The capacitor's energy reserve is [tex]\frac{1}{2} QV[/tex]
Consider a parallel plate capacitor that has a +q charge at all times.
giving a nominal fee "dq"
W.D = dw
V = d w / q
V = q/c
dw = (q/c) dq
In an electrical circuit, a capacitor is a component that is used to hold charges. A capacitor operates under the premise that when an earthed conductor is moved close to a conductor, its capacitance increases noticeably. As a result, a capacitor has two plates with equal and opposite charges that are spaced apart.
total W.D. in levying a fine plus Q
[tex]\int\limits dw = \int\limits^Q_0 (q/c) dq[/tex]
w = [tex]\frac{1}{c} \frac{Q^2}{2}[/tex]
The energy created by the work is then stored in the form of energy,
[tex]E = \frac{Q^2}{2C}[/tex]
and
[tex]Q = \frac{1}{2} CV^2[/tex]
[tex]Q = \frac{1}{2} QV[/tex]
The capacitor's energy reserve is
[tex]E = \frac{Q^2}{2C}[/tex]
[tex]E = \frac{1}{2} QV[/tex]
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Which of the following setup will the induced current be equal to zero?
There is a zero induced magnetic field in the image shown in A.
When would the induced current be zero?
We know that the principle of electromagnetic induction states that there would be an induced emf only when there is a change in the induced magnetic flux. In this case, we would have to look at each of the images so as to know where there is no change in the magnetic flux.
The induced current is zero in a conductor when there is no change in magnetic field passing through it as shown in image A.
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If f is the fraction of the light transmitted through the two polarizers, express f in terms of theta1 and delta theta12 (delta theta12=theta2-theta1
In this problem, y-polarized light passes through two polarizers. We need to look at the intensity of the light after passing through the first polarizer.
What is polarizer?With respect to the initial intensity and the angle between the transmission axis of the first polarizer and the y-axis, the intensity i 1 after passing through the first polarizer is the initial intensity. Multiply cos squared theta 1 before passing through the first polarizer. where theta 1 is the angle between the initial polarization direction of the light and the axis of motion of the first polarizer. So this is the intensity after passing through the first polarizer, which comes from the men's law in part b.
We need to know the intensity of the light after passing through the second polarizer, i.e. before entering the second polarizer. Their intensity is i 1 , which is the intensity after passing through the first polarizer, so i is 2 i 1 x cos 2 cos 2 alpha. where alpha is the angle between the two polarizers and the angle between the two polarizers is theta 2 - theta. 1 and theta 2 minus theta 1 can be written as delta theta 12 points. So this is the intensity after passing through his second polarizer. Now we need to find the fraction of light transmitted through the two polarizers with respect to theta 1 and the angle difference between the two polarizers. Therefore, i 2 equals i 1 cos delta squared, and theta 12 equals i 1 . Since we don't square cos theta 1, the part that passes through the two polarizers is the final light that passes through the second polarizer with the intensity. I 2 at the initial intensity. This is the part that passes through the two polarizers and is equal to cos squared theta 1. From this equation, i 2 on i does not give cos squared theta 1 times cos squared delta theta 12 . Now we need to find f like this cos squared theta 1 times cos squared delta theta 12 delta. Theta 12 is the difference in polarization angles of Theta 2 minus Theta. 1 theta 1 equals 36 degrees. Theta 2 is 56 minus theta 136 degrees. From this we get the fraction 0.5 8 points. This is the break and the solution is now complete.
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if you point toward the zenith today and point there again 45 days later, you will have pointed twice in the same direction relative to the
if you point toward the zenith today and point there again 45 days later, you will have pointed twice in the same direction relative to the your horizon
We put more restrictions and limitations on ourselves than what a balanced horizon requires. Sometimes we rely too much on our optimism and joy, losing sight of the reality of the situation. A horizon is actually trying to teach us that opportunities and difficulties are closely related to one another on the spectrum between our actions and the outcomes that follow. If we decide to choose our route and then put in the necessary effort, a horizon establishes the stage of life when positive things can occur. A warning about troublesome and troubling events is being sent by the horizon.
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A 0.018 kg marble sliding to the right at 0.42 m/s on a frictionless surface makes a elastic head-on collision with a 0.018 kg marble moving to the left at 0.32 m/s. After the collision, the first marble moves to the left at 0.27 m/s. What is the velocity of the second marble after the collision?A 0.018 kg marble sliding to the right at 0.42 m/s on a frictionless surface makes a elastic head-on collision with a 0.018 kg marble moving to the left at 0.32 m/s. After the collision, the first marble moves to the left at 0.27 m/s. What is the velocity of the second marble after the collision?
The velocity of the second marble after the collision is 0.47 m/s
According to conservation of linear momentum
The law of conservation of momentum states that in an isolated system the total momentum of two or more bodies acting upon each other remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed
M1u1 + M2u2 = M1v1 + M2v2
0.018 x 0.42 + 0.018 x 0.32 = 0.018 x 0.27 m/s + 0.018 x v2
0.00756 + 0.00576 = 0.00486 + 0.018 x v2
0.01332 = 0.00486 + 0.018 x v2
0.00846/0.018 = v2
v2 = 0.47 m/s
Hence, velocity of the second marble after the collision is 0.47 m/s
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You have isolated a highly lethal toxin from an octopus that you have reason to believe binds with high affinity to the pore opening of a voltage-gated sodium channel. To determine the effect of toxin binding, you perform a patch clamp experiment. Based on the following results, what do you conclude is the effect of the toxin on channel function (downward deflections indicate channel opening)?
Based on the results we conclude that the toxin delays channel closing.
What is toxin?A toxin is a naturally occurring organic poison created by the metabolic processes of living cells or organisms. In particular, toxins exist as proteins or proteins that have been conjugated. Organic chemist Ludwig Brieger (1849–1919)[4] coined the term "toxin," which is derived from the word "toxic."
Toxins can be small molecules, peptides, or proteins that can cause disease when they come into contact with or are absorbed by body tissues and interact with biological macromolecules like enzymes or cellular receptors. Toxins range widely in their toxicity, from typically minor (like a bee sting) to potentially fatal even at very low doses (such as botulinum toxin)
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4. A 400 kg car is traveling north at 15 m/s. It collides
with and sticks to a truck of mass 700 kg which was
traveling east at an unknown speed. The two stick
together and move initially in a direction 30 degrees
east of North. Determine the speed of the truck.
The speed of the truck is 20m/s
What is speed?
The speed of an object is described as the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time.
After the collision, the momentum of the car and the truck is given by:
p(total) = m(car) * v(total) + m(truck) * v(total)
where v(total) is the velocity of the two vehicles after the collision.
We can use the angle to find the velocity of the truck.
velocity of truck = velocity total * cos(30)
We then substitute the given values into the equation and solve for v(truck).
p(car) + p(truck) = p(total)
m(car) * v(car) + m(truck) * v(truck) = (m(car) + m(truck)) * v(total)
400*15 + m(truck) * v(truck) = (400 + 700) * v(total)
Therefore,
v(truck) = (40015 + 400v(total)) / 700
and
v(total) = v(truck) * cos(30)
v(truck) = (6000 + 400* v(truck)*cos(30)) / 700
Solving for v(truck) we get v(truck) = 20 m/s
In conclusion, the truck was traveling at 20 m/s before the collision.
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A racing car starts from rest and reaches a final speed v in a time t. If the acceleration of the car is constant during this time, which of the following statements must be true?
(a) The car travels a distance vt.
(b) The average speed of the car is v/2.
(c) The acceleration of the car is v/t.
(d) The velocity of the car remains constant.
(e) None of these.
Option - B : The average speed of the car is [tex]\frac{v}{2}[/tex] , If the acceleration of the car is constant from rest and reaches a final speed v in a time t .
The average velocity of the car is
[tex]\frac{v+v_{0} }{2}[/tex] = [tex]\frac{v + 0}{2}[/tex]
= [tex]\frac{v}{2}[/tex]
Acceleration refers to the speed at which velocity varies. Acceleration frequently, but not always, denotes a shift in speed. The direction of motion is changing, therefore an object travelling at a constant speed along a circular path is still going ahead. the rate of time-dependent velocity variation. Acceleration is a vector quantity because it has a both magnitude and a direction. The second derivative of position with respect to time or the first derivative of velocity with respect to time are also included. Acceleration is the rate at which an object's velocity varies in relation to time in physics. Newton's Second Law states that an object accelerates as a result of the total of all the forces acting on it.
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how do the following affect how can see an object? A. removing, blocking, or changing the light source, B. closing the eye, and changing the path of the light.
The following affect how can see an object is removing, blocking, or changing the light source. so, option (a) is correct.
What is light?
The electromagnetic radiation known as light is what enables the human eye to see and makes things visible. It can also be described as radiation that can be seen by humans. Light is made up of small energy packets called photons. Light moves in a straight line at all times.
What is light source?
An artificial or natural light source is anything that produces light. The Sun and stars are examples of natural light sources. Televisions and lampposts are examples of artificial lighting sources. Without light sources, we wouldn't be able to view the world around us, yet not all things we can see are light sources.
Therefore, following affect how can see an object is removing, blocking, or changing the light source. so, option (a) is correct.
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almost of stanley milgram's research subjects went all the way to what could have been a deadly jolt of electricity if the shock generator had been real. group of answer choices two-thirds three-quarters one half one-quarter
Almost two-third of Stanley Milgram's research subjects went all the way to what could have been a deadly jolt of electricity if the shock generator had been real. The word in the fill in blank is two-third.
All of the participants gave the initial mild levels of shock. Some refused to continue after about 150 volts. Others, continued to administer the shocks, under the pressure of the experimenter.
In the end, 65% of the participants continued giving the shock up to the 450 volts maximum, that shock was marked as “danger: severe shock”.
In sum, almost two-thirds of the men who participated had, shocked another person to death, all as part of a supposed experiment on learning.
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-- The complete question is, Almost __________ of Stanley Milgram's research subjects went all the way to what could have been a deadly jolt of electricity if the shock generator had been real.--
Which of the following is an accurate statement?which of the following is an accurate statement?the magnitude of a vector can be zero even though one of its components is not zero.rotating a vector about an axis passing through the tip of the vector does not change the vector.the magnitude of a vector is independent of the coordinate system used.even though two vectors have unequal magnitudes, it is possible that their vector sum is zero.it is possible to add a scalar quantity to a vector.
The accurate statement would be that the magnitude of a vector can be zero even though one of its components is not zero.
The magnitude of a vector is a scalar value that represents the length of a vector. It is calculated using the Euclidean distance formula and is independent of the direction of the vector. A vector with a magnitude of zero is known as the null vector, and it can be represented by a vector with all zero components. Thus, even though one of the components of a vector may not be zero, the magnitude of the vector can still be zero if the other components are sufficiently small.
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Your question seems to be missing, but I suppose the full question was:
"Which of the following is an accurate statement?
The magnitude of a vector can be zero even though one of its components is not zero.
Rotating a vector about an axis passing through the tip of the vector does not change the vector.
The magnitude of a vector is independent of the coordinate system used.
Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero
It is possible to add a scalar quantity to a vector."
A golf ball is hit off the ground with an initial velocity vo at an angle with respect to the horizontal. In the following questions you can safely ignore air resistance. a) Find an expression for how high in the air (verticle distance) the golf ball will travel (use vo, 0 and any other physical constants in your expression). b) Find an expression for how far (horizontal distance) the golf ball will travel. X X
An expression for how high in the air (vertical distance) the golf ball will travel is [tex]{eq}s=V_o \sin (31) t-\frac{gt^2}{2} {/eq}[/tex] and an expression for how far (horizontal distance) the golf ball will travel [tex]{eq}R=V_o \cos (31) ( t) {/eq}[/tex].
What is velocity?The scientific definition of velocity is probably similar to how you think of it. You are aware that a large displacement over a short period of time indicates a large velocity, and that velocity has units of distance / time, like miles/hour or kilometers/hour.
a) Golfer uses a six-iron with [tex]{eq}\alpha=31\enspace deg{/eq}[/tex]
The setting point at 2nd tree (14 m). Once we clear this height, we will check if the velocity we get will clear the 1st tree as well.
From Motion Equations:
[tex]{eq}s=V_o \sin (31) t-\frac{gt^2}{2} {/eq}[/tex]
since vertical distance is 14 m (minimum)
[tex]{eq}14=V_o \sin (31) t-\frac{9.81t^2}{2} {/eq}[/tex]
For Horizontal Component:
[tex]{eq}R=V_o \cos (31) ( t) {/eq}[/tex]
Since R=30+70=100
[tex]{eq}100=V_o \cos (31) ( t) {/eq}[/tex]
Getting t:
[tex]{eq}t=\frac{100}{V_o \cos (31) } {/eq}[/tex]
Substituting to 1st equation we get:
[tex]{eq}14=100 \tan (31)-4.9(\frac{100}{V_o \cos (31) })^2 {/eq}[/tex]
Solving for Initial Velocity:
[tex]{eq}V_o=38.0406\enspace m/s {/eq}[/tex]
Now, let's check if it clears the first tree.
[tex]{eq}R=V_o \cos (31) ( t) {/eq}[/tex]
Since R=30 m
[tex]${eq}t=\frac{30}{38.0406 \cos (31)} {/eq}[/tex]
[tex]{eq}t=0.92\enspace s {/eq}[/tex]
Substituting to Vertical Component:
[tex]{eq}s=V_o \sin (31) t-\frac{gt^2}{2} {/eq}[/tex]
[tex]{eq}S=13.47\enspace m {/eq}[/tex]
Since it is greater than 12 m, it clears the first tree.
Now the initial requirements are complied, let's solve for distance d (distance from the flag):
[tex]{eq}s=V_o \sin (31) t-\frac{gt^2}{2} {/eq}[/tex]
where S=0
Solving for time, we get:
[tex]{eq}t=3.9944\enspace s {/eq}[/tex]
Substituting to Horizontal Equation:
[tex]{eq}R=V_o \cos (31)(t) {/eq}[/tex]
[tex]{eq}R=130.25\enspace m {/eq}[/tex]
Solving for d:
[tex]{eq}d= (130.25)-(30+10+70) {/eq}[/tex]
[tex]{eq}d= (130.25)-(30+10+70) {/eq}[/tex]
[tex]{eq}d=20.25\enspace m {/eq}[/tex]
Thus, An expression for how high in the air (vertical distance) the golf ball will travel is [tex]{eq}s=V_o \sin (31) t-\frac{gt^2}{2} {/eq}[/tex] and an expression for how far (horizontal distance) the golf ball will travel [tex]{eq}R=V_o \cos (31) ( t) {/eq}[/tex].
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A block of metal requires a frictional force F to keep it moving with constant velocity across a surface. If the coefficient of friction is μ, then the normal force N is given by _____?
Answer: The normal force N is given by N = μ * F, where μ is the coefficient of friction and F is the frictional force required to keep the block of metal moving with constant velocity across a surface. The frictional force F is equal to the normal force N multiplied by the coefficient of friction μ. The normal force is the force exerted by the surface on the block of metal perpendicular to the surface, and it is what opposes the weight of the block and prevents it from sinking into the surface.
Explanation:
(d) for steady-level cruise, the engine thrust must equal drag and lift must equal weight. at 35,000 ft altitude, if the aircraft climbs at a rate of 500 ft/min, find the angle of climb and the proportional increment in net thrust needed to achieve this climb rate. assume l/d of 21.6.
The angle of climb is 3.2° and incremental thrust is 500 * W - (21.6) * T.
The lift-to-drag ratio (L/D) for an aircraft is equal to the ratio of lift to drag at constant velocity. For a steady-level cruise, lift must equal weight and engine thrust must equal drag. At 35,000 ft altitude, the aircraft needs an additional net thrust to climb at a rate of 500 ft/min.
To find the angle of climb
tanθ = V/g
θ = angle of climb
V = the climb rate (500 ft/min)
g = 32.2 ft/s2
tanθ = (500 ft/min)/(32.2 ft/s2)
θ = 3.2°
The lift force, L, must equal the weight of the aircraft, W. The drag force, D, must equal the thrust force, T.
L = W
D = T
The lift-to-drag ratio, L/D, is given as 21.6.
L/D = 21.6
The rate of climb is 500 ft/min.
R = 500 ft/min
Using the equation for rate of climb:
R = (T - D) / W
to get extra thrust ΔT:
ΔT = R * W - D
ΔT = 500 * W - D
= 500 * W - (L/D) * T
= 500 * W - (21.6) * T
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In 1993 the radius of Hurricane Emily was about 350 km/h. The wind speed near the center ("eye") of the hurricane, whose radius was about 30 km, reached about 200 km/h. As air swirled in from the rim of the hurricane toward the eye, its angular momentum remained roughly constant. A) Estimate the wind speed at the rim of the hurricane. B) Estimate the pressure difference at the earth's surface between the eye and the rim (Hint: The density of air (1 atm, 20 C) is 1.20 kg/m^3 .) C) Where is the pressure greater? The eye or the rim D) If the kinetic energy of the swirling air in the eye could be converted completely to gravitational potential energy, how high would the air go?
The wind speed at the rim of the hurricane is 17.14[tex]\frac{km}{hour}[/tex] and the pressure difference at the earth's surface between the eye and the rim is 1835 N/m² and the air would go high to 157.50m.
The wind speed at the rim of the hurricane will be calculated thus:
speed= [tex]\frac{200\times30}{350}[/tex]
speed= 17.14[tex]\frac{km}{hour}[/tex]
The pressure difference at the earth's surface between the eye and the rim will be:
=[tex](\frac{1}{2}\times 120\times55.56x^{2} -4.76^{2} )[/tex]
= 1835 N/m²
Kinetic Energy = Gravitational Potential Energy
[tex]\frac{1}{2}mv^{2}=mgh[/tex]
h = [tex]\frac{v^{2}}{2g}[/tex]
h=[tex]\frac{55.56^{2}}{2\times 9.8}[/tex]
h= 157.50 m
Although air can be compressed, it does not satisfy the Bernoulli equation. There are many factors that affect how the air behaves, including:
Higher altitudes have a lower temperature
Temperature and density are correlated.
High altitudes have lower pressure levels.
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Need this by midnight!! Will name brainliest if correct.
Q₁ = -2 x 10⁻⁶ C, Q₂ = -1 x 10⁻⁶ C, x = 51 cm
Calculate the magnitude of the electric field at point P in units of N/C.
Round to the nearest whole number.
(please also show explanation!)
Answer:
Rounded to the nearest whole number the electric field is 899000000
Explanation:
To calculate the magnitude of the electric field at point P, we can use Coulomb's law, which states that the force between two point charges is given by F = k * Q₁ * Q₂ / r², where k is Coulomb's constant, Q₁ and Q₂ are the charges, and r is the distance between the charges.
In this case, we are trying to find the electric field at point P, which is the force per unit charge. So we can find the force on a small test charge, q, placed at point P and divide by q to find the electric field.
F = k * Q₁ * q / x²
E = F/q
where E is electric field,
k = 8.99 x 10⁹ N.m²/C²
x = 51 cm = 0.51 m
Q₁ = -2 x 10⁻⁶ C
q = -1 x 10⁻⁶ C
Substituting these values into the equation, we get:
E = (k * Q₁ * q) / x²
E = (8.99 x 10⁹ N.m²/C² * -2 x 10⁻⁶ C * -1 x 10⁻⁶ C) / (0.51 m)²
E = -8.99 x 10⁹ N/C
The magnitude of the electric field at point P is 8.99 x 10⁹ N/C.
Rounded to the nearest whole number the electric field is 899000000 N/C.
A small object begins a free‑fall from a height of 22.0 m. After 1.10 s, a second small object is launched vertically upward from the ground with an initial velocity of 32.0 m/s. At what height ℎ above the ground will the two objects first meet?
Answer:
To find the height at which the two objects will first meet, we need to use the equations of motion for free fall and vertical upward motion.
The equation for free fall is:
h = h0 + v0t + (1/2)at^2
where h is the height of the object at time t, h0 is the initial height, v0 is the initial velocity (which is zero for free fall), and a is the acceleration due to gravity (which is 9.8 m/s^2 downward).
The equation for vertical upward motion is:
h = h0 + v0t - (1/2)gt^2
where h is the height of the object at time t, h0 is the initial height, v0 is the initial velocity, and g is the acceleration due to gravity (which is 9.8 m/s^2 downward).
We know that the first object is in free fall, and that it began at a height of 22.0 m. We also know that the second object was launched upward with an initial velocity of 32.0 m/s, 1.10 s after the first object was released.
We can use these values to find the height of the first object at the time the second object is launched:
h1 = 22.0 + 0 + (1/2)(-9.8)(1.10^2) = 20.27 m
We can use this value as the initial height for the second object:
h2 = 20.27 + 32.0(1.10) - (1/2)(-9.8)(1.10^2) = 37.47 m
Now we need to find the time at which the two objects will meet. We can use the height of the first object at the time the second object is launched, and the equation for free fall to find the time it takes for the first object to reach the height of the second object:
37.47 = 20.27 + 0 + (1/2)(-9.8)t^2
Solving for t, we find that the objects will meet at a time of approximately 1.47 seconds.
Finally, we can use this time to find the height at which they will meet:
h = 22.0 + 0 + (1/2)(-9.8)(1.47^2) = 37.47 m
So the objects will first meet at a height of 37.47 m above the ground.
when a jumbo egg was dropped from 5 meters onto a 1-inch foam surface, it fractured. which of the following changes in conditions would lead to a safe landing? select all that would. A.Change the egg size to a large egg.
B.Change the drop height to 1 meter.
C.Change the landing surface to a box of foam.
When a jumbo egg was dropped from 5 meters and fractured upon landing on a 1-inch foam surface, there were two changes in conditions that would have likely led to a safe landing. Option B and C are correct.
The first change is to lower the drop height. The force of the impact is proportional to the height from which the egg is dropped, so reducing the height would reduce the force of the impact and make a safe landing more likely. For example, if the height was reduced to 1 meter, the force of the impact would be one fifth of what it was when dropped from 5 meters.
The second change is to provide more cushioning upon impact. The 1-inch foam surface did not provide enough cushioning to absorb the force of the impact and protect the egg, but using a box of foam as the landing surface would increase the amount of cushioning and reduce the force of the impact. The more cushioning there is, the less the force of the impact will be and the more likely it is that the egg will have a safe landing.
In conclusion, reducing the drop height and providing more cushioning upon impact are two changes in conditions that would have led to a safe landing for the jumbo egg when dropped. It is important to keep in mind that the specifics of each situation will affect the outcome, and it is necessary to consider various factors, such as the size and type of egg, the height and surface upon landing, and the speed and angle of impact, to determine the best way to ensure a safe landing.
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you have a stopped pipe of adjustable length close to a taut 62.0 cm , 7.25 g wire under a tension of 4510 n . you want to adjust the length of the pipe so that, when it produces sound at its fundamental frequency, this sound causes the wire to vibrate in its second overtone with very large amplitude. the speed of sound in air is 344 m/s .
The required length of the pipe when tension in the pipe is given is calculated to be 0.1144 m.
The length of the taut is given as L = 62 cm = 0.62 m
Mass of the wire is given as 7.25 g = 7.25 x 10⁻³ kg
Tension in the wire = 4510 N
The speed of sound is 344 m/s.
We first determine the wave's speed on a string to get the length of the pipe by:
v = √F/μ ----(1)
where,
v = speed
F = tension
μ = linear density
m is the mass, and L is the length, so = m/L.
Thus, v = √FL/m = √(4510)(0.62)/(7.25 x 10⁻³) = √(385.68 x 10³) = 10 ×√(3856.8) = 621.03 m/s
Now, we use to determine the wire's frequency
f = n v /L
where, f is frequency
Second overtone has large amplitude, n = 3
f = 3(621.03)/2×0.62 = 1502.49
Using the second equation, we can now determine the pipe's length. the frequency of the pipe and the wire is the same, therefore,
f = n v /2L
n = 1, fundamental frequency
L = v/2f = 344/(2×1502.49) = 344/3004.98 = 0.1144 m
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A 3kg book is resting high on a book shelf. If the book has 73.5 J of potential energy, how high is the shelf?
2.5m
If this book slipped off the shelf and fell all the way to the ground, how much kinetic energy would it have the instant it hit the ground (if we ignore air resistance)?
____J
Answer:
0 J
Explanation:
1. We know that U = mgh,
h = U/mg
or h = 73.5/3*9.8 = 2.5 m
2. When the book falls on the ground, there will be no kinetic energy by the book as the book will once again be stationary, and will convert this kinetic energy to other forms, so your answer must be 0 J.
A particle undergoes three consecutive displacements given by vectors D1 = (2.5î − 3.5ĵ − 3.0 k) mm, D2 = (2.5î − 2.0ĵ + 3.0 k) mm, and D3 = (−8.5î + 9.0ĵ + 8.0 k) mm. a-Find the resultant displacement vector of the particle (in mm).
D = mm (b) What is the magnitude of the resultant displacement (in mm)? mm
(c) If all displacements were along one line and in the same direction, how far would the particle travel (in mm)? mm
a) The resultant displacement vector of the particle is given by the vector sum of all three displacement vectors, which is D = D1 + D2 + D3 = (-5î + 3.5ĵ + 8.0k) mm.
What is resultant displacement?Resultant displacement is a vector which describes the total change in position from the starting point to the ending point. It is calculated by adding the individual displacements of the same body in different directions. Resultant displacement is the magnitude of the displacement vector which is the shortest distance between the two points.
b) The magnitude of the resultant displacement is given by the magnitude of the resultant vector, which is
|D| = √(-5)² + 3.5² + 8.0² = 8.9 mm
c) If all displacements were along one line and in the same direction, then the particle would travel the distance of the magnitude of the resultant vector, which is 8.9 mm.
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Nonreflective coatings on camera lenses reduce the loss of light at the surfaces of multilens systems and prevent internal reflections that might mar the image. Find the minimum thickness of a layer of magnesium fluoride (n = 1.38) on flint glass (n = 1.66) that will cause destructive interference of reflected light of wavelength 455 nm near the middle of the visible spectrum. Non-Reflective Coatings: The camera lenses are provided with anti-reflective coatings, which works on the principle of destructive interference of light reflected from the interface. The coating provides double interfaces, one with air, another with lens. When light reflects from both the interfaces, it undergoes destructive interference, and therefore reflection of light is minimised.
The minimum thickness of the magnesium fluoride coating to cause destructive interference of reflected light of wavelength 455 nm is 144 nm.
The minimum thickness of the magnesium fluoride coating that will cause destructive interference of reflected light of wavelength 455 nm can be calculated using the formula for the optical thickness of a coating:
t = m * λ / (4 * (n1 - n2))
where:
t = minimum thickness of coating
m = an integer, representing the order of the destructive interference
λ = wavelength of light (455 nm)
n1 = refractive index of air (approximately 1)
n2 = refractive index of flint glass (1.66)
For destructive interference to occur, the optical thickness of the coating must be equal to an odd multiple of one-quarter of the wavelength of light. In this case, we will use m = 1:
t = 1 * 455 nm / (4 * (1 - 1.66))
t = approximately 144 nm
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A freight company uses a compressed spring to shoot 1.90 kg packages up a 1.00 m-high frictionless ramp into a truck. The spring constant is 391 N/m and the spring is compressed 32.0cm.
1. What is the speed of the package when it reaches the truck?
2. A careless worker spills his soda on the ramp. This creates a 50.0 cm-long sticky spot with a coefficient of kinetic friction 0.300. Will the next package make it into the truck?
a. The speed of the package when it reaches the truck is 1.7 m/sec.
b. No, the next package will not make it into the truck.
a. The speed of the package when it reaches the truck is calculated using the equation for potential energy, PE = 1/2kx², where k is the spring constant and x is the amount of compression (30 cm).
PE = 1/2(500N/m)(0.30m)²
PE = 4.5 J
The kinetic energy, KE, of the package when it reaches the truck is equal to the potential energy, so:
KE = 4.5 J
Using the equation KE = 1/2mv², where m is the mass of the package (2.0 kg) and v is the velocity, we can calculate the velocity.
4.5 J = 1/2(2.0 kg)(v²)
v = 1.7 m/sec
b. The package will not make it into the truck due to the increased friction from the sticky spot. The energy dissipated due to friction will be greater than the kinetic energy of the package, resulting in the package not having enough energy to make it up the ramp.
Complete Question:
A freight company uses a compressed spring to shoot 2.0kg packages up a -high frictionless ramp into a truck, as FIGURE P10.51 shows. The spring constant is 500N/m and the spring is compressed 30cm.
a. What is the speed of the package when it reaches the truck?
b. A careless worker spills his soda on the ramp. This creates a 50-cm-long sticky spot with a coefficient of kinetic friction 0.30. Will the next package make it into the truck?
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Which one to pick
the steps that involve hydrogen during photosynthesis
The steps are shown, but they are not in the correct order.
1 - Water is broken down into oxygen and hydrogen.
2 - Glucose is broken down to be used by plants.
3 - Hydrogen combines with carbon dioxide to form glucose.
4 - Hydrogen enters the plant as part of water.
The correct order of steps (4,1,3,2) that show how hydrogen is involved during photosynthesis is as follows:
4 - Hydrogen enters the plant as part of water.1 - Water is broken down into oxygen and hydrogen.3 - Hydrogen combines with carbon dioxide to form glucose.2 - Glucose is broken down to be used by plants.What is Photosynthesis?Green plants use the process of photosynthesis to create their own nourishment with the help of solar energy.
Certain compounds are necessary for photosynthesis and are employed as reactants. Water, carbon dioxide, and solar light energy are some of these substances.
The correct steps are 4, 1, 2, 3
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An air-conditioning system requires a 34-m-long section of 12-cm-diameter ductwork to be laid underwater. Determine the upward force the water will exert on the duct. Take the densities of air and water to be 1.3 kg/m3 and 1000 kg/m3, respectively.
The upward force the water will exert on the dust is 3770.3 Newton. The result is obtained by using the formula for buoyant force.
What is buoyant force?According to Archimedes principle, the buoyant force is the upward force exerted by a fluid on an object placed in them. The magnitude of the buoyant force is equal to the weight of a fluid displaced by an object.
The buoyant force can be expressed as
Fb = ρgV
Where
Fb = buoyant forceρ = density of fluidg = acceleration due to gravityV = volume of object immersed under the fluidWe have a ductwork with
L = 34 md = 12 cm = 0.12 mρ air = 1.3 kg/m³ρ water = 1000 kg/m³Find the upward force by the water on the duct!
The upward force exerted is called the buoyant force. So, we can solve the problem by using the formula above.
We find the volume immersed under the water.
V = πr²L
V = π(½d)²L
V = ¼πd²L
V = ¼(3.14)(0.12)²(34)
V = ¼(3.14)(0.12)²(34)
V = 0.384336 m³
We use g = 9.81 m/s². The upward force will be
Fb = ρgV
Fb = 1000 × 9.81 × 0.384336
Fb ≈ 3770.3 Newton
Hence, the water will exert the upward force of 3770.3 Newton on the duct.
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Determine the stiffness kt of the single spring such that the force f will stretch it by the same amount s as the force f stretches the two springs. express kt in terms of stiffness k1 and k2 of the two springs.
The stiffness of the single spring kt is k1 + k2, if the force f stretches it by the same amount s as the force stretches the two springs.
The force f will stretch the single spring and the two springs by the same amount s if the following equation is satisfied:
f / kt = s
f / (k1 + k2) = s
where kt is the stiffness of the single spring, k1 and k2 are the stiffnesses of the two springs, f is the force, and s is the stretch.
Solving for kt, we get:
kt = f / s = k1 + k2
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consider a charging capacitor. it turns out that there is a magnetic field in the space between the capacitor plates essentially equal to that outside the plates, even though there is no (real) current between the plates. (a) compute the magnetic field in the loop l. assume full symmetry so that the field is purely azimuthal.
The magnetic field in the loop l is equal to the magnetic field outside the loop, which is assumed to be purely azimuthal.
A magnetic field is a region of space in which a magnetic force is exerted by a magnet, electric current, or moving charged particles. This force is what causes a compass to point north and is responsible for many of the phenomena associated with electricity and magnetism.
For a symmetrical capacitor, the magnetic field between the capacitor plates is equal to the magnetic field outside the plates, as there is no real current between the plates. Therefore, the magnetic field in the loop l is equal to the magnetic field outside the loop, which is assumed to be purely azimuthal. Thus, the magnetic field in the loop l is equal to the azimuthal component of the magnetic field outside the loop, which can be calculated using the equation:
B = μ0*I/2πr,
where μ0 is the permeability of free space, I is the current in the loop, and r is the radius of the loop.
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Which of the following mechanisms is most important quantitatively for the exchange of electrolytes across capillaries?
Bulk flow is the most important mechanism for the exchange of electrolytes across capillaries.
This is because the capillary walls are permeable to electrolytes, allowing them to move freely through the capillary wall to be exchanged between the interstitial fluid and the blood. This is known as bulk flow, and it is responsible for the majority of electrolyte exchanges between the two fluids.
In addition to bulk flow, other mechanisms are involved in the exchange of electrolytes across capillaries. These include:
Diffusion is the process of molecules moving from an area of higher concentration to an area of lower concentration. Osmosis is a special kind of diffusion, where a solvent (usually water) is moved from an area of lower solute concentration to an area of higher solute concentration. Active transport is the movement of molecules against a concentration gradient, and is powered by energy from ATP.Learn more about capillaries:
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Explain how gravity is at the center of many of the motion and force equations. How does gravity impact sound waves.
Answer:
Gravity is at the center of many motion and force equations because it is a fundamental force that affects the motion of objects in the universe. The force of gravity can be described by Newton's law of gravitation, which states that two objects in the universe are attracted to each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
This force of gravity affects the motion of objects in the universe, including the motion of sound waves. Sound waves are disturbances that propagate through a medium, such as air or a solid, and transfer energy from one location to another. The presence of a gravitational field can alter the speed and path of sound waves.
For example, the speed of sound is influenced by the local pressure and temperature of the medium, and these can be affected by gravity. In a uniform gravitational field, the pressure decreases with height, which can result in a reduction in the speed of sound. In contrast, if the medium is accelerating, such as in a rocket, the effective gravity experienced by the medium can change, which can alter the speed of sound.
In summary, gravity plays a central role in many motion and force equations, and it can also impact the behavior of sound waves by altering the speed and path of the waves in a gravitational field.
Explanation:
Gravity is one of the four fundamental forces and it attracts all the matter with mass.
What is the interaction between gravity and sound wave?Contrary to popular belief, heavy metal music isn't actually heavy. The mass of sound waves is negative, and they can interact through gravity. So, sound rises, to put it another way.
By accounting for intricate particle interactions that had previously been disregarded, Angelo Esposito at Columbia University in New York and his colleagues estimated the link between sound and gravity. According to their findings, sound waves should have a detrimental effect even though it is minor.
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Determine the algebraic sign of alex's x velocity and y velocity at the instant he leaves the ground at the edge of the crevasse.
Alex's velocity as he leaves the ground is +,0 after it leaves the player's hand at the instant before he leaves the ground is +,-.
at the highest point of the ball,
A group of terms combined using addition, subtraction, multiplication, and division constitute an algebraic expression.
Expressions made from constants and variables are known as algebraic expressions. Any value is possible for a variable. For instance, the formula 6 x + 5 comprises two terms. The variable, its coefficient, and the constant term are represented by the numbers 7 x, 5 y.
Consequently, the algebraic expression just before he rises off the ground is positive and negative.
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A worker carries cement blocks weighing 1.50 X 102 N each, up a ladder onto a scaffold
8.00 m high at a constant velocity. The worker carries them at a rate of 2 blocks per
minute.
How much work is done by the worker in 10.0 minutes?
How much work is done in 1.00 hour?
The work that is done in 10 minutes is 6000 J
Work that is done in one hour is 36000 J
What is work done?Work is done when a force acts on an object and causes it to move in the direction of the force. The amount of work is calculated as the product of the force and the distance over which it acts.
Now we know that the work that have been done by the person that is carry the block is;
Work = Force * Distance
Force = 1.50 X 10^2 N
Distance = 8.00 m
Work = 1.50 X 10^2 N * 8.00 m
= 1200 J
Work done in 10 minutes = 5 * 1200 J = 6000 J
Work done in one hour = 30 * 1200 = 36000 J
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