The turning-point angles is θ = 9.666 degrees if the child has a speed of 0.80 m/s when the ropes are vertical.
As per the details provided in the above question are as bellow,
The speed at bottom = v = 0.8 m/s
The length of the rope = l = 2.3 meter
The Work Energy Theorem provides us with,
The energy an item has as a result of motion is known as kinetic energy. A force must be applied to an item in order to accelerate it. We must put forth effort in order to apply a force. After the job is finished, energy is transferred to the item, which then moves at a new, constant speed.
Change in kinetic energy = net work done
[tex]0 - 0.5mv^2 =[/tex]- mgl (1-cosθ)
[tex]0.5 \times 0.8^2[/tex] = 9.8 x 2.3 (1-cosθ)
angle θ = 9.666 degrees
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Note:- The correct question would be as bellow,
A child swings back and forth on a swing suspended by 2.3m -long ropes.
Find the turning-point angles if the child has a speed of 0.80 m/s when the ropes are vertical.
6. An ice skater is spinning at 60 RPM when she pulls in her arms and undergoes an angular acceleration of 10 rad/s"" for 0. 6 seconds. What was her final RPM and how many rotations did she spin during this time?
The final RPM of ice skater is 116.38.
RPM's meaning?RPM's meaning? per revolution
RPM, which stands for revolutions per minute, is a measure of how quickly a machine is operating at any one time. RPM is a measure used in automobiles to indicate how often the crankshaft completes one full rotation each minute as well as how frequently each piston rises and falls in its cylinder.
Briefing:
ω₀ = 6.2π rad/s
α= 10π rad/s
t = 4.2 s
Find: ω
ω = αt + ω₀
ω = 10 (0.6 s) + 6.2π rad/s
ω = 116.38RPM
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How does changing the mass or speed of a moving object before it collides with
another object affect the forces on those objects during the collision?
PLEASE HURRY
Answer:
When two objects collide, the forces that are exerted on each other are determined by their masses and speeds. If the mass of one of the objects is increased, the force that it exerts on the other object during the collision will also increase. Similarly, if the speed of one of the objects is increased, the force that it exerts on the other object during the collision will also increase. In general, the greater the mass and speed of an object, the greater the force that it will exert on another object during a collision. However, it is important to note that the direction of the forces will remain the same, regardless of the masses or speeds of the objects involved.
does initial velocity equal final velocity when doing a one dimenstion free fall problem if you throw a ball up
If we assume at time instance t= 0, then the same thing happens. initial velocity is equal to final velocity
During a free fall, only the gravitational force acts on a body. The initial velocity of the body is zero during free fall.
Vertical motion is symmetrical - the distance and time are the same in the rise as in the fall; the final velocity will have the same magnitude as the initial velocity but in the opposite direction. Horizontal components will never be effected by gravity; it is constant velocity motion
The average velocity is the ratio of the total distance traveled to the total time taken. This can happen in two cases, first if the initial velocity and the final velocity are equal to the average velocity and there is no change in the velocity for the entire trip
Velocity is the measure of the amount of distance an object covers in a given amount of time. Here's a word equation that expresses the relationship between distance, velocity and time: Velocity equals distance travelled divided by the time it takes to get there.
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2. what property of tissue does a proton density image show? what tr and te times do we need to achieve proton density imaging?
In a proton density image the tissue magnetization, RF signal intensity, and image brightness are.
Proton Mail is the world's largest cozy e-mail provider. It gives end-to-cease encryption and plenty of different splendid safety capabilities to maintain your communications non-public. Even the company hosting your emails has no manner of reading them, so you can rest confident that they cannot be studied via third events either.
It has a completely, very wealthy internal shape. you could have heard that protons are made up of 3 smaller basic particles known as quarks, two united states, and one down quark to be particular, but it is only the top of the particle iceberg, as proton researcher Paul Reimer explains.
One or extra protons are present in the nucleus of every atom. They provide the attractive electrostatic crucial force which binds the atomic electrons. The quantity of protons in the nucleus is the defining belongings of an element and is referred to as the atomic quantity.
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under the influence of its drive force, a snowmobile is moving at a constant velocity along a horizontal patch of snow. when the drive force is shut off, the snowmobile coasts to a halt. the snowmobile and its rider have a mass of 136 kg. under the influence of a drive force of 205 n, it is moving at a constant velocity whose magnitude is 5.50 m/s. the drive force is then shut off. (a) calculate the distance in which the snowmobile coasts to a halt. (b) calculate the time required for the snowmobile to stop.
A) 13.2 m, The snowmobile moves at a constant speed when the drive force is engaged; as the acceleration is zero, there is no net force. On the other hand, the net force is the product of two forces acting on the snowmobile: the driving force, F, and the frictional force, Ff: F-Ff=0, Ff=F.
(b) 4.2 s, The relationship between the snowmobile's acceleration and time t is given by: a=v-u/t, The time it takes the snowmobile to stop is 4.2 seconds after rearranging for t and entering numbers.
How do you define magnitude?The simplest definition of magnitude in physics is "distance or quantity." In either an absolute or relative meaning, it displays the size or motion of an object.
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what is the difference between fresnel and fraunhofer diffraction? are they different physical processes? explain.
The Fraunhofer process is typically simpler to study even though they are physically the same processes and have distinct features. Fresnel diffraction, players who are near to one another, and non-parallel light rays
Participants in the Fraunhofer diffraction are far apart, and the light beams are parallel.
When plane waves are incident on a diffracting object and the diffraction pattern is observed far enough away from the object (a distance satisfying Fraunhofer condition) (in the far-field region), as well as when it is observed at the focal plane of an imaging lens, the Fraunhofer diffraction equation is used to model the diffraction of waves in optics. The Fresnel diffraction equation, on the other hand, predicts the diffraction pattern that is produced close to the diffracting object (in the near field area).
Although Joseph von Fraunhofer was not directly engaged in the formulation of the theory, the equation bears his name.
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where is the center of gravity of the man doing the classic yoga poses shown in (figure 1)?
The center of gravity of the man doing the classic yoga poses will be as shown in first figure.
The Center of Gravity is the theoretical point in the body where the body's total weight is expected to exert force. It is important to know the center of gravity because it predicts the behavior of a body's movement when obeying gravity. It is also used in the construction of static structures such as buildings and bridges.
In a modern gravitational field, the center of gravity is identical to the center of mass. However, the two concepts do not always coincide. For the moon, the center of mass is very close to its geometric center. However, its center of gravity is slightly lower than Earth's due to the strong gravitational force of the nearby moon.
In a symmetrically shaped object made of homogenous materials, the center of gravity will match the body's geometric location. However, an asymmetrical object consisting of many components with different dimensions will have its center of gravity at some distance from its geometric center. In the hollow body or irregularly shaped body, the center of gravity in a point outside the body material.
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what is the expected mass of a potassium-39 nucleus, based on the total mass of its protons and neutrons?
The total mass of the protons and neutrons in a potassium-39 nucleus is 6.5307 x 10^-26 kilograms.
The mass of a potassium-39 nucleus can be calculated based on the total mass of its protons and neutrons. Potassium-39 is a stable isotope of potassium with 19 protons and 20 neutrons in its nucleus. The mass of a proton is approximately 1.6726 x 10^-27 kilograms, and the mass of a neutron is approximately 1.6749 x 10^-27 kilograms.
Therefore, the total mass of the protons in a potassium-39 nucleus is 19 x 1.6726 x 10^-27 = 3.18094 x 10^-26 kilograms. The total mass of the neutrons in a potassium-39 nucleus is 20 x 1.6749 x 10^-27 = 3.3498 x 10^-26 kilograms.
The total mass of the protons and neutrons in a potassium-39 nucleus is therefore 3.18094 x 10^-26 + 3.3498 x 10^-26 = 6.5307 x 10^-26 kilograms. This is the expected mass of a potassium-39 nucleus, based on the total mass of its protons and neutrons.
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a generator supplies 100 v to a transformer's primary coil, which has 50 turns. if the secondary coil has 500 turns, what is the secondary voltage?
According to the question if the secondary coil of transformer has 500 turns, the secondary voltage is 1000 V.
What are transformers and what varieties exist?Transformers for power, transformers for distribution, and transformers for isolation, in that sequence. We have Dual Winding Transformer and Autotransformers based on windings. We offer Core Type Transformers, Shell Type Transformers, and Berry Type Transformers based on core designs.
Briefing:For an ideal transformer
Vs/Vp=Ns/Np
Given that primary voltage V =100 V
Number of turns in primary N = 50 turns
Number of turns in srcondary Ns = 500 turns
Therefore
Vs/100=500/50
Hence voltage across secondary Vs = 1000 V
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17. two identical waves undergo pure constructive interference. is the resultant intensity twice that of the individual waves? explain your answer.
According to the question, two identical waves undergo pure constructive interference, resultant intensity is quadruple individual wave intensity.
What is sound wave interference?When two or even more sound waves are present at once from distinct sources, they interact with one another to create a new wave. The combination of all previous waves results in the new wave. Interference is the term for wave interaction.
What is a good illustration of interference?The reflecting light from an oil coating floating on water is one of the best illustrations of interference. Another illustration is the thin coating of a soap bubble (shown in Figure 1), which, when illuminated by either natural or synthetic light sources, reflects a variety of lovely colors.
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A rightward force is applied to a 6-kg object to move it across a rough surface at constant
velocity. The object encounters 15 N of frictional force. Use the diagram to determine the
gravitational force, normal force, net force, and applied force.
Fnorm = 58.8 N; Fnorm = 58.8 N; Fapp = 15 N; Fnet = 0 N. In the case of constant velocity, a = 0 m/s/s and Fnet = 0 N, Fgrav = m • g • 9.8 m/s/s • 6 kg • 58.8 N Ffrict = Fapp = 15 N since there is no horizontal acceleration.
A rightward force is what?A book is moved across a desk with a rightward acceleration by applying a rightward push to it. Consider the effects of friction. Pass over air resistance. Static Friction = Normal Force x Static Friction Coefficient is the formula for calculating static friction.
How can I determine force?Newton's second law of motion provides the definition of the force formula: An object's force is equal to its mass times its acceleration. F = m ⨉ a. To apply this formula, you must use SI units for force (newtons), mass (kilograms), and acceleration (meters per second squared).
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A box is released from rest and slides down a ramp in a closed system. Even though the box speeds up, its kinetic energy at the bottom of the ramp is less than the potential energy that it had at the top of the ramp.
What best explains why the box’s final kinetic energy is less than its initial potential energy?
In a closed system, kinetic energy is always less than potential energy.
Some potential energy was converted into thermal energy due to friction.
The acceleration due to gravity became smaller as the box slid down the ramp.
In a closed system, total energy is constantly being lost to outside objects.
The best explanation why the box’s final kinetic energy is less than its initial potential energy is that some potential energy was converted into thermal energy due to friction.
option B is the correct answer.
What is the law of conservation of energy?
The law of conservation of energy states that energy can neither be created nor destroyed but can be converted from one form to another.
According to law of conservation of energy, we have the following energy conversion process.
potential energy to kinetic energykinetic energy to potential energychemical energy to electrical energypotential energy to heat and kinetic energy, etcIn absence of friction, the potential energy of the box at the top of the ramp is equal to the kinetic energy of the box at the bottom of the ramp.
In the presence of friction, some potential energy will be converted into thermal energy due to friction and the final kinetic energy will be smaller than the initial potential energy.
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Answer:
The answer above is correct (I just did it on Edge.) - It's option B!
Explanation:
Hope this helped - brainliest would be greatly appreciated!
Have a great day :D
a boy rides his bicycle which has wheels of radius 27.0 cm. if the boy accelerates from rest to a speed of 11.2 m/s in 24.0 s, what is the angular acceleration (in rad/s2) of the tires? (enter the magnitude.)
The angular acceleration is 0.01533rad/s.
We are given that,
Radius = r = 27.0cm
Speed = v = 11.2 m/s
Time = t = 24.0 s
Therefore , We shall first find the linear acceleration before calculating the angular acceleration from one of the linear motion kinematics equations and the initial velocity u will be 0.
v = u + at
a = v/t
a = (11.2m/s)/(27.0×10⁻²m)
a = 0.414 ×10⁻²m/s²
Now , calculating the angular acceleration,
a = α × r
α = a/r
α = (0.414 ×10⁻²m/s²)/(27.0×10⁻²m)
α = 0.01533rad/s
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what is the resistance of a conductor that carries a current of 120 amperes when the potential difference between its ends is 240 volts?
The resistance of a conductor that carries a current of 120 amperes when the potential difference between its ends is 240 volts = 2 Ω
Electrical resistanceElectrical resistance is the force that opposes the flow of current, it's a component that can reduce the speed and quantity of the flow of electrons in an electric circuit.
The formula for electrical resistance can be seen to have several components, namely R is the resistance (Ω), V is the voltage (V), and I is the current strength (A).
The equation:
R = V/I
We have,
Current strength = 120 A
The potential difference between its ends = 240 V
So, the resistance of a conductor that carries a current of 120 amperes when the potential difference between its ends is 240 volts:
R = 240 V / 120 A
= 2 Ω
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you are holding short for an intersection departure on runway 8 with the sign in front of you. which way should you turn when taxiing onto the runway to depart runway 8?
With the sign in front of you, you are waiting in short formation for an intersection taxiing on runway 8. In order to depart from runway 8, you should turn left as you enter the runway.
In contrast to towing or pushback, where the aircraft is moved by a tug, taxing (sometimes written taxying) is the movement of an aircraft on the ground under its own power. Although the name refers to vehicles with wheels most often, it also covers vehicles with skis or floats.
Taxiways are used by airplanes to go between locations on an airport, such as from a hangar to the runway. The takeoff roll and landing rollout, which are the accelerating run and descending run along a runway, respectively, before takeoff and landing, respectively, are not referred to as "taxiing."
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a 25-kg crate is pushed across a frictionless horizontal floor with a force of 20 n, directed 20o below the horizontal. the acceleration of the crate is:
1.75 m/s2 is the crate's acceleration.
mass=25kg, f=20n.
In terms of physics, what is frictionless?A surface is said to be frictionless if it has a force acting on any thing that is practically zero or insignificant, meaning that there is no resistance between the surface and the material, allowing the object to slide and move freely without any friction.
Can one walk on a frictionless surface?Every every activity that requires the interaction of two surfaces and motion involves friction, with the exception of space walks, which you may conduct without any resistance. Because there won't be any contact force to propel the individual forward, one cannot walk in the absence of friction.
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Dad pulls his daughter Sarah (Sarah and sled combined mass 60 kg) on a sled, pulling on a rope with a force of 300 N at an angle of 30° above the horizontal. If we neglect friction force: What is the normal force acting on the sled/Sarah system?
Answer: Fn = 450 N
Explanation:
Part of the tension acts in the upward y-direction, reducing the normal force.
ΣFy = Fn + Ftsin(30)-Fg
0 = Fn + (300 N)sin(30) - (60 kg)(10 m/s^2)
0 = Fn + 150 N - 600 N
0 = Fn - 450 N
Fn = 450 N
when a nucleus of 235u undergoes fission, it breaks into two smaller, more tightly bound fragments. t or f
The fragments reaction is 7.59 MeV/nucleon and 8.39 MeV/nucleon
What is nucleus ?
Neutrons and protons, which have opposite electric charges, make up atomic nuclei. The strongest basic force now understood, known as the strong force, is what holds these things together. A normal atom's nucleus generally holds more than 99.9% of the atom's mass yet takes up considerably less than.01 percent of its volume.
What is fission ?
When a neutron collides with a bigger atom, it excites it and causes it to split into two smaller atoms, which are known as fission products. This process is known as fission. A chain reaction might start as a result of additional neutrons that are also emitted. Huge amounts of energy are produced during the splitting of each atom.
1) m_proton + m_netron + m_electron - m_U
= 92*1.007276466812 + 92*5.4857990943e-4 + 143*1.008664916 - (235.0439299)
= 1.9151 u
= 931.494061 * 1.9151 MeV
= 1784 MeV
= 1784/235 = 7.59 MeV/nucleon
2) m_proton + m_netron + m_electron - m_Cs
= 55*1.007276466812 + 55*5.4857990943e-4 + 82*1.008664916 - (136.9070895)
= 1.2338 u
= 931.494061 * 1.2338 MeV
= 1149 MeV
= 1145/137 = 8.39 MeV/nucleon
Therefore, the fragments reaction is 7.59 MeV/nucleon and 8.39 MeV/nucleon.
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A wire of cross sectional area of 6 * 10 ^ - 5 * m ^ 2 length 50cm stretches by 0.4mm under a load of 3000N. What is the Young's Modulus of the wire?
The Young's Modulus of the wire of length 50 cm is 4.0×10⁵ N/m.
What is young's modulus?Young's modulus is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression.
To calculate the young's modulus of the wire, we use the formula below.
Formula:
γ = (F/A)/(L/e).................. Equation 1Where:
γ = Young's modulusF = ForceA = AreaL = Length of the wiree = ExtensionFrom the question,
Given:
F = 3000 NA = 6×10⁻⁵ m²L = 50 cm = 0.05e = 0.4 mm = 4×10⁻⁴ mSubstitute these values into equation 1
γ = (3000/6×10⁻⁵)/(0.05/4×10⁻⁴)γ = 4.0×10⁵ N/mHence, the Young's Modulus is 4.0×10⁵ N/m.
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a pair of french bikers rode from paris to qatar for the world cup. a total of 7,000 kilometers in __ months.
From Paris to Qatar for the world cup, two French riders traveled by bicycle. In three months, 7,000 kilometers overall.
The Fédération Internationale de Football Association (FIFA), the world's governing organization of association football, and its senior men's national teams compete in the FIFA World Cup, commonly referred to as the World Cup. With the exception of 1942 and 1946, when it was postponed due to World War II, the tournament has been conducted every four years since its inception in 1930. The current winners are France, who captured their second championship during the 2018 competition in Russia.
The structure uses a qualification round to choose the teams that advance to the tournament phase, which occurs over the previous three years. 32 teams fight for the title at sites in the host country or nations during the tournament round.
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A simple harmonic wave of wavelength 18.7 cm and amplitude 2.34 cm is propagating in the negative x-direction at 38.0 cm/s.
Part A. Find its angular frequency.
Part B. Find its wave number.
Part C. Write a mathematical expression describing the displacement y of this wave (in centimeters) as a function of position x and time t measured in cantimeters and seconds, respectively. Assume the maximum displacement occurs at x = 0 when t = 0 .
a) Angular frequency is 12.75 rad/s b) The wave number is 33.59m c)
y ( x ,t) = 2.34 x sin(33.59 x - 12.75t)
Given,
wavelength = λ = 18.7 cm
= 0.187 m
amplitude , A = 2.34 cm
v = 0.38 m/s
A) angular frequency = ?
f = v/λ
f = 0.38/1.87 = 2.03
angular frequency ,
ω = 2π f
ω = 2π x 2.03
ω = 12.75 rad/s
B) the wave number,
K = 2π/λ = 33.59m
c) as the wave is propagating in -x direction, the sign is positive between x and t
y ( x ,t) = A sin(k x - ω t)
y ( x ,t) = 2.34 x sin(33.59 x - 12.75t)
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if the amplitude increases to 0.20 mm , by what factor does the bug's maximum kinetic energy change?
The bug's maximal kinetic energy changes as 16 times of Kinetic energy before amplitude increases when the amplitude approaches 0.20 mm.
The amplitude of a wave is its largest displacement. The wave's greatest velocity is now expressed as its amplitude, which is: v =Aw= K/M.
Now, the square of the wave is directly proportional to the kinetic energy of a system. As a result, the wave's maximum kinetic energy is given by KE = k/2A^2, which means that
KE1/KE2 = A1^2/A2^2 where KE1 is the kinetic energy prior to the amplitude (A1) increasing and KE2 is the kinetic energy following the amplitude increasing (A2)
Due to that,
The bug's entire vertical journey was S = 0.10m
The wave's amplitude is equal to half of the whole distance from the top to the bottom, hence its value is (A) = S/2 = 0.1/2 = 0.05m.
Now that the wave's amplitude has increased to 0.20 m, KEA = KE1/KE2 = A1^2/A2^2
KE1/KE2 = (0.05)^2/(0.20)^2, which equals 0.0025/0.04 = 0.0625.
KE2 then equals 16KE1
Therefore, the largest change in kinetic energy is (KE2) = 16KE1.
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Find complete question: A bug on the surface of a pond is observed to move up and down a total vertical distance of 0.10 m, lowest to the highest point, as a wave passes. What is the amplitude of the wave? If the amplitude increases to 0.20 m, by what factor does the bug's maximum kinetic energy change?
A boat travels 12.0 m while it reduces its velocity from 9.5 m/s to 5.5 m/s. What is the magnitude of the boat’s acceleration while it travels the 12.0 m?
a. 1.3 m/s2
b. 2.5 m/s2
c. 3.0 m/s2
d. 7.5 m/s2
The magnitude of the boat’s acceleration while it travels 12.0 m is b. 2.5 [tex]ms^{-2}[/tex]
u= 9.5 [tex]ms^{-1}[/tex]
v= 5.5 [tex]ms^{-1}[/tex]
s= 12 m
From the given data we can use,
[tex]v^{2} -u^{2} =2as[/tex]
to calculate acceleration.
[tex]v^{2} -u^{2} =2as[/tex],
Where,
v is the final velocity,
u is the initial velocity,
a is the acceleration and
s is the distance covered.
Substituting the values we have,
[tex]v^{2} -u^{2}[/tex]= 2×a×s
[tex](5.5)^{2}[/tex] - [tex](9.5)^{2}[/tex]= 2 ×a×12
a= [tex]\frac{(5.5)^{2} -(9.5)^{2}}{(2)(12)}[/tex]
a= [tex]\frac{(30.25)^{2} -(90.25)^{2}}{(24)}[/tex]
a=[tex]\frac{-60}{2000}[/tex]
a=-2.5 [tex]ms^{-1}[/tex]
(The negative sign says that it is a negative acceleration )
Therefore the magnitude of the boat's acceleration is -2.5 [tex]ms^{-1}[/tex]
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what is the current i(t) in the circuit at time t after the switch is closed? express your answer in terms of q0 , l , c , and other variables given in the introduction.
If the current i(t) in the circuit at time t after the switch is closed in terms of q0 , l , c the differential equation will be V(t) = (q0/C) × e^(−t/RC )
The equation for V(t) would be V(t)=E(RC)(dV(t)/dt) if a battery with EMF E was present in the circuit. With respect to V(t), this differential equation is no longer homogenous. But it can be resolved by simply substituting Vb(t)=V(t)E. This substitution has the effect of removing the E term and producing an equation for Vb(t) that is the same as the equation you solved for V(t). When a battery is supplied, the capacitor's initial condition is typically that it is completely discharged at time t=0.
In these circumstances, the solution will appear as V(t)=E(1et/(RC)) Since the voltage across the capacitor is zero at time t=0 according to this solution, is 0 at time t=0 since the capacitor wasn't charged at that point, and it climbs asymptotically to E.
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What are three thing you reearched about how earthquake tart and how they travel
Whenever the ground is hit with enough force to crack or break, an earthquake results. Tectonic plate boundaries are linked to the majority of earthquakes.
What is earthquake explain?An earthquake is a quick movement of geological materials beneath the earth's surface that causes the ground to shake violently or weakly. The tectonic plate boundary is where the earthquakes start.
What is earthquake and its effects?The earthquake is the sudden energy released from the earth's crust that causes the earth's surface to shake. Seismic waves, also called S waves, are consequently produced. The type and severity of an earthquake are based on the local seismic activity.
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find the weight of a car on a 12 degree slope if the force required to push the car up the hill is 650 lbs g
The weight of the car on the 12 degree slope is 546.72 lbs. This weight is important to know for various reasons, such as calculating the amount of force and energy required to move the car up the hill.
The weight of a car on a 12 degree slope can be calculated using the formula:
Weight = Force * sin(Slope Angle)
Therefore, the weight of the car on the 12 degree slope can be calculated as follows:
Weight = 650 lbs * sin(12°)
Weight = 546.72 lbs
The weight of a car on a 12 degree slope is important to know for various reasons. For example, if the car is being driven up the slope, it is important to know the weight of the vehicle to ensure that it will be able to make it up the hill. Additionally, knowing the weight of the car on the slope can help engineers and designers to calculate the amount of force and energy required to move the car up the hill.
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The planet mercury orbit around the sun is an ellipse eccentricity 0.206 length of major axis us 1.16×10 the power of 8 km. the sun at one focus
1,What is the maximum distance from mercury to the sun
2,what is the minimum distance b/n them
The maximum distance from mercury to the sun is 0.58 * 10⁸ km.
The minimum distance b/n them is 0.46 * 10⁸ km.
What is the distance about?The shape of an elliptical orbit can be described by its eccentricity, which is a measure of how "flattened" the ellipse is. An eccentricity of 0 indicates a circular orbit, while an eccentricity of 1 indicates a parabolic orbit.
In the case of Mercury's orbit, the eccentricity is given as 0.206, which means that the orbit is slightly flattened, but still close to circular. The length of the major axis of the ellipse is given as 1.16 * 10⁸ km.
To find the maximum distance from Mercury to the sun (also known as the aphelion), we need to find the distance from the center of the ellipse to the farthest point on the ellipse (which is at the top of the major axis). This distance is equal to half of the length of the major axis. Thus, the maximum distance from Mercury to the sun is:
1.16 * 10⁸ km / 2 =0.58 * 10⁸ km
To find the minimum distance between Mercury and the sun (also known as the perihelion), we need to find the distance from the center of the ellipse to the closest point on the ellipse (which is at the bottom of the major axis). This distance is equal to half of the length of the major axis times the square root of 1 - (eccentricity)². Thus, the minimum distance between Mercury and the sun is:
[tex](1.16 x 10^8 km / 2) * \sqrt{(1 - (0.206)^2) } = 0.46 * 10^8 km[/tex]
Therefore, Note that the sun is located at one of the foci of the elliptical orbit, rather than at the center. However, since the eccentricity of Mercury's orbit is relatively small (0.206), the distance from the center of the ellipse to either focus is very close to the distance from the center to the top or bottom of the major axis, and the difference can be ignored for most purposes.
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a block of mass 0.482 kg is hung from a vertical spring and allowed to reach equilibrium at rest. as a result, the spring is stretched by 0.630 m. find the spring constant.
The spring constant of the spring is 7.497 N/m.
The given parameters;
mass of the block, m = 0.482 kg
extension of the spring, x = 0.630 m
additional extension, = 0.338 m
The spring constant of the spring is calculated as follow
F = mg
Kx = mg
K = mg/x
K = 0.482 × 9.8 / 0.630 = 7.497N/m
F = -kx.
The spring constant, or k, is the proportional constant. It is a gauge of the spring's rigidity. A spring exerts a force F = -kx in the direction of its equilibrium position when it is stretched or compressed to a length that deviates by an amount x from its equilibrium length. The spring constant is calculated by dividing the force required to extend or compress a spring by the length it goes up or down. It is used to assess the stability or instability of a spring, The spring's stiffness is quantified by the spring constant, or k. For various springs and materials, it differs. The stiffer the spring is and the harder it is to stretch, the greater the spring constant.
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A 150-kg object takes 1.5 minutes to travel a 2,500-meter straight path. It begins the trip traveling 120 meters per second and decelerates to a velocity of 20 meters per second.
What was its acceleration?
Responses
(A) −1.11 m/s2
(B) −0.3 m/s2
(C) +1.11 m/s2
(D) +80 m/s2
Answer: So the answer is (A) -1.11 m/s^2.
Explanation: To solve this problem, we need to use the formula for average acceleration, which is given by:
a = (vf - vi) / t
Where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time.
Plugging in the values given in the problem, we get:
a = (20 m/s - 120 m/s) / (1.5 minutes * 60 seconds/minute) = -100 m/s / 90 seconds = -1.11 m/s^2
So the answer is (A) -1.11 m/s^2.
if you placed 1.00 c of positive charge on the earth and 1 c of negative charge 384,500 km away on the moon, how much force would the positive charge on the earth experience
If you placed 1.00 coulomb (C) of positive charge on the Earth and 1 C of negative charge 384,500 km away on the Moon, the positive charge on the Earth would experience a gravitational force of attraction towards the negative charge on the Moon.
The gravitational force of attraction between two charged particles is given by the formula:
F = (k * q1 * q2) / r^2where F is the gravitational force, k is the Coulomb constant, q1 and q2 are the charges of the two particles, and r is the distance between them.
Plugging in the values provided, we get:
F = (8.99 x 10^9 N*m^2/C^2) * (1 C) * (1 C) / (384,500 km)^2
= 2.34 x 10^-9 N.
This is a very small force due to the large distance between the two charges and the relatively small magnitude of their charges.
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