The distance between charge 1 and 3 is equal to 20 cm and the force between charge 1 and 3 is equal to force between charge 1 and 3 that is 0.9 Newton and the force between charge 2 and 3 is equal to 1.41 Newton.
What are charges?Electric charges are basic property of matter carried by some elementary particles that governs how the particles are affected by an electric or magnetic field. Electric charge, which can be positive or negative, occurs in discrete natural units and is neither created nor destroyed.
What is coulomb's law?Coulomb's law states that like charges repel and opposite charges attract, with a force proportional to the product of the charges and inversely proportional to the square of the distance between them.
Given:
Magnitude on charge 1 = 4 μC
Magnitude on charge 2 = 4 μC
Magnitude on charge 3 = 1 μC
Distance between charge 1 and 2 = 32 cm
Distance of charge 3 from center of charge 1 and 2 = 12 cm
Distance between charge 1 and 3 can be find using Pythagoras theorem.
Distance between charge 1 and 3 = √(256 + 144)
Distance between charge 1 and 3 = 20cm
Similarly Distance between charge 2 and 3 = 20cm
Force between charge 1 and 3 can be found using coulomb law.
Force between charge 1 and 3 = (9 × 4 × 1)/40
Force between charge 1 and 3 = 36/40
Force between charge 1 and 3 = 0.9 Newton
Similarly using symmetry, force between charge 2 and 3 = 0.9 Newton
Force between charge 1 and 2 =(9 × 4 × 4)/102
Force between charge 1 and 2 = 1.41 newton
Therefore the distance between charge 1 and 3 is equal to 20 cm and the force between charge 1 and 3 is equal to force between charge 1 and 3 that is 0.9 Newton and the force between charge 2 and 3 is equal to 1.41 Newton.
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Why does hitting a magnet with a hammer cause the magnetism to be reduced?
Hitting a magnet with a hammer cause the magnetism to be Physical disruption and vibration damage the material's order, demagnetizing it.
Explanation:There are numerous methods for demagnetizing a magnet.
A magnet, as we know, has magnetic moments, which are the arrangements of molecules in a specific direction.
The hammer causes the magnetic poles of the magnet to point in opposite directions, causing the magnet to bend.
When we repeatedly hammer on a magnet, the magnetic dipoles inside the magnet are released from their ordered configuration.
Magnetism is known to be caused by the presence of magnetic moments.
As a result, when we hammer it, the dipoles are perturbed, lose their orientation, and magnetic moments cease to exist. As a result, the magnet will become demagnetized.
What is Magnetism?The force that magnets use to either attract or repel one another is known as magnetism.
Electric charges in motion are what generate magnetism. Every substance is made of small particles known as atoms.
Electrons, which are charged particles, are found in every atom. Electrons spin like tops around an atom's nucleus, or center. Their mobility causes an electric current to flow, causing each electron to act as a miniature magnet.
Another strongly magnetic substance must enter the magnetic field of an existing magnet in order to be magnetized. A magnet's magnetic field is the area of magnetic force that surrounds it.
An electric current can magnetize some compounds.
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Imagine that the entire Sun, of mass MS , collapses to a sphere of radius Rg such that the work required to remove a small mass m from the surface would be equal to its rest energy mc² . This radius is called the gravitational radius for the Sun.
(b) Find a numerical value for Rg .
The value of radius (Rg) is 1.475km .
Given,
The mass of the sun = Ms
Radius of the sphere = Rg
work required to remove a small mass (m) from the surface would be equal to its rest energy mc^2 .
The given radius (Rg) is called the gravitational radius for the sun.
We know,
Gravitational potential energy or work done
= Ug = GMs×m/Rg
the given rest energy = E =mc^2
As, it is given that the required work or energy is equal to rest energy,
thus, Ug=E
GMs×m/Rg = mc^2
Rg = GMs/c^2
We know,
G = 6.67×10^-11 N. m^2/kg^2
Ms = 1.99×10^30 kg
c = 3×10^8 m/s
Thus, Rg = 6.67×10^-11 × 1.99×10^30 / (3×10^8)^2
Rg = (13.2733×10^19)/(9×10^16 )
Rg = 1.4748×10^3 m
Rg = 1.475km
Hence, The value of radius (Rg) is 1.475km .
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What creates a magnetic field? More than one answer may be correct. (a) a stationary object with electric charge (b) a moving object with electric charge (c) a stationary conductor carrying electric current (d) a difference in electric potential (e) a charged capacitor disconnected from a battery and at rest Note: In Chapter 34, we will see that a changing electric field also creates a magnetic field
Electricity can be applied to a wire to produce a magnetic field. Charged particles that are in motion produce all magnetic fields. Due to the continually moving electrons inside, even the magnet on your refrigerator is magnetic.
Describe the magnetic field?Magnetic forces can be observed in a magnetic field, an electric current, a changing electric field, or a vector field around a magnet. Magnetic compass needles and other permanent magnets line in the direction of magnetic fields similar to those found on Earth. Electrically charged particles are forced to move in a circular or helical path via magnetic fields. The operation of electric motors is generated by this force, which is applied to electric currents in wires in a magnetic field.
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an iron bolt of mass 72.0 g hangs from a string 38.8 cm long. the top end of the string is fixed. without touching it, a magnet attracts the bolt so that it remains stationary, but is displaced horizontally 27.0 cm to the right from the previously vertical line of the string.
The weight of the iron bolt is 0.706N
What do you mean by the vertical line of the string?A line that is perpendicular to the surface or another line that is regarded as the base is the vertical line. In coordinate geometry, the vertical lines are often perpendicular to the horizontal lines and parallel to the y-axis. Any straight line that runs from top to bottom or bottom to top is considered to be a vertical line. Standing lines are another name for vertical lines. The vertical lines that we typically draw connect the bases of a square or a rectangle. We shall examine the idea of the vertical line and its characteristics in this essay.
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The charge per unit length on a long, straight filament is -90.0μC/m . Find the electric field (a) 10.0cm
The electric field for 10 cm is 16.2 MN/C
Length of the straight filament = (10cm) (1m/100cm) = 0.1
Electric field for the straight conductor = [tex]E = \frac{2k_{e} \lambda}{r}[/tex]
E = [2(8.99 × 10^9 N·m^2/C^2)(90.0 × 10^-6 C/m)] / 0.1 m
E = 16.2 MN/C
The electric field is directly radially inward, toward the filament.
Electric field is a force produced by a charge near its surroundings. This force is exerted on other charges when brought in the vicinity of this field. SI unit of electric field is N/C (Force/Charge).
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the electric field at 2 cm from the center of long copper rod of radius 1 cm has a magnitude 3 n/c and directed outward from the axis of the rod. (a) how much charge per unit length exists on the copper rod? (b) what would be the electric flux through a cube of side 5 cm situated such that the rod passes through opposite sides of the cube perpendicularly?
a)The charge per unit length (in C/m) exists on the copper rod is
3.34×10⁻¹² C/m
b) The electric flux through a cube is 0.018 N.m²/C
Electric field = it is a physical field that surrounded by electric charge particle and exert force on another charge particles.
Radius of copper rod = 1 cm. = 0.01m
The electric field strength = 3 N/C.
The electric field at 2 cm from the center of a long copper rod.
a)The charge per unit length (in C/m) exists on the copper rod.
The electric field at a point can be given as
E = λ/2πε₀r
where
λ is linear charge density
ε₀ is the permittivity in free space
r is the radius
λ = E*2πε₀r
= 3 ×2×3.14×8.85×10⁻¹² ×2×10⁻²
λ = 3.34×10⁻¹² C/m
The charge per unit length (in C/m) exists on the copper rod is
λ = 3.34×10⁻¹² C/m
b) side of the cube is 5cm
charge enclosed inside rod is given by :
q = λ L
using the equation of gauss law
Ф = q/ε₀
using this in the above equation we get
q(enclosed) = λ L/ε₀
q = 3.34×10⁻¹² C/m × 5× 10⁻²m / 8.85×10⁻¹²C²/N.m²
= 0.018 N.m²/C
the electric flux through a cube is 0.018 N.m²/C
a)The charge per unit length (in C/m) exists on the copper rod is
3.34×10⁻¹² C/m
b) The electric flux through a cube is 0.018 N.m²/C
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When alcohol is rubbed on your body, it lowers your skin temperature. Explain this effect.
When alcohol is rubbed on your body, it lowers your skin temperature due to evaporative cooling.
What is Boiling point?The temperature at which the vapor pressure of a liquid is equal to the pressure of the atmosphere on the liquid and varies according to substances and their components.
When alcohol is rubbed on your body, it lowers your skin temperature, it evaporates and is referred to an endothermic reaction which entails absorption by the body.
Alcohol has a very low boiling point which is why rubbing it on the body will lead to evaporative cooling which will produce a cooling effect and is the most appropriate choice.
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A 25 kg block is pulled with an applied force of 200 N across a horizontal surface. The block experiences a frictional force of 75 N.a. Draw a free-body diagram for the block, including all forces acting on the block.
b. Determine the net force acting on the block.
c. Calculate the acceleration of the block.
Answer:
see attachment for the answer.
Explanation:
Brainliest Given:
Reflection is when a wave hits a surface and bounces off of it. Light can bounce off of a mirror so you can see yourself, and sound can bounce off of a wall so you hear an echo.
Refraction is when waves bend when they go into a different substance. This makes objects underwater look like they’re in a different spot than they actually are, and can make your straw look ‘crooked’ in your glass.
Diffraction is when waves bend as they go through openings, and around corners or objects. Sound diffracts more than light does, so it is easy to hear things around corners but impossible to see them.
Interference happens when the crests of two waves meet and build a bigger one, or a crest and trough come together and make a smaller one. This can make sound louder or softer, and light brighter or dimmer.
Decide which type of wave interaction is described below:
1. You can see the mountain peaks on the surface of a lake.
2. You try and spear a fish in a pond, but it hits just next to it.
3. You can still hear a concert even though you are in the parking lot.
4. Students are talking normally in the cafeteria, but it sounds very loud in there.
5. A big wave in a pool hits another wave, and it becomes mostly flat.
6. You use your window as a mirror.
7. Part of your fishing pole drops in the water, and it looks like it broke.
8. You hear a car in the driveway, even though you are on the other side of the house.
Answer: 1. Reflection
2. Refraction
3.Diffraction
4. Diffration
5.Interference
6. Reflection
7. Refraction
8. Diffraction
Good luck !
as a ferromagnetic object gets closer to the magnet, the magnetic force pulling the object decreases exponentially.
Ferromagnetic substance are strongly attractive to a magnet.
Ferromagnetic material are those materials which shows magnetic property also in the absence of external magnetic field
It's Atom have permanent dipole moment present in domains.
These are used in the industry.
example of ferromagnetic substance are nickel, iron ,Cobalt etc
When ferromagnetic object is placed in a magnetic field the domains will oriented in the direction of magnetic field even after the removal of applied magnetic field it will not change the shows that it become a permanent magnet.
Magnetic force on ferromagnetic object depends on the strength of the object and also size of the object
The given question is incomplete. The complete question is.
as a ferromagnetic object gets closer to the magnet, the magnetic force pulling the object decreases exponentially
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In a transverse wave, the motion of the disturbance is in what direction relative to the wave motion?.
In a transverse wave, the motion of the disturbance is perpendicular to the direction of the wave motion.
A wave is a disturbance that travels through a medium. Depending on the direction of movement of the individual particles relative to the direction of the propagation of the wave, waves can be divided into longitudinal wave and transverse waves.
A transverse wave is a type of wave in which the individual particles of the medium move in a perpendicular direction relative to the direction of wave propagation. This phenomenon can be observed on a water wave. If we place a floatable object on a rippled water surface, it tends to oscillate up and down. This is because the water molecules are also oscillating up and down, perpendicular to the direction of the wave.
Other examples of transverse waves include electromagnetic waves and seismic waves.
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buoyancy: a steel ball sinks in water but floats in a pool of mercury, which is much denser than water. where is the buoyant force on the ball greater?
The buoyant force on the ball in the pool of mercury is greater.
What do you mean by buoyant force?An object is subject to the buoyant force of the liquid ( fully or partially submerged in a liquid ). An object won't sink in a liquid if its buoyant force (pointing upward) exceeds its weight (pointing downward) on the object. A fluid's buoyancy, also known as its upthrust, is the upward force it exerts in opposition to the weight of an object that is partially or completely submerged. The weight of the fluid on top causes pressure in a fluid column to rise with depth. As a result, the pressure at the bottom of a fluid column is higher than at the top.
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Which of the following is most likely to form when tectonic plates move away from each other?
Group of answer choices Below.
A. Continental Rift
B. Fault
C. Subduction Zone
D. Trenches
Answer:
Continental Rift
Explanation:
I had earth science in 2020-2021 my freshman year. Rifting can be caused when hot material from a mantle plume reaches the base of a continental plate and causes the overlying lithosphere to heat up. In addition to this the upwards movement of the plume against the base of the plate results in extensional forces which can cause rifting.
what is the major cause of the earth’s magnetic field? the earth’s liquid outer core the earth’s liquid outer core the earth’s magnetic lithosphere the earth’s magnetic lithosphere charged particles from the sun charged particles from the sun magnetic materials on the earth’s surface
The earth's liquid outer core is the major cause of the earth’s magnetic field.
What is magnetic field?The magnetic influence on moving electric charges, electric currents, and magnetic materials is described by a magnetic field, a vector field. A force acting on a charge while it travels through a magnetic field is perpendicular to both the charge's motion and the magnetic field. The magnetic field of a permanent magnet attracts or repels other magnets as well as ferromagnetic elements like iron. A magnetic field that varies with location will also exert a force on a variety of non-magnetic materials by changing the velocity of those particles' outer electrons. Electric currents, like those utilised in electromagnets, and electric fields that change over time produce magnetic fields that surround magnetised things.
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What is the position when t = 18 s?
Joe walks 36m north followed by 90m east. What is his magnitude of displacement
from the start?
Answer: 90m - 36m = 54 m from the start! Best of luck!
A proton is projected in the positive x direction into a region of a uniform electric field →E =(-6.00 × 10⁵) i^ N/C at t=0 . The proton travels 7.00 cm as it comes to rest. Determine (b) its initial speed, and
The initial speed of the proton that is projected in the positive x direction into a region of a uniform electric field is 2.84×〖10〗^6 m/s
The equation of motions expresses the speed of an object with initial velocity u, final velocity v, and distance s, as;
v^2= u^2+2 a.s
Making u the subject of the formula,
u^2= -2 a.s
Given that:
a=5.76×〖10〗^13 m/s^2
s =7.00cm or 0.07m
Inserting values,
u^2= -2 ×(-5.76×〖10〗^13 m/s^2)×0.07m
u^2=8.06×〖10〗^12 m^2/s^2
Therefore,
u= √8.06×〖10〗^12 m^2/s^2
u=2.84×〖10〗^6 m/s
Therefore, the initial speed of the proton is 2.84×〖10〗^6 m/s
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the hydrogen-line emission spectrum includes a line at a wavelength of 434 nm. what is the energy of this radiation? (h
The energy of this radiation is 4.58 x 10⁻¹⁹ joules.
What is radiation?
Ionizing and non-ionizing categories of radiation are typically distinguished based on the energy of the radiated particles. Ionizing radiation carries energies greater than 10 eV, which is enough to ionize atoms and molecules and break chemical bonds. This distinction is important since these compounds differ significantly in how poisonous they are to living creatures. Ionizing radiation is typically produced by radioactive materials that release radiation in the form of photons, electrons, or positrons. Other sources include secondary cosmic rays that interact with Earth's atmosphere to produce muons, mesons, positrons, neutrons, and other particles, as well as X-rays from radiography examinations used in medicine.
Calculations:
wavelength = 434nm = 434 x 10⁻⁹m
planck's constant = h= 6.626 x 10 ⁻³⁴ J
E =?
by using the formula;
E = hc /λ
value for c is 3 x 10⁸ m/s
E is equal to (6.626 x 10 34 J)(3 x 108 m/s) / 434 x 109m.
E = 1.9878 x 10⁻²⁵ / 434 x 10⁻⁹m
E = 4.58 x 10⁻¹⁹ joules
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What is true about the nodes and antinodes of a standing wave? a. they decrease in number with time. b. they remain in a fixed position. c. their position keeps changing with time. d. they increase in number with time.
The nodes and antinodes of a standing wave always remain in a fixed position.
In a standing wave, the nodes and anti-nodes are present at fixed points.
The pattern of a standing wave shows that nodes result from destructive interference and anti-node result form constructive interference.
From a rest position, if we observe nodes and anti-node positions then we can see that nodes have zero displacement while anti-nodes are points that exhibit maximum displacement between two waves.
To put it simply, in Physics, the nodes and anti-nodes are two integral phases of a standing wave.
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HELP!!
A football is kicked straight up into the air; it hits the ground
5.2 s later.
a) What was the greatest height reached by the ball? Assume l
is kicked from ground level.
b) With what speed did it leave the kicker's foot?
Q|C A bat, moving at 5.00 m/s , is chasing a flying insect. If the bat emits a 40.0 -kHz chirp and receives back an echo at 40.4 kHz , (a) what is the speed of the insect?
The speed of the insect is 3.03m/s.
What is speed?The speed of an object, also known as v in kinematics, is a scalar quantity that refers to the size of the change in that object's position over time or the size of the change in that object's position per unit of time. The instantaneous speed is the upper limit of the average speed as the duration of the time interval gets closer to zero. The average speed of an object over a period of time is calculated by dividing its distance traveled by the length of the interval. Distance divided by time is the dimension of speed.
Explanation:
The frequency that is received by the source after the reflection is given by,
[tex]f_{1} =f_{0} (\frac{V-v}{V-V_{b} } )(\frac{V+v_{b} }{V+v} )[/tex]
[tex]40.4=40 (\frac{343-v}{343-5} ) x (\frac{343+5}{343+v} )\\[/tex]
[tex]v=3.03 m/s[/tex]
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when a 0.30 kg mass is suspended from a massless spring, the spring stretches a distance of 2.0 cm. let 2.0 cm be the rest position for the mass-spring system. the mass is then pulled down an additional distance of 1.5 cm and released.calculate the period of resulting oscillation in si units.
When a 0.30 kg mass is suspended from a massless spring, the spring stretches a distance of 2.0 cm, with an additional distance of 1.5cm,
Mass m= 0.30 kg
Distance x = 2.0 + 1.5 cm = 0.035 m
Since spring constant k = [tex]{\frac{mg}{x}[/tex] , (g=9.81)
k = [tex]{\frac{0.3*9.81}{0.035}[/tex] = 84.085 N/m
ω = [tex]\sqrt{\frac{k}{m} }[/tex] = [tex]\sqrt{\frac{84.085}{0.3} }[/tex] = 16.74 rad/sec
T = [tex]\frac{2\pi }{w}[/tex] = [tex]\frac{2*3.14}{16.74}[/tex] = 0.375 sec
The spring constant is the force required to stretch or compress the spring divided by the distance the spring is lengthened or shortened. It is used to determine the stability or instability of a spring and thus the system for which it is intended.
Therefore the time period of resulting oscillation is 0.375 sec.
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Four toy cars are moving at a constant speed until they experience an unbalanced force of 12 n each. Which toy car would have an acceleration of 3 m/s2 ?.
Answer: the car mass with four would have an accelaration
Explanation:
Three solid plastic cylinders all have radius 2.50cm and length 6.00cm. Find the charge of each cylinder given the following additional information about each one. Cylinder (a) carries charge with uniform density 15.0 nC/m² everywhere on its surface. Cylinder
By the charge density, the surface area of the cylinder charge is 0.20 nC.
We need to know about charge density to solve this problem. The charge density can be determined as
λ = Q / A
where λ is charge density, Q is charge and A is surface area.
The parameter given is the charge density and the solid cylinder shape which are :
λ = 15 nC/m²
r = 2.5 cm = 0.025 m
L = 6.0 cm = 0.06 m
Find the surface area of cylinder
A = 2πrL + 2πr²
A = 2π. 0.025. 0.06 + 2 . π . 0.025²
A = 0.0134 m²
Find the charges
Q = λ x A
Q = 15 x 0.0134
Q = 0.20 nC
Hence, the surface area of the cylinder charge is 0.20 nC.
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M The following charges are located inside a submarine: 5.00μC,-9.00μC, 27.0μC , and -84.0μC (b) Is the number of electric field lines leaving the submarine greater than, equal to, or less than the number entering it?
Since the net electric flux which is − 6.89 × 10^6 V⋅m through the hull of the submarine is negative, the number of electric field lines leaving the submarine is less than the number entering it.
A submarine (or sub) is a watercraft capable of independent operation underwater. It differs from a submersible, which has the more limited underwater capability. Most large submarines consist of a cylindrical body with hemispherical (or conical) ends and a vertical structure, usually located amidships, that houses communications and sensing devices as well as periscopes. In modern submarines, this structure is the "sail".
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I can’t think of the answer for this question
The car started 15 ml west of Mulberry road.
Consider the East-West route as the x-axis, and place Mulberry Road's intersection at x = 0. This implies that, the west of the intersection is -ve and the east side will be represented positive.
Given the car ends up at 18 mi West to the intersection, implies that it ends at -18mi from x = 0. Also given the total displacement = - 33mi.
Hence, initial position = final position - displacement
= -18 - (- 33)
= -18 + 33
= 15 mi. So, the car started from 15mi from the Mulberry road and from the East of it.
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Quick Quiz 40.2 While standing outdoors one evening, you are exposed to the following four types of electromagnetic radiation: yellow light from a sodium street lamp, radio waves from an AM radio station, radio waves from an FM radio station, and microwaves from an antenna of a communications system. Rank these types of waves in terms of photon energy from highest to lowest
The order of decreasing photon energy is FM radio, AM radio, yellow light, and microwaves.
Electromagnetic radiation: The electromagnetic field's waves, which are conveying electromagnetic radiant energy through space, are what make up electromagnetic radiation. It consists of X-rays, gamma rays, microwaves, infrared, light, and radio waves. These waves are all a component of the electromagnetic spectrum.
Microwave radiation has wavelengths between one meter and one millimeter, which correspond to frequencies between 300 MHz and 300 GHz, respectively.
Radio waves: The electromagnetic spectrum's longest wavelengths, which are found in radio waves, are normally found at frequencies of 300 gigahertz and below.
The radio waves have the highest photon energy and the lowest is microwaves.
So, the highest to lowest order is as follows:
FM radio, AM radio, yellow light, and microwaves.
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A uniform, rectangular block made of steel has dimensions 1. 00 cm×2. 00 cm×3. 00 cm. It is placed on a wooden board, and then the board is tilted until the block begins to slide down the board. Which face of the block should be in contact with the board, so that it begins to slide at the shallowest angle?.
Dimensions of a steel block that is uniformly rectangular are 1. 00 cm, 2. 00 cm, and 3. 00 cm. It starts to slide at the shallowest angle whenever the block's face comes into contact with the board.
What do you mean by an angle?An angle is formed when the two straight lines or rays meet at a common endpoint. The common point of the contact is called the vertex of an angle. The word angle comes from Latin word named ‘angulus,’ meaning “corner.”
In general, an angle is a figure created in Euclidean geometry by two rays that have a common terminus and are referred to as the vertices and sides of the angle, respectively.
The angles produced by the beams are always contained in the plane that comprises two rays.
In conclusion, the block will start to slide at the angle that offers the least resistance once its face makes contact with the board.
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S Show that the difference between decibel levels β₁ and β₂ of a sound is related to the ratio of the distances r₁ and r₂ from the sound source byβ₂ - β₁ = 20 log( r₁ / r₂)
Decibels are used to measure sound (dB). A motorcycle engine operating is roughly 95 dB louder than regular conversation, which is around 60 dB louder than a whisper.
What do you mean by decibel level?A relative unit of measurement, the decibel (symbol: dB), is equal to one-tenth of a bel (B). It uses a logarithmic scale to express the ratio of two values of a power or root-power quantity. The power ratio between two signals with a one-decibel difference in level is 101/10 (or roughly 1.26), and the root-power ratio is 10120. (approximately 1.12). The unit can convey an absolute value or a change in the relative value. When used in this method, the unit symbol is frequently followed by letter codes that denote the reference value. In the latter situation, the numeric value reflects the ratio of a value to a fixed reference value. A typical suffix is "V" for the reference value of 1 volt, for instance (e.g., "20 dB").
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A motorboat cuts its engine when its speed is 10. 0m/s and then coasts to rest. The equation describing the motion of the motorboat during this period is v=vi e^⁻ct, where v is the speed at time t, vi is the initial speed at t=0 , and c is a constant. At t=20. 0s , the speed is 5. 00m/s (c) Differentiate the expression for v(t) and thus show that the acceleration of the boat is proportional to the speed at any times
The acceleration of the motorboat is proportional to the speed.
The speed of the motorboat when it cuts its engine =
10 m/s
The motion of a motorboat is v.
[tex]v = v _{i} \: e ^{ - ct}[/tex]
[tex]10= v _{i} \: e ^{ - ct} = (v _{1})(1)[/tex]
[tex] v _{i} = 10 \:m /s[/tex]
At t = 20. seconds.
v = 5 m/s
[tex]5= 10 \: e ^{ - c(20 \: s)}[/tex]
[tex] e ^{ - c(20 \: s)} = 0.500[/tex]
At t = 40 seconds.
[tex]v = 10 \: e ^{ - 40 \: c}[/tex]
[tex] = \frac{10}{0.250} [/tex]
= 2.50 m/s
Acceleration of the motor boat is,
[tex]a = \frac{dv}{dt} [/tex]
[tex] = \frac{d}{dt} \: v = v _{i} \: e ^{ - ct}[/tex]
[tex] = v _{i} \: e ^{ - ct}(-c)[/tex]
[tex]= -c(v _{i} \: e ^{ - ct})[/tex]
a = -cv
The acceleration of the motorboat is negative constant into speed.
Therefore, the acceleration of the motorboat is proportional to the speed.
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