Please Help me! Please show all work!
Jeremiah the Bullfrog rode a roller coaster around a loop. Being a good friend, he took some measurements for you during his journey. The 1.5kg amphibian noted that at the bottom of the loop, the speed of the roller coaster was 33m/s. You know from the informational poster next to the entrance that the loop has a radius of 22m. How much force did the seat exert on Jeremiah at the bottom of the loop?
Answers
74.25 N much force did the seat exert on Jeremiah at the bottom of the loop.
What is centripetal force?This is an acceleration technique. When an item is moving in a circle, it is moving ahead while being turned by a consistent force that is directed inward. The Centripetal Force is the name given to this internal resultant force.
Given that,
Mass (m) = 1.5 kg
speed (v) = 33 m/sec
radius (r) = 22m
As we know,
centripetal force (F) = mv²/r
or, F = [1.5 × (33)²] / 22
or, F = 74.25 N
So, 74.25 N much force the seat exert on Jeremiah at the bottom of the loop.
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Related Questions
Disregarding air resistance, what is the speed of a ball dropped from 12 feet just before it hits the ground? (Use 1 ft = 0.30 m, and use g = 9.8 m/s2.)
2.4 m/s
8.4 m/s
10.8 m/s
15.3 m/s
Answers
Answer:
[tex]8.4\; {\rm m\cdot s^{-1}}[/tex].
Explanation:
Let [tex]x[/tex] denote the displacement of the ball. It is given that [tex]x = 12\; {\rm ft}[/tex]. Apply unit conversion and ensure that the displacement [tex]x\![/tex] of the ball is measured in meters:
[tex]\begin{aligned}x &= (12\; {\rm ft})\, \frac{(0.30\; {\rm m})}{(1\; {\rm ft})} = 3.6\; {\rm m}\end{aligned}[/tex].
Let [tex]u[/tex] denote the initial velocity of the ball, and let [tex]v[/tex] denote the velocity of the ball right before it hits the ground. Note that since the question states the ball was "dropped", assume that the ball was initially at rest with initial velocity [tex]u = 0\; {\rm m\cdot s^{-1}}[/tex].
Under the assumptions, the acceleration [tex]a[/tex] of the ball will be constantly [tex]a = g = 9.8\; {\rm m\cdot s^{-2}[/tex].
Rearrange the SUVAT equation [tex]v^{2} - u^{2} = 2\, a\, x[/tex] to find the final velocity [tex]v[/tex] of the ball right before landing:
[tex]\begin{aligned}v &= \sqrt{u^{2} + 2\, a\, x} \\ &= \sqrt{(0\; {\rm m\cdot s^{-1}})^{2} + 2\, (9.8\; {\rm m\cdot s^{-1}})\, (3.6\; {\rm m})} \\ &= 8.4\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
Answer: B (8.4 m/s)
Explanation:
a motorcycle has a mass of 250 kg. it goes around a 13.7 m radius turn at 96.5 km/h. what is the centripetal force on the motorcycle?
Answers
A motorcycle has a mass of 250 kg. it goes around a 13.7 m radius turn at 96.5 km/h. 9720 N is the centripetal force on the motorcycle.
To find the centripetal force on the motorcycle, we can use the formula for centripetal force:
F = m * a
where F is the centripetal force, m is the mass of the object, and a is the centripetal acceleration. To find the centripetal acceleration, we can use the formula for centripetal acceleration:
a = v^2 / r
where a is the centripetal acceleration, v is the velocity, and r is the radius of the curve. In this case, we know that the mass of the motorcycle is 250 kg, the velocity is 96.5 km/h, and the radius of the curve is 13.7 m. To find the centripetal acceleration, we need to convert the velocity from km/h to m/s. Since 1 km/h is equal to 1000 m/3600 s = 0.2778 m/s, the velocity in m/s is 96.5 km/h * 0.2778 m/s/km/h = 26.7 m/s.
For centripetal force and centripetal acceleration, we get:
F = m * a
= 250 kg * (v^2 / r)
= 250 kg * (26.7 m/s)^2 / 13.7 m
= 9720 N
Therefore, the centripetal force on the motorcycle is 9720 N.
Gravity is the centripetal force that drives astronomical orbits according to Newtonian mechanics. The tension of the rope provides the centripetal force on an object that is swinging around on the end of a rope in a horizontal plane. The rope illustration is a pull-related example. In some situations, such as when a wall's natural reaction serves as the centripetal force for a wall of death or a Rotor rider, the centripetal force can also be provided as a "push" force.
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Which phrase describes a risk associated with producing energy in a nuclear power plant?
Answers
Answer:
Production of wastes needing long-term storage
Explanation:
A man whoe Ma i 40kg walk up a flight of 20 tep each 150mm height in 10ec. Find the average power developed. (g=10m-2)
Answers
A man whose mass is 40kg walk up a flight of 20 step each 150mm height in 10 sec. The average power developed is 12.0 W.
The average power developed by the man as he walks up the stairs, you need to know the work he does and the time it takes him to do it. First, you can find the work done by the man by multiplying his weight (which is equal to his mass multiplied by the acceleration due to gravity) by the distance he travels:
= Work = (40 kg) x (10 m/s^2) x (20 steps x 0.150 m/step)
= 120 J
Then, you can divide the work done by the time it takes to do it to find the average power developed:
= Power = Work / Time
= 120 J / 10 s
= 12.0 W
So, the average power developed by the man as he walks up the stairs is 12.0 W.
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some time later, kid a was spinning with the same speed that kid c had originally. what would kid a's centripetal acceleration be if his distance from the center of the merry-go-round was r
Answers
Centripetal refers to “center-seeking” Quantifies the change in directionof the velocity The acceleration is directed toward the center of the circle of motion.
The magnitude of the centripetal acceleration is given by V^2/r, the direction is toward the center of the circle. The tangential component of the acceleration is due to changing speed. The centripetal component of the acceleration is due to changing direction.
When an object is rotating at a constant angular velocity, the whole object has a constant angular velocity. Therefore, every mint on the turntable has the same, constant angular velocity.
The acceleration which causes the tangential velocity to change direction is called Centripetal acceleration. Centripetal acceleration is always in toward the center of the circle.
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Determine how much heat needs to be transferred to 1 kg of ice at -10C to turn it into water at 15C. The specific heat capacities of ice and water are 2.1 and 4.2 kJ, respectively, the specific heat of melting of ice is 330 kJ/kg
Answers
Answer: If you drop ice into hot water will result in the ice melting
Explanation:
the cosmic microwave background is almost perfectly uniform in all directions, except for very small deviations in its temperature. what do scientists think these small deviations represent?.
a. varying redshift and blueshift due to motions of gas in the early universe
b. region of slightly higher helium abundance in the early universe
c. the warmer spots represent regular matter and the cooler spots represent dark matter
d. regions of slightly density that made it possible for galaxies form
Answers
In a case whereby cosmic microwave background is almost perfectly uniform in all directions, except for very small deviations in its temperature. what the scientists think these small deviations represent is d. regions of slightly density that made it possible for galaxies form.
What is the cosmic microwave background?The Cosmic Microwave Background can be descibed as the cooled remnant of the first light which could ever travel freely throughout the Universe it can be seen as the 'fossil' radiation, which an be considered as the furthest that any telescope can see.
It should be noted that the density i can be of two types, whereby one is absolute density, and the other is relative density hgowever the Relative density can be described as the specific gravity, and this is the ratio of the density of a material to the density of reference material.
Therefore, option D is correct.
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a proton is accelerated by a uniform 360 n/c electric field. find the kinetic eergy and the velocity of the proton after it has traveled 50
Answers
The kinetic energy is 2.88 × 10-17 J and the velocity of the proton will be 180 m/s
The kinetic energy of the proton is given by
KE = qV = (1.60217662 × 10-19 C) (360 N/C) (0.50 m)
= 2.88 × 10-17 J, The velocity of the proton is given by:
V = (360 N/C) (0.50 m) =0.360 x 0.50 = 0.180 m/s .
This means that after the proton has traveled 50 cm, it will have a kinetic energy of 2.88 × 10-17 J and a velocity of 180 m/s. This result is because the electric field is uniform and constant, and the proton is accelerated by the same amount throughout its journey. This means that the velocity and kinetic energy of the proton will increase linearly with the distance traveled. The electric field provides the proton with a constant acceleration, and as the proton travels further, it gains more kinetic energy and a higher velocity.
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a thin rod of mass m and length l is suspended vertically from a frictionless pivot at its upper end. a mass m of putty traveling horizontally with a speed υ strikes the rod at its cm and sticks there. Explain why the intial angular momentum is what it is?
Answers
The rotating equivalent of linear momentum in physics is called angular momentum, also known as moment of momentum or rotational momentum.
Conservation of Angular Momentum m v (L/2) = I w => w^2 = m^2 v^2 L^2/(4 I^2)---------eq1
Conservation of Energy (1/2) I w^2 = (m + M)g h----------------eq2 where h = height of the center of mass
Relate h to h': h' = height from the bottom a= angle between rod and the normal
(L/2 -(L/2) cos(a)) = h (L - L cos(a))=h' => h=h'/2--------------------------eq3
Compute I=moment of inertia I=m(L/2)^2 + (1/12) M L^2 + M(L/2)^2 I= [(L^2)/4](m + 4M/3)------------------eq4
Plug eq1 and eq3 into eq2 (1/2) I m^2 v^2 L^2/(4 I^2) = (m + M)g h'/2 Solve for h' h'=m^2 v^2 /((m + M)g)
Then use eq4 to get the final result h'=m^2 v^2 /((m + 4M/3)(m + M)g)
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what happens if the woman suddenly slides closer to the hub by 0.400 m? (select all that apply.)
Answers
The new net torque is in the opposite direction and hhas greater magnitude than that of previous.
What is torque?The force that can cause an object to rotate along an axis is measured as torque. Similar to how force accelerates an item in linear kinematics, torque accelerates an object in an angular direction.
A vector quantity is a torque. The force acting on the axis determines the direction of the torque vector.
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an object is placed just inside the focal point of a converging lens. describe the image (mark all that apply).
Answers
As you move the object closer and closer to the focal point, the image will become further and further away kind of image results from putting anything in front of the focal
A converging lens's focal point is just outside the image result for an item. explain the picture (mark all that apply).
In reality, it is possible to generalize that the image will always be situated behind the mirror whenever the item is situated between the focal point (F) and the mirror. In certain circumstances, the image will be larger than the thing and upright (not inverted).
Kind of image results from sandwiching an object between No image is created when the object is at the focal point. although the refracted beams do not converge or diverge. The light rays cannot create an image since they are moving parallel to one another after refractive error.
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the gas in a cylynder absorbs 850 kj of heat, and the subsequent expansion does 455 kj of work on the surroundings. what is the change in the systems internal energy
Answers
The change in the systems internal energy is 400KJ.
ΔE = Q - W
but, Qin > 0
Win < 0
ΔE = 850 - 450 = 400KJ
As with the static rest mass energy of its constituent matter, the internal energy cannot be readily measured, and knowledge of all of its components is rarely interesting. In contrast to its absolute value, the internal energy is only primarily concerned with changes in thermodynamics. Instead, it is typical to specify a reference state and gauge how a thermodynamic process differs from this state. Matter is transferred, energy is released as heat, or thermodynamic work is performed to change the internal energy. The system's attributes, including changes in temperature, entropy, volume, and molar composition, are used to measure these processes. The system is referred to as closed when matter transfer is inhibited by impermeable containment walls. Neither matter if the confining walls fail.
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when making your turn you should accelerate at the apex of the turn. group of answer choices true false
Answers
The statement "when making your turn you should accelerate at the apex of the turn" is false.
It is generally not advisable to accelerate at the apex of a turn. In fact, it is generally recommended to slow down or maintain a constant speed while turning, in order to maintain control and avoid oversteering.
Accelerating at the apex of a turn can cause the vehicle to lose traction and potentially lose control. This is especially true if the surface is slippery or the vehicle is traveling at a high speed.
Instead of accelerating at the apex of a turn, it is generally recommended to gradually increase speed as the vehicle exits the turn, once it is back on a straight stretch of road. This allows the vehicle to maintain stability and control while turning, and helps to prevent accidents.
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if the distance of a galaxy is 5 mpc, what is its recessional velocity if the hubble constant is 70 km/s/mpc?
Answers
The distance of galaxy is given as 5Mpc. and the Hubble's constant is 70(km/s)/Mpc.
To find the recessional velocity of the galaxy
Hubble found that the tendency of recessional velocity is to increase with the distance of galaxy, therefore recessional velocity is directly proportional to the distance of the galaxy
The relation between recessional velocity and the distance of the galaxy can be expressed using Hubble's law.
substituting the values we get
V=70 (km/s)/ mpc [tex]\times[/tex]5Mpc
V = 350km,
Therefore the recessional velocity will be 350 km/s.
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if you represented earth's history by a line that is 2 m long, how long a segment (in cm) would represent the 400 million years since life moved onto the land?
Answers
If you represented earth's history by a line that is 2 m long then, the segment length in 400 million years will be 43.2 cm.
The entire history of the Earth is represented by a line 5 meters long.
The age of the Earth is 4.6 billion years.
That means a length of 5 meters or 500 cm (1m = 100cm, so 5m = 5× 100 = 500 cm) represents 4.6 billion years, i.e 4600million years. (As 1 billion years = 1000 million years)
We have to calculate the length of the segment for 400 million years.
In 4600 million years, the segment length is = 500 cm
In 1 million years, the segment length will be = 500 / 4600 = 0.108 cm
In 400 million years, the segment length will be = 0.11 × 400 = 0.108 × 400 = 43.2 cm
Therefore, the segment length in 400 million years will be 43.2 cm.
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a fairground ride spins its occupants inside a flying saucer-shaped container. if the horizontal circular path the riders follow has an 8.90 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration 1.50 times that due to gravity? (you do not need to enter any units.)
Answers
There are 17.1 revolutions per minute will the riders be subjected to a centripetal acceleration 1.50 times that due to gravity
Acceleration is the rate at which velocity changes over time, both in terms of speed and direction. A point or object travelling in a straight path is accelerated if it accelerates or decelerates. Even if the speed is constant, motion on a circle is accelerated because the direction is always changing.
The centripetal acceleration can be written as: a =
r \sω \s²
Where is the angular velocity. Equating this to the question: r²= 2.25 g
7.00 2 = 2.25 9.81
When we solve for, we get: = 1.78
Angular velocity is defined as the rate of change of angle = 2 T.
Where T is the time span (time for one revolution)
As a result, we can solve for T.
= 3.5
As a result, it completes one rotation every 3.5 seconds. It will finish in one minute:
60 /3.5
= 17.1 rotations.
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Wwhat was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?
Answers
The speaker's power output is 785.398 W assuming uniform spherical spreading of the sound and neglecting absorption in the air.
Given the Sound Intensity = I and
the Loudspeaker Distance = r = 2.5m
Sound level produced(β) : 130 dB
The formula for calculating sound intensity is:
β = 10logI/I0
130 = 10logI/10-12
13 = logI/10-12
10^13x10^-12 = I
I = 10 W/m^
A = area, hence power (P) = IA = 4πr^2
P = 10X 4X 3.14X (2.5)^
P = 785.398W
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At a rock concert, a dB meter registered 130 dB when placed 2.5 m in front of a loudspeaker on stage. (a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?
A table tennis ball is dropped onto the flour from a height
€ 4m and It rebounds to a height of 3m. If the time of
ontact with the floor is o.ols, what is the magnitude and
irection of the acceleration during the contact.
Answers
The acceleration of the ball during the contact is 1652 m/s^2 in upward direction.
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).
The velocity of the ball before hitting the floor in downward direction:
u = √(2gs)
= √(2×9.8×4) m/s
= 8.85 m/s.
The velocity of the ball after hitting the floor in upward direction:
v = √(2gs)
= √(2×9.8×3) m/s
= 7.67 m/s.
Hence, the acceleration of the ball during the contact in upward direction is: a = change in velocity/time duration
= (7.67 - (-8.85))/0.01 m/s^2
= 1652 m/s^2
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What is the best response that shari’s friend could make? she could agree with shari because the pendulum is at the same height and would have the same gravitational potential energy at both positions. she could agree with shari because the pendulum has the same amount of mechanical energy throughout its swing. she could disagree with shari because the pendulum converts kinetic energy into gravitational potential energy, then back into kinetic energy. she could disagree with shari because the pendulum converts gravitational potential energy into kinetic energy, then back into gravitational potential energy.
Answers
The best response that shari’s friend could make was that She could disagree with Shari because the pendulum converts gravitational potential energy into kinetic energy, then back into gravitational potential energy.
What is the pendulum's greatest potential?The ball is momentarily immobile at the height of the swing. Due to its elevated position above the surface, it possesses the maximum potential energy. The system of the ball on the pendulum string has the same overall quantity of energy at every point in the swing.
The pendulum's energy is continuously transformed from gravitational potential to kinetic, and vice versa. The pendulum on the left swings more quickly than the pendulum on the right because shorter pendulums swing more quickly than larger ones do.
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SOMEONE PLEASE HELP ME!!!
The velocity-time graph for an object is shown. How can the total displacement of the object be determined?
Answers
Answer:
Below
Explanation:
The area under the graph will represent the displacement .
Remember displacement = velocity * time
so the total displacement will be Area 1 - Area 2
is there an angle of incidence between 0∘ and 90∘ such that all of the light will be reflected?
Answers
A beam of light in the air encounters a transparent block with index of refraction n=1.53. Some of the light is reflected and some is refracted. There will be no such angle of incidence between [tex]$0^{\circ}$[/tex] and [tex]$90^{\circ}$[/tex] such that all of the light will be reflected.
In geometric optics, the angle of incidence is the angle between a ray incident on a surface and the normal, or line perpendicular to the surface at the point of incidence. Any type of wave, including microwave, X-ray, optical, and acoustic, may create a ray.
The refractive index of an optical medium is a dimensionless quantity that indicates how well that medium bends light in optics. The refractive index controls how much light is refracted or twisted when it enters a substance.
[tex]\begin{aligned}\mu & =\frac{1}{\sin c} \\c & =\sin ^{-1}\left(\frac{1}{\mu}\right) \\& =\sin ^{-1}\left(\frac{1}{1.53}\right) \\& =40.83\end{aligned}[/tex]
First condition it should be remembered that if the incident angle is from denser medium to rarer medium at or greater than [tex]$40.33^{\circ}$[/tex], all light will be reflected but in this Question, the condition is the opposite.
Hence, there should not be such an angle.
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The complete question should be:
A beam of light in the air encounters a transparent block with index of refraction n=1.53. Some of the light is reflected and some is refracted.
Is there an angle of incidence between [tex]$0^{\circ}$[/tex] and [tex]$90^{\circ}$[/tex] such that all of the light will be reflected?
(a) Yes, at an angle greater than [tex]50^{\circ}[/tex]
(b) Yes, at an angle less than [tex]50^{\circ}[/tex]
(c) No.
an object in free fall has a speed of 60 m/s. one second later its speed is
Answers
An object in free fall has a speed of 60 m/s. One second later its speed is 70m/s.
We're asked to find the speed of an object in free fall one second after it has a speed of 60m/s. An object in free fall means that the only force affecting its motion is gravity. To do this, we can use the equation
vy=v°y+ayt
where:
vy is the velocity at time (what we're trying to find) voy is the initial velocity (60m/s in this case, because it's assumed to be travelling downward, which is taken to be the negative y- axis) ay is the acceleration, equal to -g, which is 9.81m/s is the time, which in this case is 1 second.Plugging in known values, we have Vy=60m/s(9.81m/s²)(1s) =-70m/s rounded to 2 (or 1, technically) significant figures.
This the velocity of the object (which is why it includes a sign). The speed is simply the magnitude of this, which is a positive quantity.
speed = 70m/s
You also could have solved this problem neglecting the signs of the initial velocity and acceleration in the above equation:
speed = 60m/s +(9.81m/s²)(1s) = 70m/s
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in an average human, basic life processes require energy to be supplied at a steady rate of 100 w .What daily energyintake, in Calories, is required to maintain these basic processes?This is the minimum daily caloric intake needed to avoidstarvation.
Answers
The daily equivalent of 6.27 106 joules is 1500 calories, which the average person consumes daily. This is roughly equivalent to the energy needed to drive a car for 15 minutes.
Even while sleeping, a creature still needs energy. This is because our bodies continue to go through a variety of energy-intensive biological processes when we sleep.
Even when we are asleep, our hearts continue to beat in order to circulate blood throughout the body. Additionally, the heart requires energy to beat. As a result, the heart requires a constant flow of energy to function.
Therefore, 1 watt = 1 joule/second, so 100 w there needs to be 100 joules.
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a solid sphere of mass m and radius r rolls without slipping along a table at speed v. what is its kinetic energy? (given for solid sphere i
Answers
The kinetic energy of a solid sphere is (1/2)mv² + [(2/5)mr²] × ω² × r for having mass m and radius r rolls without slipping.
We know that if property of sphere is defined, it means that linear and rotational kinetic energy is possible.
For rotational energy, we need to know about moment of inertia and angular acceleration.
For solid sphere moment of inertia is given by the expression=(2/5)mr² where m is the mass and r is the radius of the sphere
Now, we know that for angular acceleration we need angular velocity which can be calculated by the linear velocity which can be calculated by the formula
v=ω×r where v is the linear velocity ,ω is angular velocity and r is the radius of the object.
So,ω=v/r
Now we know that angular acceleration(α)=ω² × r
Therefore, rotational energy is =I × α = [(2/5)mr²] × ω² × r
Now, we know that kinetic energy is given by =(1/2)mv² where m is the mass and v is the velocity of a solid sphere.
So, kinetic energy of sphere is =linear kinetic energy + rotational kinetic energy
=>kinetic energy = (1/2)mv² + [(2/5)mr²] × ω² × r
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what is the frequency of an electromagnetic wave that has the same wavelength as a 3.5 khzkhz sound wave in water?
Answers
7.095 × 10⁵ KHz is the frequency of an electromagnetic wave that has the same wavelength as a 3.5 KHz sound wave in water.
What is the frequency?The pace at which current changes direction each second is known as frequency. One hertz (Hz), which is a unit of measurement used internationally, equals one cycle per second. One hertz (Hz) is one cycle every second. A full alternating current or voltage wave is referred to as a cycle.
The number of waves that pass a specific place in a predetermined period of time is known as the wave frequency. A wave passes a fixed point in one hertz (Hz), the SI unit for wave frequency, in one second. A wave with a higher frequency has more energy than a wave with a lower frequency of the same amplitude.
Given that,
frequency = 3.5 KHz
As we know,
V = fλ
As, the electromagnetic wave that has the same wavelength, thus
V/f = constant
Therefore,
V₁/V₂ = f₁/f₂
now, f₁ = (V₁/V₂)× f₂
or, f₁ = [(3 × 10⁸) / 1480] × (3.5 × 10³)
or, f₁ = 7.095 × 10⁸ Hz
or, f₁ = 7.095 × 10⁵ KHz.
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compared to when the cosmic microwave background was first released, the radiation of the cosmic microwave background today is blank and has most of its photons at blank wavelengths.
Answers
The radiation of the cosmic microwave background today is blank and has most of its photons at longer wavelengths.
Gamma rays have extremely small wavelengths that are only a small portion of the size of atoms, whereas other wavelengths can extend as far as the universe because the relationship between wave frequency and wavelength is inverse. Although it isn't always stated explicitly, electromagnetic radiation's wavelengths are typically expressed in terms of the vacuum wavelength, regardless of the medium they are traveling through. Electromagnetic radiation's behavior is influenced by its wavelength. wavelength x frequency equals the speed of light. Energy equals Planck's constant times frequency. Wave number in cm equals 1/wavelength. A rough estimate of the wavelength size is shown along with the wavelengths of various regions of the electromagnetic spectrum.
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the system moves upward with a constant velocity of 10 ft/s. what is the reading on the bathroom scale (in pounds)
Answers
The reading on the bathroom scale is W = 230 lbs.
Solution:
Since acceleration is zero, so weight remains the same on scale
W = 230 lbs
Acceleration is the rate of change of velocity over time, both in terms of velocity and direction. A point or object moving in a straight line accelerates as it accelerates or decelerates. Circumferential motion is accelerated because it always changes direction even at constant velocity.
Acceleration is the change in velocity over time. Whenever a change in velocity or acceleration in the direction of movement occurs. At constant velocity, acceleration is zero. Deceleration is called negative acceleration or deceleration.
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Find the area of the region that lies inside both curves.
r^2 = 2 sin(2θ), r = 1
Answers
The area of the region that lies inside both curves r² = 2sin(2θ), r = 1 is -0.1287 square units.
Since the curves are:
r² = 2sin(2θ) and
r = 1.
We find their point of intersection.
So, r² = r²
= 2sin(2θ) = 1²
= 2sin(2θ) = 1
= sin(2θ) = 1/2
= 2θ = sin⁻¹(1/2)
= 2θ = π/6
= θ = π/12
Thus, we integrate the area from θ = 0 to θ = π/12
Now the area A of the region between two curves between θ = α to θ = β is =
= A = ∫ (r²-r'²) dθ [from 0 to π/12]
So, the area between the curves r² = 2sin(2θ), r = 1 between θ = 0 to θ = π/12 is =
= A = ∫ (r²-r'²) dθ [from 0 to π/12]
= A = (2sin2θ dθ - 1²) dθ [from 0 to π/12]
= A = 0.1278
So, the area of the region that lies inside both curves r² = 2sin(2θ), r = 1 is -0.1287 square units.
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how are radio communications usually affected by the charged particles that reach earth from solar coronal holes?
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Charged particle emissions interact with the magnetosphere of the earth to produce geomagnetic storms or disturbances.
Communication systems suffer harm from solar storms. Some radio frequencies are absorbed during geomagnetic storms while others are reflected, resulting in rapidly fluctuating signals and unexpected propagation patterns (reproducing or multiplying in unplanned directions). Amateur and public radio are frequently interfered with. The atmospheric circumstances that radio waves meet, like clouds and precipitation, reflect, absorb, scatter, refute, and diffract them. Importantly, different air conditions have distinct effects on radio waves. A different type of disturbance that might impact radio communications is a coronal mass ejection, or CME. Although in many ways superior to flares, CMEs were not identified until spacecraft were able to study the Sun from orbit.
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what produces the retrograde motion of mars, and what geometric arrangements did ptolemy use to explain this motion?
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Due of Earth's far bigger orbit than Mars', as Earth passes it, Mars seems to be going backwards. Ptolemy postulated that planets orbited on epicyles that revolved around deferents to explain this.
Mars experiences retrograde motion when Earth, which moves more quickly than Mars, passes it. Due to this, Mars seems to move westward in retrograde motion, which is the real or apparent travel of a body in a direction that differs from that of the majority of solar system members' (direct) movements or the motion of other astronomical systems with a preferred direction of motion. All of the planets, with the exception of Venus and Uranus, rotate counterclockwise on their own axes as seen from a location in space north of the solar system (from a large distance above the North Pole of the Earth). Venus and Uranus, therefore, exhibit retrograde rotation. Fewer than half of the known satellites of the planets exhibit retrograde rotation.
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