To solve this problem, we need to use the principles of Newton's laws of motion and rotational dynamics.
a. To determine FT1 and FT2, we can use the equation for the net force in the direction of motion of each block. For block m1, the net force is:
FT1 - m1g = m1a
where g is the acceleration due to gravity and a is the acceleration of the blocks. Solving for FT1, we get:
FT1 = m1(g + a)
Substituting the values given in the problem, we get:
FT1 = 7.96(9.81 + 1) = 87.4 N
For block m2, the net force is:
m2g - FT2 = m2a
Solving for FT2, we get:
FT2 = m2(g - a)
Substituting the values given in the problem, we get:
FT2 = 10(9.81 - 1) = 88.1 N
Therefore, the tensions in the two parts of the string are:
FT1 = 87.4 N and FT2 = 88.1 N
b. To find the net torque T acting on the pulley and determine its moment of inertia I, we can use the equation for the torque due to a force acting at a distance from the axis of rotation. In this case, the tension in the string exerts a force on the pulley, causing it to rotate.
The torque due to FT1 is:
τ1 = FT1r
where r is the radius of the pulley. The torque due to FT2 is:
τ2 = -FT2r
where the negative sign indicates that the torque is in the opposite direction to τ1.
The net torque T acting on the pulley is the sum of τ1 and τ2:
T = τ1 + τ2 = (FT1 - FT2)r
Substituting the values we found earlier, we get:
T = (87.4 - 88.1)(0.029) = -0.02 Nm
Since the blocks are accelerating to the right, the pulley must be accelerating to the left. Therefore, the net torque T must be negative.
To determine the moment of inertia I of the pulley, we can use the equation for the torque due to the acceleration of a rotating object:
T = Iα
where α is the angular acceleration of the pulley. Since the pulley is not sliding or slipping, we know that the linear acceleration of the blocks is equal to the tangential acceleration of the pulley, which is given by:
a = rα
where a is the linear acceleration of the blocks and r is the radius of the pulley.
Substituting for α in the equation for torque, we get:
T = I(a/r)
Rearranging, we get:
I = (Tr)/a
Substituting the values we found earlier, we get:
I = (-0.02)(0.029)/1 = -0.00058 kgm^2
Since the moment of inertia cannot be negative, we know that we made an error in our calculation. The most likely cause is a sign error in the torque calculation. We should check our work and try again to find the correct value of I.
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The resistance, r, to electricity of a cylindrical-shaped wire is given by the equation r = startfraction p l over pi d squared endfraction, where p represents the resistivity of the wire’s material, l represents the length of the wire, and d represents the diameter of the wire. what happens to the resistance of the wire as the diameter approaches 0?
As the diameter of the wire approaches to zero, the resisitance approaches infinity.
What is resistance?Electrical resistance is the physical capacity of any body to oppose the flow of electric current even when there is an applied potential difference, capacity calculated by Ohm's First Law, and, according to the International System of Units (IS), is measured in ohms.
With that being said, and knonwing that:
R = Resistance; p = Resistivity; L = Length; d = Diameter
It is possible to calculate the resistance of the wire by:
[tex]R = p\frac{L}{A}[/tex]
Where A is calculated by:
[tex]A = \frac{\pi d^{2} }{4}[/tex]
Changing in the first formula:
[tex]R = p\frac{L}{\pi d^{2} } \\\\R = p\frac{4L}{\pi d^{2} }[/tex]
Knowing that when the diameter tends to zero resistance tends to infinity, it is possible to say that resistance of the wire will tend to infinity when the diameter approaches zero.
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Answer:
The resistance approaches infinity.
Explanation:
100% Correct
A 16.9 kg monkey is swinging on a
5.32 m long vine. It starts at rest,
with the vine at a 43.0° angle.
How much PE does the monkey
have?
(Unit = J)
The potential energy of the monkey at the given position is 600.9 J.
What is potential energy?Potential energy is the energy stored in a body that depends upon the relative position of various parts of the body.
It increases with increase in the height of the object above the ground level.
Potential energy of the monkeyThe potential energy of the monkey is calculated as follows;
P.E = mgh
P.E = mg (L sin43)
where;
m is mass of the monkey, given as 16.9 kgg is acceleration due to gravity, given as 9.8 m/s²L is length of the vine given as 5.32 mSubstitute the given parameters and solve potential energy of the monkey
P.E = (16.9)(9.8)( 5.32 x sin 43)
P.E = 600.9 J
Thus, the potential energy of the monkey at the given position is 600.9 J.
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Objects a and b each have a mass of 25 kilograms. object a has a velocity of 5.98 meters/second. object b is stationary. they undergo a perfectly elastic collision in one dimension. what is the total kinetic energy of the system after the collision?
The total kinetic energy of the system after collision is 223.5J
In elastic collision kinetic energy and momentum are conserved.
According to the question
mass of object a = 25kg
mass of object b = 25 kg
initial velocity of a u1 = 5.98 m/s
initial velocity of b u2 = 0
so from momentum conservation-
mau1 + mbu2 = (m1+m2)v
25kg × 5.98m/s + 25×0 = (25+25)v
v = 2.99 m/s
Now the total kinetic energy after the collision will be:
final kinetic energy = 1/2 (m1+m2) v²
= 1/2 (25+25)× (2.99)²
= 223.5 J
Thus, total kinetic energy of the system after collision is 223.5J
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The motor ___________ currents listed in NEC Tables 430.247 through 430.250 shall be used to determine the ampacity of motor circuit conductors and short-circuit and ground-fault protection.
The motor full load currents listed in NEC Tables 430.247 through 430.250 shall be used to determine the capacity of motor circuit conductors and short-circuit and ground-fault protection. This is further explained below.
What is currents?Generally, Moving through an area of water or air where there is less movement than the water or air itself, an eddies
In conclusion, Using the full load currents indicated in NEC Tables 430.247 through 430.250, the capacity of motor circuit conductors and short-circuit and ground-fault protection for motors should be determined.
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A projectile is launched with initial velocity vo. If a second projectile is launched with half of the initial velocity of the first projectile. Compare the range of the second projectile with the first one:
Comparison of the range:
If a second projectile is launched with half of the initial velocity of the first projectile. The range of the second projectile is one-fourth of the first one.
Calculation:
Step-1:
It is given that the first particle has an initial velocity of [tex]v_0[/tex], and the second particle has an initial velocity of [tex]\frac{v_0}{2}[/tex]. It is required to compare the range of the second projectile with the first one.
It is known that the range of a projectile is calculated as,
[tex]R=\frac{u^{2} \sin 2 \theta}{g}[/tex]
Where u is the initial speed, g is the acceleration due to gravity, and [tex]\theta[/tex] is the angle at which the particle is thrown.
This problem [tex]\theta[/tex] is the same in both cases.
Step-2:
Therefore the range of the first projectile is,
[tex]R_1=\frac{v_0^{2} \sin 2 \theta}{g}[/tex]
The range of the second projectile is,
[tex]$$\begin{aligned}R_2&=\frac{(\frac{v_0}{2})^{2} \sin 2 \theta}{g}\\&=\frac{v_0^2\sin 2 \theta}{4g}\\\end{aligned}$$[/tex]
Therefore,
[tex]$$\begin{aligned}\\\frac{R_2}{R_1}&=\frac{1}{4}\\\Rightarrow R_2&=\frac{1}{4}R_1\\\end{aligned}\\$$[/tex]
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step by step process please
I know the ans but not the process
pic attached
Answer:
[tex]\huge\boxed{\sf F= 350 \ N}[/tex]
Explanation:
Considering pivot as the central point,
Key:
Torque = Force F × radius rAnticlockwise torque = Clockwise torque[tex]F_1r_1=F_2r_2[/tex]
Here,
Anticlockwise force is FClockwise force is 600 N[tex]r_1=70+50= 120 \ cm = 1.2 \ m[/tex][tex]r_2=70 \ cm = 0.7 \ m[/tex]Solution:Substitute the givens in the above formula.
[tex]F(1.2)=600(0.7)\\\\F(1.2)=420\\\\Divide \ 1.2 \ to \ both \ sides\\\\F=420/1.2\\\\F= 350 \ N\\\\\rule[225]{225}{2}[/tex]
The focal length of the objective of a telescope is 75.0 cm. While the eyepiece has a focal length of 6.00 cm, what is the magnifying power of this telescope
The magnifying power of this telescope is 12,5.
What is a telescope?
The telescope is an optical instrument that aims to allow the observation of large objects at long distances, such as galaxies, stars and planets. It consists of two parts: the objective, which can be a lens or a curved mirror, and the eyepiece, made up of a set of lenses.
With that being said and knowing that:
The focal length of the objective of a telescope (fo) = 75cm; The focal length of the eyepiece of a telescope (fe) = 6cm.
[tex]M = \frac{fo}{fe}[/tex]
Changing the values:
[tex]M = \frac{75}{6} = 12,5[/tex]
So, The magnifying power of this telescope is 12,5.
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What does a dielectric do to a capacitor?
A dielectric fabric is used to split the conductive plates of a capacitor. This insulating cloth significantly determines the properties of a component. The dielectric constant of fabric determines the amount of strength that a capacitor can keep while voltage is applied.
A capacitor is an electrical component that attracts energy from a battery and stores the power. Internal, the terminals connect with metal plates separated by way of a non-engaging in substance. While activated, a capacitor quickly releases electricity in a tiny fraction of a 2d.
Capacitor, a tool for storing electric electricity, together with two conductors in near proximity and insulated from each different. A simple example of this sort of garage tool is the parallel-plate capacitor.
A capacitor is a tool that shops electric power in an electric-powered area. it is a passive digital thing with terminals. The effect of a capacitor is called capacitance.
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Aluminum and copper wires of equal length are found to have the same resistance. What is the ratio of their radii
Answer:
R = ρ L / A resistance of wire
ρC / ρA = [RC AC/ LC] / [RA AA/ LA} = AC / AA
Since resistance and length are the same for both wires where A is the area of the wire
ρC / ρA = rC^2 / rA^2 where r is the radius of the wire
(ρC / ρA)^1/2 = rC / rA
rC / rA = (1.72 / 2.83)^1/2
rC / rA = .780 radius of copper wire is .780 of aluminum wire
The only source of light in a room is the lightbulb shown. An opaque disk is placed in front of the bulb. A screen is then placed successively at positions A, B, and C. At which screen position(s) does the disk cast a shadow that is completely dark at the center
On screen A the opaque disk cast a shadow that is completely dark at the center
opaque is defined as difficult to understand or not allowing light to pass through. The appearance of a black sheet of paper is an illustration of opaqueness. The study of astrophysics is an illustration of opaque.
An opaque object illuminated by a point source of light is said to produce a crisp shadow whose dimensions may be determined using geometry. This is according to geometric optics. The computation process is quite simple. Light beams are uniformly emitted from the source in all directions. These rays can be visualized as lines radiating straight out from the source. When a light source encounters an opaque object, the light rays cease moving away from the source.
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3. A car, initially at rest, travels 48 m in 4 s along a straight line with constant
acceleration. Determine the magnitude of the acceleration of the car.
Answer and Solution:
Magintude of Acceleration = 6 m/s -2
given - Initial velocity = 0
Time = 4s
Distance travelled = S = 48m
Acceleration = a = ?
Thus,
S= ut + 1/2 at2
The rate at which an object's speed changes, or the pace at which velocity changes, is known as acceleration. Newton's second law states that acceleration is inversely proportional to mass and directly proportional to the total sum of all forces acting on an item. It's simple math: if a thing is being pushed by a number of forces, you need to add them up (they may be acting in different directions), then divide the total force by the mass of the object.
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In nineteenth century, physical science was divided into discipline. .
Answer:
Here! Try this Website!: www.britannica.com › science › physical-science physical science | Definition, History, & Topics | Britannica. So you will learn a lot more about science, history, and topics about it!
Answer:i have no idea
Explanation:
A mass m is attached to an ideal massless spring. When this system is set in motion with amplitude a, it has a period t. What is the period if the amplitude of the motion is increased to 2a?.
When amplitude of motion increases to 2a the time period remains the same.
The formula for spring mass system is given by
T = 2π√m/k
where, k = spring constant
m= mass of spring
T = time period
So, from here we get to know that time period is independent of amplitude, so we increase or decrease the amplitude of system there will be no effect on Time period of spring mass system.
Thus, when amplitude of motion increases to 2a the time period remains the same.
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In a bell-shaped curve, the x-axis (horizontal direction) of the graph represents which of the following
X-axis represents the value of a particular characteristic; characteristics of an organism can include such traits as size and color.
What is a bell-shaped curve?
A typical sort of distribution for a variable is the bell curve, commonly referred to as the normal distribution. The normal distribution graph, which has a symmetrical bell-shaped curve, is what gave rise to the phrase "bell curve."
The highest point on the curve, or the top of the bell, denotes the most likely outcome in a set of data (its mean, mode, and median), while all other potential outcomes are symmetrically distributed around the mean, resulting in a downward-sloping curve on each side of the peak. The bell curve's standard deviation provides information about its width.
The x-axis represents a variable's value, while the y-axis provides information about the likelihood that we will see that value.
I understand the question you are looking for is this:
In a bell-shaped curve, the x-axis (horizontal direction) of the graph represents which of the following?
a. The value of a particular characteristic; characteristics of an organism can include such traits as size and color.
b. The number of individuals
c. Time
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Pure (r)-mandelic acid has has [α]d = 150°. If a mixture of (r)-mandelic acid and (s)-mandelic acid has [α]d = 120°, what is the enantiomeric excess of (r)-mandelic acid in the mixture?
The enantiomeric excess of (r)-mandelic acid in the mixture IS 80%.
The optical rotation of the mandelic acid was measured on a Perkin rotation of the optically active mandelic acid. Ethanol isn't always a suitable solvent for resolution due to the fact the salts are very soluble in it.
Enantiomers excess = (mixture/pure) × 100
⇒ excess enantiomers = +120/+150 × 100
⇒ excess enantiomers = 80%
A Racemic aggregate Is An equal aggregate Of two Enantiomers And Has a specific Rotation of 0° (Optically Inactive) the 2 components of “racemic acid” are (2S,3S)-tartaric acid, that is levorotatory, or (–); and (2R, 3R) tartaric acid, that is dextrorotatory.
Mandelic acid loosens the bonds that adhere the dead or antique pores and skin cells to the pores and skin surface. This allows the shedding of antiques.
The angle of rotation in ranges of the plane of polarization of a ray of monochromatic light that passes via a tube lengthy containing the substance.
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Numerical implementation of wavelength-dependent photonic spike timing dependent plasticity based on VCSOAï¼»
A photonic system exemplifying the biological neural process of spike timing dependent plasticity (STDP) is experimentally demonstrated using nonlinear polarization rotation. STDP represents the neuronal responses for learning based on input/output timing, order, and sequence.
What is Photonic implementation of spike timing dependent plasticity with weight-dependent learning window based on VCSOA ?according to the present synapse weight, we implement the optical spike timing dependent plasticity (STDP) with weight-dependent learning window in a VCSOA with double optical spike injections,
and numerically investigate the corresponding weight-dependent STDP characteristics. The simulation results show that, the bias current of VCSOA has significant effect on the optical STDP curve.After introducing an adaptive variation of the bias current according to the present synapse weight, the optical weight-dependent STDP based on VCSOA can be realizedLearn more about Spike timing dependent plasticity here:
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A kettle was tested for its energy efficiency. Its power rating was 900 W. Over the course of 4 minutes and 30 seconds, its useful energy output was 0.05 kWh. How do I answer this ?
A kettle was tested for its energy efficiency. Its power rating was 900 W. Over the course of 4 minutes and 30 seconds, its useful energy output was 0.05 kWh
Energy is referred to by scientists as the capacity for work. People have figured out how to transform energy from one form to another and then use it to accomplish tasks, making modern civilization possible.
Thermal energy, radiant energy, chemical energy, nuclear energy, electrical energy, motion energy, sound energy, elastic energy, and gravitational energy are among the several types of energy.
The ability to perform tasks is referred to as energy. Formula. Potential energy is the energy that an object has stored because of its position and height, and it may be calculated using the following formula: P.E. equals mgh.
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is the Earth bigger than the moon
Answer:
Yes
Explanation:
The Earth is about 4x bigger than the moon. Scientists speculate that the moon was once part of Earth, until something hit the Earth, and broke off a large chunk of it. These pieces were flung off the Earth, and began to orbit it. Slowly, the pieces were mashed together by gravity, and formed the moon.
What mass of steam at 100 ∘C must be added to 1.70 kg of ice at 0 ∘C to yield liquid water at 15 ∘C ? The heat of fusion for water is 333 kJ/kg , the specific heat is 4186 J/kg⋅C∘ , the heat of vaporization is 2260 kJ/kg .
The heat needed to turn water into ice at zero degrees is expressed as mL = 1.70*333000 = 566100 J. specific heat of vaporization is necessary to raise its temperature.
a unit mass's transition from a liquid at its boiling point to a gas at the same temperature, measured in terms of heat. is the specific heat of vaporization
The quantity of energy (enthalpy) that must be added to a liquid substance in order to convert some of that substance into a gas is known as the heat of evaporation. At 100 °C, which is the boiling point of water, the specific heat of vaporization for water is about 540 cal/g.
It should be noted that even at lower temperatures, some water molecules—those that happen to have high kinetic energy—will escape from the water's surface. When temperatures reach a specific level, known as the crucial temperature, specific heat of vaporization totally disappears.
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A 52–newton bird feeder is tied to a rope, which is attached to a tree branch. Describe the tension force of the rope.
A 52-newton tension force pulls down on the branch, and a 52-newton tension force pulls up on the bird feeder.
What is tension ?
The tension force is defined as the force that is transmitted through a rope, string or wire when pulled by forces acting from opposite sides. The tension force is directed over the length of the wire and pulls energy equally on the bodies at the ends.
Tension is the opposite of compression force. All the objects that are present in contact with each other exert a force on each other. The best example of a tension force can be seen while pulling a rope. When a pull force is applied to the rope, a significant amount of tension gets built.
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Which of the following objects is composed mostly of wood?
A. Sweater
B. Tile
C. Pencil
D. Brick
❄ Hi there.
a pencil is composed mostly of wood.
Let's check if the other choices are right.
A. Sweaters are not made of wood
B. Tiles are not made of wood
C. Pencils are made of wood
D. Bricks are not made of wood
∴ the right choice is C.
❄
Mindspore accelerates model convergence through automatic parallelism and second-order optimization.
a. True
b. False
Mindspore accelerates model convergence through automatic parallelism and second-order optimization.
The statement is a)true.
Mind Expression, MindSpore frontend, which is used to compile duties from user source code to computational graphs, control execution at some point of schooling, preserve contexts (in non-sink mode), and dynamically generate graphs (in PyNative mode).
Using a distributed structure, MindSpore leverages a local differentiable programming paradigm and new AI local execution modes to attain higher aid performance, safety, and trustworthiness.
It consists of the Ascend collection chips, Atlas series hardware, CANN chip enablement, MindSpore AI framework, ModelArts, and MindX utility enablement.
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A carnival Ferris wheel has a 15-m radius and completes five turns about its horizontal axis every minute. What is the acceleration of a passenger at his lowest point during the ride
If a Ferris wheel has a 15-m radius and completes five turns about its horizontal axis every minute then the acceleration of a passenger at his lowest point during the ride is 4.11 [tex]\text{m/s}^{2}[/tex].
Calculation:
Step-1:
It is given that the radius of the Ferris wheel is r=15 m, and the angular speed of the wheel is [tex]\omega[/tex]=5rev/min.
It is required to find the angular acceleration of a passenger at his lowest point during the ride.
The formula required to calculate the angular acceleration is, [tex]a=\omega ^2 r[/tex].
Step-2:
Now substituting the given values into the equation to get the value of the angular acceleration.
[tex]\begin{aligned}a &=\omega^{2} r \\&=(5 \mathrm{rev} / \mathrm{min})^{2}(15 \mathrm{~m}) \\&=\left(5 \mathrm{rev} / \mathrm{min} \times \frac{\left(\frac{2 \pi}{60}\right) \mathrm{rad} / \mathrm{sec}}{1 \mathrm{rev} / \mathrm{min}}\right)^{2}(15 \mathrm{~m}) \\&=(0.2741 \times 15) \mathrm{m} / \mathrm{s}^{2} \\&=4.11 \mathrm{~m} / \mathrm{s}^{2}\end{aligned}[/tex]
The acceleration is towards upwards that means towards the center of the wheel.
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The second hand of a watch completes one revolution every minute. At what phase would the second hand be if the time were 30 seconds after 1:25pm?
The phase that the second hand would be if the time were 30 seconds after 1:25pm is π radians.
Phase angle of the second hand
Angular speed of the watch is given as;
ω = 1 rev/min = 2π rad /(60 s)
when the time is 30 seconds, the phase angle is calculated as;
θ = ωt
θ = (2π rad/60s) x 30 s
θ = π radians
Thus, the phase that the second hand would be if the time were 30 seconds after 1:25pm is π radians.
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In 2020, UMass Amherst professors Jun Yao and Derek Lovley invented a generator to create electricity from:
moisture in the air
Electrical engineer Jun Yao and microbiologist Derek Lovley have developed a device that uses a natural protein to create electricity from moisture in the air, a new technology they say could have significant implications for the future of renewable energy, climate change, and the future of medicine.
What is electricity from moisture in the air ?Air Generator," or “Air-Gen,” with electrically conductive protein nanowires produced by the microbe Geobacter, discovered by Lovley some years ago.
The Air-Gen connects electrodes to the protein nanowires in such a way that electrical current is generated from the water vapor naturally present in the atmosphere.Learn more about Air Generator here:
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A rotor in a blender is rotating at 55.0 rad/s. The chef hits the Low Speed button, causing the rotor to decelerate at -40.7 rad s^2. What is its angular velocity after turning 28.8 rad? (Unit = rad/s) Remember: CCW is +, CW is-. 1 rev = 2 pl rad
26.0898 rad/s is the angular velocity of a rotor in a blender.
Given
Initial velocity (ω₁) = 55.0 rad/s
Deceleration (α) = -40.7 rad/s²
Angle (θ) = 28.8 rad
Final angular velocity (ω₂) =?
According to the angular kinematic equation
ω₂² = ω₁² + 2αθ
Put the values of ω₁, α, and θ in the equation
We get,
ω₂² = (55)² + 2(₋40.7)(28.8)
ω₂² = √680.68
ω₂ = 26.0898 rad/s
Hence, 26.0898 rad/s is the angular velocity of a rotor in a blender after turning 28.8 rad.
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According to hubble's law, with = 70 km/s , how far away is a galaxy whose recessional velocity is 6000 km/s ?
The galaxy will be D = 84.96 km far away
Hubble's law, which says simply that a galaxy's velocity (or as is sometimes plotted, its redshift) is directly proportional to its distance, also tells us something important about the state of the universe. If the universe is static and unchanging, there should be no correlation between distance and velocity.
Recessional velocity is the rate at which an extragalactic astronomical object recedes (becomes more distant) from an observer as a result of the expansion of the universe. It can be measured by observing the wavelength shifts of spectral lines emitted by the object, known as the object's cosmological redshift.
V (r) = H * D + V pec
6000 = 69.8 * D + 70
5930 / 69.8 = D
D = 84.96 km
The galaxy will be D = 84.96 km far away
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In ptolemy's system the planets orbit the earth and not the sun. how did the system explain the retrograde motion of planets like jupiter?
In ptolemy's system the planets orbit the earth and not the sun , the system explain the retrograde motion of planets like jupiter as planets move on two sets of circles, a deferent and an epicycle. It held that the planets moved along small circles that moved on larger circles around Earth, and that the combined motion sometimes resulted in backward motion.
Retrograde motion, in astronomy, actual or apparent motion of a body in a direction opposite to that of the (direct) motions of most members of the solar system or of other astronomical systems with a preferred direction of motion.
Retrograde motion is an apparent change in the movement of the planet through the sky. It is not real in that the planet does not physically start moving backwards in its orbit. It just appears to do so because of the relative positions of the planet and Earth and how they are moving around the Sun.
Claudius Ptolemy , argued that planets move on two sets of circles, a deferent and an epicycle. This explained retrograde motion while keeping the planets in their circular orbits around the Earth.
It held that the planets moved along small circles that moved on larger circles around Earth, and that the combined motion sometimes resulted in backward motion.
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A 5.10 kgkg watermelon is dropped from rest from the roof of a 18.5 mm-tall building and feels no appreciable air resistance.
Work done is by the change in the potential energy of the system. The work done by gravity is 924.63 J.
What is the Kinetic Energy?Potential energy in physics is the energy that an item retains as a result of its position in relation to other objects, internal tensions, electric charge, or other elements.The gravitational potential energy of an object, which is based on its mass and distance from another object's center of mass, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field are examples of common types of potential energy. The joule, denoted by the letter J, is the energy unit in the International System of Units (SI).Solution:
mass = 5.10 kg
height = 18.5 mm
We know that work done by the gravity on the watermelon is the change in the potential energy of the watermelon, therefore,
Work done due to gravity = change in the potential energy of the system
W = [tex]\Delta PE[/tex]
W = mg (h₀ - h₁)
W = 5.10 × 9.8 × 18.5
W = 924.63 J
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The flywheel shown has a radius of 20 in., a weight of 330 lbs, and a radius of gyration of 15 in. A 110-lb block A is attached to a wire that is wrapped around the flywheel, and the system is released from rest. The effect of friction is neglected.
The acceleration Block A is derived as a= 11.983ft/s². See explanation below.
What is the calculation deriving the above?Recall that we are given the following:
Radium = 20 inches
Weight = 330lbs
Radius of gyration = 15in
Mass of Block = 110lb
The formula for Moment of Inertia is also given as:
I = mk²
= 330 [ 15/12]²
I = 515.625 lb/ft²
To derive the moment about O, we recourse to
∈M₀ = I∝
TR = I∝
T [20/12] = 515.625 ∝
T = 309.375∝
Next, to derive the weight of the block A hanging freely,
Wa = MAg
= 110 x 32.2
= 3542 lbf
Acceleration is derived by
A = r∝
= [20/12] ∝
a = 1.667 ∝.........Lets call this equation 1
Value of the acceleration derived by Dalembert Principle
∈Fy = mAa
Wa-T = mAa
3542 - 309.375∝ = 110 x 1.667∝
3542 = 492.745∝
∝ = 7.8188 Rad/s²............Lets call this equation 2
Substituting the value of ∝ in equation 1, we have
a = 1.667∝
= 1.667 x 7.1883
a = 11.983 ft/s²
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