The active site of an enzyme catalyzes the reaction.
The active site is the region of an enzyme where substrate molecules bind and undergo a chemical response. the energetic site includes amino acid residues that form temporary bonds with the substrate (binding site) and residues that catalyze a response of that substrate (catalytic site). the active site is the part of an enzyme to which substrates bind and where a reaction is catalyzed.
The catalytic site happens subsequent to the binding site, wearing out the catalysis. It is composed of around two to four amino acids, involved in catalysis. The amino acids that form the active site are located in wonderful elements of the amino acid sequence of the enzyme.
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a study by judge and cable (2010) suggests that there is a positive relationship between weight and income for a group of men. the following data is similar to what was collected in the study. to simplify the weight variable, the men are categorized into five categories that measure actual weight relative to height from 1
The correlation is statistically significant
What is correlation?
Correlation is the propensity for two or more systems that individually display basic behavior to display complex and unique behavior when they interact. The majority of the complicated behavior of matter observed at all scales can be attributed, broadly speaking, to correlation.
What is weight?
weight is the gravitational force that pulls on an object when a larger second object, like the Earth or Moon, is present.
X Values
∑ = 24
Mean = 3
∑(X - Mx)2 = SSx = 18
Y Values
∑ = 704
Mean = 88
∑(Y - My)2 = SSy = 11076
X and Y Combined
N = 8
∑(X - Mx)(Y - My) = 330
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 330 / √((18)(11076)) = 0.7391
>r
As here r=0.7391>r_c=0.707
Hence correlation is statistically significant
Therefore, correlation is statistically significant.
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Compared to the average density of the terrestrial planets (mercury, venus, earth, and mars), the average density of the jovian planets (jupiter, saturn, uranus, and neptune) is.
The average density of the Jovian planets (Jupiter, Saturn, Uranus, and Neptune) is greater.
de
What is density?The density of a material indicates the density of that material in a given area. The density of a material is defined as its mass per unit volume. Density is basically a measure of how tightly packed a substance is. It is a unique physical property of a particular object. The principle of density was discovered by the Greek scientist Archimedes. Calculating density is easy if you know the formula and understand the units involved. The symbol ρ means density, or it can also be represented by the letter D or ρ.
Density formula: ρ = m/V, where ρ is the density, m is the mass of the object, and V is the volume of the object.
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An object executing simple harmonic motion has a maximum speed of 5.0m/s and a maximum acceleration of 0.62m/s2 .Part AFind the amplitude of this motion.Express your answer using two significant figures.Part BFind the period of this motion.Express your answer using two significant figures.
A)Amplitude of the motion, A= 40.32m
B)Period of the motion, T= 50.67 sec
What is harmonic motion?The motion that an oscillating mass experiences when restoring force is proportional to the displacement, but in opposite directions is called as harmonic motion.
The position of object around equilibrium in simple harmonic motion is :
x(t) = A cos (ωt)
A is amplitude of the motion and ω is angular frequency.
Velocity is derivative of position and given as:
v(t) = - ωA sin (ωt)
= - v₀ sin (ωt)
v₀= ωA is maximum velocity .
Acceleration is derivative of velocity and given as :
a(t)= - ω² A cos (ωt)= a₉ cos (ωt)
and a₉= ω²A is the maximum acceleration of the object.
Given: v₀= ωA= 5 m/s---(1) ; a₉= ω²A= 0.62 m/s²----(2)
From the given equation (1), we get
A) A= 5/ω
substitute this into the second equation, we find the angular frequency ω= 0.124
amplitude, A= 40.32m
B) As ω= 0.124 rad/sec
and angular frequency is related to the period as
T= 2π/ω
therefore, period , T = 2π/0.124
T= 50.67 sec
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regenerative braking uses the inertia of the vehicle to recapture energy during braking. where is this recaptured energy stored?
The kinetic energy lost during acceleration is converted back into electrical energy in the battery of the car.
What does energy mean?Electricity is regarded as having the capacity for effort by scholars. Modern civilisation is feasible because people have learned how to change energy from one form to another and then use it to complete activities.
What different types of energy exist?The six basic forms of energy are nuclear, chemical, electrical, radiant, mechanical, thermal, and thermal radiation. Studies on various kinds, such as electrochemical, acoustic, electromagnetic, and others, may be conducted.
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A single infinitely long straight piece of wire carrying a current I is split and bent so that it includes two half circular loops of radius R, as shown in the Figure. If current I1 goes through the top loop and current I2 through the lower loop (with I = I1 + I2) and if I2 = 2I1 what is the magnitude of the magnetic field at the center of the circle (k = µ0/4π)?
The magnitude of the magnetic field at the center of the circle (k = µ0/4π) is [tex]k\pi I/3R[/tex]..
Given a single infinitely long straight piece of wire is carrying a current I.
It is split and bent so that it includes two half circular loops of radius R.
Current [tex]I_{1}[/tex] goes through the top loop and current [tex]I_{2}[/tex] through the lower loop (with [tex]I=I_{1} +I_{2}[/tex]) and if [tex]I_{2}[/tex] = 2[tex]I_{1}[/tex].
Now, [tex]I=I_{1} +I_{2}[/tex]
⇒[tex]I=I_{1} +2I_{1}[/tex]
⇒[tex]I=3I_{1}[/tex]
∴[tex]I_{1}=I/3\\[/tex] and [tex]I_{2}=2I/3\\[/tex]
The magnitude of the magnetic field at the center of the circle is:
[tex]B_{z} = k\pi I_{2} /R - k\pi I_{1} /R[/tex]
[tex]B_{z} = k\pi (I_{2} - I_{1}) /R[/tex]
= [tex]k\pi I/3R[/tex]
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A coin rests on a turntable a distance r from the axis of rotation. The turntable rotates with a constant speed of v. What is the minimum coefficient of static friction between the turntable and the coin?.
The minimum coefficient of static friction between the turntable and the coin if the coin is not to slip is r (2πf)² / g .
How to calculate minimum coefficient of static friction between the turntable and the coin if the coin is not to slip ?Given ,
N=normal force acting on the coin
Normal force in the upward direction balances the weight of the coin, hence
N=mg
f=frequency of rotation Angular velocity of turntable is hence given as
w=2πf
r = distance from the axis of rotation
µ = minimum coefficient of static friction
static frictional force is given as
f= µN
f= µmg
The static frictional force provides the necessary centripetal force , hence
Centripetal force = Static frictional force
mrw² = µmg
rw² = µg
µ = rw²/g
µ = r (2πf)² / g
Therefore the minimum coefficient of static friction between the turntable and the coin if the coin is not to slip is r (2πf)² / g
The complete question is : A coin of mass m rests on a turntable a distance r from the axis of rotation. The turntable rotates with a frequency of f. What is the minimum coefficient of static friction between the turntable and the coin if the coin is not to slip?
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What are quotas simple definition?.
A quota is a trade restriction imposed by the government that limits the quantity of goods or the amount of money that a country may spend on them at one time for import or export.
Nations utilize quotas in international trade to regulate the volume of trade that takes place between them and other countries. A quota is a limit on the quantity of something or someone that is permitted or necessary.An import quota is a sort of trade restriction when a government places a cap on the quantity or price of a commodity that another country is allowed to bring into the country. A government may impose a quota, for instance, preventing a neighboring country from importing more than 10 tons of grain. A quota is the set limit on how much of something is legally permitted. Four tickets per person were no longer allowed; only two were now allowed.Thus this is the meaning of quota.
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Bridging Problem: Electric-Field Energy and Capacitance of a Conducting Sphere A solid conducting sphere of radius R carries a charge Q. Calculate the electric-field energy density at a point a distance from the center of the sphere for (a) R. (c) Calculate the total electric field energy associated with the charged sphere. (d) How much work is required to assemble the charge Q on the sphere? (e) Use the result of part (c) to find the capacitance of the sphere. (You can think of the second conductor as a hollow conducting shell of infinite radius.) (Figure 1) Where is the electric-field energy density greatest? Where is it least? Rank locations from strongest to weakest energy density. To rank locations as equivalent, overlap them. View Available Hint(s) Reset Help == ? F>ROSr< -> Greater Less Figure < 1 of 1 > The correct ranking cannot be determined. Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining
We know that capacitance due to spherical body having radius R will be C=4πEoR Now when solid sphere replaced by hollow conducing sphere the change will remain on the surface of same radius and hence:
The ability of a material object or device to store electric charge is referred to as capacitance.
1-use result is not affected as radius is same
at infinity V=KQ/r=KQ/∞=0
and potential due to charge sphere on the surface = kq/r Where k-9×10² Na²/c
Delta V=V(∞)-V®=0-kq/R
Delta v = q/4πEoR
for a sold conducting sphere, there is no electric
field inside the sphere. Hence the electric fielding!
(YXR) is zero.10 ,for r>R, U = 1/2 EoE², E=1/4πEoR Q/l^2 , U=1/2 Eo 1/(4πEoR )^2 Q^2/r^4
U(r<R),u(r>R)= o,1/2Eo(1/4πEoR)^2 (Q^2/r^4)
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calculate the rotational inertia of a meter stick, with mass 0.78 kg, about an axis perpendicular to the stick and located at the 17 cm mark. (treat the stick as a thin rod.)
The rotational inertia of a meter stick, with mass 0.78 kg, about an axis perpendicular to the stick and located at the 17 cm mark is 0.136 kg m²
Since the stick can be treated as a thin rod, the center of mass of the stick will be at its midpoint which is 0.5 m.
L = 1 m
M = 0.78 kg
I at center of mass Icm = M L² / 12
Icm = 1 * 0.78² / 12
Icm = 0.051 kg m²
From the center the 17 cm mark will be at a distance of,
d = 0.5 - 0.17
d = 0.33 m
I = Icm + M d²
I = 0.051 + ( 0.78 * 0.33² )
I = 0.051 + 0.085
I = 0.136 kg m²
Therefore, the rotational inertia is 0.136 kg m²
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one end of a string is attached to a vertical pole with the other end of the string attached to a ball that swings in a horizontal circular path, as shown. which of the following free body diagrams represents the forces exerted on the ball?
A ball is suspended from a string by its opposite end, which is fastened to a vertical pole and swings in a horizontal circle.
Weight of the ball = W
Tension in the string = T
There are only 2 forces acting on the ball it's own weight downwards and the tension on it from the string directed along the string.
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What will happen if the distance between the two objects is doubled?.
As indicated by Newton's law of attraction each article or body in the universe draws in every single item towards one another and that power of fascination is straight forwardly relative to the result of their masses and contrarily corresponding to the square of the distance between them.
The power of gravity between two articles will diminish as the distance between them increments. The two most significant elements influencing the gravitational power between two items are their mass and the distance between their focuses. As mass increments, so does the power of gravity, however an increment in distance mirrors a reverse proportionality, which makes that power decline dramatically.
At that point by Newton's All inclusive Law of Attractive energy;
F=GMm/R²
Where R is the distance between the bodies .
So , if R′ = 2R
Then, gravitational force,
F = G(Mm/R²)
After doubling the distance,
F′ = G{Mm/(2R)²} = G(Mm/4R²)
F = 4F′
Therefore, when we increase the distance between the two objects is doubled, then the gravitational force is increased four times.
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What is the acceleration due to gravity at a location where a 15. 0-kilogram mass weighs 45. 0 newtons?.
The acceleration due to gravity is 3 m/s^2
What is acceleration due to gravity ?The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity. M/s2 is its SI unit. Its vector nature—which includes both magnitude and direction—makes it a quantity. The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/s2.
An object's velocity changes when it falls freely toward the surface of the earth from a specific height. This acceleration is known as acceleration due to gravity and is symbolized by the symbol g.
In the given question
given is ; the weight = 45 N
and the mass = 15 kg
thus F = ma
or W = ma
a = W / m
a = 45 / 15
a = 3 m/s^2
thus acceleration due to gravity = a = 3 m/s^2
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what is the purpose of a voltage regulator and why is it needed in a circuit? how should the voltage regulator be wired to work properly?
Answer:
Any electrical or electronic device known as a voltage regulator keeps the voltage of a power source within allowable ranges. The voltage regulator is required to maintain voltages within the permitted range that the electrical equipment employing that voltage can tolerate. A device like this is frequently used in motor vehicles of all types to adjust the generator's output voltage to the electrical load and the battery's charging requirements. When there are too many voltage changes in electronic equipment, voltage regulators are also used.
The regulator should be connected properly as reverse polarity destroys the regulator almost instantly.
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consider the molecule below. determine the molecular geometry at each of the 3 labeled atoms. clccn has an o atom double-bonded to the first carbon (from left to right), an h atom attached to the second carbon with a wedge and an h atom attached to the second carbon with a dash. the n atom has an h atom attached with a wedge and an h atom attached with a dash. the n atom has a lone pair of electrons. the cl atom has three lone pairs. the o atom has two lone pairs. the first carbon is labeled as 1, the second carbon is labeled as 2, and the n atom is labeled as 3.
Each of the three named atoms' molecular geometry: NO "H Co 1-, 2-, and 3-trigonal planar; tetrahedral.
Describe an example of an electron.The tiniest and least massive component of an atom is an electron, which has a negative charge. In a neutral atom, the number of ions and neutrons is equal. For instance, the hydrogen atom only contains one proton and one electron. On the other hand, the uranium atom.
Why are there electrons in an atom?The atom's negatively charged particles are called electrons. An atom's whole population of electrons generates a negative electrical charge that counteracts the charge of the neutrons in the elementary particle. In comparison to the rest of the atom, electrons are quite tiny.
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the speed of light is the same for all observers, no matter what the speed of the observer or source
It is true that the speed of light in vacuum is is the same for all observers, no matter what the speed of the observer or source.
What is meant by the speed of light?It is a basic postulate of the Einstein's theory of relativity that speed of light is constant regardless of one's frame of reference. Value for the speed of light in vacuum is defined as 299,792,458 meters per second.
Speed of light can be divided into two parts:
speed of light is independent of the motion of observer. and that speed of light does not vary with time or place.To know more about speed of light, refer
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What are the advantages of quota?.
When researchers need to conduct research according to certain criteria, quota sampling is advantageous. Due to the method's filtering properties, quota sampling is extremely practical in this case.
The producers and the fortunate importers who obtain the pricey and in-demand import permits reap the full benefits of quotas. A quota differs from a tariff in this scenario. However, if import permits are put up for auction and sold to importers, the government would profit from the sale.
The sales quota is a tool to encourage the sales force's selling efforts and it sparks interest in the job. Sales quotas might be helpful when holding sales competitions. The basis for rewarding the sales team is performance relative to the sales quota.
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calculate the force of earth's gravity on a spacecraft 2.50 earth radii above the earth's surface if its mass is 1450 kg .
The force of earth's gravity on a spacecraft 2.50 earth radii above the earth's surface if its mass is 1450 kg is 1578.89. N
Force is a push or pulls upon an item because of the object's interaction with some other object. pressure is a power that can exchange the motion of an object. A force can reason an object with mass to alternate its speed, i.e., to boost up. pressure also can be described intuitively as a push or a pull. A force has each significance and course, making it a vector amount.
calculation:-
F = GMm/(Re + 2R)
= 1/9 GMm/Re²
Substituting g for GM/Re² in the above equation
Fg = 1/9mg
Substitute 1450kg for m and 9.8 m/s² for g in the above equation.
= 1/9(1450)(9.8 m/s²)
= 1578.89
The phrase 'Force' has a unique meaning. At this degree, it is absolutely appropriate to describe a force as a push or a pull. A force is not something that an object consists of or 'has in it. A force is exerted on one object through another. The concept of a force isn't always restricted to living matters or non-living matters.
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a man in a gym is holding an 8 kg weight at arm's length, a distnace of .55 m from his shoulder joint. what is the torque about his shoulder joint due to the weight if his arm is horizontal?
The center is where there is an acceleration. An 8.0 kg weight is being held at arm's length by a man at a gym, 0.55 m from his shoulder joint. If his arm is 43 N*m, what torque does the weight have on his shoulder
Explain what an acceleration is.acceleration is the rate of change in both speed and direction of velocity over time. When anything moves faster or slower in a straight line, it is said to have been accelerated.
What exactly are speed and acceleration?Acceleration. Velocity is the rate at which displacement changes. The pace at which speed changes is known as acceleration. Because it consists of both magnitude and direction, velocity is a vector quantity. Since acceleration is merely the rate at which velocity changes, it too is a vector quantity.
Torque = radius x perpendicular Force
[tex]Torque = rFsin(x) = 43 N*m.[/tex]
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how could you prove to a skeptic that the beats are an interference effect that requires both sound sources? test out your method to convince yourself that the beats require both sound sources and it is not a trick caused by one source alone.
Beats are interference patterns between two tones of different frequencies. To prove the skeptic first, play the recorded audio as there are no beats in it. Now take two sound sources with different frequencies. When both sources are turned on, we hear notes that rise and fall at equal intervals. That's what's called beats.
A frequency beat occurs when two waves with different frequencies overlap, causing alternating cycles of constructive and destructive interference between the waves.
When we tap the table with our finger, then put our ear to the table, and tap the table surface as far as 30 cm from our ear. Then the sound of beats on the table will sound louder when we put our ears on the table. So, it can be concluded that solid objects can conduct sound better than air. This is because the molecules or particles of solid objects are denser than air.
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which type of heat detector is activated by an increase in temperature in surrounding air that exceeds a set amount over a given period of time?
Rate-of-Rise Detector heat detector is activated by an increase in temperature in surrounding air that exceeds a set amount over a given period of time.
A warmth detector is a hearth alarm device designed to respond whilst the convected thermal electricity of a fireplace increases the temperature of a warmth-touchy detail. The thermal mass and conductivity of the detail regulate the price flow of heat into the detail. All warmth detectors have this thermal lag. warmness detectors have the foremost classifications of operation, "fee-of-upward thrust" and "constant temperature". the warmth detector is used to help in the discount of belongings damage.
this is the most commonplace sort of warmness detector. fixed temperature detectors perform whilst the heat-touchy eutectic alloy reaches the eutectic point converting the state from a solid to a liquid. Thermal lag delays the buildup of warmth at the sensitive detail in order that a set-temperature tool will reach its operating temperature sometime after the encompassing air temperature exceeds that temperature. The maximum common fixed temperature point for electrically connected warmth detectors is 58°C (136.4°F).
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A 0.60-kg ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.7 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N, what is the maximum speed the ball can have?
The maximum speed that the ball can have before the chord breaks is 14.57m/s.
The mass of the ball attached to the horizontal chord is 0.60 kg. The radius is 1.7m.
The maximum tension that the chord can sustain is 75N. After this the chord will break from the horizontal frictionless surface.
Because the chord is rotating, the tension will be equal to the centripetal force force, hence we can write,
Mv²/r = 75
Where,
v an r are speed and radius respectively.
Putting values,
0.60 x v²/1.7 = 75
v = 14.57 m/s.
So, the maximum speed of the ball can be 14.57 m/s.
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(17%) problem 5: consider a generator that rotates its 200 turn, 0.17 m diameter coil at 3300 rpm in a 0.95 t field. calculate the peak voltage of the generator. g
The peak voltage of the generator is 215.52 V.
Given,
Number of turns made by the generator, N = 200
Diameter of the coil = 0.17 m
So, the radius will be, r = 0.17/2 = 0.085 m
Frequency of the coil, f = 3300 rpm = 3300/60 rps
So, f = 50 rps
And the magnetic field, B = 0.95 T
The peak voltage of the generator can be calculated y the equation:
[tex]E_{0}[/tex] = N B A ω
= 200×0.95×π[tex]r^{2}[/tex]×50rps
= 200×0.95×3.14×0.085×0.085×50rps
= 215.52 Volt
Hence, the peak voltage of the generator is 215.52 V.
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What does it mean when rocks are magnetic?.
Magnetite is a special kind of rock. It sticks to magnets. Magnetite is made of a metal called iron. The iron is what sticks to magnets.
Pieces of the mineral magnetite that have been magnetized naturally are lodestones. They are magnets that are present in nature and may draw iron. Using lodestones, the phenomenon of magnetism was first discovered in antiquity. The best magnets for this test are rare earth magnets, which are inexpensive, widely available, and effective. However, there are earth rocks that can also hold a magnet, and to make matters worse, these rocks are fairly typical. Hematite and magnetite-containing rocks and minerals are the two types of rocks that are most frequently misinterpreted. For collectors and researchers, meteorites are highly valuable in terms of money and science. From a few dollars to hundreds of thousands of dollars, meteorite values can vary. Sedimentary, metamorphic, and igneous rocks all contain magnetite.
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A bullet penetrates through a wooden block and it’s velocity is doubled. What is the ratio between the bullet’s initial kinetic energy and final kinetic energy?
find the linear acceleration of block aa if there is no slipping between the cord and the surface of the wheel. express your answer in meters per second squared.
Linear acceleration of block aa is [tex]1.062 m/s^2\\[/tex].
Given,
Radius R=0.11 m
Moment of inertia I= 0.3kg[tex]m^2[/tex]
Net torque [tex]T_n_e_t = I\alpha[/tex]
[tex]= (I\alpha )/R[/tex]
So since there is no slipping, whatever is the acceleration of the block is the acceleration of the cord. And that acceleration will be the linear acceleration of the this linear acceleration of the pulley.
So let's just assume Ta. Is greater than Tb.
Ta [tex]\ge[/tex] Tb
(Ta-Tb)×R= I×(a/[tex]R[/tex])
Ta-Tb=(0.3×a)/[tex]0.11^2[/tex]
Ta-Tb = 24.8a ............(1)
(5.5×9.8) - Ta= 5.5a .......(2)
Tb-(2×9.8)=2a ............(3)
adding equation 1, 2, and 3 we get,
[tex]a_A=1.062 m/s^2[/tex]
[tex]a_B=1.062 m/s^2[/tex]
[tex]a=R\alpha[/tex]
[tex]\alpha =9.654 red/s^2[/tex]
T=(2×1.062)+19.6
Tb=21.724 N
Ta=48.06 N
Hence, Linear acceleration of block aa is [tex]1.062 m/s^2\\[/tex].
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A race-car of mass m negotiates a right hand 90o turn at constant speed v on a banked road that makes an angle θ with respect to horizontal. The radius of the turn is given by r and the time the car takes to go around the banked turn is t . The car makes the turn at high speed and, after making the banked turn, the car continues down a straight segment of road.
(A) Draw a free-body diagram which shows the forces acting on the car. Assume rolling friction and air drag are negligible (and that no propulsion force is required to maintain a constant speed). Include your coordinate axes in your drawing.
(B) Use Newton's second law to write an equation for the resulting centripetal force. Then solve the equation for the normal force of road on the tires in terms of: the mass of the car m, the radius of the curve r, time to make the curve t, banked angle θ , and any needed constants of proportionality. Simplify as possible.
(C) A race-car has a mass of 750kg and needs to take the 90o turn of radius 160m in 10.0 seconds regardless of the coefficient of static friction between the tires and the track. What should the minimum banking angle θ be?
The minimum banking angle θ be for the race-car has a mass of 750kg and needs to take the 90o turn of radius 160m in 10.0 seconds regardless of the coefficient of static friction is 21.94°.
No as the calculation :
V = regular speedN = ordinary response through the street at the tiresg = acceleration of gravityr = radius of the parththeta = banking perspectivem = mass Apply Newton's regulation withinside the vertical path we get N cos Θ= mg.Now and follow Newton's regulation withinside the horizontal path 2Now the time to make the curve is = t (given) on this time the automobile travels, s distance so the velocity of the automobile is given through from equation 2 we get.Now from equations 1 and 3, we get, This (equation four) is the simplified relation among the banking perspective, time and the radius of the path. Explanation for step 2.Apply Newton's regulation of motion Step 3/3(c).The way to every component is given in every step above.tan theta =21.94.Read more about Newton's second law:
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Which statements are true regarding resonance? Select all that apply. a. If there are two possible locations in a molecule for a double bond, then two of the electrons in that bond switch back and forth between the two locations. b. The "true" structure for a molecule that exhibits resonance is a blend of all of the possible resonance structures that can be drawn for the molecule. c. If there are unequivalent resonance structures for a given molecule, then the one that is the greatest contributor to the resonance hybrid is the lowest energy structure. d. All of the possible resonance structures for a given molecule that can be drawn exist in nature.
The statements that are true regarding resonance are, if there are two possible locations in a molecule for double bond, then two of the electrons in that bond switch back and forth between the two locations, the true structure for a molecule that exhibits resonance is a blend of all of the possible resonance structures that can be drawn for the molecule.
The resonance is the method of describing delocalized electrons within certain molecules. In this arrangement, bonding cannot be expressed by a single Lewis formula.
An ion with these delocalized electrons is represented by several resonance structures.
The effect of resonance is sharing of the double-bond character around the ring.
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A 1.8 kg uniform rod with a length of 90 cm is attached at one end to a frictionless pivot. It is free to rotate about the pivot in the vertical plane. The rod is held in the horizontal position and released from rest. Determine the rod’s linear density in SI units.
Determine the rod’s moment of inertia in SI Units.
Determine the initial angular acceleration of the rod. Determine the initial linear acceleration in the middle of the rod in SI Units.
Find the magnitude of torque in SI Units.
Answer:
ρ = 1.8 kg / .90 m = 2 kg / m linear density
Γ = m g L/2 = I α torque producing acceleration α
α = m g L/2 / I = m g L/2 / 1/3 m L^2 = 3 g / (2 *L)
α = 3 / 2 * 9.80 * / .90 s^2 = 16.3 / s^2 angular acceleration
a = L/2 α = .90 m / 2 * 16.3 / s^2 = 7.3 m/s^2 acceleration of middle of rod
A 1.8 kg uniform rod (90 cm long) pivots freely. Linear density = 2 kg/m. Moment of inertia = 0.486 kg m². Initial angular acceleration = 16.35 rad/s². Initial linear acceleration (middle) = 7.355 m/s². Torque = 7.95 Nm.
mass = 1.8 kg, length = 0.9 m
Linear density (ρ) = Mass / Length = 1.8 kg / 0.9 m = 2 kg/m
Moment of Inertia (I)-
For a uniform rod rotating about one end: I = (1/3) × m × L²
I = (1/3) × 1.8 kg × (0.9 m)² = 0.486 kg m²
Initial Angular Acceleration (α)-
Torque (τ) = I × α
Gravity provides torque
therefore, τ = m × g × L / 2
Equate the two torques and solve for α: α = (3/2) × (g / L) = (3/2) × (9.81 m/s² / 0.9 m) ≈ 16.35 rad/s²
Initial Linear Acceleration (a) at the Middle = a = α × L / 2
= 16.35 rad/s² × 0.45 m
≈ 7.355 m/s
Magnitude of Torque (τ) = I × α = 0.486 kg m² × 16.35 rad/s² ≈ 7.95 Nm
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if the string is 7.6 mm long, has a mass of 26 gg , and is pulled taut with a tension of 18 nn , how much time does it take for a wave to travel from one end of the string to the other?
If the string is 7.6 mm long, has a mass of 26 gg , and is pulled taut with a tension of 18 n then the wave take 0.104 s to travel from one end of the string to the other.
Given;
length of string, L = 7.6 m
mass of string, m = 26 g = 0.026 kg
tension on the string, T = 18 N
[tex]v = \sqrt{\frac{T}{m/L}}[/tex] where; v is the velocity of the wave
T is the tension on the string
m is the mass of the string
L is the length of the string
Thus, [tex]v = \sqrt{\frac{18}{0.026/7.6} }[/tex]
[tex]v = \sqrt{5294.11}[/tex]
[tex]v = 72.76[/tex]
Also velocity, v = distance / time
the distance the wave travels is equal to its length
[tex]v = \frac{l}{t}[/tex]
[tex]72.76 = \frac{7.6}{t}[/tex]
t = 0.104
Therefore, it will take the wave take 0.104 s to travel from one end of the string to the other.
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Add a third force that will cause the object to remain at rest. Label the new force.
The right response is to apply the new force F3 in the opposite direction of that of F2.
I have to first look for the issue in order to understand the forces. Along this instance, forces operating on an item in the vertical axis are acting in both the same direction and the opposing direction. F2 is down while F1 is up.
We must determine the length difference between F1 and F2 in order to build the vector F3 that will cancel the resulting force and allow the item to come to rest. We will have the F3 module in this fashion. The smaller of the two forces will be in this direction.
F3 will point in the same direction as F2 if F2 > F1.
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