The energy-efficient energy conversion device is a generator, one of the following.
The efficiency formula is what?Utilizing the formula below, efficiency may be represented as a ratio: Input > Output. The total quantity of beneficial work accomplished, excluding waste and spoilage, is known as output or work output. Efficiency may also be expressed in percent by dividing the ratios by 100.
What are some physics instances of efficiency?Energy is squandered less when a machine is more effective. For instance, a heat engine would be considered 75% efficient if it could convert 75% of the gasoline it received into motion while only losing 25% of it as heat.
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A circuit with a 70 V battery, a 55 Ω resistor, a resistor with 0.2 A across it, and another 55 Ω resistor in series. What is the resistance of the unknown resistor?
Answer:
350 Ω
Explanation:
The resistance of the unknown resistor can be found by using Ohm's Law, which states that the voltage (V) across a resistor is equal to the current (I) flowing through it multiplied by the resistance (R). We know the voltage (70 V) and the current (0.2 A) for the circuit, so we can find the resistance of the unknown resistor as follows:
V = IR
70 V = 0.2 A * R
R = 70 V / 0.2 A
R = 350 Ω
So the resistance of the unknown resistor is 350 Ω.
if the metal is irradiated with light of wavelength 500 nm, what is the momentum of the emitted photoelectron?
The momentum of the emitted photoelectron is [tex]8\times10^{-9}m[/tex].
What is Momentum?Simply put, momentum is the quantity of motion. Since an object has momentum if it is moving and has mass, quantity may be measured in this situation. An object lacks momentum if it is immobile.
whenever you throw a ball at a person and it hits him in the face. It shows how challenging it would have been to put a halt to the situation. In the air, a baseball is swooping. There is a big truck moving. a gun of this type shot a bullet.
How do we calculate the momentum?According to the photoelectric effect, hv=W 0 +eV.
Alternatively, hc =W 0 +eV
or [tex]500 \times 10^{-9}[/tex]
[tex](6.6×10 ^{−34} )\times(3\times10^8 )\\ \\ =2.28 \times 1.6 \times 10^{-19} +eV[/tex]
or eV=0.311019, or V=0.2
V should be V0.2 in this case.
The electron's de Broglie wavelength, = V 12.2710 10
so, λ≥2.[tex]8\times10^{-9}[/tex]
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what is the direction of the current, clockwise or counter-<:lockwise, that needs to flow in orderto lift the ball up along the z direction?
The magnetic field created by the current and the direction of the magnetic field relative to the direction of the magnetic force on the ball determine the direction of the current that must flow in order to lift the ball up along the z direction.
What is current?A stream of charged particles, such as electrons or ions, traveling through an electrical conductor or space is referred to as an electric current. The net rate of passage of electric charge through a surface or into a control container is monitored. Electric current refers to the flow of electricity in an electrical circuit as well as the amount of electricity flowing through a circuit. It is measured in amperes (A). The higher the ampere value, the more electricity flows across the circuit.
Here,
The direction of the current is often determined by applying the right-hand rule to the magnetic field and the direction of the force on the conductor. However, without further information on the intricacies of the arrangement and the exact orientation of the magnetic field, determining the exact direction of the current is impossible.
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a 0.25 kg arrow with a velocity of 12 m/s to the west strikes and pierces the center of a 6.8 kg target. a. what is the final velocity of the combined mass? b. what is the decrease in kinetic energy during the collision?
The velocity is 0.43 m/s to the west and difference in Kinetic energy is 1 J.
Together, the arrow and the target have a mass of 7.05 kg.
Using the formula p = mv, and the concept of conservation of angular momentum.
.25 x 12 + 6.8 x 0 = 7.05 x v final.
3 + 0 = 7.05 v,
and v = .43 m/s to the west.
The kinetic energy measured before and after will not be the same.
The value of KE before is [tex]\dfrac{1}{2}(0.25)12^2+ \dfrac{1}{2}(6.8) (0)^2[/tex] = 18 J.
The KE afterward is [tex]\dfrac{1}{2}(7.05)(0.43)^2[/tex],
which equals 0.65 J.
The difference is about 17 J.
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ball a with diameter d and ball b with diameter 2d are dropped from the same height. when the two balls have the same speed, what is the ratio of the drag force on ball a to the drag force on ball b? assume the reynolds number is high.
When such two balls are moving at the same speed, F1: F2 = 1: 4 will be the ratio of drag forces on balls A and B.
What in science is a force?Within science, the term "force" has to have a specific definition. At this point, describing a force as both a push or even a pull is completely acceptable. There is no substance that only an object "seems to have in it" or which it "contains" that is the force. This force is applied to one thing by another. The definition of a force comprises both living as well as non-living things.
Drag force calculation formula is = F(d) = 1/2 * C * rho*A * v²
Drag coefficient, or C
A = object area
rho = density of the moving object
v = the object's velocity
A = the object's area
F1 (force of drag on ball A) = 1/2 * C * rho * area of ball A * v²
Ball A's drag force, F2, is equal to = 1/2 * C * rho * area of ball B * v²
The only difference between the two balls is their differences in area because both are falling in the same environment and have the same speed.
F1/F2 = ball area A / ball area B= 4 * pi * r1² / 4 * pi * r2²
r1²/r2²
(d/2)²/(2d/2)²
F1 : F2 = 1 : 4
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T/F the anti-lock brake system engages every time the driver applies the brakes.
Every time the driver presses the brakes, the anti-lock brake system activates. ABS was initially created for boats. If the brake pulsates while ABS is active.
When the driver applies the brakes, does the anti-lock brake system activate?
Every time the driver presses the brakes, the anti-lock brake system activates. When ABS is engaged, a grinding sound is typical. ABS enables you to brake as hard as possible while still steering. Your ABS will not function properly if a warning light illuminates.
What are the functions of anti-lock brakes?By giving your tires some traction again in an emergency, anti-lock braking systems (ABS) assist you in steering. How It Works: aids in preventing wheel locking, potentially enabling the motorist to maneuver to safety. What It Isn't Able To Do The stopping distance may not be shortened; the pedal may shake or push back; this is okay.
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a car is moving down the highway at 65 mph when the driver is forced to brake suddenly to avoid hitting a deer. as they brake, the car's kinetic energy is converted into what? (1 point)
When conditions and hazards are present on or near a highway, a motorist is not permitted to operate a vehicle there faster than would be reasonable and prudent.
what is kinetic energy?An object's kinetic energy is the force it has as a result of motion. We have to put forth work to apply a force. After the job is finished, the object will be travelling at a new, constant speed because energy has indeed been transferred to it.
Unless otherwise indicated, 80 km/h is the max speed limit in King Edward Island. The standard speed limits are: 40 kilometres (municipalities may choose the top posted speed within their boundaries); 50 kilometres (30 mph) in urban areas; and 60 kilometres (40 mph) in school zones identified as such by the installation of signs at the intersections.
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Answer:
Into thermal energy.
Explanation:
When the breaks are applied, the kinetic energy is converted to heat, meaning it transforms into thermal energy.
which of the following should be part of solving any problem in physics? select all that apply: (a) read the problem carefully. (b) draw a picture of the situation. (c) write down the variables that are given. (d) think about which physics principles to apply. (e) determine which equations can be used to apply the correct physics principles. (f) check the units when you have completed your calculation. (g) consider whether your answer is reasonable.
All the options given should be part of solving any problem in physics.
Physics problem-solving calls for a methodical and meticulous approach. First and foremost, it's critical to attentively analyze the problem and comprehend the condition presented.
A situational drawing might aid in visualizing the issue and highlighting any crucial elements. Next, it's important to note down each and every variable that the problem provides. The next step is to consider whether physics concepts are applicable to the issue and choose the appropriate equations to apply them.
Once the calculation has been completed, it is crucial to double-check the answer's units to make sure they are formatted correctly. Finally, evaluate the reasonableness of your response and make any required modifications.
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as you look out of your dorm window, a flower pot suddenly falls past. the pot is visible for a time t , and the vertical length of your window is lw . take down to be the positive direction, so that downward velocities are positive and the acceleration due to gravity is the positive quantity g . from what height h above the bottom of your window was the flower pot dropped?
The height h above the bottom of your window was the flower pot dropped is = 1/2gt² - lw.
What is acceleration?Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).
Acceleration due to gravity is = g
Time taken to fall is = t
The length of the window is = lw
Hence, the height h above the bottom of your window was the flower pot dropped is
= distance travelled by the pot - the length of the window
= 1/2gt² - lw.
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a 20m-long metal rod has a radius of 1.0 cm and a resistance of 3.2 x 10-5 ohms. what is the resistivity of the metal?
A 20m long metal rod has a radius of 1.0 cm and a resistance of 3.2 x 10-5 ohms. The resistivity of the metal is 5.0 * 10 -8 ohm - m.
The value of the metal's resistivity must be determined in accordance with the question.
resistivity = π* r * R / L
= 3.14 * 0.01 * 0.01 * 3.2*10^-5 / 0.20 m
= 5.0 * 10 ^ -8 ohm - m
The Greek letter omega () represents resistance, which is measured in ohms. Ohms are named after the German physicist Georg Simon Ohm (1784-1854), who studied the relationship between voltage, current, and resistance. Ohm's Law is credited to him.
All materials, to some extent, resist current flow. They are divided into two categories:
Conductors are materials with very little resistance that allow electrons to move freely. Silver, copper, gold, and aluminum are just a few examples.
Insulators: Materials with high resistance to electron flow. Rubber, paper, glass, wood, and plastic are just a few examples.
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When light is transmitted or reflected, is any energy absorbed?
Yes, when light is transmitted or reflected, some energy can be absorbed by the medium or the surface it encounters, reducing the intensity of the light. This is why materials can appear to be colored or opaque.
How is reflection an important aspect for seeing?Reflection is an important aspect of seeing, as it enables us to see objects by allowing light to bounce off of them and reach our eyes. Light from a source reflects off its surface, and then enters our eyes, allowing us to perceive the object and its location in space.
What are the factors that can damage our eye?Eyes can be damaged in a variety of ways like physical trauma, UV exposure, Infections, Degenerative conditions, chemical exposure, etc.
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a 0.800 kg block is attached to a spring with spring constant 17.5 n/m . while the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 50.0 cm/s . what are
The block may move up to 19.7 cm from its resting position, and its oscillations last for a period of 2.76 seconds.
Displacement formula: What is it?The final position less the starting position is known as displacement.
The greatest displacement is:
The simple harmonic motion equation can be used to determine the block's maximum displacement:
x = A * cos (wt)
where w is the angular frequency, t is the time, and A is the amplitude. The block's starting velocity can be used to compute the amplitude:
A = v0 / w
The spring constant can be used to determine the angular frequency:
Sqrt(k / m) = w
Where k is the spring constant and m is the block's mass.
Replacement of values
A = 50.0 cm/s/sqrt(17.5 N/m/0.800 kg), and w = sqrt(17.5 N/m/0.800 kg).
w = 2.32 rad/s, with A = 19.7 cm
The maximum displacement is equal to the amplitude:
x = A = 19.7 cm
The oscillation's time scale:
The angular frequency can be used to calculate the oscillation's period:
T = 2 * pi / w
Replacement of values
T = 2.76 s = 2.32 rad/s / 2 * pi
Therefore, the oscillation's period is roughly 2.76 seconds.
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the plot depicts the position versus time of a toy car in one dimension. during which time interval(s) is the car going backward?
The plot depicts the position versus time of a toy car in one dimension. during 4 — 6 seconds and 0—2 seconds intervals is the car going backward.
Time in PhysicsTime in physics is determined by its measurement. This measurement requires extreme precision, which leads to the requirement that time be considered a linear continuum that is indivisible and not quantized. However, with sophisticated tools, time is now measured accurately using modern atomic time standards such as TAI and UTC.
In classical/non-relativistic physics, time is a scalar quantity and the general concept used is absolute time. Meanwhile, in relativity, time is understood as something relative. In contrast, Quantum Mechanics states that in fact time may not be a central concept in quantum theory as in classical physics and there is actually no such thing as quantum time.
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A circuit with a battery, a 1 Ω resistor, a 15 Ω resistor, and a 23 Ω resistor in series. The total current is the system is 8.8 A. What is the voltage of the battery?
Answer:
Below
Explanation:
Series resistances are additive: V = IR = (8.8)(1 + 15+23) = 343.2 v
true or false: if a hard magnetic material is heated above its curie temperature and then cooled back to room temperature it will regain its original permanent magnetization.
The claim that a hard magnetic material will restore its initial permanent magnetization if heated above its curie temperature and subsequently cooled to room temperature is untrue.
When a magnetic substance reaches its Curie temperature, what happens?The alignment of a material's magnetic moments is compelled into a disordered state when it reaches its Curie temperature. On the basis of the same concept, a material's magnetic strength gradually decreases when it is subjected to progressively greater temperatures.
If a magnet is heated to a high temperature, what will happen?If heated over its melting point or for an extended period of time, a magnet will permanently lose its magnetic force at a temperature of about 80 °C.
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move 2 meters east and move 4 meters west what is the distance
The person has covered a distance of 6m.
What is the difference between distance and displacement?
Distance is the total length of the path covered by an object, whereas displacement is the change in position of an object from its starting point. In other words, distance is a scalar quantity that refers to "how much ground an object has covered," whereas displacement is a vector quantity that refers to "how far out of place an object is."
For example, if an object moves from point A to point B, the distance covered is the total length of the path from A to B, whereas the displacement is the shortest possible distance from A to B in a straight line. Displacement has both magnitude and direction, while distance only has magnitude.
The distance that has been covered by the person that has been moving can be obtained from;
2 m + 4m
= 6m
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Most electromagnets have a core?
A) Why is iron usually used for the core
B) What would happen if you used steel instead
Iron has strong ferromagnetic properties and that is why it is used as core in electromagnets. However, iron can easily be demagnetized but steel cannot. Steel forms permanent magnet.
What is an electromagnet ?An electromagnet is a material which can form a magnetic field in the presence of an electric field. The magnetic field strength depends on the nature of the material as well the strength of the electric field.
Iron is a metal exhibiting strong ferromagnetic properties. The magnetic field lines can align along the applied field and it can be lost when the applied field is removed.
Therefore, iron can be demagnetized when the switch is off. If we use steel instead it would be very difficult to demagnetize and will form a permanent magnet.
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what is energy efficiency? if a machine is not 100% efficient does it violate the law of conservation of energy? why or why not?
Energy efficiency refers to the use of less energy to perform the same tasks.
Meanwhile law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another; a machine's efficiency below 100% does not violate the law of conservation of energy because some energy is inevitably lost as waste heat during energy conversion processes.
Energy efficiency refers to the ability to perform a task using the minimum amount of energy necessary. Energy efficiency is important because it helps reduce the energy consumption and greenhouse gas emissions that result from energy production.
A machine that is not 100% efficient does not violate the law of conservation of energy because energy is not destroyed, only converted from one form to another. When energy is converted from one form to another, some energy is inevitably lost as waste heat. According to the principle of energy conservation, energy can neither be created nor destroyed; rather, it can only be transformed from one form into another.
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what is the repulsive force between two pith balls that are 10.3 cm apart and have equal charges of 34.0 nc?
The repulsive force between two pith balls is F = 9.8 × 10^(-4) N
It can be calculated using Coulomb's law, which states that the force between two point charges is 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:
F = k × q1 × q2 / r^2
where k is the Coulomb constant (9 × 10^9 N × m^2 / C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between them. With the given charges of 34.0 nC and a separation of 10.3 cm, we can calculate the repulsive force as follows:
F = (9 × 10^9 N × m^2 / C^2) × (34.0 × 10^(-9) C)^2 / (0.103 m)^2
F = 9.8 × 10^(-4) N
The resulting force will be a positive value, indicating repulsion.
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when rolled down a mountainside at 7.0 m/s, the horizontal component of its velocity vector was 1.8 m/s. what was the angle of the mountain surface above the horizontal?
The angle of the mountain surface above the horizontal is calculated to be 75°.
Velocity of an object rolled is given as 7 m/s.
Horizontal component of velocity is given as 1.8 m/s.
Drawing a triangle, V becomes the hypotenuse and Vx becomes the adjacent side. We get the formula from that image using the characteristics of a right triangle.
Therefore, cos x = Vx / V.
where, x is the angle we are calculating
The formula's cos x value is obtained by substituting the given values: cos x = 1.8 m/s / 7 m/s = 0.257.
x = cos⁻¹(0.257) = 75 degrees
Thus, the angle of the mountain surface above the horizontal is calculated to be 75 degrees.
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. a rock is suspended from a scale reads 20.0 n. a beaker of water (having a density of 1000 kg/m3) is raised up so the rock is totally submerged in the water. the scale now reads 12.5 n. what is the density of the rock?
Density of the rock after submerging in a beaker of water is 2.67ˣ10³Kg/m³.
We are given some quantities like Force = 20.0 N,Density = 1000 kg/m³.We need to calculate the mass of the rock firstly when it is reading 20N.
Similarly,the scale new reads 12.5 N,we need to again find the mass of the rock.
Using formula of force,we know that
F=mg
=>20N=m×10
=>m=20/10
=>m=2kg.
Now,Scale reads 12.5 N after rock is totally submerged so mass of rock after submerged.We need to calculate the mass of rock
Using formula of force,
F=mg
=>12.5=m×10
=>m=12.5/10
=>m=1.25Kg.
The scale reads 12.5 N = 1.25 kg so it is displacing 0.75 kg of water
We need to calculate the volume of rock using volume of water it displaces.Since,density is given we need to use the formula of volume which is given by
Volume=mass/density
=>V=0.75/1000
=>V=7.5×10⁻⁴m³
After finding the volume,we need to calculate the density of the rock.
Using formula of density,
density=mass/volume
=>density=2kg/7.5×10⁻⁴m³
=>density=2666.66kg/m³
=>density=2.67ˣ10³Kg/m³
Hence, density of rock is 2.67ˣ10³Kg/m³.
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a car moving at a steady 10 m/s on a level highway encounters a bump that has a circular cross-section with a radius of 30 m. the car maintains its speed over the bump. what is the apparent weight of the 60.0-kgpassenger when the car is at the top of the bump?
(A) Apparent weight when the car is at the top of the bump is 388 newton. (B) Speed at which the car loses contact with the bump road is 17.15 m/s.
What is weight?In science and engineering, weight of an object is defined as the force acting on the object due to gravity.
Given, r = 30 m ; v = 10 m/s and m = 60 kg
A) Let N be normal reaction.
And at the bump
N = mg - mv² / r
N = 60 x 9.8 - 60 x 10 x 10 / 30 = 588 - 200
N = 388 newton
Part B) Then contact loose, N = 0
So, mg = mv² / r
v² = r x g = 30 x 9.8 = 294
v = 17.15 m/s.
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Note: The question given on the portal is incomplete. H. Here is the complete question.
Question: A car moving at a steady 10 m/s on a level highway encounters a bump that has a circular cross-section with a radius of 30 m. The car maintains its speed over the bump. What is the normal force exerted by the seat of the car on a 60 kg passenger when the car is at the top of the bump? Part B) what speed does the car lose contact with the bump road?
a lion can produce a roar with a sound intensity level of 114 db at a distance of 1.00 m . what is the sound intensity level at a distance of 4.00 m ? assume that intensity obeys the inverse-square law.
A lion can produce a roar with a sound intensity level of 114 db at a distance of 1.00 m . The intensity level at 4 m from the lion is 16 DB.
Though it is a unit of pressure rather than sound, the decibel, or dB, is frequently used to measure sound levels. A decibel is a logarithmic unit that expresses a physical quantity's relationship to a reference level.
The square of the distance has an inverse relationship with the decibel intensity.
I₂ = D₁²
I₁ D₂²
The sound intensity level at one meter is 114 dB.
I₂ = 1²
114 4²
I₂ = 16 Db
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a pendulum bob is released from some initial height such that the speed of the bob at the bottom of the swing is 0.99 m/s. what is the initial height of the bob?
the initial height of the bob of pendulum is approximately 0.9801 m
The following equation can be used to calculate the pendulum bob's initial height:
h = [tex]v^2 / 2g[/tex]
where g is the acceleration brought on by gravity ([tex]9.8 m/s2[/tex]), v is the speed of the bob at the swing's bottom, and h is the starting height.
replacing the specified values:
h = [tex](0.99 m/s)^2 / (2 * 9.8 m/s^2)[/tex]
h = 0.9801 m
As a result, the bob's starting height is roughly 0.9801 m.
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What happens if both the speed and radius of a circular path of a body doubled and what will be the effect of it on centripetal acceleration?
If both the speed and radius of a circular path of a body are doubled then centripetal acceleration will also be doubled.
What Is Centripetal Acceleration?The characteristic of an object moving in a circular path is known as centripetal acceleration. Centripetal acceleration is the term for any moving object whose acceleration vector is directed toward the center of the circle. The centripetal acceleration formula is as follows:
[tex]a_c=v^2 /r[/tex]
where v is the angular speed and r is the radius.
Now for the given question,
Original centripetal acceleration,
[tex]a=v^2 /r[/tex]
New centripetal acceleration,
[tex]a^{'} =(2v)^2 /2r\\\\=2v^2/r\\=2a[/tex]
Hence, centripetal accelearation is also doubled.
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an earth satellite moves in a circular orbit 769 km above the earth's surface. the period of the motion is 81.1 min. what is the magnitude of the centripetal acceleration of the satellite in m/s2?
The magnitude of the centripetal acceleration of the satellite is [tex]8.162 m/s^2.[/tex]
Centripetal acceleration: What is it?Centripetal acceleration is the term used to describe the speed of a body moving in a circular path. Since velocity is a vector quantity (it has a magnitude, a speed, and a direction), it varies as a body moves in a circular motion, causing acceleration. The circle's center is the direction in which the acceleration is pointed. Meters per second squared are used to measure centripetal acceleration. This acceleration is brought on by a force known as centripetal force, which is also pointed in the direction of the circle's center.
Given, h = 769 km
[tex]Rearth = 6.38 x 10^6m\\Rtotal = 6.38 \times 106769 \times 10^3 \\Rtotal = 4.90 \times 10^6 \\T = 81.1 \times 60 = 4866 sec \\V = 2\pi \times r \\V = 2\times 4.90 \times 10 4866 \\Linear Velocity, V = 6,324 m/s \\[/tex]
Now, the Magnitude of Centripetal Acceleration = Total
(6324)2 Magnitude of centripetal acceleration = 4.90 x 10
Magnitude of centripetal acceleration =[tex]8.162 m/s^2[/tex]
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if the braking distance for your car at a certain speed is 200 ft and, after reacting to a situation, you have managed to stop your car in 4.0 s, then the magnitude of the acceleration was
The magnitude of acceleration will be: [tex]a = \frac{2}{4^2} \left( 200 \text{ ft} - v_0 \cdot 4.0 \text{ s} \right)[/tex]
The magnitude of the acceleration can be found using the equation of motion for the uniformly accelerated motion:
[tex]$$d = v_0 t + \frac{1}{2} at^2$$[/tex]
where d is the braking distance,
v_0 is the initial speed,
t is the time taken to stop, and
a is the magnitude of the acceleration.
Given that the braking distance is 200 ft, and the time taken to stop is 4.0 s, we can write:
[tex]$$200 \text{ ft} = v_0 \cdot 4.0 \text{ s} + \frac{1}{2} a \cdot 4.0^2 \text{ s}^2$$[/tex]
Solving for a, we find:
[tex]a = \frac{2}{4^2} \left( 200 \text{ ft} - v_0 \cdot 4.0 \text{ s} \right)[/tex]
Note that v_0 is not given, so we cannot determine the exact value of a.
However, we can see that the magnitude of the acceleration is proportional to the difference between the braking distance and the product of the initial speed and time taken to stop.
The greater the difference, the greater the magnitude of the acceleration.
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discuss the physical origin of the quantization of energy of a particle confined to moving inside a one-dimensional box or on a ring.
We can model this as an infinite square well in which the particle's potential energy inside the box is zero and the potential energy outside is infinite. Therefore, the particle's quantum number is 4.86 × 10⁻²
The expression of wave function for a particle in one dimensional box is given as
φ(x) = ( √2/L ) sin ( nπx/L )
now we input our given figures, the limit of the particle to find it within the center of the box is
xₓ = L/2 + 20% of L/2
xₓ = L/2 + (0.2)L/2
xₓ = 3L/5
And the lower limit is,
x₁ = L/2 - 20% of L/2
x₁ = L/2 - (0.2) L/2
x₁ = 2L / 5
The expression for the probability of finding the particle within the center of the box is
P = ∫ˣₓ₁ ║φ(x)║² dx
P = ∫ ³L/⁵ ₂L/₅║(√2/L) sin ( nπx/L)║²dx
= 2/L ( ∫ ³L/⁵ ₂L/₅║sin ( nπx/L)║²dx
= 2/L ( ∫ ³L/⁵ ₂L/₅ (( 1 - cos ( 2πn x/L)/2) dx)
The particle is in its first excited state, then
n =2
Then calculate the particle's quantum number as follows;
= 2/L ( ∫ ³L/⁵ ₂L/₅ (( 1 - cos ( 2π(2)x/L)/(2)) dx)
= 1/L ( ∫ ³L/⁵ ₂L/₅ (( 1 - cos ( 4πx/L)/2) dx
= 1/L ( x - (L/4π)sin (4πx/L)) ³L/⁵ ₂L/₅
= 1/L ((3L/5) - (L/4π) sin (( 4π(3L/5)/L)) - (( 2L/5) - (L/4π)sin ( 4π(2L/5)/L)))
= 1/L ( L/5 + L/4π (sin(8π/5) - sin ( 12π/5)))
Use the trigonometric formula to solve the above equation
Sin A – sin B = 2sin ( A-B/2) cos (A+B/2)
Calculate the particle's quantum number as follows
P = 1/L ( L/5 + L/4π (sin(8π/5) - sin ( 12π/5)))
= 1/5 + 1/4π ( 2sin( (8π/5 -12π/5 ) / 2 ) cos ( (8π/5 + 12π/5) / 2 ))
= 1/5 + 1/2π ( -sin(2π/5) cos2π
= 1/5 - 1/2π ( sin (2π/5)(1))
= 0.0486 (10⁻²)(10²)
= 4.86 × 10⁻²
Therefore, the particle's quantum number is 4.86 × 10⁻²
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a quarterback throws a football with angle of elevation and speed . find the horizontal and vertical components of the velocity vector.
The projectile's displacement horizontally as a result of velocity is shown by the horizontally velocity component (vx). The component of vertical velocity (vy).
What do a vector's horizontal and vertical components mean?The vector's horizontal portion spans from its source to its farthest x-coordinate. From of the x-axis to a vector's highest point, the vertical component runs. The vector and the two parts combine to form a right triangle.
What exactly is a velocity vector?A velocity vector shows the rate of change in an object's position. The magnitude of a velocity vector represents an object's velocity, while the vector's direction represents an object's direction.
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the position of a particle moving along the y-axis has a position given by . is there any time interval during which the particle is not moving?
There is no such time interval when the particle is not moving during its motion in the y-axis.
The position of the particle in the y axis is give by the relation,
y = 0.20+8t-10t²
Differentiating with respect to time,
dy/dt = 8-20t
Now, we know,
dy/dt = speed
So,
Speed = 8-20t
For not moving the particle should have zero speed at that moment, so putting speed = 0,
8-20t = 0
8 = 20t
t = 20/8
t = 2.5 second
Now, here we are asked of any "interval" now any specific moment where the particle is at rest, because speed is only zero at only one moment, there is no such interval of zero speed, also, it might be possible that at 2.5s the particle is turning so we cannot be sure.
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Complete question - The position of a particle moving along the y axis has a position given by y = 0.20+8t-10t². Is there a time interval during which the particle is not moving?