To solve this problem, you can use the equations of motion for rotational motion under constant acceleration:
ωf = ωi + αt --(1)
θ = ωit + 0.5αt^2 --(2)
where ωi is the initial angular velocity, ωf is the final angular velocity, α is the angular acceleration, t is the time elapsed, and θ is the angular displacement.
Using equation (1), we can find the angular acceleration of the wheel:
α = (ωf - ωi)/t
= (30.0 rad/s - 10.0 rad/s)/20.0 s
= 1.0 rad/s^2
Using equation (2), we can find the total angular displacement of the wheel during the 20.0 seconds:
θ = ωit + 0.5αt^2
= 10.0 rad/s × 20.0 s + 0.5 × 1.0 rad/s^2 × (20.0 s)^2
= 400.0 rad
To find the time at which the wheel has undergone half of this angular displacement, we can use equation (2) again:
θ/2 = ωit + 0.5αt^2
Rearranging and solving for t, we get:
t = [(-ωi) ± sqrt(ωi^2 + 2αθ)]/α
Since we are looking for a positive time, we take the positive root:
t = [(-10.0 rad/s) ± sqrt((10.0 rad/s)^2 + 2 × 1.0 rad/s^2 × 400.0 rad)]/1.0 rad/s^2
≈ 12.4 s
Therefore, the answer is B, 12.4 s.
footballer shoots ball has mass (m) with force (F), ball gains velocity from force its value is 6m/s. the ball stops after 10sec. So magnitude of momentum of ball after 3.333 sec. is....... kg.m/sec. ( choose the best answer)
3m
4m
6m
8m
The magnitude of momentum of the ball after 3.333 sec is 10F/3 kg.m/sec. None of the options provided match this answer exactly.
What is Momentum?
Momentum is a physical property of an object that describes its motion. It is defined as the product of an object's mass and velocity, and it is a vector quantity, which means it has both magnitude and direction.
The magnitude of momentum of the ball after 3.333 sec can be calculated using the equation:
p = m * v
where p is momentum, m is mass, and v is velocity.
Given that the ball gains a velocity of 6m/s from the force and stops after 10 seconds, we can calculate the mass of the ball as:
v = F * t / m
6 = F * 10 / m
m = 10F / 6
m = 5F / 3
Now, we can calculate the momentum of the ball after 3.333 sec using the above equation:
p = m * v
p = (5F / 3) * (6 * 3.333 / 10)
p = (5F / 3) * 2
p = 10F / 3
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5. 7.0 tons of coal are burned to generate 3.6 x 104 kwh of electricity. what is the efficiency of the generator? answer
The efficiency of generator when 7.0 tons of coal are burned to generate 3.6 x 10^4 kwh of electricity is 74.1%.
The efficiency of the generator is the ratio of the useful output of energy to the input of energy. It is a measure of how much of the energy that is put into a system actually gets transformed into useful output energy.
To calculate the efficiency, we need to determine the useful energy output and the energy input. Then we can find the efficiency by dividing the useful energy output by the energy input.
Given that 7.0 tons of coal are burned to generate 3.6 x 10^4 kwh of electricity.
Here, we have to find the efficiency of the generator.
We need to convert the given tons of coal into joules.
1 ton of coal = 2.5 x 10^10 J
So,7.0 tons of coal = 7.0 x 2.5 x 10^10 J = 1.75 x 10^11 J
The input energy is 1.75 x 10^11 J
Useful output energy is given as 3.6 x 10^4 kWh.
We need to convert kWh into joules.
1 kWh = 3.6 x 10^6 J
Therefore, 3.6 x 10^4 kWh = 3.6 x 10^4 x 3.6 x 10^6 J = 1.296 x 10^11 J
The efficiency of the generator is given as
Efficiency = (Useful output energy / Input energy) x 100
Substituting the values, we get,
Efficiency= (1.296 x 10^11 / 1.75 x 10^11) x 100= 0.741 x 100= 74.1%
Therefore, the efficiency of the generator is 74.1%.
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Calculate the momentum and velocity of:
a) An electron having a de Broglie wavelength of 2.0 × 10-⁹ m.
b) A proton of mass 1.67 x 10-27 kg and a de Broglie wavelength of 5.0 nm.
19. Calculate the associated de Broglie wavelength of the electrons in an electron beam which has
been accelerated through a pd of 4000V.
20. An alpha particle emitted from a radon-220 nucleus is found to have a de Broglie wavelength of
5.7 x 10-15 m. Calculate the energy of the alpha particle in MeV.
We can apply the de Broglie equation: = h/p, where h is the Planck constant (6.626 x 10-34 J.s), p is the momentum, and is the wavelength. P = h/ = (6.626 x 10-34 J.s)/(2.0 x 10-9 m) = 3.313 x 10-25 kg.m/s is the result of solving for p.
How is an electron's wavelength determined?Using the de Broglie relation between the momentum p and the wavelength of an electron (=h/p, where h is the Planck constant), the wavelength of an electron is computed for a given energy (accelerating voltage).
How can one determine an electron's de Broglie wavelength?To get the electron's wavelength, use the de Broglie wave equation, hmv.
Step 2 is to compute. λ=hmv=6.626×10−34J⋅s(9.11×10−31kg)×(3.00×108m/s)=2.42×10−12m.Step 3: Consider your outcome. This minute wavelength
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While the platform is rotating, the hanging mass remains attached to the test mass and is not removed from the platform. - True - False
False is the proper response. The magnitude of velocity is constant in a uniform circular motion. Therefore, the assertion is true.
How does the frequency or number of revolutions change when the washer's bulk rises?
The frequency increased with increasing bulk. The second formula can also be used to describe this relationship. The equation demonstrates the direct connection between acceleration and mass in the presence of constant load and diameter. The outcome is that an increase in mass causes an increase in velocity.
A uniformly moving item has a centripetal force that is constantly directed toward the center of the circle it is traveling in. When the applied circular path force is released, the item will travel on a single direction parallel to the curving route at a certain location.
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14.
a) The concept of the photon was important in the
development of physics throughout the last century.
Explain what is meant by a photon.
b) The diagram shows a photocell. When the metal surface
is exposed to electromagnetic radiation, photoelectrons
are ejected. The collector collects the photoelectrons
and the sensitive ammeter indicates the presence of a
tiny current.
i. For a certain frequency and intensity of
radiation, the ammeter shows a current of
1.2 x 10-7 A. Calculate:
glass bulb
metal
radiation
1. The energy of each photon.
2. The maximum kinetic energy of each photoelectron.
3. The current in the photocell.
Vacuum
1. The charge reaching the collector in 5.0 s.
2. The number of photoelectrons reaching the collector in 5.0 s.
ii. The work function energy of the metal is 3.5 x 10-19 J and the incident radiation has
a frequency of 7.0 x 10¹4 Hz. Calculate the maximum kinetic energy of an ejected
photoelectron.
iii. The intensity of the incident radiation is doubled, but the wavelength is kept
constant. State the effect this has on each of the following:
Answer:
a) A photon is a quantum of electromagnetic radiation. It is a particle-like entity that carries energy proportional to its frequency.
b)
i.
The energy of each photon can be calculated using the equation E = hf, where h is the Planck constant. The frequency of the radiation is not given in the question, so it cannot be calculated.
The maximum kinetic energy of each photoelectron can be calculated using the equation KEmax = hf - Φ, where Φ is the work function. Since the frequency is not given in the question, this cannot be calculated.
The current in the photocell is given as 1.2 x 10^-7 A.
To calculate the charge reaching the collector in 5.0 s, we can use the equation Q = It, where Q is the charge, I is the current, and t is the time. Thus, Q = (1.2 x 10^-7 A)(5.0 s) = 6.0 x 10^-7 C.
To calculate the number of photoelectrons reaching the collector in 5.0 s, we can use the equation Q = Ne, where N is the number of electrons and e is the elementary charge. Thus, N = Q/e = (6.0 x 10^-7 C)/(1.6 x 10^-19 C/electron) = 3.75 x 10^12 electrons.
ii.
The maximum kinetic energy of an ejected photoelectron can be calculated using the same equation as in part 1, with the values given in the question: KEmax = hf - Φ = (6.626 x 10^-34 J s)(7.0 x 10^14 Hz) - 3.5 x 10^-19 J = 4.62 x 10^-19 J, or 2.88 eV.
iii.
Doubling the intensity of the incident radiation while keeping the wavelength constant will increase the number of photons incident on the metal surface, and thus increase the number of photoelectrons emitted per second. This will result in an increase in the current in the photocell. However, it will not change the energy of each photon or the maximum kinetic energy of each photoelectron, since these values depend only on the frequency of the radiation.
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kayla has two magnets. she would like to know how much magnetic energy is stored in each one. what would be the best way for her to determine which magnet has the most magnetic energy?
Kayla can determine which magnet has the most magnetic energy by performing an experiment using a magnetic pendulum.
What is a magnet?
A magnet is an object that has a magnetic field surrounding it. The magnetic field is what allows magnets to attract or repel other magnets. Magnets can be natural or man-made. A magnetic pendulum is a simple device that consists of a magnet hanging on a string.
When the magnet is brought near to another magnet, it will either be attracted or repelled. By measuring the amount of force required to move the magnet, Kayla can determine which magnet has the strongest magnetic field and therefore the most magnetic energy.
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a photon undergoing compton scattering has an energy after scattering of 80 kev, and the electron recoils with an energy of 25 kev. find the wavelength of the incident photon. find the angle at which the photon is scattered. find the angle at which the electron recoils.
The wavelength of the incident photon is 2.48 x [tex]10^{-11}[/tex] m. The angle at which the photon is scattered is 0.24 radians. And the angle at which the electron recoils is 0.48 radians.
Calculating the Wavelength of the Incident Photon:
The wavelength of the incident photon can be calculated using the equation
λ = h/p, where h is Planck's constant and p is the momentum of the photon.
The momentum of the incident photon can be calculated using the equation p = E/c, where E is the energy of the incident photon and c is the speed of light.
Therefore, substituting the energy of the incident photon (80 keV) in the equation, we can calculate the momentum of the incident photon:
p = 80 keV/ (3 x [tex]10^8[/tex] m/s) = 2.67 x [tex]10^{-24}[/tex] kg.m/s
Therefore, the wavelength of the incident photon can be calculated using the equation:
λ = h/p
= 6.63 x [tex]10^{-34}[/tex] J.s/ (2.67 x [tex]10^{-24}[/tex] kg.m/s )
= 2.48 x [tex]10^{-11}[/tex] m
Calculating the Angle at which the Photon is Scattered:
The angle at which the photon is scattered can be calculated using the Compton scattering equation, which is
Δθ = (h/mc) (1 - cos θ),
where Δθ is the change in the angle of the photon's trajectory, h is Planck's constant, m is the mass of the electron, and θ is the angle at which the photon is scattered.
The mass of the electron can be calculated using the equation m = [tex]E/c^2[/tex], where E is the energy of the electron and c is the speed of light.
Therefore, substituting the energy of the electron (25 keV) in the equation, we can calculate the mass of the electron:
m = 25 keV/ (3 x [tex]10^8[/tex] [tex]m/s)^2[/tex]
= 8.33 x [tex]10^{-36}[/tex] kg
Therefore, the angle at which the photon is scattered can be calculated using the Compton scattering equation:
Δθ = (h/mc) (1 - cos θ)
= (6.63 x [tex]10^{-34}[/tex] J.s/ (8.33 x [tex]10^{-36}[/tex] kg) (1 - cos θ)
= 0.24 radians.
Calculating the Angle at which the Electron Recoils:
The angle at which the electron recoils can be calculated using the equation θ = 2Δθ,
where Δθ is the change in the angle of the photon's trajectory.
Therefore, substituting the value of Δθ (0.24 radians) in the equation, we can calculate the angle at which the electron recoils:
θ = 2Δθ
= 2 x 0.24
= 0.48 radians.
Thus, the wavelength of the incident photon is 2.48 x [tex]10^{-11}[/tex] m, the angle at which the photon is scattered is 0.24 radians, and the angle at which the electron recoils is 0.48 radians.
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Figure 3 shows a scuba diver ascending from 20 m below the surface where the water temperature is 10 °C, to the surface, where the temperature is 25 °C and the pressure is 1.01 × 10 Pa.
Calculate the pressure the diver is subiected to at 20 m below the surface of the water
[Density of water = 1025 kg m-31
[Acceleration due to gravity, g = 10 m s]
The pressure the diver is subjected to at 20 m below the surface of the water is approximately 3.15 × 10^5 Pa.
From the given information, we know that the pressure at the surface of the water is 1.01 × 10^5 Pa. We need to find the pressure the diver is subjected to at 20 m below the surface.
We can use the formula for pressure at a depth in a fluid:
P = ρgh + P0
where:
P is the pressure at the given depth
ρ is the density of the fluid
g is the acceleration due to gravity
h is the depth of the fluid
P0 is the atmospheric pressure at the surface (in this case, at the water's surface)
We are given the density of water (ρ = 1025 kg/m^3), the acceleration due to gravity (g = 10 m/s^2), and the depth of the water (h = 20 m). We can plug these values into the formula:
P = ρgh + P0
P = (1025 kg/m^3)(10 m/s^2)(20 m) + 1.01 × 10^5 Pa
P ≈ 3.15 × 10^5 Pa
Therefore, the pressure the diver is subjected to at 20 m below the surface of the water is approximately 3.15 × 10^5 Pa.
What is pressure?
Pressure is defined as the force per unit area applied perpendicular to the surface of an object or fluid. It is a scalar quantity and is usually measured in units of pascals (Pa) or pounds per square inch (psi).
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The weight of a dum bell is 500 n. It is lifted over a bodybuilder’s head at a distance of 0.7 meters. What is the work done by the bodybuilder on the dum bell?
350 J
714.2 J
500 J
1.4 x 10-3 J
Explanation:
W = F * d <==== ( Force * distance)
500 N * .7 m = 350 J
The sun appears larger than other visible stars because it is ______ than they are.
brighter
bigger
hotter
closer
The sun appears larger than other visible stars because it is closer than they are.
The sun appears larger than other visible stars because it is closer than they are. The Sun is a star that is found at the center of our Solar System. The Sun contains around 99.86% of the total mass of the Solar System. The Sun is also known as Sol, which is the source of life for our planet. The Sun is the brightest object in our Solar System.
The sun appears larger than other visible stars because it is closer than they are. Although the sun is one of the smallest stars in the universe, it appears larger and brighter than any of the other visible stars in the sky because it is closer to the Earth than any of the other stars. This is due to the fact that the Sun is the nearest star to the Earth, and as a result, it appears larger and brighter than any of the other visible stars.
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jet is flying due north relative to the ground the speed of the jet relative to the ground is 155 m s the wind at the jet's altitude is 40.0 m s toward the northeast 45.0 north of east suppose that the x axis is directed eastward and the y axis is directed northward find the speed of the jet relative to the air its airspeed
The velocity of the jet relative to the air (its airspeed) is 156 m/s to the east.
We can solve this problem using vector addition. Let the velocity of the jet relative to the air be represented by vector A, and the velocity of the wind relative to the ground be represented by vector B.
The velocity of the jet relative to the ground is the vector sum of vectors A and B. We can find the magnitude and direction of vector A by using the Pythagorean theorem and trigonometry:
A² + B² = C²
where C is the magnitude of the velocity of the jet relative to the ground:
C = √(A² + B²) = √((155 m/s)² + (40.0 m/s)²) = 162 m/s
The direction of vector A can be found using the tangent function:
tan θ = B/A
where θ is the angle between vector A and the x-axis:
θ = tan⁻¹(B/A) = tan⁻¹((40.0 m/s)/(155 m/s)) = 14.1° north of east
Therefore, the velocity of the jet relative to the air (its airspeed) is:
A = C*cos(θ) = (162 m/s)*cos(14.1°) = 156 m/s to the east
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which is more likely to interfere with compass readings, ac current in your refrigerator or dc current when you start your car? explain.
AC current in your refrigerator is more likely to interfere with compass readings than DC current when you start your car.
Compass readings are interfered with by the magnetic fields that AC current and DC current generate. AC current generates a continuous magnetic field that oscillates, while DC current generates a steady magnetic field. Because of the oscillations, AC magnetic fields are much more likely to interfere with a compass than DC magnetic fields.
AC current's magnetic field is of greater intensity and flux density than DC current. The magnetic field generated by a refrigerator's AC motor is one of the main sources of electromagnetic interference that can disturb magnetic compass readings, particularly those in automobiles.
AC motors use a lot of energy, which produces magnetic fields that can interfere with the compass readings. The electrical system of a car uses DC, which generates a relatively steady magnetic field. When a car's engine is started, the battery is subjected to high levels of electrical noise, which can affect other electrical systems in the vehicle.
However, the interference produced is not strong enough to affect the compass reading when compared to the magnetic field produced by the AC motor in a refrigerator.
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given that organic molecules need to react in order to produce life, this suggests we should search for worlds in the solar system that have a. rocky surfaces b. an atmosphere c. organic molecules on their surfaces d. either an atmosphere, or a surface or subsurface liquid medium such as water, or both.
Given that organic molecules need to react in order to produce life, this suggests we should search for worlds in the solar system that have:
A rocky surface, as these surfaces provide the solid foundation needed for the organic molecules to bond and react together.An atmosphere, as this provides the organic molecules with the air needed for their reactions.Organic molecules on their surfaces, as these molecules are necessary for life to form.Either an atmosphere, or a surface, or subsurface liquid media such as water, or both, as these are necessary components for the reactions of organic molecules to take place.
Organic molecules are chemical compounds that include carbon and hydrogen atoms that are produced by living organisms. These molecules play a crucial role in the formation of life on Earth. Life on Earth began about 4 billion years ago with the formation of organic molecules in the oceans. In the search for life beyond Earth, scientists are searching for signs of organic molecules in other worlds in the solar system.
There are several criteria for finding life on other planets. The first criterion is that the planet must have either an atmosphere, or a surface or subsurface liquid media such as water, or both. This is because organic molecules need to react in order to produce life. Without an atmosphere or a liquid medium, the organic molecules will not react, and life cannot form.
The second criterion is that the planet must have organic molecules on its surface. Organic molecules can be produced by living organisms, or they can be produced by non-living processes such as meteorite impacts or volcanic activity. If organic molecules are found on the surface of a planet, it suggests that the planet has the potential to support life.
Therefore, we should search for worlds in the solar system that have either an atmosphere, or a surface or subsurface liquid media such as water, or both.
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all other things being equal, would a lens with a short focal length or a long focal length be better as a fire starter? drag the terms on the left to the appropriate blanks on the right to complete the sentences. resethelp smaller focal length lens creates an image that is blank bright.target 1 of 2 to burn fire we need high light intensity, hence we need the image to be brighter, that means the lens with blank focal length will be more effective.
A lens with a shorter focal length is better as a fire starter because it creates an image that is brighter. To burn a fire, we need a high light intensity. This means that the lens with a smaller focal length will be more effective.
Shorter focal length lenses create a bright, highly focused light beam which is ideal for a fire starter. A longer focal length lens produces a dimmer and more spread out light beam which would not be suitable for this purpose. When using a shorter focal length lens, the light is focused more narrowly and with more intensity, creating the necessary light intensity needed to start a fire.
Shorter focal length lenses also typically have larger apertures which allow more light to pass through the lens, resulting in a brighter image. Additionally, a shorter focal length lens also has a wider field of view which allows more light to enter the lens. This further contributes to the brightness of the image.
In conclusion, when all other things are equal, a lens with a shorter focal length is better as a fire starter because it creates a brighter image that has the necessary light intensity needed to start a fire. The wider field of view and larger aperture of a shorter focal length lens allows more light to pass through and create a brighter image.
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A velocity vs time graph is very useful because:
A. the slope is velocity and the acceleration
B. the acceleration is the area under the curve
C. the slope is the acceleration and the displacement is the area under the curve
D. the slope is the displacement and the velocity is the area under the curve
The acceleration is shown by the graph's slope. The acceleration is likewise decreasing because the curve's slope is getting flatter and less steep.
Why does a velocity against time graph's slope increase?Acceleration is equivalent to the slope of a velocity against time graph. The ratio of the change in the y-axis to the change in the x-axis is the formula for slope. This is the same as the acceleration equation. Hence, acceleration is equal to the slope of a velocity vs. time graph.
What does a graph of velocity versus time show?Acceleration is indicated by a velocity-time graph's slope.
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If a 64 kg person is 134 meters above the ocean on a cliff, what is the person’s gravitational potential energy?
Hello and greetings lilliepruiett.
The gravitational potential energy of a person with a mass of 64 kg who is at a height of 134 meters, is 84044.8 Joules.
Explanation:It is an exercise in gravitational potential energy, which is the energy that an object possesses due to its position in a gravitational field.
This potential energy can be calculated using the following formula:
Epg = mgh
where:
Epg is the gravitational potential energy in joules (J).m is the mass of the object in kilograms (kg).g is the acceleration due to gravity in meters per second squared (m/s²).h is the height of the object in meters (m) with respect to a reference point.This formula states that gravitational potential energy increases as mass, height, or gravity increases.
We are told that a person of mass 64 kg is over the ocean on a cliff, with a height of 134 meters, knowing the acceleration of gravity is 9.8 m/s². We calculate the Epg.
To calculate the Epg, we add the formula and substitute the data in it. It is not necessary to clear the formula, because we are calculating the Epg, so
Epg = m × g × h
Epg = 64 kg × 9.8 m/s² × 134 m
Epg = 84044.8 J
The gravitational potential energy of a person with a mass of 64 kg who is at a height of 134 meters, is 84044.8 Joules.
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Answer:
The person’s gravitational potential energy is 84044.8 Joules.
Explanation:
The gravitational potential energy (GPE) of an object is given by the formula:
[tex]\sf\qquad\dashrightarrow GPE = m \times g \times h[/tex]
where:
m is the mass of the objectg is the acceleration due to gravity (9.8 m/s² on Earth)h is the vertical distance from a reference pointPlugging in the given values, we get:
[tex]\sf\qquad\dashrightarrow GPE = 64\: kg \times 9.8\: m/s^2 \times 134\: m[/tex]
[tex]\sf\qquad\dashrightarrow GPE = \boxed{\bold{\:\:84044.8\: Joules\: (J)\:\:}}[/tex]
Therefore, the person’s gravitational potential energy is 84044.8 Joules.
Which one of the following is an electronic system used by the NYSE for directly transmitting orders to designated marktet makers? O Pillar system O Garage order flow O Big Room system O Order NET SLP network
The electronic system used by the NYSE for directly transmitting orders to designated market makers is the Pillar system (option A).
The Pillar system is an electronic trading platform used by the New York Stock Exchange (NYSE) that enables direct transmission of orders from traders to designated market makers. The system is designed to improve speed, reliability, and efficiency of trading by automating the process of order routing and execution.
The Pillar system replaces the NYSE's previous trading platform, the NYSE Classic, and was introduced in 2017 as part of the exchange's efforts to modernize and streamline its operations. The system is intended to provide a more seamless and integrated trading experience for market participants.
Option A is the correct answer.
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pilar is playing with a remote-controlled toy boat in a lake. she navigates the boat 400 m away from herself, keeping it at a constant speed. steering it back toward herself, pilar navigates the boat over the same route and at the same speed for 2 minutes, and then she increases the boat's speed by 10 m/min. the return trip is 60 seconds faster. how long does the return trip take?
Pilar is playing with a remote-controlled toy boat in a lake. she navigates the boat 400 m away from herself, keeping it at a constant speed, the return trip takes 3 minutes.
To find the time it takes for the return trip:
On the initial trip away from herself, Pilar navigates the boat 400 m away, which takes:
Time = Distance / Speed
= 400 m / v m/min
= 400/v min
1. The time for the first 2 minutes of the return trip at the same speed:
Time = 2 min
2. The time for the remaining distance at the increased speed:
The increased speed is "v + 10" m/min. The time for this segment is given as 60 seconds (1 minute) less than the initial trip:
Time = (400 m) / (v + 10) m/min
= (400/v - 1) min
The total time for the return trip is the sum of the time for the two segments:
Total time = 2 min + (400/v - 1) min
Now,
Total time = 2 min + (400/v - 1) min
= 60 seconds faster than the initial trip
Since 60 seconds is equal to 1 minute, we have:
Total time = 2 min + (400/v - 1) min = 2 min + 1 min
Simplifying the equation:
400/v - 1 = 1
400/v = 2
v = 400/2
v = 200 m/min
So,
Total time = 2 min + (400/v - 1) min
Total time = 2 min + (400/200 - 1) min
Total time = 2 min + (2 - 1) min
Total time = 2 min + 1 min
Total time = 3 min
Thus, the return trip takes 3 minutes.
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the mean lifetime of an electronically excited state in a molecule is 5 ns. if this state emits at 500 nm, calculate the uncertainty in the emitted wavelength
The uncertainty in the emitted wavelength is approximately: 0.013 nm.
The mean lifetime of an electronically excited state in a molecule is 5 ns. If this state emits at 500 nm, calculate the uncertainty in the emitted wavelength.
The uncertainty in the emitted wavelength can be calculated using the relation given below,Δλ = h/(4πmc)τ
Here, Δλ is the uncertainty in the emitted wavelength is Planck’s constant
m is the mass of an electron
c is the speed of light in vacuum
t is the lifetime of the excited state
Therefore, substituting the given values we have,Δλ = (6.626 × 10^-34)/(4π × 9.1 × 10^-31 × 3 × 10^8 × 5 × 10^-9)≈ 0.013 nm (approximately)
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1.
(a)
Beams of red light of wavelength 700 nm and green light of wavelength 550 nm are incident
normally on a diffraction grating which has 5000 lines per cm. Bright spots (maxima) are
observed on a distant screen.
LIT
(i) State one use of a diffraction grating.
You can use it in microwaves
(ii) Show clearly that the grating spacing, d is 2.0 x 10 m.
20×10....
(iii)
53-9°
Show clearly which of the two colours would give a second order maximum at an
angle of diffraction between 33° and 34°.
131
11 S
LIT
wavelength....
The green light of wo
give a second order maximum because
It has a shorter wavelength so the
diffraction will meet on the obstacks.
(b) (i) Show that the maximum order possible is given by
d
2
275
would
121
Del
(ii) Determine the maximum order for
(I) the green light,
550 =
2
(II) the red light.
700nm
3.50
2
Assuming that the diffracted beams from both lights only overlap at n = 0, determine
the total number of bright spots which can be observed.
Nu
A diffraction grating can be used, for example, to divide light into its many wavelengths or colours, enabling spectroscopic examination. We have the following by applying the grating spacing formula, d = 1/N, where N is the number of lines per unit length:
When red light with a wavelength of 625 nm generally incident?Normally, red light with a wavelength of 625 nm is impinge on an optical diffraction grating with a line density of 2 105 m
Is a diffraction grating typically the site of an electromagnetic wave incident?A diffraction grating often experiences an electromagnetic wave impinge on it. A second-order maximum is generated at a 30° angle to the grating's normal. There are 5000 lines per cm on the grating.
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if an object rolls down a ramp, how does the velocity of that object at the bottom of the ramp compare with the height of the object at the top?
If an object rolls down a ramp, the velocity of that object at the bottom of the ramp will be greater than the height of the object at the top.
This is because the potential energy of the object is converted to kinetic energy as it rolls down the ramp.
How is velocity calculated?Velocity is calculated by dividing the distance covered by the time taken. It is usually measured in meters per second (m/s) or kilometers per hour (km/h). If the ramp is sloped, the acceleration of the object depends on the angle of the ramp and the force of gravity.
To calculate the velocity of an object rolling down a ramp, we need to use the equation:
v = √(2gh)
where,
v is the velocity of the object at the bottom of the ramp
g is the acceleration due to gravity (9.8 m/s²)
h is the height of the ramp.
This formula applies if we assume there is no friction and air resistance.
Factors affecting velocity:
Several factors can affect the velocity of an object rolling down a ramp. These factors include the angle of the ramp, the height of the ramp, the mass of the object, the force of gravity, and friction between the object and the ramp. As the angle of the ramp increases, the velocity of the object also increases.
As the height of the ramp increases, the velocity of the object also increases. As the mass of the object increases, the velocity of the object decreases. As the force of gravity increases, the velocity of the object also increases. As the friction between the object and the ramp increases, the velocity of the object decreases.
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a softball of mass 0.220 kg that is moving with a speed of 4.0 m/s (in the positive direction) collides head-on and elastically with another ball initially at rest. afterward the incoming softball bounces backward with a speed of 2.0 m/s. calculate the velocity of the target ball after the collision.
The velocity of the target ball after the collision will be 1.32 / m².
Velocity of the target ball after the collision = (m1u1 + m2u2) / (m1 + m2)
Here, m1 = mass of the incoming softball = 0.220 kgm² = mass of the target ball = ?
u1 = initial velocity of the incoming softball = 4.0 m/su2 = initial velocity of the target ball = 0 m/sv1 = final velocity of the incoming softball = -2.0 m/s (because the incoming softball is bouncing backward)
v2 = final velocity of the target ball = ?
Substituting the given values in the above formula, we get:
v2 = (m1u1 + m2u2 - m1v1) / m2v2 = (0.220 x 4.0 + 0 x 0 - 0.220 x (-2.0)) / m2v2 = (0.880 + 0.440) / m2v2 = 1.32 / m²
Therefore, the velocity of the target ball after the collision is 1.32 / m².
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9. what must the orbital height (above the surface) of a satellite that is in geosynchronous with a point on the earth's equator?
A geosynchronous satellite must be in an orbit with a height of approximately 35,786 km (22,236 miles) above the surface of the Earth at the equator.
This height is referred to as the "geosynchronous orbital height" or the "Clarke orbit". In order for a satellite to be in geosynchronous with a point on the Earth's equator, it must have an orbital height of approximately 35,786 kilometers above the Earth's surface.
What is Geosynchronous?Geosynchronous is a term that refers to an orbit in which a satellite orbits the Earth at the same rate as the Earth rotates. As a result, the satellite appears to remain in a fixed position relative to an observer on the ground. Satellites that are placed in geosynchronous orbit are used for a variety of purposes, including communications, meteorology, and remote sensing. They're also useful for military purposes.
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a satellite in a circular orbit around earth experiences a centripetal acceleration of 8.62 m/s2 . the tangential speed of the satellite is 7.65 x 103 m/s. the radius of earth is 6.38 x 106 m. what is altitude of the satellite?
The altitude of the satellite is 2.24 × 10⁷ m.
Given, the centripetal acceleration of the satellite is a = 8.62 m/s²,
the tangential speed of the satellite is v = 7.65 × 10³ m/s,
the radius of the earth is R = 6.38 × 10⁶ m
We can find the altitude (h) of the satellite from the relation;
a = (v² / R) + (v² / h)
where, v is the tangential velocity, R is the radius of the Earth, h is the altitude of the satellite
Substitute the given values to calculate h;
a = (v² / R) + (v² / h)
8.62 = (7.65 × 10³)² / (6.38 × 10⁶) + (7.65 × 10³)² / h
h = (7.65 × 10³)² / (8.62) - (6.38 × 10⁶)h = 2.24 × 10⁷ m
Therefore, the altitude of the satellite is 2.24 × 10⁷ m.
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using the coils from the e/m apparatus, how much current do you need to pass through the coils to create a magnetic field strength of 0.575 gauss in the center of the coils? use
Using the coils from the e/m apparatus, the current you need to pass through the coils to create a magnetic field strength of 0.575 gauss in the center of the coils is: 0.255 amperes.
To create a magnetic field strength of 0.575 gauss in the center of the coils from an e/m apparatus, you need to pass an electric current of 0.255 amperes through the coils. The magnetic field strength, B, produced by a current-carrying coil is proportional to the current I and inversely proportional to the coil's radius,
r: B = μ₀NI/2r,
where μ₀ is the permeability of free space and N is the number of turns in the coil.
To determine the current required to produce a magnetic field strength of 0.575 gauss in the center of the coils, we can rearrange the equation and solve for I.
Thus, I = 2rB/μ₀N. Using the given information, we can calculate that 0.255 amperes are needed to create a magnetic field strength of 0.575 gauss in the center of the coils from an e/m apparatus.
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Complete Question:
Using the coils from the e/m apparatus, how much current do you need to pass through the coils to create a magnetic field strength of 0.575 Gauss in the center of the coils? Use Rcoil = 0.145 m. All other necessary information is provided in the lab manual. Enter your answer in units of Amps, rounded to three decimal places.
9. Thermal energy (heat) is defined as
A. the sum of all the kinetic energies of all the particles in an object
B. the average of all the kinetic energies of all the particles in an object
C. the sum of all the numbers of particles in an object
D. the average number of particles in an object
Answer:
The correct answer is A. Thermal energy (heat) is defined as the sum of all the kinetic energies of all the particles in an object.
According to Huygens’ wave theory, every point on the wavefront behaves as a source of (A) secondary waves (B) stationary waves (C) surface waves (D) beatsRead more on Sarthaks.com - https://www.sarthaks.com/1200121/according-huygens-wave-theory-every-point-the-wavefront-behaves-source-secondary-waves
According to Huygens’ wave theory, every point on the wavefront behaves as a source of secondary waves.
What is Huygens' wave theory?Christiaan Huygens, a Dutch mathematician and physicist, created the Huygens' wave theory. It's a hypothesis that light waves can be seen as tiny wavefronts that are each a spherical wave. According to Huygens, every point on a given wavefront acts as a secondary source of waves in Huygens' wave theory. Huygens' wave theory states that every point on a wavefront behaves as a source of secondary waves.
The Huygens' principle or Huygens-Fresnel principle states that light waves are generated from every point on a wavefront. It specifies that each point on a wavefront serves as a secondary source of spherical waves. This theory enables researchers to determine how light waves move and the laws that govern their propagation.
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if 54 j of work are needed to stretch a spring from 14 cm to 20 cm and 90 j are needed to stretch it from 20 cm to 26 cm, what is the natural length of the spring?
The natural length of the spring is 17 cm. Given that a 54J of work is needed to stretch a spring from 14 cm to 20 cm and 90J of work is needed to stretch it from 20 cm to 26 cm.
Let L be the natural length of the spring.
Initial length of the spring = 14 cmFinal length of the spring = 26 cmTotal energy required to stretch the spring from natural length to 26 cm = 54 + 90 = 144 J
Total extension of the spring = (26 - L) cmTotal energy required to stretch the spring from natural length to 20 cm = (54 / 144) × 90 = 33.75 J
Total extension of the spring = (20 - L) cm
Now we need to equate the total extensions of the spring to find the natural length of the spring.(20 - L) + (26 - L) = 12cm46 - 2L = 12L = 17 cm
Therefore, the natural length of the spring is 17 cm.
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when he displacement of a mass on a spring is half the amplitude of the oscillation, what fraction of the mass's energy is kinetic energy?
Answer:
PE = 1/2 K x^2 potential energy
when x = A
PEt = 1/2 k A^2 total potential energy
If x = A / 2
PE 1/2= 1/2 k A^2 / 4
PE1/2 / PEt = 1/4
Thus the PE at 1/2 the displacement is 1/4 the total
Since PE + KE = constant
3/4 the mass's energy will be KE at 1/2 the amplitude
what was the speed of the 600 g glider just before impact? one end of a massless, 30-cm -long spring with spring constant 25 n/m is attached to a 250 g stationary air-track glider; the other end is attached to the track. a 600 g glider hits and sticks to the 250 g glider, compressing the spring to a minimum length of 22 cm .
The speed of the 600 g glider just before impact is 1.98 m/s.
It is given that: Mass of the stationary air-track glider, m1 = 250 g = 0.25 kg, Length of the spring, l = 30 cm = 0.3 m, Spring constant, k = 25 N/m, Mass of the incoming glider, m2 = 600 g = 0.6 kg, The length of the compressed spring is 22 cm = 0.22 m.
To solve the problem, we can use the principle of conservation of momentum. The momentum of an object is the product of its mass and velocity.
momentum = mass x velocity
Before collision:
In the beginning, the stationary glider is at rest. Hence, its initial momentum is zero. However, the incoming glider has momentum of:
m2 × u (where u is the initial velocity of the incoming glider)
After collision:
The two gliders stick together and move with a common velocity, v. Using the principle of conservation of momentum, we can write:
m2 × u = (m1 + m2) × v
Substituting the given values:
0.6 kg × u = (0.25 kg + 0.6 kg) × v0.6
u = 0.85v
Dividing both sides by 0.85, we get:
v = 0.706 m/s
But we are required to find the speed of the incoming glider just before impact (i.e., u). To find u, we can use the principle of conservation of energy. Since the spring is compressed and not released, the total mechanical energy is conserved.
Initially, the glider had only potential energy stored in the compressed spring. The potential energy stored in the spring is given by the formula:
potential energy = 1/2 k x²
where x is the distance by which the spring is compressed before the collision.
Hence, initially the incoming glider had a potential energy of:
potential energy = 1/2 × 25 N/m × (0.3 m - 0.22 m)²= 0.5 × 25 N/m × (0.08 m)²= 0.04 J
This potential energy is converted into kinetic energy of the two gliders after collision. Hence, we can write:
1/2 (m1 + m2) v² = potential energy
Substituting the values:
1/2 (0.25 kg + 0.6 kg) v² = 0.04 JV² = 0.04 / 0.425V² = 0.0941
Taking square root of both sides:
v = 0.3066 m/s
The speed of the incoming glider just before impact is therefore:
u = 2.29 m/s - 0.3066 m/su = 1.98 m/s
Therefore, the speed of the 600 g glider just before impact is 1.98 m/s.
Note: The question is incomplete. The complete question probably is: One end of a massless, 30-cm -long spring with spring constant 25 n/m is attached to a 250 g stationary air-track glider; the other end is attached to the track. a 600 g glider hits and sticks to the 250 g glider, compressing the spring to a minimum length of 22 cm. What was the speed of the 600 g glider just before impact?
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