The potential difference between the head and the tail of a displacement vector that points at right angles to a uniform electric field is zero (0).
A uniform electric field refers to the electric field having the same magnitude and direction at all points in space. A uniform electric field is created by two parallel plates that have the same charge density and are close enough to each other that the edges can be ignored. The electric field strength of a uniform electric field is constant, which means that the direction and magnitude are the same at all points in space.
The potential difference between the head and tail of a displacement vector that points at right angles to a uniform electric field is zero (0). It is because the potential difference between two points is equal to the negative of the work done per unit charge in moving a positive test charge from one point to another point. When a displacement vector that points at right angles to a uniform electric field is moved from one point to another, no work is done because the electric field and displacement vector are perpendicular. As a result, the potential difference is zero.
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if two flutists play their instruments together at the same intensity, is the sound twice as loud as that of either flutist playing alone at that intensity? why or why not?
No, the sound wouldn't be twice as loud as that of either flutist playing alone at that intensity. The increase in sound intensity would be less than twice as loud.
This is because when two sound waves coincide, the amplitude of the resulting sound wave is the sum of the amplitudes of the individual sound waves. That is, when two identical sound waves come together, they create a new sound wave that is slightly louder than the original sound wave, but not twice as loud.
Furthermore, sound intensity is affected by the distance from the sound source, and when two flutists are playing together, the sound waves produced have to travel further before they reach the listener, thus reducing the intensity of the sound.
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how much thermal energy in calories is absorbed by 750.0g of water when its temperature increases from 15.4c t 86.3c
750.0 g of water at a temperature of 15.4°C will absorb 9,117.2 calories of thermal energy to increase its temperature to 86.3°C. This can be calculated by using the specific heat formula:
Q = m * c * ΔT
where:
Q = thermal energy (calories)
m = mass of water (g)
c = specific heat (calories/g°C)
ΔT = change in temperature (°C)
Therefore:
Q = 750.0 g * 4.184 calories/g°C * (86.3°C - 15.4°C)
Q = 9,117.2 calories
Thermal energy is the energy generated in the form of heat. It is a type of kinetic energy that is produced by moving particles that makeup matter. The movement of molecules generates heat energy in the form of kinetic energy. The faster the molecules move, the more thermal energy is generated.
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A long solenoid has 100 turns/cm and carries current i. an electron moves within the solenoid in a circle of radius 2.30 cm perpendicular to the solenoid axis. the speed of the electron is 0.0460c (c speed of light). find the current i in the solenoid.
The current in the solenoid becomes 3.56 A.
How to find current in the solenoid?
Number of turns in the solenoid, n = 100 turns/cm
Radius of the circular path of electron, r = 2.30 cm
Speed of electron, v = 0.0460c, where c is the speed of light
To find: Current in the solenoid, i
Formula used: Magnetic field inside the solenoid,
B = μ0ni Where, μ0 = 4π × 10⁻⁷ T m/A is the permeability of free spaceSolution:
The force on a moving electron in a magnetic field is given by
F = Bev
Where B is the magnetic field, e is the charge of an electron and v is its velocity.
The force acting on the electron provides the necessary centripetal force for the electron to move in a circle of radius r.
So,
Bev = (mev²)/r
where me is the mass of an electron
On simplifying the above equation, we get
Be = (mev)/r
Put the value of B from the formula of magnetic field inside the solenoid, B = μ0ni
we get
μ0ni = (mev)/r
Solve for i,
i = (mev)/(μ0nr)
Substitute the given values and solve
i = (9.109 × 10⁻³¹ kg × 0.0460c × 3 × 10⁸ m/s)/(4π × 10⁻⁷ T m/A × 100 turns/cm × 2.30 cm)i
= 3.56 A
Therefore, the current in the solenoid is 3.56 A.
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the photo at right was taken through a specroscope. what color was the pigment extract used to produce this spectrum? what colo(s) did this extract absorb?
Light is a form of energy. All the properties of light can be explained by Considering the Wave length and lespuscutar theory.
The Wave Theory states that waves are how light moves across space. When Visible light is passed through a prim it is split up into seven colours which corresponds to definite wave length. a phenomenon Called dispersion. The study of interaction between matter and electromagnetic radiation is defined as spectroscopy.
A spectrophotometer is a device which detect the percentage transmittance of light radiation. When light of certain intensity and frequency range is passed through the Sample Thus the instrument Compare the intensity of the transmitted light with that of the incident light.
A spectroscope is a device that divides light into its individual wavelengths to produce a spectrum.
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What is the transfer of thermal energy called?
Answer:
Conduction
Explanation:
The process by which heat energy is transmitted through collisions between neighboring atoms
the rotational speed of a flywheel increases by 40%. by what percent does its rotational kinetic energy increase? explain your answer.
The rotational kinetic energy of a flywheel increases by 80% when its rotational speed increases by 40%. This is because the rotational kinetic energy of a flywheel is directly proportional to the square of its angular velocity.
The rotational speed of a flywheel increases by 40%. The percentage increase in its rotational kinetic energy is approximately 96.8%. Suppose the initial rotational speed of the flywheel is n1 and the initial rotational kinetic energy is K.E.1. After the speed of the flywheel is increased by 40 percent, the new speed is n2 = n1 + 0.4n1 = 1.4n1.
Then the new kinetic energy K.E.2 of the flywheel is given by K.E.2 = (1/2)I(n2^2)where I is the moment of inertia of the flywheel.Since n2 = 1.4n1, we have [tex]K.E.2 = (1/2)I(1.96n1^2) = 0.98I(n1^2).[/tex].
Therefore, the percentage increase in the rotational kinetic energy of the flywheel is approximately 96.8%.
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discuss how errors due to earth curvature and refraction can be eliminated from the differential leveling process.
Errors due to earth curvature and refraction can be eliminated from the differential leveling process by using the trigonometric leveling method.
This method utilizes the principle of triangles to determine the height difference between two points on the Earth's surface.
The trigonometric method begins by measuring the horizontal angle between two points, then the vertical angle between the same two points, and finally the distance between the points.
The trigonometric method is not affected by the curvature of the Earth or refraction since the vertical angle is measured at a given distance instead of the line of sight.
Therefore, the measurements of the angles and distances remain unaffected.
The trigonometric leveling process is as follows: first, an instrument is set up at point A. A second instrument is then set up at point B, and both instruments are leveled.
The horizontal angle between the two points is then measured with a theodolite, followed by the vertical angle. Lastly, the distance between the two points is measured using a tape measure.
After all the measurements are taken, the results are then used in a trigonometric formula to calculate the difference in elevation between the two points.
This method eliminates errors due to refraction or the Earth's curvature, since the elevation difference is not determined by the line of sight, but rather by the measured angles and distance.
The trigonometric leveling method is the best method to eliminate errors due to the Earth's curvature and refraction from the differential leveling process.
This method uses trigonometric principles and measurements to accurately calculate the difference in elevation between two points.
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CQ6.07 Given: L = 26 mH (milli H) The inductor current i changes 9.1 A/ms (Amps per milli sec) for a short while. What is the voltage across the inductor during this period? VL = ?? V
The voltage across the inductor during the period when the current changes at 9.1 A/ms with an inductance of 26 mH is 236.6 V.
An inductor is an electrical component that stores energy in a magnetic field when a current passes through it. An inductor is a device that opposes any change in the current flowing through it. The inductor is represented by the symbol L and is measured in henries (H).
The difference in electrical potential between two points in a circuit is known as voltage. The unit of voltage is volts (V).
The voltage across an inductor can be calculated using the formula:
[tex]v = L(di/dt)[/tex]
where v is the voltage, L is the inductance, and [tex]di/dt[/tex] is the rate of change of current.
Substituting the given values, we get:
[tex]v = 26\ mH \times (9.1 \ A/ms)[/tex]
Note that the units for inductance and rate of change of current must be consistent, so we convert the inductance to henries (H) and the rate of change of current to amps per second (A/s):
[tex]v = 0.026\ H \times (9100 \ A/s)[/tex]
[tex]v = 236.6 \ V[/tex]
Therefore, the voltage across the inductor during this period is 236.6 V.
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The sound level produced by one singer is 71.8 dB. What would be the sound level produced by a chorus of 45 such singers (all singing at the same intensity at approximately the same distance as the original singer)? Answer in units of dB.
The sound level produced by a chorus of 45 singers would be approximately 88.3 dB.
How to find the sound level produced by a chorus of 45 singers?Assuming that the sound level of each singer is independent and the same, the sound level produced by a chorus of 45 singers can be calculated using the following formula:
L2 = L1 + 10 log (N2/N1)
where:
L1 = the sound level of one singer = 71.8 dB
N1 = the number of singers in the original group = 1
N2 = the number of singers in the new group = 45
L2 = the sound level of the new group
Substituting the values in the formula, we get:
L2 = 71.8 + 10 log (45/1)
L2 = 71.8 + 10 log (45)
L2 = 71.8 + 16.5
L2 = 88.3 dB
Therefore, the sound level produced by a chorus of 45 singers would be approximately 88.3 dB, assuming all the singers are singing at the same intensity at approximately the same distance as the original singer.
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in which region are the temperatures and pressures at which it's possible to change the phase of x by raising or lowering the temperature?
The region in which it is possible to change the phase of x by raising or lowering the temperature is: phase transition region.
This region is typically marked by an increase in pressure and a decrease in temperature. Temperature and pressure are inversely proportional to one another within this region, meaning that as pressure increases, temperature decreases and vice versa.
The exact temperature and pressure at which the phase transition occurs depends on the type of material being transitioned and its individual characteristics. For example, water boils at 100°C and 1 atm of pressure while other substances may have different boiling points.
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a 170-hz sound travels through pure helium. the wavelength of the sound is measured to be 5.92 m. what is the speed of sound in helium?
The speed of sound in pure helium is approximately 1006.4 m/s.
When a sound wave travels through a medium, it produces a series of compressions and rarefactions in the medium, which causes the particles of the medium to vibrate. The speed of sound in a particular medium depends on the physical properties of the medium, such as its density, elasticity, and temperature.
The speed of sound in helium can be calculated using the formula,
speed of sound = frequency x wavelength
Given that the frequency of the sound is 170 Hz and the wavelength is 5.92 m, we can plug in these values and get,
speed of sound = 170 Hz x 5.92 m
speed of sound = 1006.4 m/s
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how long must a 0.70- mm -diameter aluminum wire be to have a 0.42 a current when connected to the terminals of a 1.5 v flashlight battery?
To determine the length of an aluminum wire required to carry a certain current, one must use the formula: r = (ρL) / (πr²), where r is the radius of the wire, ρ is the resistivity of the wire, and L is the length of the wire is 48.54 m.
What is the length of the wire?A 0.70 mm diameter aluminum wire has a radius of 0.35 mm or 0.00035 m. The resistivity of aluminum is 2.82 × 10⁻⁸Ωm. The formula for current is:
I = V / R
where, V is voltage, and R is resistance. We can rearrange this to:
R = V / I
Plugging in the given values of 0.42 A and 1.5 V gives R = 3.571 Ω. The resistance of a wire is given by:
R = ρL / A
where, A is the cross-sectional area of the wire, and ρ is its resistivity.
We know the resistivity of aluminum and the radius of the wire, so we can calculate the cross-sectional area of the wire:
A = πr² = 3.1416 × (0.00035 m)² = 3.848 x 10⁻⁷ m². Substituting all the values in the formula for the resistance of the wire and solving for L gives:
L = RA / ρ = (3.571 Ω) × (3.848 x 10⁻⁷ m²) / (2.82 × 10⁻⁸ Ωm) = 48.54 m.
Therefore, the aluminum wire must be 48.54 m long to have a current of 0.42 A when connected to the terminals of a 1.5 V flashlight battery.
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what is the equation to find the equivalent resistance, req, of two resistors in series, r1 and r2? group of answer choices
The equivalent resistance of resistors in series is always greater than the individual resistances. This is because the total resistance of the circuit is the sum of the resistances, and therefore the electric current has to overcome more resistance to flow through the circuit as compared to when a single resistor is used.
To find the equivalent resistance, req, of two resistors in series, r1 and r2, the following equation is used:
Req = R1 + R2
Where Req is the equivalent resistance of the series circuit,
R1 is the resistance of the first resistor,
R2 is the resistance of the second resistor.
Resistors in a circuit are the components that oppose the flow of electric current. When two resistors are connected in series, they are connected end to end so that the electric current flows through one resistor before flowing through the second one.In a series circuit, the equivalent resistance, req, is calculated as the sum of the individual resistances of the resistors connected in series.
Therefore, to find the equivalent resistance of two resistors in series, R1 and R2, we add the resistance values of the two resistors, as shown in the formula above.
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Two large parallel metal plates carry opposite charges. They are separated by 10 cm and p. D of 500 volts is applied on them. What is the magnitude of electric field strength between them? compute the work done by the field on a change of 2x10^-9 as it moves from higher to lower part?
(a) The magnitude of electric field in the region between the plates is [tex]\mathbf{9 , 2 5 0}$ $\mathrm{V} / \mathrm{m}$.[/tex]
(b) The magnitude of the force the field exerts on a particle with the given charge i[tex]s $2.22 \times 10^{-5} \mathrm{~N}$.[/tex]
(c) The work done by the field on the particle as it moves from the higher potential plate to the lower is[tex]$8.88 \times 10^{-7} \mathrm{~J}$.[/tex]
(d) the change of the potential energy is[tex]$8.88 \times 10^{-7} \mathrm{~J}$.[/tex]
(a) The magnitude of electric field in the region between the plates is calculated as;
[tex]$$\begin{aligned}& E=\frac{V}{d} \\& E=\frac{370}{40 \times 10^{-3}} \\& E=9,250 \mathrm{~V} / \mathrm{m}\end{aligned}$$[/tex]
(b) The magnitude of the force the field exerts on a particle with the given charge is calculated as follows;
[tex]$$\begin{aligned}& F=E q \\& F=9,250 \times 2.4 \times 10^{-9} \\& F=2.22 \times 10^{-5} \mathrm{~N}\end{aligned}$$[/tex]
(c) The work done by the field on the particle as it moves from the higher potential plate to the lower is calculated as follows;
[tex]$$\begin{aligned}& W=F d \\& W=2.22 \times 10^{-5} \times 40 \times 10^{-3} \\& W=8.88 \times 10^{-7} \mathrm{~J}\end{aligned}$$[/tex]
(d) the change of the potential energy is calculated as;
[tex]$$\begin{aligned}& \Delta U=q \Delta V \\& \Delta U=q\left(V_1-V_2\right)\end{aligned}$$$$\text { DeltaU }=2.4 \times 10^{-9}(370)$$$$\Delta U=8.88 \times 10^{-7} \mathrm{~J}$$[/tex]
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Full Question: Two large, parallel, metal plates carry opposite charges of equal magnitude. They are separated by a distance of 40.0 mm, and the potential difference between them is 370 V
A. What is the magnitude of the electric field (assumed to be uniform) in the region between the plates?
B. What is the magnitude of the force this field exerts on a particle with a charge of 2.40 nC ?
C. Use the results of part (b) to compute the work done by the field on the particle as it moves from the higher-potential plate to the lower.
D. Compare the result of part (c) to the change of potential energy of the same charge, computed from the electric potential.
suppose you have an atwood machine with two different masses m and m. what are the external forces acting on this system?
The external forces acting on this system are: gravity and the tension in the string.
An Atwood machine is a system consisting of two masses, m, and m, connected by a string that passes over a pulley. In this system, the external forces are gravity and the tension in the string. Gravity pulls both masses downward, while the tension in the string acts in opposite directions on the two masses, pulling the heavier one down and the lighter one up.
The tension in the string is determined by the masses m and m and the acceleration of the system. If m is the heavier mass and m is the lighter mass, the tension in the string will be greater than if both masses had the same weight. This is because the tension must balance the gravitational forces on the two masses. The greater the mass, the greater the gravitational force, and the greater the tension in the string must be to balance it.
The acceleration of the system is determined by the masses, the tension in the string, and the amount of friction in the system. The greater the tension, the greater the acceleration, and the smaller the mass, the greater the acceleration. Friction acts against the acceleration, reducing the net acceleration of the system.
In summary, the external forces acting on an Atwood machine with two different masses m and m are gravity and the tension in the string. The tension in the string is determined by the masses and the acceleration of the system, while the acceleration is determined by the masses, the tension in the string, and the amount of friction in the system.
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the reason distance has a greater effect on the force of gravity between our earth and moon is because the distance between them is
The reason distance has a greater effect on the force of gravity between our Earth and Moon is because the distance between them is relatively large.
The reason distance has a greater effect on the force of gravity between the Earth and the Moon is because the force of gravity between two objects decreases with the square of the distance between them. This is known as the inverse square law of gravity.
The force of gravity between two objects is proportional to the product of their masses, and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as,
F = G * (m1 * m2) / r^2
where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
In the case of the Earth and the Moon, their masses are fixed, so the only variable that affects the force of gravity between them is the distance. As the distance between the Earth and the Moon increases, the force of gravity between them decreases rapidly, according to the inverse square law.
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--The complete question is, Fill in the blank, the reason distance has a greater effect on the force of gravity between our earth and moon is because the distance between them is ________________.--
g what is the relationship between the wavelength of light, its color, and the energy of its photons?
Shorter wavelengths of light correspond to higher frequencies, and higher frequencies of light correspond to more energy in the photons. This means that the color of light is related to the energy of its photons: the higher the frequency of light, the higher the energy of its photons and the closer the color is to the blue end of the visible light spectrum.
The relationship between the wavelength of light, its color, and the energy of its photons is as follows:
The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. In simpler terms, the shorter the wavelength of light, the greater the energy of its photons, while the longer the wavelength of light, the less energy its photons possess. The relationship between the wavelength of light and its color is also direct in that different colors are a result of light waves of different wavelengths.
The color spectrum ranges from red (longest wavelength) to violet (shortest wavelength), with colors in between, such as orange, yellow, green, blue, and indigo. This spectrum represents the visible part of the electromagnetic spectrum, with ultraviolet and infrared light having shorter and longer wavelengths, respectively. The energy of photons from these parts of the spectrum follows the same pattern as visible light, with ultraviolet photons possessing more energy than visible light photons and infrared photons possessing less energy than visible light photons.
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true or false: energy is the capacity to do work and work is anything that involves moving matter against an opposing force.
The given statement "Energy is the capacity to do work and work is anything that involves moving matter against an opposing force" is TRUE. Energy is the capacity to do work, which is defined as any action that requires the application of a force to move matter. This includes tasks such as lifting a book, pushing a door open, or running.
Energy refers to the capacity of a physical system to perform work. Energy is generally used to complete tasks, such as moving an object from one location to another, heating up or cooling down a material, or lighting up a room. Work is defined as the transfer of energy to an object via a force applied to the object over a given distance, as per the statement. Work is usually identified as the displacement of an object through a force applied to it in the direction of its displacement against an opposing force.Energy and work are two distinct but interrelated concepts in physics. Energy is the capacity to perform work, and work is the transfer of energy from one object to another through a force acting over a distance. Energy and work are both expressed in joules (J), the unit of energy in the International System of Units (SI).
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a record turntable is rotating at 33 1 3 rev/min. a watermelon seed is on the turntable 7.3 cm from the axis of rotation. (a) calculate the acceleration of the seed, assuming that it does not slip. (enter the magnitude.)
Assuming that it does not slip, the acceleration of the seed is 0.89 m/s².
The acceleration of the seed can be calculated using the formula for centripetal acceleration:
a = (v²) / r
where a is the centripetal acceleration, v is the velocity of the seed, and r is the distance from the axis of rotation to the seed.
To use this formula, we need to first convert the rotational speed of the turntable from rev/min to radians per second. There are 2π radians in one revolution, so:
ω = (33 1/3 rev/min)(2π rad/rev)(1 min/60 s) = 3.49 rad/s
The velocity of the seed can be calculated from the tangential velocity formula:
v = rω
where v is the tangential velocity of the seed.
Substituting the given values, we get:
v = (0.073 m)(3.49 rad/s) = 0.255 m/s
Now we can use the formula for centripetal acceleration:
a = (v²) / r
Substituting the values we have calculated, we get:
a = (0.255 m/s)² / 0.073 m = 0.89 m/s²
Therefore, the acceleration of the seed is 0.89 m/s² assuming that it does not slip.
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turns people upside down. people should not drop down. this is due to: gravity. inertia. seat belts. centrifugal force.
The given statement "turns people upside down" and "people should not drop down" are both due to the centrifugal force.
What is Centrifugal Force?Centrifugal force is defined as the apparent force that tends to move a rotating body away from the center of rotation. When an object moves in a circular path, a force must act towards the center of the circle to keep it moving in a circle. This force is known as the centripetal force.
The opposite force that acts to push the object away from the center of the circle is called centrifugal force. So, the given statement "turns people upside down" and "people should not drop down" are both due to the centrifugal force.
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a load of 12 kg stretches a spring to a total length of 15 cm, and a load of 30 kg stretches it to a length of 18 cm. find the natural (unstretched) length of the spring.
The natural length of the spring is therefore 12.97 cm.
The natural length of the spring is found by calculating the spring constant using the Hooke's law formula. Spring constant (k) = Force (F) / extension (x). The natural length of the spring refers to the length of the spring when it is not carrying any load. Hooke's law states that the force required to extend or compress a spring by a distance x is proportional to that distance. Mathematically, F=kx, where F is the force applied, x is the displacement from the equilibrium position, and k is the spring constant. To find the natural length of the spring, we need to calculate the spring constant.
To do this, we use the data given in the problem. A load of 12 kg stretches the spring to a total length of 15 cm. We can find the force applied by multiplying the load by the acceleration due to gravity (g), which is 9.8 m/s^2. Thus, F = mg = 12 * 9.8 = 117.6 N. The extension of the spring is given as x = 15 cm - x0, where x0 is the natural length of the spring. Thus, x = 0.15 m - x0. Substituting these values into Hooke's law, we get: k = F/x = 117.6/(0.15 - x0)
Similarly, when a load of 30 kg stretches the spring to a length of 18 cm, we can find the force applied as F = mg = 30 * 9.8 = 294 N. The extension is given as x = 0.18 m - x0. Substituting these values into Hooke's law, we get: k = F/x = 294/(0.18 - x0)
Now we have two equations for k, so we can set them equal to each other: 117.6/(0.15 - x0) = 294/(0.18 - x0) Cross-multiplying and simplifying, we get: 117.6(0.18 - x0) = 294(0.15 - x0) 21.168 - 117.6x0 = 44.1 - 294x0 176.4x0 = 22.932 x0 = 0.1297 m
The natural length of the spring is therefore 12.97 cm.
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the speed of sound in air is approximately the same for all wavelengths. what evidence is there that this is true?
The speed of sound in air is approximately the same for all wavelengths.
Step by step Explanation :
The evidence that this is true is the following:
The speed of sound in air is approximately the same for all wavelengths. This is proved by the fact that a sound wave is an atmospheric disturbance that propagates as a longitudinal wave through the air, travelling as a pressure wave that causes areas of compression and rarefaction.
The speed of sound in air is constant and is determined by the average kinetic energy of the air molecules. This is why the speed of sound is the same for all wavelengths.
When the temperature of air is held constant, the speed of sound in air is constant. This is the primary reason why the speed of sound in air is practically constant at a given temperature.
The wavelengths of sound range from about 17 meters for the lowest audible frequency (about 20 Hz) to about 17 millimeters for the highest audible frequency (about 20,000 Hz).
The speed of sound in dry air at room temperature is around 343 meters per second, but it may vary depending on a variety of factors, including humidity, temperature, and pressure.
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What type of element gains electrons in ionic bonding, and what type of charge will it create?
Explanation:
Nonmetals tend to gain electrons and become anions. For example, in Fig. 2.22 A, a neutral oxygen atom (O), with eight protons and eight electrons, gains two electrons. This gives it two more negative charges than positive charges and an overall charge of 2–.
Suppose you are standing on a skateboard or on in-line skates and you toss a backpack full of heavy books toward your friend. What do you think will happen to
you and why? Explain your answer in terms of Newton's third law of motion.
Answer: According to Newton's third law of motion, when you toss a backpack full of heavy books towards your friend while standing on a skateboard or in-line skates, there will be an equal and opposite reaction force acting on you, causing you to move in the opposite direction, which may be backward due to the conservation of momentum.
Which traits are controlled by polygenic inheritance? Select four options.
red hair
hazel eyes
blood type
length of corn ears
birth weight
fur color of palomino horses
Answer:
All options except fur color of palomino horses and blood type
Answer:
A, B, D, and E
Explanation:
a 4.0 kg body has two times the kinetic energy of an 8.5 kg body. calculate the ratio of the speeds of these bodies.
The ratio of the speeds of these bodies is 2.06
The kinetic energy of an object is equal to 1/2mv^2.
For the 4.0 kg body, the kinetic energy is 1/2 (4.0 kg)v^2
For the 8.5 kg body, the kinetic energy is 1/2 (8.5 kg)u^2
Given that the kinetic energy of the 4.0 kg body is twice the kinetic energy of the 8.5 kg body, we can set up the following equation:
1/2 (4.0 kg)v^2 = 2 * (1/2 (8.5 kg)u^2)
Simplifying the equation, we have:
2 (4.0 kg)v^2 = (8.5 kg)u^2
Solving for the ratio of the speeds, we get:
v^2/u^2 = (8.5 kg)/(2 (4.0 kg)) = 4.25
Therefore, the ratio of the speeds of the two bodies is equal to the square root of 4.25, which is approximately equal to 2.06.
So, the 4.0 kg body is moving at approximately 2.06 times the speed of the 8.5 kg body.
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a 60 kg dancer applies a horizontal force of -800 n on the dance floor. the dancer's acceleration will be
The acceleration of the dancer who applies a horizontal force of -800 N on the dance floor will be 13.33 m/s².
The formula used to calculate acceleration is as follows:F = m × a
where,F is the force,m is the mass, and,a is the acceleration
Substituting the given values in the above formula, we get:
-800 N = 60 kg × a
We can solve this equation for a, which will give us the acceleration of the dancer.
a = (-800 N) / (60 kg) = -13.33 m/s²
Therefore, the acceleration of the dancer will be 13.33 m/s².
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a ball is thrown upward from the ground with an initial speed of 35 m/s; at the same instant, another ball is dropped from a building 5.0 m high. after how long will the balls be at the same height?
The time taken by both balls to be at the same height is 1.02 seconds.
The time taken by two balls to be at the same heightGiven,Initial speed of the ball that is thrown upward from the ground, u = 35 m/s,Initial height of the ball that is dropped from a building, h = 5.0 m,Finding out the time taken by both balls to be at the same height,Time taken by ball that is thrown upward from the ground, t = ?
For the first ball (that is thrown upward from the ground), the acceleration, a = -9.8 m/s² (negative because it's going against the gravity).Using the formula of motion,S = ut + 1/2 at²where,S = height of the ball above the ground, t = time taken by the ball to reach that height, and u = initial speed of the ball that is thrown upward from the ground.
Here, h = S and u = 35 m/s, and a = -9.8 m/s². Then putting the values we get,h = ut + 1/2 at²5 = (35)t + 1/2 (-9.8)t²5 = 35t - 4.9t²----------------(1)Also, for the second ball (that is dropped from a building), the time taken to reach the ground can be found using the formula, h = 1/2gt². Here, h = 5.0 m.
Therefore,5 = 1/2 × (-9.8) × t²5 = -4.9t²t² = -5/-4.9t² = 1.02t = √1.02
Therefore, the time taken by both balls to be at the same height is 1.02 seconds.
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The formula for speed is Total Distance / Total Time. Based on the data table below, what is the
average speed after 2 minutes? Please show all calculations.
Time (min.) Distance (m)
0
1
2
3
0
50
75
90
Answer:
To find the average speed after 2 minutes, we need to calculate the total distance covered in 2 minutes and divide it by 2.
Total Distance after 2 minutes = 75m
Total Time after 2 minutes = 2 minutes
Average Speed after 2 minutes = Total Distance / Total Time
Average Speed after 2 minutes = 75m / 2 min = 37.5 m/min
Therefore, the average speed after 2 minutes is 37.5 m/min.
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what is the approimate electrostatic force between two protons seperated bvy a distance of 1.0x10^-6
The electrostatic force between two protons separated by a distance of 1.0 × 10^-6 m is 2.3 × 10^-8 N.
Electrostatic force is the force between two electrically charged objects. This force can either be attractive or repulsive.
It is proportional to the product of the two charges and inversely proportional to the square of the distance between them.
The force is defined by Coulomb's law which states that:
The electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is given as:F = kq1q2/r2
WhereF is the electrostatic forcek is Coulomb's constantq1 and q2 are the charges of the two particles is the distance between the two particles in meters.
The value of Coulomb's constant is 9.0 × 10^9 Nm^2/C^2.Let's consider two protons separated by a distance of 1.0 × 10^-6 m. The charge on each proton is +1.6 × 10^-19 C.
F = kq1q2/r2F = (9.0 × 10^9 Nm^2/C^2)(+1.6 × 10^-19 C)(+1.6 × 10^-19 C)/(1.0 × 10^-6 m)^2F = 2.3 × 10^-8 N
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