Order from fastest to slowest
[tex]1\geq 2\geq 3\geq 4\geq 5[/tex]
Sort the items in order of speed. Overlap items to rank them equally.
The wheel in the is rolling to the right without slipping.
Rank in order, from fastest to slowest, the speeds of the points labaled 1 through 5.
Rank items from fastest to slowest. To rank items as equivalent, overlap them.
an sphere is pure rolling speed of context point 5 meet be zero w.r.t ground.
Hence, v-ωR=0
v=ωR
[tex]v_5_/_g\geq v_5_/_c+v_c_/_g...............(1)[/tex]
part.5
speed= 0 [tex]v_5=0[/tex]
part.2
[tex]v_2=\sqrt{v^2+v^2}[/tex]
[tex]= \sqrt{2} v[/tex]
=(1.414)v
part.3
[tex]v_3= \sqrt{v^2[/tex]ω[tex]^{2}[/tex][tex]R^2/4[/tex] = 1.118v
part. 1
[tex]v_1[/tex]=v+ωR
=2v
part. 4
[tex]v_4[/tex]=v
order from fastest to slowest
[tex]1\geq 2\geq 3\geq 4\geq 5[/tex]
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a driver should not try to pass a large vehicle when that vehicle is making a turn because the driver will not be visible to the driver of the large truck. a) on the left b) on the right c) at all d) all of the above
When a large truck is turning, a driver shouldn't attempt to pass it on the right since the large truck's driver won't be able to see them.
What makes it a driver?The term "driver" has a history dating back to the 15th century and is used to describe a person who drives working animals, particularly pack or draft horses.
What exactly does a driver do?Transporting goods or people safely from one place to another is the primary duty of a driver. They must adhere to traffic regulations and plan their route properly, and they must always get enough fuel in the tank to get where they're going.
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You redo the primitive yo yo experiment (Figure 1), but instead of holding the free end of the string stationary, you move your hand vertically so that the tension in the string equals 2M /3. What is the vertical acceleration of the yo yo's cena of mass? Does it accelerate upward or downward? Express your answer to three significant figures and include the appropriate units. Enter positive value of the acceleration is directed upward and negative value if the acceleration is directed downward.
The vertical acceleration of the yo yo cena of mass is 0.66 m/s².
We know that, T = M*a
And T is given as 2M/3
2M/3 = M*a
So, a = 0.66 m/s²
Acceleration is the general term for any process where the velocity changes. There are only two ways to accelerate either by increasing the speed or decreasing direction, or both. The reason for this is that velocity includes both a speed and a direction.
You cannot possibly be accelerating if you don't also change you direction and speed, regardless of how swiftly you are travelling. Due to this, a jet experiences no acceleration even when it is moving at a high speed. In this case, 800 miles per hour, because its velocity is constant.
When it lands, the jet will accelerate as it slows down and quickly come to a stop.
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The amount of air drag on an 0. 8n flying squirrel dropping vertically at terminal velocity is?.
The amount of air drag on an 0. 8n flying squirrel dropping vertically at terminal velocity is 0.8 N.
What speed is terminal velocity?The speed that an object reaches when it freely falls through a gas or liquid is known as the terminal velocity. A parachutist who waits to open the chute will typically reach a terminal velocity of around 150 miles per hour (240 km/h). A mist of minute oil droplets settles with an incredibly low terminal velocity, whereas raindrops fall at a considerably lower terminal velocity. An object compelled to go faster than its terminal velocity will slow down to this constant velocity upon release; an object dropped from rest will increase its speed until it achieves terminal velocity.Therefore, an object reaches terminal velocity when its speed is no longer growing or decreasing and its acceleration (or deceleration) is zero.To learn more about velocity, refer to
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in your drawings for the field of the bar magnet, where are the field lines closest together? where are they farthest apart? what is the significance of a concentration of field lines?
The magnetic field is the strongest at the poles of a magnet, so the lines are closer to each other at poles, and farthest at the center outside the magma.
Magnetic lines being close together mean a strong magnetic field and lines far apart from each other mean a weak magnetic field.
Magnetic field lines are like streamlines in fluid flow, they represent something continuous, and a different resolution would show more or fewer lines. Various phenomena have the effect of displaying magnetic field lines as though the field lines were physical phenomena.
Magnetic field Magnetic field strength is one of two ways that the intensity of a magnetic field can be expressed. Technically, a distinction is made between magnetic field strength H, measured in amperes per meter (A/m), and magnetic flux density B, measured in Newton-meters per ampere (Nm/A), also called teslas (T).
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suppose that 20 j of work is needed to stretch a spring from a0 cm to 2a0 cm. 80 j of work is needed to stretch it from a1 cm to 2a1 cm. what is the natural length of the spring. note that a0 and a1 are some constants and the unit is cm instead of m
The needed length of spring or the natural length is ( 12a₀²- a₁²)( 8a₀- 2a₁).
Let L be the natural length,
Since 20J of work is demanded to stretch the spring from a₀ cm to 2a₀ cm,
We have,20 = k / 2(( 2a₀- L) ²-( a₀- L) ²)--------- eq 1
Again,80 J of work is demanded to stretch the spring from a₁ cm to 2a₁ cm,
80 = k / 2(( 2a₁- L) ²-( a₁- L) ²)---------- eq 2
Now, eq 2 / eq 1
k/ 2(( 2a₀- L) ²-( a₀- L) ²) k/ 2(( 2a₁- L) ²-( a₁- L) ²)
= (80/20)a₁( 3a₁- 2L)/ a₀( 3a₀- 2L)
= 43a₁ ²- 2La₁/ 3a₀ ²- 2La₀ = 43a₁ ²- 2La₁
= 12a₀ ²- 8La₀L( 8a₀- 2a₁)
= 12a₀ ²- 3a₁ ²L
= ( 12a₀ ²- 3a₁ ²)( 8a₀- 2a₁)
Therefore the needed length of spring or the natural length is ( 12a₀²- a₁²)( 8a₀- 2a₁).
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g capacity, the ability of the material/structure to safely resist load without breaking or damage, depends on?
Ductility determines whether a material or structure can safely withstand a load without breaking or suffering damage.
Ductility: What is it?A material's ductility is a mechanical property that refers to how easily it can be drawn from. In the field of materials science, ductility refers to how much plastic deformation under tensile stress a material can withstand before breaking. Ductility is a top priority in both engineering and manufacturing.
It describes a material's suitability for specific manufacturing processes (like cold working) and its capacity to withstand mechanical overload. Among the metals that are frequently referred to as ductile are copper and gold. Not all metals, like cast iron, can fail brittlely; some can instead fail ductilely. Polymers can be thought of as ductile materials because they typically allow for plastic deformation.
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within the deep cold zone, average temperature and salinity . a. remain fairly constant with depth. b. increases and decreases, respectively. c. decrease with depth. d. increase with depth.
The average salinity in the deep cold zone increases with depth. The average temperature in the deep cold zone decreases with depth.
Salinity in the ocean is how much salt is in ocean water. Near the surface, the salinity could change.
Salinity will decrease after rainfall.Salinity will increase after evaporation on a sunny day.Sunlight can affect the temperature of the water. But only about 200 m from the surface. Below 200 m, the sunlight cannot get through.
According to hydrostatic pressure, as deeper as the ocean, the pressure increase. When the pressure increase, the temperature will decrease.
In the deep cold zone, there is a water current called thermohaline circulation which carries colder and saltier water to the deeper parts of the ocean. This circulation makes in the deep cold zone the temperature decrease and the salinity increase.
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A carnival game consists of a two masses on a curved frictionless track, as pictured below. The player pushes the larger object so that it strikes the stationary smaller object which then slides follows the curved track so that it rises vertically to a maximum height, hmax. The masses are equipped with elastic bumpers so that the impact between them is an elastic collision. If the larger object has a mass, M = 7.76 kg and the smaller object has a mass of m = 1.86 kg, then with what velocity, v0, should the player release the larger object so that the smaller object just reaches the target maximum height of hmax = 3.0 m above the horizontal portion of the track?
Velocity 1.90 m / s , v0, should the player release the larger object so that the smaller object just reaches the target maximum height of hmax = 3.0 m above the horizontal portion of the track.
What is Velocity?
The directional speed of an item in motion, as measured by a specific unit of time and viewed from a certain point of reference, is what is referred to as velocity.
In this exercise we are given the maximum height data, with energy we can know how fast the body came out
Final mechanical energy, maximum height
EMF = U = m g h
Initial mechanical energy, in the lower part of the track
Em₀ = K = ½ m v²
Em= EMF
½ m v² = m g h
v = √ 2gh
Now we can use the moment to find the speed with which objects collide
The large object has a mass M = 5.41 kg a velocity starts v₁₀, the small object has a mass m = 1.68 kg an initial velocity of zero v₂₀ = 0 and final velocity v
Initial before the crash
p₀ = M v₁₀ + 0
Final after the crash
pf= = M v1f + m v
po=pf
M v₁₀ = M v1f + m v
As the shock is elastic the kinetic energy is conserved
[tex]$$\begin{aligned}& K_0=K_f \\& 1 / 2 M v_{10}{ }^2=1 / 2 M v_{1 f^2}+1 / 2 m v^2\end{aligned}$$[/tex]
Let's write the system of equations
[tex]$$\begin{aligned}& M v_{10}=M v_{1 f}+m v \\& M v_{10}{ }^2=M v_1 f^2+m v^2\end{aligned}$$[/tex]
We cleared vif in the first we replaced in the second
[tex]$$v_{1 f}=\left(\mathrm{M} \mathrm{v}_{10}-\mathrm{mv}\right) / \mathrm{M}$$[/tex]
M v₁₀² = M (M v₁₀ - mv)² / M² + m v²
M v₁₀² = 1 / M (M² v₁₀² - 2mM v v₁₀ + m² v²) +m v²
v₁₀² (M - M) + 2 m v v₁₀ - v² (m2 + m) / M = 0
2 m v₁₀ - v (m + 1) m/ M = 0
v₁₀ = v (m +1) / (2M)
Let's substitute the value of v
v1₁₀= √ (2gh) (m +1) / (2M)
Let's calculate
v₁₀ = √ (2 9.8 3) (1+ 1.68) / (2 5.41)
V₁₀ = 7.668 (2.68) / 10.82
v₁₀ = 1.90 m / s
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exhibit 6-5 the weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. refer to exhibit 6-5. what percentage of items will weigh between 6.4 and 8.9 ounces? a. .2881 b. .1145 c. .4617 d. .1736
The percentage of items will weigh between 6.4 and 8.9 ounces 0.4617.
In science and engineering, the burden of an object is the force performing on the item because of gravity. a few well-known textbooks outline weight as a vector quantity, the gravitational force performed on the object. Others outline weight as a scalar quantity, the importance of the gravitational pressure.
Retaining your weight inside the ordinary range is an important part of healthful growing old. As in other tiers of existence, elevated body mass index (BMI) in older adults can growth the chance of developing fitness issues. those encompass heart ailments, excessive blood strain, stroke, and diabetes.
Bad sleep, sedentary activities, and consuming too many processed or sugary meals are simply some of the habits that could increase your hazard of weight advantage. yet, some simple steps — together with mindful ingesting, workout.
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What is the Goldilocks zone?
A. It is the depth within the Earth’s crust where gold can be found.
B. It is a range of distance from a star where temperatures are right for liquid water to exist.
C. It is the distance from a star where pressures are right for an atmosphere to form.
D. It is the temperature range where porridge is just right.
The Goldilocks zone is a range of distance from a star where temperatures are right for liquid water to exist (option B).
What is the Goldilocks zone?The Goldilocks zone is a zone around a star where a planet could experience temperatures like those on Earth, allowing for the possible existence of liquid water and of life.
The Goldilocks Zone also called habitable zone refers to that range of distance with the right temperatures for water to remain liquid.
Only one planet so far is known to be habitable for life and that planet is Earth. On Earth, water is a critical ingredient for life.
If a planet’s orbit takes it too close to its parent star, then it will be too hot for liquid water to exist, and if it’s too far out it will be too cold. However, the actual distances involved, that define habitable or Goldilocks zone vary between stars.
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A force of 570 N keeps a certain ideal spring stretched a distance of 0.900 m.
Part A:
What is the potential energy of the spring when it is stretched 0.900 mm?
Express your answer with the appropriate units.
Part B:
What is its potential energy when it is compressed 9.00 cm?
Express your answer with the appropriate units.
Hooke's law states that the elongation of a material is proportional to the applied stress within the elastic limits of the material.
Using Hooke's law
F = kx
570 = k * 0.9
k = 712.5 N/m
(a) energy at x = 0.8 m
U = 0.5 k x^2 = 0.5* 712.8* 0.8^2
U = 228 J
(b) U = 0.5 * 712.8* 0.09^2
U = 2.887 J
Elastic potential energy is the potential energy released as a result of the deformation of an elastic body. B. Spring extension is stored. This is equal to the work done to stretch the spring, which depends on the spring constant k and the stretched distance. The force exerted by the spring is the restoring force that helps return the spring to its equilibrium length.
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an electric utility company supplies a customer's house from the main power lines 120 v with two copper wires, each of which is 80.0 m long and has a resistance of 0.108 per 300 m. (a) find the voltage at the customer's house for a load current of 110 a.
At the customer's home, the voltage (potential difference) for such a load current at 110 an is 116 V
What is the difference in electric potential, explained simply?Electron pressure is quantified by the electric potential difference, commonly referred to as voltage. Because of their mutual repulsion, it is dependent on how closely the particles are packed and may be viewed as a measurement of "how desperately the electron want to move."
Briefing:P.d. at the house = Source P.d. - P.d in the lines
Also, Potential difference, V = current * resistance
Let the resistance be R:
R/(80 + 80)m = 0.108 Ω/300 m
R = 0.0576 Ω
P.d. in the lines = 110 * 0.0576 = 6.34V
P.d. at the house = 120 - 6.34= 113.66
P.d. at the house = 113.66 V
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photons in a beam of light with wavelength l have momentum p. if the wavelength is doubled, the momentum is:
When a beam of a photon with wavelength (λ) is doubled, momentum (p) will be halved.
What is Wavelength?
The distance in a wave between a given position and the same point in the following wave cycle. This can be from peak to peak, from trough to trough, from null to null, etc. The formula E = hν = hc/λ, where E is energy, h is Planck's constant, is frequency, c is the speed of light, and is the wavelength, relates wavelength to energy and frequency.
What is Momentum?
The definition of momentum is "mass in motion." Since every item has mass, if it is moving, it must have momentum because its mass is in motion. The amount of motion and the speed of the motion are the two factors that determine how much momentum an item possesses. The factors of mass and velocity affect momentum. According to an equation, an object's momentum is determined by multiplying its mass by its velocity.
Momentum = mass • velocity, (p = mv)
Hence, When a beam of a photon with wavelength (λ) is doubled, momentum (p) will be halved.
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in a collision between a 50-ton bulldozer and a compact car, which vehicle will experience the greater impact force?
The vehicle that weighs less will be hit harder in a collision between two moving objects at the same speed; the more massive and heavy the vehicle, the more energy and momentum it will generate.
Which vehicle will experience the greater force of impact?When two objects come into contact, a force of impact is created. The impact or striking power of your vehicle increases with speed. According to the rules of physics, speed increases cause an increase in the force of impact. A car's force of impact will therefore increase four times if its speed is doubled. The impact increases ninefold when the speed is tripled. Consequently, hitting something at these speeds is equivalent to crashing off a one-, four-, or nine-story building, respectively.In a collision between two moving objects at the same speed, the lighter object will be hit harder since its energy and momentum are greater than those of the heavier one. The lighter, smaller vehicle will decelerate more quickly and might even be propelled in the opposite direction from where it was originally moving.To Learn more About vehicle that weighs less refer to:
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It takes a car 1. 75 h to go from mile marker 10 to mile marker 115. What is the average speed of the car? responses 1. 6 mph 1. 6 mph 60 mph 60 mph 65 mph 65 mph 183 mph.
The car travels at an average speed of 60 mph the entire way.
The parameters are as follows:
t = 1.75 hours for the car's motion;
[tex]x_{1}[/tex] = 10 miles for its initial position, and
[tex]x_{2}[/tex] = 115 miles for its final position.
The following formula is used to determine the car's overall mileage:
Distance traveled =[tex]x_{2} -x_{1}[/tex] = 115 miles - 10 miles = 105 miles
Thus, the distance traveled is 105 miles.
The following formula is used to determine the vehicle's average speed during the entire journey:
Average Speed = Distance traveled/Time Taken
Average Speed = 105 miles/ 1.75 hours = 60 miles per hour
As a result, the car travels at an average speed of 60 miles per hour.
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I need a detailed answer
The mass of the beam, given that the beam is balanced is 400 g
How do I determine the mass of the beam?First, we shall re-conctruct the diagram given to better understand what we are looking for. Please see attached photo.
In the attached photo,
M is the mass of the beamNote: The mass of the beam act at the centre of the beam
Now, we shall determine the mass of the beam as follow:
Clock wise moment = M × 10Anti-clock wise moment = 200 × 20Mass of beam (M) =?Anti-clock wise moment = Clock wise moment
200 × 20 = M × 10
4000 = M × 10
Divide both sides by 10
M = 4000 / 10
M = 400 g
Thus, from the above calculation, we can conclude that the mass of the beam is 400 g
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Which of the following refers to the motion of an object falling straight down
with only the force of gravity acting on it?
OA. Free fall
OB. Air resistance
OC. Gravity
OD. Projectile motion
Answer:
D
Explanation:
projectile motion
is the answer
a small artery has a length of 1.6 ✕ 10−3 m and a radius of 2.4 ✕ 10−5 m. if the pressure drop across the artery is 1.8 kpa, what is the flow rate (in mm3/s) through the artery? (assume that the temperature is 37°c.)
The flow rate (in mm3/s) through the artery is [tex]7.031 * 10^-^1^1 m^3/s[/tex]
What is Poiseuille's Law?
Poiseuille's Law can be used to explain the fluid flow through an IV catheter. According to this, the viscosity (μ), pressure gradient (P), length (L), and diameter (r) of the tubing are all important variables that affect fluid flow (Q).
It is given by equation
Δp = 8μLQ / π[tex]R^4[/tex]
where,
Δp = pressure difference between the two ends
μ = dynamic viscosity
L = length of pipe
Q = volumetric flow rate
π = pi
R = pipe radius
Given,
Length of artery L = [tex]1.6 * 10^-^3m[/tex]
Radius R = [tex]2.4 * 10^-^5m[/tex]
Pressure Δp = 1.8 kPa = [tex]1.8 * 10^3 Pa[/tex]
Viscosity μ = [tex]2.084 * 10^-^3 Pa. s[/tex]
Subsituting the values in equation,
Δp = 8μLQ / π[tex]R^4[/tex]
Q = Δp × π[tex]R^4[/tex] / 8μL
Q = [tex]\frac{(1.8 * 10^3) (3.14)(2.4 * 10^-^5)^4}{8 * (2.084* 10^-^3)(1.6 * 10^-^3)}[/tex]
Q = [tex]7.031 * 10^-^1^1 m^3/s[/tex]
The flow rate (in mm3/s) through the artery is [tex]7.031 * 10^-^1^1 m^3/s[/tex]
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What is the complete factorization of 8x2 − 8x + 2?
The complete factorization is 2 (2x-1)².
What is factorization?Factorization is a way of dividing mathematical algebraic statements into their components. The components will produce the original phrase if we multiply them once more.
Factorization is a way of dividing mathematical algebraic statements into their components. If we multiply the components again, we get the original equation.
Factorising is the opposite of extending brackets. Fully factorizing an expression implies putting it in brackets and removing the greatest common factors. Finding the largest common factor between each item in the phrase is the simplest method of factorization.
Given,
= 8x² - 8x +2
= 8x² - (4+4)x +2
= 8x² - 4x + 4x +2
= 4x (2x -1) -2 (2x-1)
= (4x-2) (2x-1)
= 2 (2x-1) (2x-1)
= 2 (2x-1)²
Thus, complete factorization is 2 (2x-1)².
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two particles are separated by a certain distance. the force of gravitational interaction between them is f0 . now the separation between the particles is tripled. find the new force of gravitational interaction f1 . express your answer in terms of f0 .
According to the given statement the force would be F0=9×F1.
What does the term "gravitational" mean?involving or pertaining to the attraction between two components: Ocean tides rise and fall due to the moon's gravitational pull. of or pertaining to a strong inclination or movement in the direction of something or someone: There has been a lot of research on why they gravitate toward harmful conduct.
What is gravitational force, for instance?The force that now the earth applies to a body is referred to as gravitational force. The downhill and upward motion with water in rivers and streams, as well as the upward motion of something like a ball when it's thrown, are examples of motion brought on by gravitational force.
Briefing:Isaac Einstein's universal law general gravitational is the formula that describes the attraction forces between two masses (m) that are separated from one another by a distance (r) (F=Gmm/r2).
Using the values listed in the question as a guide:
F0= Gm₁m₂÷r²
F1=Gm₁m₂÷(3r)²
We obtain by dividing F0 but also F1:
F0=9×F1
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6. conical surface of constant density find the moment of iner?tia about the z-axis of a thin shell of constant densthe cone 4x 2 4y 2 - z 2
We need to find the rotational inertia of the shell about the axis of rotation.
What is rotational inertia?Inertia of rest the inability of a body to change by itself its state of rest is called inertia of rest. Inertia of direction. The inability of a body to change by itself its direction of motion. Inertia of motion: The inability of the body to change by itself its state of motion is called inertia of motionYou tend to move forward when a sudden break is applied.You feel a backward force when the bus moves quickly from rest.Dusting bed with a broom removes dust due to inertia of rest.when you shake a branch the leaves get detached.According to Newton's first law of motion, an object with a given velocity maintains that velocity unless acted on by an external force. Inertia is the property of matter that makes this law hold true.Any item that can be turned has rotational inertia as a quality. It's a scalar value that indicates how complex it is to adjust an object's rotational velocity around a certain axis.Then the moment of inertia about the y-axis of the thin semicircular region of constant density will be.When a car makes a sharp turn at a high speed, the driver tends to get thrown to another side due to inertia of direction.The spark coming out of a grinding stone is tangential to the rotating stone due to directional inertia.The mud from the wheels of a moving vehicle flies off tangentially.[tex]I_{y} = (\frac{1}{8}) \pi r^{4}[/tex]
x = r cos θ
y = r sin θ
dA = r dr dθ
Then the moment of inertia about the x-axis will be
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for a parallel flow double pipe heat exchanger insulated from its surroundings, the mean outlet temperature of the initially cold fluid can exceed the mean outlet temperature of the initially hot fluid.
The final heat of your substance can be calculated by adding the temperature change to the starting point.Your water's final temperature would be 24 + 6, or 30 degrees Celsius, for instance,if the temperature was 24 degrees when it began.
What is the formula for the beginning temperature?Simple: Change in temperature divided by initial temperature.Grams are used to express the mass.T=TfTi, where Transfer function is the final temperature while Ti is the initial temperature, gives the change in temperature.
What distinguishes initial from final?In physics, an object's initial position is its starting point for motion, and its final position is where it comes to rest.
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the light we see from the most distant known quasar was emitted around 10 gyrs ago. what was happening with our sun (and therefore earth) 10 gyrs ago? what was happening with the milky way galaxy at this time?
10 billion years ago, the sun was likely in its early stages of formation. At this time, the Milky Way was still in the process of collapsing and starting to form stars.
What is Milky Way?
The galaxy that contains our Solar System is known as the Milky Way, and its name refers to how it appears to us on Earth: a hazy band of light in the night sky made up of stars that are too close together to be seen individually. The Milky Way is a disk-shaped structure, but when viewed from Earth, it looks like a band. In 1610, Galileo Galilei used his telescope for the first time to separate the band of light in to the individual stars. Most astronomers believed that the Milky Way held all of the universe's stars until the early 1920s.
Gas and dust clouds were beginning to collect, and the first stars and proto-planetary disks were beginning to form. The Milky Way was also likely forming its spiral arms, as the young stars began to move around the center of the galaxy. As the stars aged, they began moving further away, creating the spiral arms that we see today.
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determine the moment of inertia of a 8.20 kg sphere of radius 0.793 m when the axis of rotation is through its center
The moment of inertia of the sphere when the axis of rotation is through its center be 2.063 kg-m².
What is moment of inertia?The sum of the products generated by multiplying each particle's mass by the square of its distance from the axis results in the moment of inertia (I), which is always expressed with respect to that axis.
Given parameters:
Mass of the sphere: m = 8.20 kg.
Radius of the sphere: r = 0.793 m.
Hence, the moment of inertia of the sphere when the axis of rotation is through its center be = 2/5 mr²
= 2/5 × 8.20 × 0.793 × 0.793 kg-m².
= 2.063 kg-m².
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hree children are riding on the edge of a merry-go-round that is 115 kg, has a 1.7-m radius, and is spinning at 24 rpm. the children have masses of 32, 34, and 40 kg. (a) if the children with masses of 34 and 40 kg move to the center of the merry-go-round, what is the new angular velocity in rpm?
The new angular velocity in rpm is
27.7 rpm
M = 115 kg be the mass of the merry-go-round,
r = 1.7 m be its radius,
m1 = 32 kg,
m2 = 34 kg,
m3 = 40 kg be the masses of the three children,
ω = 22 rpm be the angular velocity with all children at the edge,
ω' (to be calculated) be the angular velocity after m2 is moved to the center.
The conservation of angular momentum can be used to resolve this.
The angular momentum before and after the move must be equal.
But there are two presumptions we must make.
1) The merry-go-round has a consistent disc shape. Although it is improbable, if the merry-go-round has a more widespread. The issue gets more complex due of its convoluted shape.
2) The kids are on the merry-go-outer round's edge. Regardless of where the kids are, the issue is easily fixable.
but, since I have no information, I'll guess it's on the edge.
In general, a mass m at the edge contributes mr²ω to the angular momentum.
The rotating uniform disk contributes Mr²ω/2 to the angular momentum.
Now we can equate the total angular momentum after the move to the total
angular momentum before the move.
Mr²ω'/2 + m1r²ω' + m3r²ω' = Mr²ω/2 + m1r²ω + m2r²ω + m3r²ω
From that express
ω' = ω(M/2 + m1 + m2 + m3)/(M/2 + m1 + m3)
Substituting actual numbers
ω' = 22×(115/2 + 32 + 34 + 40)/(115/2 + 32 + 40) = 27.7 rpm
Hence, new angular velocity in rpm is 27.7 rpm
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the maximum speed of a child on a swing is 4.9 m/s. the child's height above the ground is 0.70 m at the lowest point in his motion. how high above the ground is he at his highest point
1.925 m high above the ground is he at his highest point.
As per the question,
V=4.9 m/s
h= 0.70 m (child's height above the ground at the lowest point in the motion)
Height of the child above the ground at his highest point=h’
H=h’-h
1/2mV²=mgH (g=9.8m/s²)
V²=2gH [V=2g(h’-h)]
V=√ 2×9.8×(h’-0.70)
(4.9)²=19.6(h’-0.70)
24.01=19.6h’-13.72
37.73=19.6h’
37.73/19.6=h’
1.925=h’
What is motion?In physics, motion is defined as a change in a body's position or orientation over time. Translation is the term for motion along a line or a curve. Rotation is another motion that modifies a body's orientation.
What is periodic motion?Periodic motion is defined as a motion that repeats at regular periods of time.
The motion of a youngster on a swing is periodic because the motion of a swing also repeats after short intervals.
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the swirling gas that collects around a compact object, as its binary companion transfers material to it, is called
NOT an event horizon is its binary counterpart, which transports matter to it.
What is an object in a sentence?To refer to the item or person that is the target of an action, we typically use the word "object." Alternatively, the recipient. In a sentence, a verb's action is transferred to a noun or pronoun as a direct object. It typically responds to the what- or whom-questions regarding the verb.
What is a picture or an object?Icons, cursors, buttons, sprites, and other complicated artworks can be made from a collection of simple visual pieces called image objects. Without having to sketch a single pixel, Image Objects let you express creativity.
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a 0.160-g puck strikes and embeds itself in a 6.4 kg block. the block moves off at 1.2 m/s. what was the puck's speed?
The puck's speed was 7.2 m/s.
What is speed?
Despite their similarities, speed and velocity have very different meanings, just as distance as well as displacement do. Speed, which is a scalar quantity, is the "speed at which an object is moving." The rate that an object travels a distance can be assumed of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object moving slowly, which travels a relatively short distance within the same amount of time. Zero speed refers to an object that is not moving at all.
The puck's speed can be determined by solving the equation for momentum conservation. Momentum is conserved when the total momentum before an interaction is equal to the total momentum after the interaction. In this case, the equation looks like this:
m_P * v_P + m_B * v_B = (m_P + m_B) * v_F
Where m_P is the mass of the puck, v_P is the initial velocity of the puck, m_B is the mass of the block, v_B is the initial velocity of the block, and v_F is the final velocity of the block.
Plugging in the given values, we get:
0.160 * v_P + 6.4 * 1.2 = (0.160 + 6.4) * 1.2
Solving for v_P, we get:
v_P = 7.2 m/s
Therefore, the puck's speed was 7.2 m/s.
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Nasa’s orion spacecraft, which left earth last week, flew within 81 miles of the surface of which celestial body on monday?.
Nasa’s Orion spacecraft, which left earth last week, flew within 81 miles of the surface of the moon on Monday as part of Artemis I mission.
What is the Artemis I mission?On Nov. 16, 2022, Artemis blasted off on a nearly month-long mission to orbit the moon and return to Earth. Although there are no humans on board, the mission is meant to prepare the way for crews to land on the moon in the future. On November 21, 2022, flying day six of the Artemis I mission, the Orion spacecraft captured this monochrome image of the moon with its optical navigation camera. NASA's mission controllers lost touch with Orion when it passed behind the moon, as expected. Due to complications with the fuelling process, bad weather, and other factors, earlier launch attempts had to be scrubbed.On Monday, NASA's Orion spacecraft sped past the far side of the moon, coming within 81 miles of the surface.To learn more about Artemis I mission , refer:
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A 30-cm-diameter, 1.4 kg solid turntable rotates on a 1.4-cm-diameter, 450 g shaft at a constant 33 rpm. When you hit the stop switch, a brake pad presses against the shaft and brings the turntable to a halt in 12 seconds. Part A How much friction force does the brake pad apply to the shaft?
0.628N friction force is applied by the brake pad to the shaft when a 30-cm-diameter, 1.4 kg solid turntable rotates on a 1.4-cm-diameter, 450 g shaft at a constant 33 rpm and when you hit the stop switch, a brake pad presses against the shaft and brings the turntable to a halt in 12 seconds.
To determine the friction force applied by the brake pad to the shaft, first we need to calculate the moment of inertia of the solid turn table. Let's consider the moment of inertia of turn table as a disk then -
I = MR²/2
where M= mass of the turntable=1.4 kg
R= radius of the turntable
= diameter of the turntable/2
R= 30cm/2 = 15cm or 0.15m
substituting the value -
I = 1.4kg*(0.15)²/2
I = 0.0157kg-m²
When we hit the stop switch, a brake pad presses against the shaft and brings the turntable to a halt in 12 seconds so the acceleration (α) will be-
α = (ωf-ωi)/t
The initial angular speed (ωi) of the turntable = 33rpm or 3.45rad/s
The final angular speed (ωf) of the turntable = 0 rad/s
so,
α = (0 rad/s - 3.45 rad/s)/12s
α = -0.28rad/s²
Now, the frictional force applied by the brake pad is-
Torque = I x α
from dynamics of rotational motion
r x f = I x α
f = (I x α)/r
where r = radius of the distance from the pivot point so
1.4cm/2 or 0.007m
f = (0.0157kg-m²) * (0.28 rad/s²)/ 0.007m
f = 0.628N
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