No, the kinetic energy of the electron will not change.
The relationship of electron moving in a circular orbit in a uniform magnetic field:The electron receives no work from the magnetic force. In actuality, the magnetic force's work is provided by:
where F is the magnetic force, d is the electron's displacement, and is the angle between the force's direction and the electron's motion.
However, because the magnetic pull is always perpendicular to the charged particle's direction and velocity, there is no work done.
The work-energy theorem states that the change in an electron's kinetic energy is equal to the work that has been done on it; therefore, because there has been no work done, the electron's kinetic energy has not changed.
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gravity on the moon is 1.6 m/s2. what is the gravitational potential energy of a 1200-kg lander resting on top of a 350-m hill? j
The energy that an object has due to its location in a gravitational field is known as gravitational potential energy. GPE = mgh is the formula for gravitational potential energy. GPE = 1200(1.6)(350) = 672000 J
What is the source of gravitational potential energy?If an object is located at a height that is higher (or lower) than the zero height, it has gravitational potential energy. If an object is situated on an elastic media in a position other than the equilibrium position, it has elastic potential energy.
How is the energy of gravitational potential stored?By utilizing a pump, crane, or engine to raise a mass to a specific height, gravity batteries can store gravitational potential energy. Depending on the mass of the object and also how high it was lifted, the mass now retains a specific gravitational potential energy after being raised.
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Ali and kris are driving to a city that is 120 miles from their house. They have already traveled 20 miles, and they are driving at a constant rate of 50 mi/h. Write a function that models their distance from home as a function of time. What is a reasonable domain for this situation?.
The remaining distance that would result from multiplying the speed by the time t will be added to the 20 miles that make up the total distance. The domain's response would be 0 t 2.
By distance, what do you mean?The distance or amount of between two objects, points, etc. The condition or fact of being far from another in space; distance. a straight line in space It would take too long to walk seven miles in one hour. A wide body of water encircled the ship.
What are length and distance?A segment's or a room's dimensions are examples of things that can be measured in terms of length. Distance is the separation between two things, like two cities and two points.
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a 45.0-kg woman stands up in a 60.0-kg canoe 5.0 m long. she walks from a point 1.00 m from one end to a point 1.00 m from the other end. if you ignore resistance to motion of the canoe in the water, how far does the canoe move during this process?
Answer:
Measure the CM from the left end of the canoe
M x = (45 * 1 + 2.5 * 60) M = 105
x = (45 + 150) / 105 = 1.86 m from left end
After she walks 3 m the CM is from the left end
M y = (45 * 4 + 60 * 2.5)
y = (45 * 4 + 60 * 2.5) / 105 = 3.14 m
The left end of the canoe has moved 1.28 m to left
(The CM cannot move without an external force)
Check:
She increases the CM by 45 (3 - 1.28) = 77.4
Canoe movement decreases the CM by 60 * 1.28 = 76.8
1.28 is close
Assume that the light emitted by a hot filament or hot metal bar is made to pass through a low density gas, and the emergent light is then analyzed in a spectrometer; what kind of spectrum is seen in this case?.
we will see absorption line spectrum in this case.
We see Absorption lines usually as dark lines, or lines of reduced intensity, on a continuous spectrum. In this example when the light emitted by a hot filament or hot metal bar is made to pass through a low density gas, and the emergent light is then analyzed in a spectrometer, then we can see the absorption spectrum.
Dark line comes When electrons go from one energy level to another, the difference in those energy level is a specific value, and not a range of values. they will absorb the photons if they are transitioning upwards towards a higher energy, corresponding to the wavelength of light which has the specific amount of energy they need to ascend.
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an electron is moving with a velocity of 4.3 x 106 m/s in a uniform magnetic field of strength 3.5 t. the velocity vector makes a 55o angle with the magnetic field. what is the magnitude of the magnetic force on the electron?
The magnetic force on the electron is 2 x 10^(-12) N
What is the magnitude of the magnetic force on the electron?
Magnetic force can be defined as the attraction or repulsion force that arises between electrically charged particles because of their motion.
The velocity of the electron is
v = 4.3 x 106 m/s
The strength of the uniform magnetic field is B = 3.5 T
The angle between the velocity of the electron and the magnetic field is 55 degrees.
Also, the charge on the electron is
e = 1.6 X 10 power minus 19 C
The magnetic force can be calculated as
F = Bev sin θ
Substituting the given values we can find the total magnetic force.
The magnetic force on the electron is 2 x 10^(-12) N
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The reason that most seti programs choose to listen at microwave radio frequencies is that.
The reason that most SETI programs choose to listen at microwave radio frequencies is that microwaves are the most energy-efficient way to send information.
What is radio frequencies?Radio frequencies are used in transmitters, receivers, computers, televisions, mobile phones and other communication devices. Radio frequencies are also used in carrier current systems such as telephones and control circuits.In 2021 ARPANSA will publish the standard.Standards for limiting exposure to radio frequency fields - 100 kHz to 300 GHz. The ARPANSA RF standard specifies limits for human exposure to RF EMR in the frequency range 100 kHz to 300 GHz.Microwaves have a frequency range of 109 Hz (1 GHz) to 1000 GHz and corresponding wavelengths of 30 to 0.03 cm. Within this spectrum range there are many important communication system applications in both military and civilian settings.To learn more about radio frequencies from the given link :
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If a car collides with a moving bus, what type of relationship exists between the force of the car and the force of the bus?.
The correct answer is forces are equal but opposite in direction between car and bus.
What do we mean by Collision?
When two objects collide, forces of equal magnitude and opposite direction are applied to each object. Such pressures frequently result in one thing gaining momentum and gaining speed while the other object slows down (lose momentum).
The force applied to an object to cause an impact—a change in momentum—on it is referred to as the impact force, or momentum. Technically speaking, the Car and the bus would have exerted and felt the same amount of impact force in the event of a collision. Because every action has a corresponding and opposing response, according to Newton's third law.
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What does "jettison" mean? Why are parts of the spacecraft jettisoned?
Answer: 1. throw or drop (something) from an aircraft or ship
2.to ensure mission success just in case the first one fails.
Explanation:
A ball is pushed downhill with an initial velocity of 3. 0 m/s. The ball rolls down a hill with a constant acceleration of 1. 6 m/s2. The ball reaches the bottom of the hill in 6. 0 s. What is the ball's velocity at the bottom of the hill?.
The ball's velocity at the bottom of the hill is 12.6 m/s. The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity.
Velocity can be defined as the rate at which something moves in a specific direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off. Because the velocity vector is scalar, its absolute value magnitude will always equal the motion's speed. Additionally, it is inversely proportional to transit duration and proportionate to displacement. Its measurement is in meters per second (m/s). The velocity formula is shown below: V = s/t.
Where V is the end velocity, u the beginning velocity, a the acceleration, and t the duration,
We obtain the response by substituting the data. 12.6 m/s.
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an archer shoots a bow horizontally from the same height as the target's bull's-eye, located 25.2 m away. the bow is shot with a speed of 76.9 m/s. how far below the center of the bull's-eye does the arrow hit the target?
The calculated value is a = 16.24°. If the initial speed is the same, launch angles closer to 45° 45° 45° give a longer maximum horizontal distance (range).
These launches have a better balance of the initial velocity components that optimize the horizontal velocity and time in the air. The black dots represent measurements, such as the estimated 3D locations of the object based on the 2D images, while the bullseye represents the true value, such as the true location of the object. Let a be the projectile's angle.
37 sin a° is the vertical component.
Vertical component: 37 cos °
Time to achieve peak height equals (37 sin a°)/9.8
[2(37 sin a°)/9.8](37cos a°)(horizontal travel) = 75
75*9.8/37*37 = 2sin a° + cos a°
sin 2a° = 0.537
2a° = 32.47°
a = 16.24°
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A 1000-kg car is moving at 30 m/s around a horizontal unbanked curve whose radius is 100 m. What is the magnitude of the friction force required to keep the car from sliding?.
The magnitude of the friction force required to keep the car from sliding is 13112 N.
Calculation:-
friction force = centripetal force
= mv^2 / R
= 1000*30^2 / (200/2)
= 9000 N
so option B) 9000 N is the correct answer
15) net force = mv^2 / R
= 250*(96.5*5/18)^2 / 13.7
= 13112 N = 1.31*10^4 N
Friction is the force resisting the relative motion of sturdy surfaces, fluid layers, and material factors sliding towards each specific. There are numerous styles of friction Dry friction is a strain that opposes the relative lateral movement of two stable surfaces in touch.
Friction is the shape of contact pressure. It exists between the surfaces that are in touch. The frictional force relies upon the character of the floor in contact. The rougher the ground, the extra friction is involved. The frictional force is proportional to the urgent pressure, which is the burden of the body. it's miles impartial of the place of the touch.
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how close were your wavelength measurements to the accepted values of wavelengths for the various gases as listed below? what factors do you think might have contributed to any differences, and how might they have affected your measurements?
The accepted values of wavelengths for Hydrogen is a simple atom with a simple spectrum. Besides the three lines we may be able to see in 410 nm.
Gamma rays have incredibly short wavelengths that are only a small percentage of the size of atoms, but other wavelengths can extend as far as the cosmos, despite the fact that the relationship between wave frequency and wavelength is inverse. Although it is not often stated explicitly, electromagnetic radiation wavelengths are frequently represented in terms of the vacuum wavelength, regardless of the medium they pass through.
Electromagnetic radiation's behavior is influenced by its wavelength. Wavelength times frequency equals the speed of light. Energy is obtained by multiplying frequency by the Planck constant. The wave number in centimeters is 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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A solar eclipse happens when…
A. the Moon’s shadow crosses Earth’s surface.
B. the Earth’s shadow crosses the Sun’s surface.
C. the Earth’s shadow crosses the Moon’s surface.
D. the Sun’s shadow crosses the Moon’s surface.
Answer:
A. the Moon's shadow crosses Earth's surface.
Explanation:
When the Moon orbits Earth, the Moon moves between the Sun and Earth. When this happens, the Moon blocks the light of the Sun from reaching Earth. This causes an eclipse of the Sun or a solar eclipse. During a solar eclipse, the Moon casts a shadow onto Earth.
Answer:
a) Moon’s shadow crosses Earth’s surface.
Explanation:
A solar eclipse happens when the Moon’s shadow crosses Earth’s surface. Hence, the option (a) is correct answer.
Need help with both questions
Answer: 2) c 3) c
Explanation:
The difference between starting time and ending time is the elapsed time.
F = ma (Newton's 2nd Law of Motion)
The velocity selector in in a mass spectrometer consists of a uniform magnetic field oriented at 90 degrees to a uniform electric field so that a charge particle entering the region perpendicular to both fields will experience an electric force and a magnetic force that are oppositely directed.
If the uniform magnetic field has a magnitude of 12.1 mT, then calculate the magnitude of the electric field that will cause a proton entering the velocity selector at 43.4 km/s to be undeflected. Give your answer in units of kV/m.
The magnitude of the electric field that will cause a proton to enter the velocity selector and to be undeflected is 0.525 kV/m.
When a proton enters a region with a uniform electric and magnetic field, the magnetic force and the electric force will affect the motion of the protons. The electric field is perpendicular to the velocity of a proton. The magnetic field is perpendicular to both the velocity of the proton and the electric field and has an opposite direction to the electric force. When the proton is undeflected it means the forces balance.
F electric = F magnetic
qE = qvB
E = vB
[tex]v = \frac{E}{B}[/tex]
v = velocity of the proton (m/s)E = the magnitude of the electric field (V/m)B = the magnitude of magnetic field (T)Parameter
B = 12.1 mT = 12.1 x 10-3 T = 1.21 x 10-2 Tv = 43.4 km/sConvert velocity to m/s
[tex]v = 43.4 \times \frac{1 \: km}{1 \: s} = 43.4 \times \frac{1,000 \: m}{1 \: s}[/tex]
v = 43.4 x 103 m/s
v = 4.34 x 104 m/s
Calculate the magnitude of the electric field
E = B x v
E = 1.21 x 10-2 x 4.34 x 104
E = 525.14 V/m
[tex]E = \frac{525.14}{1,000}[/tex]
E = 0.525 kV/m
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What is the mass of an object if it takes a net force of 1,022 N to accelerate at a rate of 24 m/s2?
find A, Fn, and Fg
42.58 kg is the mass of an object if it takes a net force of 1,022 N to accelerate at a rate of 24 m/s2
F=ma
F= force= 1,022 N
m= mass=?
a=acceleration=24 m/s2
F=ma
a=F/m
a= 1,022 N/24 m/s2
a=42.58 kg
In physics, mass is used to express inertia, a property common to all matter. In essence, it is the resistance of a mass of matter to changing its course or speed in response to the application of a force.
The more mass a body has, the less of a change an applied force makes. Using Planck's constant, the kilogram, the ISU's unit of mass, is equivalent to 6.62607015 1034 joule seconds (SI). One kilogram is multiplied by one square meter per second to yield one joule.
Since the second and the meter have already been defined in terms of other physical constants, the kilogram is determined by precise measurements of Planck's constant.
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if a proton moves from point 1 to point 2 on an isoline with the same voltage, how much work is done
There is no net work done because of absence in any difference between the potentials.
What is work done to shift a proton?The potential difference between two points in a circuit equals the amount of work done in moving a unit charge from one point to another. If the two points are at the same potential, no NET work is done to move the test charge from one point to another. Some parts of the path may have had positive work done, while other parts of the path may have had negative work done.
Work done = Charge × change in potential
W = q × ΔV
q = 1.6 × 10⁻¹⁹ C
ΔV = 0
W = 1.6 × 10⁻¹⁹ × 0
W = 0
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A student builds an electromagnet using a battery, an iron nail. And some insulated wire. The wire is wrapped around the nail 50 times and then connected to the battery. What changes could the student make to increase the strength of the electromagnet?.
To enhance the strength of the electromagnet, the student must enlarge the nail, wrap additional wire around the nail, increase the voltage of the battery, and enlarge the nail.
How does an electromagnet work?An electromagnet's mechanics are not extremely sophisticated. Wrapping a piece of conductive wire, usually copper, around a metal object accomplishes the task.
Until electricity is applied, this looks to be nothing more than a jumbled collection of parts, much like Frankenstein's monster.
An electromagnet, on the other hand, does not need to be activated by a storm. A current is introduced and flows through the wire, which can be supplied by a battery or another power source.
Therefore, to enhance the strength of the electromagnet, the student must enlarge the nail, wrap additional wire around the nail, increase the voltage of the battery, and enlarge the nail.
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10pa is acting on an area of 0.5m2
Answer:
Explanation:
F = p·A =10·0.5 = 5 N
Which of the following potential problems with question wording have been identified by cognitive psychologists? (Check all that apply.) a) unfamiliar technical terms
b) vague or imprecise terms
c) ungrammatical sentence structure
d) phrasing that overloads working memory
e) embedding the question with misleading information
Option d) phrasing that overloads working memory, potential problems with question-wording have been identified by cognitive psychologists.
Cognitive psychology is the look at mental procedures, along with memory, attention, belief, and language processing, and the way they affect human behavior. Cognitive psychologists expand strategies to assist folks that are experiencing difficulties with one or more of those processes.
Cognitive psychologists normally earn either a Ph. D as a doctor of Philosophy or a Psy. D as a medical doctor of Psychology in cognitive psychology. Similar to psychology coursework, they need education in studies techniques, statistics, neuroscience, and cognitive mastering.
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A 2 kg toy caramels at a speed of 5 m/s if a child applies a three new enforce for 2 m in the same direction the car is already moving how much work is done on the car
The work done on the car is equal to the force applied to the car multiplied by the distance over which that force is applied. In this case, the force is applied for 2 meters, so the work done is equal to 3 Newtons multiplied by 2 meters, or 6 Joules.
What is force?
A force is indeed an influence that can alter an object's motion in physics. An object with mass can change its velocity, or accelerate, as a result of a force. An intuitive way to describe force is as a push or even a pull. A force is a vector quantity because it has both direction and magnitude. It is calculated using the newton SI unit (N). Force is denoted by the letter F. (formerly P). The net force acting on an object seems to be equal to the rate that its momentum changes over time, according to Newton's second law in its original formulation. This law suggests that an object's acceleration is directly proportional to the total force acting on the object if the object's mass remains constant.
Work is defined as force multiplied by distance, so the work done on the car is (3 N)(2 m) = 6 Nm. Since 1 Nm = 1 J, the work done on the car is 6 J.
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A cheetah has a mass of 60 kg. It produces a force of 480 n between its feet and the ground. What is its acceleration?.
A cheetah with a mass of 60 kg and a force of 480 N accelerates at a rate of 8 m/s2.
The acceleration of an object is equal to the net force exerted on it divided by its mass, or a = F m, in accordance with Newton's second rule of motion. The force applied divided by the mass of the item yields the acceleration of a moving body. the following:
Mass Force (N) Acceleration (m/s2) (kg)
In response to your inquiry, a cheetah weighs 60 kg and exerts 480 N of force.
Acceleration = 480 x 60
Acceleration equals 8m/s2.
Therefore, the cheetah's acceleration for a mass of 60 kg and a force of 480 N equals 8 m/s2.
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The right answer is "8 m/s²"
Answer explanation:
Acceleration = force / mass
= 480 N / 60 kg
= 8 m/s2
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A 20 m long, uniform bridge of weight 100 kN is supported at each end by pillars, as shown. The pillars exert forces T₁ and T2 on the ends of the bridge. What are the values of T₁ and T2 when a van of weight 24 kN is on the bridge, 5 m from the left-hand pillar?
Answer
T1=68 kN
Explanation:
A 20 m long, uniform bridge of weight 100 kN is supported at each end by pillars, as shown. The pillars exert forces T₁ and T2 on the ends of the bridge. What are the values of T₁ and T2 when a van of weight 24 kN is on the bridge, 5 m from the left-hand pillar is T1=68 kN
What are the types of force ?Force can be defined as pushing or pulling of any object resulting from the object’s interaction or movement, without force the objects can not be moved, can be stopped or change the direction.
Force is a quantitative interaction between two physical bodies, means an object and its environment, there are different types of forces in nature.
If an object in its moving state will be either static or motion, the position of the object will only be changed if it is pushed or pulled and The external push or pull upon the object called as Force.
The contact force types are the force that occurs when we apply some effort on an object such as Spring Force, Applied Force, Air Resistance Force, Normal Force, Tension Force, Frictional Force
Non-Contact forces are another type of forces occur from a distance such as Electromagnetic Force, Gravitational Force, Nuclear Force
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if you were travelling outward from the earth in a space shuttle at an altitude of 68.9 km you would be in the
The virtually massless subatomic particle known as a neutrino seldom interacts with ordinary matter and travels through space at nearly the speed of light.
Although they can originate from a wide range of sources, the majority of neutrinos that travel through the Earth come from the Sun, which beams untold quantities of them our way every second. The vast majority of these neutrinos travel through the Earth and you and then emerge from the other side as if nothing ever happened. About 100 billion neutrinos from the Sun pass through your thumb each second to give you an idea of scale. If you extrapolate that to Earth, you end up with a lot of zeros.
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A ski lift is used to transport people from the base of a hill to the top. If the lift leaves the base at a velocity of 15. 5 m/s and arrives at the top with a final velocity of 0 m/s, what is the height of the hill? round the answer to the nearest tenth. M.
The heigh of the hill is 12.26m that is calculated from the law of conservation of energy.
What is conservation of energy?In physics, the law of conservation of energy states that the total energy of an isolated system remains constant ; it is said to be conserved over time.
How to calculate the height of the hill using the law of conservation of energy?
The height of the hill can be calculated from the law of conservation of energy as initial velocity (kinetic energy) transforms into potential energy (height).
KE = U
Where,
KE = kinetic energy = 1/2 * mv^2
U = potential energy = mgh
So
1/2 * mv^2 = mgh
h = 1/2 * (v^2)/g
h = 1/2 * 15.5^2/9.8
h = 12.26m (rounded to the nearest tenth)
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The ladder shown is 3.0 m long and the coefficient of static friction between the floor and ladder is 0.50. There is no friction between the wall and the ladder. What is the minimum angle (in degrees) that the ladder can make with the floor without slipping?
This is a static equilibrium problem. The sum of the torques equals zero, the sum of the forces along x equals zero, and the sum of the forces along y equals zero. Use the point where the ladder contacts the ground as the axis of rotation. At the minimum angle, you're getting the maximum possible value of static
45° s the minimum angle (in degrees) that the ladder can make with the floor without slipping defying friction.
F=μmg
" Moment along the bottom of ladder "
[tex]0.5 Lmg cos \theta=LF_wsin \theta[/tex]
[tex]0.5 Lmg cos \theta=L \mu mg sin \theta[/tex]
[tex]0.5 cos \theta=mu sin \theta[/tex]
[tex]\theta=tan^-1(0.5 )/(\mu)[/tex]
Θ= 45°
Physical friction is all around us. Static friction is the resistance to an object moving along a route. Finally, explain it with a simple example. Consider the common activity we all engage in: walking. While working, we are continuously in contact with the floor. As we advance our feet, motion pushes on the earth as we travel backward.
The fact that friction operates in the opposite direction from relative motion is one important aspect to be aware of in order to decrease friction. This phenomenon might be helpful for slowing down the action until it eventually stops.
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an 8.0-g bullet is shot into a 4.0-kg block, at rest on a frictionless horizontal surface (see the figure). the bullet remains lodged in the block. the block moves into an ideal massless spring and compresses it by 8.7 cm. the spring constant of the spring is 2400 n/m. the initial velocity of the bullet is closest to
The velocity of the bullet is 1100 m/s.
When the bullet lodges into the block, as there is no net external force, the momentum of the system will be conserved. After that when the block + bullet system compresses the spring, the energy of the system remains conserved. The kinetic energy is conserved into the potential energy of the spring.
Velocity is the directional speed of an object in movement as an illustration of its price of the trade-in position as found from a particular frame of reference and as measured through a specific standard of time.
Calculation:-
Mass of block, M = 4 Kg
Mass of bullet, m = 8 g = 0.008 Kg
Compression in spring, x = 8.7cm = 0.087 m
Let's first solve the energy conservation,
K.E. = P.E.
(1/2)(M+m)V2 = (1/2)kx2
V2 = 2400*(0.087)2/(4+0.008)
V2 = 4.53
V = 2.13 m/s
Now, conserving the momentum,
mv = (M+m)*V
v = (4+0.008)*2.13/0.008
The velocity of the bullet, v = 1066.6 m/s
Rounding to the velocity as 1100 m/s
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The number of objects that have been observed to be orbiting in the kuiper belt is approximately.
The hundreds of thousands of icy bodies larger than 100 km have been observed to be orbiting in the Kuiper belt is approximately.
What is Kuiper belt?
The region beyond Neptune known as the Kuiper Belt is made up of countless stellar objects orbiting the sun. Solid methane, ice, and ammonia make up belt objects. The belt's orbit deviates from the orbital plane and can be inclined by up to 19 degrees. Scientists searched for Planet X as a possible explanation for the origin of the belt.
What is orbit?
An orbital is a region where it is possible to estimate the likelihood of finding any electron, whereas an orbit is a fixed path that electrons follow around the atom's nucleus.
The Kuiper Belt is thought to contain a trillion comets or more and hundreds of thousands of icy bodies bigger than 100 km (62 miles).
Therefore, there may be hundreds of thousands of icy bodies larger than 100 km have been observed to be orbiting in the Kuiper belt is approximately.
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cables provide most of the support to keep a suspension bridge up. the elastic force of tension pulling u is 28,000 N and the force of gravity is 28,000 N down. find the net force
The net force to keep a suspension bridge up is zero, 0N.
An action-reaction pair of forces acting at each end of the aforementioned elements is tension. Consider a rope. Aside from the ends, every portion of the rope experiences tension force in both directions. The attached weight exerts force and tension on one side of the ends. The tension of the string fluctuates under different conditions. The net force formula is provided by when the body is at rest.
The tension exerted on an item is determined by adding the products of its mass, acceleration, and gravitational force. It is denoted mathematically as follows:
T = mg + ma
Where,
T is tension
m is mass
a is acceleration
g is the acceleration due to gravity
Here,
T = 28000N
mg = 28000N
ma = T - mg
ma = 28000 - 28000
ma = 0N
The net force to keep a suspension bridge up is zero, 0N.
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How high would a skater need to start on a previous incline to make it up and around a loop that is 6.1meters high?
The skater need to start 7.525 meter high.
Let,
The skater need to start on a previous incline at height = h.
Mass of the skater = m
Given, height of the loop = 6.1 meter.
Radius of the loop; r = 6.1/2 meter = 3.05 meter.
Let to make it up and around a loop that is 6.1meters high, the man required minimum velocity v on the highest point of the loop.
So, centripetal force at highest point = weight of the man
⇒ mv²/r = mg
⇒ v = √(gr)
Then, potential energy of the skater at height h is = mgh.
And, minimum energy of the skater at the highest point of the loop is = potential energy + minimum kinetic energy.
= mg(2r) + 1/2 mv²
= 2mgr + 1/2 mgr
= 5/2 mgr
According to conservation of energy,
potential energy of the skater at height h = minimum energy of the skater at the highest point of the loop
⇒ mgh = 5/2 mgr
⇒ h = 5/2 r =( 5/2 )× 3.05 meter = 7.525 meter.
Hence, required height is 7.525 meter.
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