y^{2}\hat{j}[/tex]
At x = 0.3 and y = 0.6, we can find the acceleration as:
[tex]\vec{a}=-87\hat{i}+97.2\hat{j}[/tex] (in SI unit)
Then the magnitude of the acceleration on that point is:
[tex]a=\sqrt{(-87)^{2}+(97.2)^{2}}\approx 130.44[/tex] (SI Unit)
What is the electric field strength inside the capacitor? What is the potential energy of a proton at the midpoint of the capacitor?
Answer:
2.4*10^-17 J
Explanation:
E = V/d = 300 V / 3*10^-3 m = 1.0*10^5 V/m
Voltage at midpoint = E*d = 1.0*10^5 V/m * 1.5*10^-3 m = 150 V
ΔV = 300 V - 150 V = 150 V
Charge of a proton = 1.6*10^-16 C
U = qΔV = (1.6*10^-16 C)(150V) = 2.4*10^-17 J
The electric field strength inside the capacitor is 100,000 V/m, the Potential difference at the midpoint is 150V, and the potential energy of a proton at the midpoint of the capacitor is 2.403 x 10⁻¹⁷J.
What is a capacitor?A capacitor is an electronic device that stores electrical energy in an electric field between two conducting plates separated by a dielectric material. When a voltage difference is applied across the plates, a charge is stored on each plate, creating an electric field between the plates. The capacitor can then release this stored electrical energy when needed.
The energy stored in a capacitor is given by the formula:
U = [tex]\frac{1}{2}[/tex]CV²
Where
U =the energy stored in the capacitor,
C = the capacitance of the capacitor,
V =the voltage difference across the plates.
Capacitance is a measure of the ability of a capacitor to store charge and is given by the formula:
C = εA/d
Where C = the capacitance,
ε = the permittivity of the dielectric material between the plates,
A = the area of the plates,
d =the distance between the plates.
Here in the question
To calculate the electric field strength inside the capacitor, we can use the formula:
E = V/d
Where E = the electric field strength,
V =the voltage difference between the plates,
d =the distance between the plates.
In this case, the distance between the plates is d=3mm =0.003m,
the voltage difference is between 0V to 300V.
Now, the electric field strength inside the capacitor is:
E = V/d = 300V/0.003m = 100,000 V/m
To calculate the potential energy of a proton at the midpoint of the capacitor, we can use the formula:
U = qV
Where U = the potential energy,
q =the charge of the particle,
V =the voltage difference between the plates.
In this case, we need to know the charge of the proton.
The charge of a proton = +1.602 x 10⁻¹⁹ C.
At the midpoint of the capacitor, the proton will experience a potential difference of 150V (half of the 300V voltage difference).
Now, the potential energy of the proton at the midpoint of the capacitor is:
U = qV = (1.602 x 10⁻¹⁹ C) x (150V) = 2.403 x 10⁻¹⁷J
Therefore, the electric field strength is 100,000 V/m and the potential energy of a proton at the midpoint of the capacitor is 2.403 x 10⁻¹⁷J.
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A combination of two identical resistors connected in series has an equivalent resistance of 12. ohms. What is the equivalent resistance of the combination of these same two resistors when connected in parallel?
Answer:
R1 + R2 = R = 12 for resistors in series - so R1 = R2 if they are identical
2 R1 = 12 and R1 = R2 = 6 ohms
1 / R = 1 / R1 + 1 / R2 for resistors in parallel
R = R1 * R2 / (R1 + R2) = 6 * 6 / (6 + 6) = 3
The equivalent resistance would be 3 ohms if connected in parallel
Express this as y=mx + c
1.
[tex] \frac{1}{y} = \alpha ( {x - 6)}^{ - b} [/tex]
Answer:
let alpha be y,
1/2=y(x-6)^(-b)
1/2=y(1/x-6)
1/2=y/x-6
x-6=2y
x-6/2=y
(1/2)x-(6/2)=y
y=(1/2)x-3
Two identical spheres, A and B, carry charges of
+6 microcoulombs and -2 microcoulombs,
respectively. If these spheres touch, what will be
the resulting charge on sphere A?
The resulting charge in sphere A from the two given different charges is determined as +2 μC.
Resulting of the two speheres
The resulting charge of the two spheres is determined by suming the two individual charges together as shown below;
Resulting charge = +6 μC - 2 μC
Resulting charge = +4 μC
Charge in sphere AThe resulting charge will be distributed uniformly between the two spheres and charge in sphere A and B will be equal.
Charge in sphere A = charge in sphere B = ¹/₂ x +4 μC = + 2 μC
Thus, the resulting charge in sphere A from the two given different charges is determined as +2 μC.
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How do kinetic and potential energy transfer to one throughout a roller coaster ride?
Answer:
As the cars ascend the next hill, some kinetic energy is transformed back into potential energy. Then, when the cars descend this hill, potential energy is again changed to kinetic energy. This conversion between potential and kinetic energy continues throughout the ride.
Explanation:
hope it helps U
How does the gravitational force between two objects change if the distance between the objects doubles?
a)
The force decreases by a factor of 4.
b)
The force decreases by a factor of 2.
c)
The force increases by a factor of 4.
d)
The force increases by a factor of 2.
if the distance between the objects is doubled the force is reduced by a factor of 4
Whats is gravitational force?Gravitational force is the force of attraction between objects in the universe.
f = G * m1 * m2 / r^2
f = gravitational force
G = gravitational constant
m1 = mass of object 1
m2 = mass of object 2
r = distance between the objects
From the formular, the gravitational force and the distance is an inverse relationship so increasing the distance by a factor results to reduction of the force by the square of the factor. hence doubling the distance which is distance mutiplied by 2 will lead to reduction of the force by 2^2 = 4
Therefore: The force decreases by a factor of 4.
hope it helps
A ball is dropped off of a building and falls past a window that is 2.2m long. If it takes .28s for the ball to cross the window what is the distance from the top of the building to the top of the window?
Answer:
oh what do you believe this one
In absence of friction, to bring an object to rest
a. a force must act in the same direction of its direction of motion
b. a force may not be necessary
C. the object will come to rest by itself
d. a force must act in the opposite direction of its direction of motion
You want to improve your dominant trait score, and you decide to take daily walks by yourself. What trait will you strengthen with this activity?
Muscles such as quadriceps, hamstrings, the calf muscles and the hip adductors get stronger by walking.
Which muscles get stronger due to walking?The quadriceps, hamstrings, the calf muscles and the hip adductors are the muscles which get stronger by doing walking because impact is produced on these muscles while walking. Walking is a good exercise which have many health benefits.
So we can conclude that muscles such as quadriceps, hamstrings, the calf muscles and the hip adductors get stronger by walking.
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Answer:
introversion is the correct answer
Explanation:
God bless! Have a great day!
Parallel field lines evenly spaced and all pointing left labeled B. There is a point with a vector down labeled v. There is a circle next to the point labeled F. Use the right-hand rule for magnetic force to determine the charge on the moving particle. This is a charge.
By using the right-hand rule for magnetic force to determine the charge on the moving particle, it's a negative charge.
What is magnetic force?It should be noted that the magnetic force simply means the attraction or repulsion that arises between electrically charged particles.
The right-hand rule for magnetic force states that to determine the direction of the magnetic force, one should point the right thumb in the direction of the velocity.
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Answer:
Particle q1 has a charge of 2.7 μC and a velocity of 773 m/s. If it experiences a magnetic force of 5.75 × 10–3 N, what is the strength of the magnetic field?
✔ 2.8
T
In the same magnetic field, particle q2 has a charge of 42.0 μC and a velocity of 1.21 × 103 m/s. What is the magnitude of the magnetic force exerted on particle 2?
✔ 0.12
N
Explanation:
Hope this helps
Starting from Newton’s Third Law F₁₂ = -F₂₁ derive the Law of Conservation of Momentum for an elastic collision.
From Newton’s Third Law, the Law of Conservation of Momentum for an elastic collision is derived as m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
Newton's third lawThis law states that action and reaction are equal and opposite. That is the force applied to an object is equal to the reaction received by the object.
F₁₂ = -F₂₁
m₁a₁ = -m₂a₂
m₁v₁/t = -m₂v₂/t
m₁v₁ = -m₂v₂
m₁v₁ + m₂v₂ = 0
For an elastic collision involving two objectsThe sum of the initial momentum must be equal to sum of final momentum.
let initial velocity = ulet final velocity = vm₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Thus, from Newton’s Third Law, the Law of Conservation of Momentum for an elastic collision is derived as m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
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Write any two differences between series combination and parallel combination of cells.
Answer:
Your answer is attached above
Hope it helps
TC
have a great time
A tire on a car is rolling smoothly. Its center of mass is moving at 18 m/s. How fast is the top of the tire moving in m/s
For a tire on a car is rolling smoothly and It's center of mass is moving at 18 m/s, the speed of the top of the tire is mathematically given as
Vtop=36m/s
What is the speed of the top of the tire?Generally, the equation for the relationship between the top and the core is mathematically given as
Vtop=2*(vcore)
Threrefore
Vtop=2*18
Vtop=36m/s
In conclusion, the speed of the top
Vtop=36m/s
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a bulb rated 100 watt 120 volt is connected across a 120 volt source find the current in the bulb and power consumed by it
As it mentioned
100W/120VSo
power is 100W
Now
Current be I
[tex]\\ \rm\rightarrowtail I=\dfrac{P}{V}=\dfrac{100}{120}=\dfrac{5}{6}=0.8A[/tex]
A solenoid has 450 loops each of radius 0.0254 m. The field increases from 0 T to 3.00 T in 1.55 s. What is the EMF generated in the coil? (Hint: What is the area of a circle) (Unit = Volts)
Answer:
0.175 second
Explanation:
i hope it helps
"A ball with a mass of 0.1 kg is rolling at a velocity of 5 m/s. What is its
momentum?" What Given is the 5 in this problem? *
mass
velocity
acceleration
momentum
Answer:
velocity
Explanation:
because the si unit of mass is kg, velocity is m/s, acceleration is m/S2 , moment is kgm2/s . so 5 is given as velocity.
An elastic string of length 20cm stretch by 7mm under a load 50N . The strain in the spring is?
Answer:
0.035
Explanation:
7÷1000
=0.007m
0.007/0.2
=0.035
Mechanical strain of an elastic substance is the ratio of its change in length to the original length. The strain of the elastic string of length 20 cm when stretched by 7 mm is 0.035.
What is strain ?Strain is a physical quantity used to express the change in dimension of an elastic material. It is the ratio of change in length to the original length. Stress is the force that causing the deformation.
According to Hook's law of elasticity, the strain is directly proportional to the strain. They show a linear relation. Let L be the original length of a string and its change in length be ΔL.
Thus, strain = ΔL / L
Given that, the change in length = 7 mm = 0.7 cm
original length of the string = 20 cm
strain = 0.7 cm/ 20 cm
= 0.035
Therefore, the strain of the elastic string of length 20 cm when stretched by 7 mm is 0.035.
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The terminal velocity of a 3 × 10^-5 raindrop is about 9 m/s. Assuming a drag force Fd = −bv, determine (a) the value of the constant b and (b) the time required for such a drop, starting from rest, to reach 63% of terminal velocity.
Based on the data provided, the value of the constant b is 3.27 × 10^-5 kg/s and the time required to reach 63% of terminal velocity is 0.58 s.
What is terminal velocity?The terminal velocity of a body is the velocity at which the body falls at constant velocity through a fluid.
For the falling raindrop, let positive direction be downwards and negative direction upwards,
mass of the raindrop, m = 3×10-5 kg velocity at time t, is v(t)terminal velocity, v0 = 9 m/sgravitational acceleration, g = 9.81 m/s²The raindrop experiences a downward gravitational force mg, and an upward drag force -bv.
The total force at a time t is given as
F(t) = mg - bv(t)a)
Terminal velocity is achieved then the total force is 0,
0 = mg - bv0
Therefore
b = mg/v0
Substitutingthe values:
b = (3 × 10^-5 × 9.8)/9
b = 3.27 × 10^-5 kg/s
b) Applying Newton's Second Law
F = ma
where
a = v/tF = mgTherefore,
mg = mv/t t = v/g
however, t is at 63% velocity
thus:
t = 0.63v/g
t = 0.63 × 9 /9.8
t = 0.58 s
Therefore, the value of the constant b is 3.27 × 10^-5 kg/s and the time required to reach 63% of terminal velocity is 0.58 s
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Two bodies of specific heats S1 and S2 having the same heat capacities are combined to form a single composite body. What is the specific heat of the composite body?
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Heat capacity of body 1 :
[tex]\qquad \sf \dashrightarrow \:m_1s_1[/tex]
Heat capacity of body 2 :
[tex]\qquad \sf \dashrightarrow \:m_2s_2[/tex]
it's given that, the the head capacities of both the objects are equal. I.e
[tex]\qquad \sf \dashrightarrow \:m_1s_1 = m_2s_2[/tex]
[tex]\qquad \sf \dashrightarrow \:m_1 = \dfrac{m_2s_2}{s_1} [/tex]
Now, consider specific heat of composite body be s'
According to given relation :
[tex]\qquad \sf \dashrightarrow \:(m_1 + m_2) s' = m_1s_1 + m_2s_2[/tex]
[tex]\qquad \sf \dashrightarrow \:s' = \dfrac{ m_1s_1 + m_2s_2}{m_1 + m_2}[/tex]
[tex]\qquad \sf \dashrightarrow \:s' = \dfrac{ m_2s_2+ m_2s_2}{ \frac{m_2s_2}{s_1} + m_2 }[/tex]
[ since, [tex] m_2s_2 = m_1s_1 [/tex] ]
[tex]\qquad \sf \dashrightarrow \:s' = \dfrac{ 2m_2s_2}{ m_2(\frac{s_2}{s_1} + 1)}[/tex]
[tex]\qquad \sf \dashrightarrow \:s' = \dfrac{ 2 \cancel{m_2}s_2}{ \cancel{m_2}(\frac{s_2}{s_1} + 1)}[/tex]
[tex]\qquad \sf \dashrightarrow \:s' = \dfrac{ 2 s_2}{ (\frac{s_2 + s_1}{s_1} )}[/tex]
[tex]\qquad \sf \dashrightarrow \: s' = \dfrac{2s_1s_2}{s_1 + s_2} [/tex]
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why some aqutatic plants float an water give reason science subjects class 4
A car accelerates to a speed of 55 m/s within the span of 8 seconds. If its acceleration
was 4 m/s2, what was its initial velocity? Show all work and units for full credit.
The initial velocity of a car that accelerates to a speed of 55 m/s within the span of 8 seconds is 23m/s.
How to calculate initial velocity?The initial velocity of a moving body can be calculated using the following formula:
a = v - u/t
Where;
a = acceleration (m/s²)v = final velocity (m/s)u = initial velocity (m/s?t = time (seconds)According to this question, a car accelerates to a speed of 55 m/s within the span of 8 seconds. If its acceleration was 4 m/s², the initial velocity is calculated as follows:
4 = 55 - u/8
32 = 55 - u
u = 55 - 32
u = 23m/s
Therefore, the initial velocity of a car that accelerates to a speed of 55 m/s within the span of 8 seconds is 23m/s.
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The figure (Figure 1) shows a pV diagram for 4.00×10−3 mole of ideal H2 gas. The temperature of the gas does not change during segment bc. What volume does this gas occupy at point c?
The volume that the gas will occupy based on the temperature given will be 0.80 liters.
How to calculate the volume?From the information, it was stated that the figure shows a pV diagram for 4.00×10−3 mole of ideal H2 gas and that the temperature of the gas does not change during segment bc.
Therefore, the volume will be:
= (0.20) × (2.0/0.50)
= 0.20 × 4
= 0.80
In conclusion, the volume is 0.80 liters.
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Which material is a good heat conductor ?
Answer:
wood lighters gasoline hope it helps
Explanation:
Pls helppppp my last question!
Answer:
load
a generator, a light bulb (load) and a closed switch
Explanation:
as explained in the other question, the fan is using generated electric energy to create mechanical movement. as such it is a load on the grid or circuit or net.
and electric power can only flow, if there is a closed (uninterupted) circuit from the power source to a load and back.
any open switch is an interruption of the circuit.
a buzzer is a kind of switch. it closes the circuit (and puts a load on) only when somebody presses it.
by the way, a closed circuit without a load will "destroy" (short circuit) the power source or at least the wires (burn through).
Which term describes living things?
A) We shiver when we get cold.
B) Moss on the side of the tree is active even though it looks still.
C) Human kidneys produce urine.
D) A rabbit gets nutrients from a carrot.
Answer:
Explanation:
define key terms related to the muscular, skeletal, and nervous systems
Answer:
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Topic : Heat
1. Why can anyone put their fingers beside the flame of a lit candle without getting burned, but not above the flame?
2. What is the purpose of putting holes near the top of a metal lampshade?
3. A metal spoon is placed in one of two identical cups of hot coffee. Which cup will be cooler after a few minutes?
A disk of radius a has a total charge Q uniformly distributed over its surface. The disk has negligible thickness and lies in the xy plane.
What is the electric potential V(z) on the z axis as a function of z , for z>0 ?
What is the magnitude E of the electric field on the z axis, as a function of z , for z>0 ?
The electric potential V(z) on the z-axis is : V = [tex](\frac{Q}{a^2} ) [ (a^2 + z^2)^{\frac{1}{2} } -z[/tex]
The magnitude of the electric field on the z axis is : E = kб 2[tex]\pi[/tex]( 1 - [z / √(z² + a² ) ] )
Given data :
V(z) =2kQ / a²(v(a² + z²) ) -z
Determine the electric potential V(z) on the z axis and magnitude of the electric fieldConsidering a disk with radius R
Charge = dq
Also the distance from the edge to the point on the z-axis = √ [R² + z²].
The surface charge density of the disk ( б ) = dq / dA
Small element charge dq = б( 2πR ) dr
dV [tex]\frac{k.dq}{\sqrt{R^2+z^2} } \\\\= \frac{k(\alpha (2\pi R)dR}{\sqrt{R^2+z^2} }[/tex] ----- ( 1 )
Integrating equation ( 1 ) over for full radius of a
∫dv = [tex]\int\limits^a_o {\frac{k(\alpha (2\pi R)dR)}{\sqrt{R^2+z^2} } } \,[/tex]
V = [tex]\pi k\alpha [ (a^2+z^2)^\frac{1}{2} -z ][/tex]
= [tex]\pi k (\frac{Q}{\pi \alpha ^2})[(a^2 +z^2)^{\frac{1}{2} } -z ][/tex]
Therefore the electric potential V(z) = [tex](\frac{Q}{a^2} ) [ (a^2 + z^2)^{\frac{1}{2} } -z[/tex]
Also
The magnitude of the electric field on the z axis is : E = kб 2[tex]\pi[/tex]( 1 - [z / √(z² + a² ) ] )
Hence we can conclude that the answers to your question are as listed above.
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how does the gravitational pull of the blue supergiants impact the direction of your star?
Answer:
Blue supergiants represent a slower burning phase in the death of a massive star. Due to core nuclear reactions being slightly slower, the star contracts and since very similar energy is coming from a much smaller area (photosphere) then the star's surface becomes much hotter.
Explanation:
I know this may not be the answer youre looking for, but hopefully this can help somehow!
A 100 Ohm, 200 Ohm, and 400 Ohm resistors are in parallel with each other. What is the equivalent
resistance? Which resistor would draw the most current, and why?
Answer:
1/R = 1/R1 + 1/R2 + 1/R3
1/1 + 1/2 + 1/4 = 1 + .5 + .25 = 1.75
1/1.75 = .572
multiplying this by 100 gives us
R = 57.2 ohms
The smallest resistor (100 ohms) will draw the most current
(One can also use R = R1 R2 R3 / (R1 R2 + R1 R3 + R2 R3)
Hi there!
We can use the following equation to solve for equivalent resistance:
[tex]\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}[/tex]
We can plug in the givens and solve.
[tex]\frac{1}{R_T} = \frac{1}{100} + \frac{1}{200} + \frac{1}{400} \\\\\frac{1}{R_T} = 0.175\\\\R_T = \frac{1}{0.175} = \boxed{57.143 \Omega}[/tex]
The resistor that would draw the most current is the 100 Ohm resistor because current chooses the path of LEAST RESISTANCE. This can also be proved mathematically with the following:
For resistors in parallel, the POTENTIAL DIFFERENCE (VOLTAGE) is the same.
Since I = V/R, a smaller 'R' means a larger 'I'. Thus, the smallest resistor would have the greatest current through it.