The pulse traveled 1.25 cm in 2.5s. with 0.5 cm/s
From the equation of motion in 2 dimensions d = v*t ...... ( i )
As
v= d/t so d=v*twhere the time taken is 2.5 s
the velocity of pulse is 0.5 cm/s
to find the distance covered in a given time which a velocity of 0.5 m/s
so from equation (i)
d= v*t..........................(from i)d = 0.5 * 2.5d= 1.25So the distance it will be covered is 1.25 cm
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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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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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The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of 2.00 103 N with an effective perpendicular lever arm of 3.40 cm, producing an angular acceleration of the forearm of 165 rad/s2. What is the moment of inertia of the boxer's forearm
Answer: The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of 2.00 103 N with an effective perpendicular lever arm of 3.40 cm, producing an angular acceleration of the forearm of 165 rad/s2. Then, the moment of inertia of the boxer's forearm will be 0.412Nm/rad/sec2.
Explanation: To find the correct answer, we have to know more about the moment of force or torque.
What is Torque?Torque is the measure of turning effect of a force.If the object rotates about an axis, then the perpendicular distance from the axis to the line of action of the force is called the lever arm.Torque is measured by the product of force and the lever arm.If r is the position vector of the point of application of force, then torque T is,[tex]T=rFsin\alpha[/tex], where, [tex]\alpha[/tex] will be the angle between r and F.
Torque in terms of moment of inertia [tex]I[/tex] and the angular acceleration [tex]\beta[/tex] will be,[tex]T=I\beta[/tex]
Where, [tex]I=r[/tex]×m
How to solve the problem?Given that,[tex]F=2*10^3N\\r=3.40*10^-2m\\\beta =165 rad/sec^2[/tex]
From the above equation of T, we can produce the equation of moment of inertia as,[tex]I=\frac{T}{\beta } =\frac{rFsin\alpha }{\beta } \\where, sin\alpha =1.\\Thus,\\T=\frac{rF}{\beta } =\frac{68}{165} =0.412Nm/rad/s^2.[/tex]
Thus, we can conclude that, moment of inertia of the boxer's forearm will be, 0.412Nm/rad/sec².
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An object of mass 1.00 kg is attached to a vertical spring with spring constant 100 N/m. The object is held at rest in a position such that the spring is stretched upward a distance 1.00 cm beyond its undisturbed length. If the object is released, how far will it drop before coming to rest
The object will drop 5 cm if released before coming to rest.
How far will the object fall?We know from Hooke's law that the work that is done when the spring is stretched is given by the formula;
W = 1/2 kx^2
k= 100 N/m
x = 1.00 cm or 0.01 m
W = 0.5 * 100 * 0.01
W = 0.5 J
Now;
W = mgh
h = W/mg
m = 1.00 kg
g = 9.8 m/s^2
h = 0.5 J/1.00 kg * 9.8 m/s^2
h = 0.05 m or 5 cm
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One method of getting a tight fit, say of a metal peg in a hole in a metal block, is to manufacture the peg slightly larger than the hole. The peg is then inserted when at a different temperature than the block. Should the block be hotter or colder than the peg during insertion
The block should be colder than the peg during insertion.
To find the answer, we have to know more about the thermal expansion of metal.
What is thermal expansion of metal?Metals' Thermal Expansion The phenomenon of material expanding on heating and contracting on cooling is now well-known. An object changes in size when heated. Depending on the body's form. It is known as linear expansion if the expansion takes place linearly.The peg should be warmer than the metal block. Since the metal peg is made larger, the temperature of the metal block should be lower than that of the peg in order for the metal block's thermal expansion to provide a tight fit when the peg is inserted into the hole and the temperature rises.Due to the metal's tendency to expand as temperature rises, the hole's size decreases. As a result, at the time of insertion, the metal block's temperature should be lower than the peg's temperature.Thus, we can conclude that, the block should be colder than the peg during insertion.
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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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The international Space Station (ISS) orbits the Earth once every 90 mins at an altitude of 409 km. How high would it have to be in order to be to be in geosynchronous orbit
It would have to be 36,719 Km high in order to be to be in geosynchronous orbit.
To find the answer, we need to know about the third law of Kepler.
What's the Kepler's third law?It states that the square of the time period of orbiting planet or satellite is directly proportional to the cube of the radius of the orbit.Mathematically, T²∝a³What's the radius of geosynchronous orbit, if the time period and altitude of ISS are 90 minutes and 409 km respectively?The time period of geosynchronous orbit is 24 hours or 1440 minutes.As the Earth's radius is 6371 Km, so radius of the ISS orbit= 6371km + 409 km = 6780km. If T1 and T2 are time period of geosynchronous orbit and ISS orbit respectively, a1 and a2 are radius of geosynchronous orbit and ISS orbit, as per third law of Kepler, (T1/T2)² = (a1/a2)³a1= (T1/T2)⅔×a2= (1440/90)⅔×6780
= 43,090 km
Altitude of geosynchronous orbit = 43,090 - 6371= 36,719 kmThus, we can conclude that the altitude of geosynchronous orbit is 36,719km.
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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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please help me to find out my mistake
From the calculation, the speed of sound at 10 K is 63.5 m/s.
What is the speed of sound?We know that the speed of sound is directly proportional to the temperature of the body thus we can write;
V1/V2 = √T1/T2
Then;
T1 = 0 degrees or 273 K
T2 = 10 K
V1 = 330 m/s
V2 = ?
330/T2 = √273/10
330/T2 = 5.2
330 = 5.2T2
V2 = 330/5.2
V2 = 63.5 m/s
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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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Which of these is most likely to create a boating hazard around river bridges?
a) boats slowing as they approach the bridge
b) cars crossing the bridge
c) debris collecting around pilings
d) bridges swaying due to wind and waves
Debris collecting around pilings is most likely to create a boating hazard around river bridges.
The option (c) is the correct option.
Boating Hazards:
Dams, submerged items, freezing water, rapidly changing weather, sunstroke, and current are just a few of the dangers that boaters may encounter. It's not always easy to see these risks. These risks must be recognized by boaters, and they must always be prepared to prevent hazards.
Operator negligence is the most frequent reason for boating accidents, according to US Coast Guard (USCG) recreational boating statistics from 2019. Inattentiveness on the part of the operator can result in crashes, people falling overboard, and slip-and-fall incidents on board, all of which can result in life-threatening injuries.
The greatest places to find more about any potential local risks are marinas and local boaters. Check any nearby marine charts as well to learn about potential dangers and how to avoid them.
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a charged partocle produces an electric field with a magnitude of 2.0 N/C at a point that is 50cm away from the particle
The charge on the particle is 5.6 × 10⁻¹¹ C.
Calculation:The magnitude of an electric field produced by a charge is given by:
E = q/ 4πε₀r²
where,
E = electric field
q = charge
r = distance
1/4πε₀ = 8.99 × 10⁹ Nm²/C²
Given,
E = 2.0 N/C
r = 50 cm = 0.5 m
To find,
q =?
Put the values in the above equation:
E = q/ 4πε₀r²
q = E (4πε₀r²)
q = 2.0 × (0.50²)/ 8.99 × 10⁹
q = 5.6 × 10⁻¹¹ C
Therefore, the particle has a charge of 5.6 × 10⁻¹¹ C.
What is an electric field?The physical field that surrounds each electric charge and acts to either attract or repel all other charges in the field is known as an electric field. Electric charges or magnetic fields with different amplitudes are the sources of electric fields.
I understand the question you are looking for is this:
A charged particle produces an electric field with a magnitude of 2.0 N/C at a point that is 50 cm away from the particle. What is the magnitude of the particle's charge?
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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
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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17% Part (a) Calculate the x-component of the electric field at point P due to charge Q1. Write your answer in units of N/C.
The x component would be Ex = 412 x cos 49° = 270 N/C
Assume there is a small positive charge located at point P. By definition the magnitude of the electric field at point P due to charge Q1 is
E = kQ1/d2
where k is the coulomb constant and d is the straight line distance from Q1 to P.
The distance is the hypotenuse of the triangle formed by Q1, Q2, and P.
d = √0.065^2 + 0.075^2 = 0.099 m at an angle of θ = arctan 7.5/6.5 = 49°.
|E| = 8.99 x 10^9 Nm^2 C^-2 x 0.45 x 10^-9 C/ 0.099^2 m^2 = 412 n/C
The x component would be Ex = 412 x cos 49° = 270 N/C
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Two boys with masses of 40 kg and 60 kg stand on a horizontal frictionless surface holding the ends of a light 10-m long rod. The boys pull themselves together along the rod. When they meet the 40-kg boy will have moved what distance?.
When they meet the 40-kg boy would have moved a distance of 6 m.
Distance moved by the 40 kg boyApply the principle of center mass;
Take the 40 kg mass as the reference point;
X(40 kg) = (40kg x 0 + 60kg x 10 m)/(40 kg + 60 kg)
X(40 kg) = (600)/(100)
X(40 kg) = 6 m
Thus, when they meet the 40-kg boy would have moved a distance of 6 m.
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When the absolute value of the price elasticity of demand falls in the range 0 to 1, demand is said to be _____.
When the absolute value of the price elasticity of demand falls in the range 0 to 1, demand is said to be inelastic.
A good or service that has an income elasticity of demand between zero and 1 is considered a normal good and income inelastic. If a good or service has an income elasticity of demand below zero, it is considered an inferior good and has negative income elasticity.
Inelastic is an economic term referring to the static quantity of a good or service when its price changes. Inelastic means that when the price goes up, consumers' buying habits stay about the same, and when the price goes down, consumers' buying habits also remain unchanged.
Price elasticity of demand is a measurement of the change in consumption of a product in relation to a change in its price. A good is elastic if a price change causes a substantial change in demand or supply.
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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
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:
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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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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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.
You are looking down on a 20 kg beam resting on a horizontal, frictionless surface. The beam is 2 m long and can pivot about one end. A small 0.1 kg rock slides across the surface at 400 m/s and hits the middle of the beam, embedding itself inside. What is the angular speed of the rod after the impact (in rad/s)
The angular speed of the rod after the impact is 1.49 rad/s
What is angular speed?
The rate of change of angular displacements is known as angular speed.
Angular speed is a scalar measure of the rotating object.
What is Angular momentum?
It is the property of a rotating body given by the product of the moment of inertia and the angular velocity of the rotating object.
Angular momentum is expressed as follows:
L=m*v*r
Here,
mass of beam, M =20 kg
mass of rock, m =0.1 kg
length of the beam, L =2 m
length where rock slides, l = (L / 2), l = 1 m
velocity of rock, v =400 m/s
As here the Torque on which the system is zero implies that the angular momentum is conserved.
Initial angular momentum for rock: I(ri) = m*v*r
Final angular momentum for rock: I(rf) = m*w*r^2
Final angular momentum for beam: I(bf) = 1/3 (M*L^2w)
Now, According to the conservation of momentum:
m*v*r = m*w*r^2 + 1/3 (ML^2w)
w = m*v*r / ( mr^2 + 1/3 ML^2 )
w = 0.1 *400*1 / ( (0.1 * 1) + 1/3 20* 2^2 )
w = 1.49 rad / s
The angular speed of the rod after the impact is 1.49 rad/s
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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]
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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airs of conductors carrying current into or out of the power-supply components of electronic equipment are sometimes twisted together to reduce magnetic-field effects. Why does this help
Answer: Pairs of conductors carrying current into or out of the power-supply components of electronic equipment are sometimes twisted together to reduce magnetic-field effects. This is for reducing the area of the loop and hence reducing the inductance and suffer less interference or improving electromagnetic compatibility.
Explanation: To find the answer, we need to know more about Twisted pairs.
What is twisted pairs?Twisted pairs are simply conductors carrying current into and out of the power supply components of the electronic equipment, which are sometimes twisted together to reduce magnetic field effects.It can be able to minimize the area of the loop around the circuit. thus, the magnetic field from each wire will cancels each other.This will reduce the inductance as well as interference caused by the nearest fields.Twisting them will defines a transmission line impedance.Thus, we can conclude that, the twisted pairs are used for reducing the area of the loop and hence reducing the inductance and suffer less interference or improving electromagnetic compatibility.
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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 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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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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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]
Learn more about the range of a projectile here:
https://brainly.com/question/17016688
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