Just as waves spread out when a boat moves in water or a stone is thrown in a pond, gravitational waves are distortions in the curvature of space-time caused by motions of matter that propagate with the speed of light.
It turns out that one type of gluon chain behaves in the four-dimensional spacetime as the graviton, the fundamental quantum particle of gravity. In this description, gravity in four dimensions is an emergent phenomenon arising from particle interactions in a gravityless, three-dimensional world.
Since matter carries energy, such objects will have a gravitational field and so they will distort space-time. So one way in which a charge or a magnet will distort space-time is by virtue of its matter.
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the forearm in the figure(figure 1) accelerates a 3.2 kg ball at 7.5 m/s2 by means of the triceps muscle, as shown. a) Calculate the torque needed. Ignore the mass of the arm. Answer in m*Nb) Calculate the force that must be exerted by the triceps muscle. Answer in N
The calculated answer for the torque is 7.812 Nm and the force is 25.2 N
In the given question, we have to find the torque needed and the force exerted by the triceps muscle.
We know that, when there is a net torque on the system, it causes angular acceleration and the angular momentum is no more conserved.
Here let be the arm is massless.
The torque can be written as
τ=Iα
Where I is the moment of inertia.
α is the angular acceleration.
So,
τ=mR^2 α
τ=mRa
Here we have used the relationship between angular and tangential acceleration, which is: α=a/R.
The position vector is: R = 0.31
The mass is: m =3.6
The tangential acceleration is: a =7 m/s2
So, the torque will be,
τ=3.6*0.31*7
=7.812
So, the required torque is 7.812 Nm.
And we know that torque is: τ=F.R
So, force is F = τ/r
= 7.812/0.31
=25.2 N
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What is 4-dimensional Euclidean space?
How can there be 4 mutually perpendicular directions?
In mathematics, a Euclidean space is a geometric space in which the distance between two points is measured using the Euclidean distance formula. In 4-dimensional Euclidean space, there are 4 mutually perpendicular directions, which are commonly referred to as the x, y, z, and w directions. These directions are perpendicular to each other, meaning that they form right angles with one another.
The concept of 4-dimensional Euclidean space can be difficult to visualize, as it is a concept that exists beyond our everyday three-dimensional world. However, we can think of it as an extension of three-dimensional space, in which there is an additional direction (the w direction) that is perpendicular to the x, y, and z directions. This additional direction allows for the representation of additional information or variables in the space.
For example, in four-dimensional Euclidean space, we could represent the position of a point using four coordinates (x, y, z, w) rather than just three (x, y, z). This additional coordinate could represent a variety of different quantities, such as time, energy, or some other physical property.
The brakes of a 1000kg car exert 3000N. How long will it take the car to come to a stop from a velocity of 30meter per second and how far will the car travel during this time?
If the car is traveling at 30 meters per second, it will take 10 seconds to halt. A 1,000 kilogram car's brakes produce 3000 N of force.
Which is greater, velocity or speed?In contrast to speed, velocity represents the direction and speed of an object's motion since it follows a path. As a result, velocity is a vector, whereas speed is a scalar.
What distinguishes speed from acceleration?The rate at which a displacement varies is measured by its velocity. Accelerated speed changes are experienced. Its velocity is an vector quantity since it is composed of two parts. Acceleration is also a vector quantity since it is simply the rate about which velocity varies.
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An air-filled parallel-plate capacitor has plates of area 2.60 cm2 separated by 2.50 mm. The capacitor is connected to a(n) 17.0 V battery. (a) Find the value of its capacitance. pF (b) What is the charge on the capacitor? рC c) What is the magnitude of the uniform electric field between the plates? N/C
a) The value of its capacitance is 0.90 pF
b) The charge on the capacitor is 15.3 pC
c) The magnitude of the uniform electric field between the plates is 6.8 N/C.
given that :
are of the parallel plate capacitor = 2.60 cm²
distance d = 2.5 mm
potential = 17 V
a) The value of its capacitance is :
C = Eo A / d
= ( 8.85 × 10⁻¹² C² / N . m ) ( 2.60 × 10⁻⁴ m²) / 2.50 × 10⁻³
= 0.90 × 10⁻¹² F
= 0.90 pF
b) The charge on the capacitor is :
q = CVo
q = 0.90 × 10⁻¹² F × 17 V
q = 15.3 × 10⁻¹² C
q = 15.3 pC
c) The magnitude of the uniform electric field between the plates is :
E = Vo / d
E = 17 / 2.50 × 10⁻³
E = 6.8 N/C
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the de broglie wavelength of a 0.0810 gram bullet traveling at the speed of 658.3 m/s is m.
The de broglie wavelength of the bullet of mass 0.081 g is 1.24×10⁻³⁸ m
What is wavelength?Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space or along a wire.
To calculate the de broglie wavelength, we use the formula below.
Formula:
λ = h/mv................... Equation 1Where:
λ = de broglie wavelength of the bulletm = Mass of the bulletv = Velocity of the bulleth = Planck's constantFrom the question,
Given:
h = 6.62×10⁻³⁴ J/Hzm = 0.081 = 0.000081 kgv = 658.3 m/sSubstitute these values into equation 1
λ = (6.62×10⁻³⁴)/(0.000081×658.3)λ = 1.24×10⁻³⁸ mHence, the de broglie wavelength of the bullet is 1.24×10⁻³⁸ m
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131 53i is an artificially made radioactive isotope of iodine, produced during the operation of nuclear power plants and the detonation of nuclear bombs. exposure to high concentrations of 131 53i represents a serious risk for human health. however, small doses of this radioactive isotope are put to good use in medical studies. 131 53i is widely used in treating thyroid cancer and in diagnosis of abnormal liver and kidney function.
Part A
What is emitted when the radioactive nucleus of 131 53I decays to form the stable isotope of xenon 131 54Xe?
part B
What is the energy Q released when 131 53Idecays and 131 54Xe is formed? The atomic mass of 131 53I is 130.906118 u and the atomic mass of 131 54Xe is 130.90508 u.
Part C
The newly formed xenon nucleus is left in an excited state. Thus, when it decays to a state of lower energy a gamma ray is emitted. If the wavelength of the emitted gamma ray is 3.44×10−12 m , what is the decrease in mass, ΔmXe, of the xenon nucleus as a result of this decay?
A . The emitted particle is β⁻.
The radiactive isotope ¹³¹ I ₅₃ decays into ¹³⁵Xe₅₄ by emitting a beta particle and an information .
¹³¹ I ₅₃ --> ¹³⁵Xe₅₄+ β⁻ +v + Q
Therefore, The emitted particle is β⁻.
B .the energy Q released when 131 53I decays and 131 54 Xe is formed is 0.966MeV
Q= Δmc²
= (130.906118u - 130.90508u - 0.32*10⁻⁴u)(931.5MeV/c²)
= 0.966MeV
C . the decrease in mass, ΔmXe, of the xenon nucleus is 3.87*10⁻⁴ u.
= hc/λ
= [tex]\frac{(6.625*10^{-34} )(3*10^{8} m/s)}{3.44*10^{-12} }[/tex]
= 0.3605 MeVj
Δm = (0.3065)MeV([tex]\frac{1u}{931.5Mev/c^{2} }[/tex])
= 3.87*10⁻⁴ .
Mass is a quantitative measure of inertia in physics and a fundamental property of all matter. In effect, it is the resistance that an object offers to changes in velocity or position when a force is applied. The greater the mass of an object, the smaller the change caused by an applied force.
Mass can be experimentally defined as the inertia of a body, a measure of its resistance to acceleration (change in velocity) when a net force is applied. An object's mass also determines the strength of its attraction to other bodies. size. A 2kg cast iron weight used for scales. The decrease in mass, ΔmXe, of the xenon nucleus is 3.87*10⁻⁴ u
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A fighter jet is traveling at 515m/s directly away from a communication antenna that broadcasts at 406 MHz. What change in frequency does the fighter jet observe?
The fighter jet notices a change in frequency of 697 Hz.
rom Doppler's effect, f' = f(1 - u/c)
Here, c denotes the speed of light, u is the speed of the fighter jet, and f is the frequency of the antenna's broadcast.
so, f' = f(1 - u/c)
⇒f'/f = 1 - u/c
⇒(f - f')/f = u/c
⇒∆f = fu/c
so change in frequency, ∆f = fu/c
now f = 406 × 10⁶ Hz , u = 515 m/s and c = 3 × 10^8 m/s
so, ∆f = (406 × 10^6 × 515)/(3 × 10^8)
= 69696.67 × 10^-2
= 696.9667 Hz ≈ 697 Hz
Because of this, the fighter jet measured a 697 Hz change in frequency.
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A fighter jet is traveling at 515m/s directly away from a communication antenna and that broadcasts at 406MHz.
The antenna is a device that is used for transmitting and receiving signals, which represent some information. antennas play a major role in the case of wireless communication system as the antenna effectively converts electromagnetic waves to electronic signals. antennas are the basic components of any electrical circuit, because it provides interconnecting links between transmitter and free space or free space and receiver.
The purpose of an antenna is to collect and convert electromagnetic waves to electronic signals. In communication antenna, the same antenna can be used for both transmission and reception.
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(a) In unit-vector notation, what is the torque about the origin on a particle located at coordinates (0 m, -2.0 m, 2.0 m) due to force F1 with components F1x = 5.0 N and F1y = F1z = 0?(b) In unit-vector notation, what is the torque about the origin on a particle located at coordinates (0 m, -3.0 m, 2.0 m) due to force F2 with components F2x = 0, F2y = 3.0 N, and F2z = 5.0 N?
The torque about the origin is [tex]$2.0 \mathrm{Nm} \hat{i}-8.0 \mathrm{Nm} \hat{j}-12.0 \mathrm{Nm} \hat{k}$[/tex].
What is torque?
Torque[tex]$\vec{T}$[/tex] is the cross product between force [tex]$\vec{F}$[/tex] and vector position [tex]$\vec{r}$[/tex] respect a fixed point (in our case the origin):
[tex]\vec{\tau}=\vec{r} \times \vec{F}$$[/tex]
There are multiple ways to calculate a cross product but we're going to use most common method, finding the determinant of the matrix:
[tex]$\vec{r} \times \vec{F}=-\left[\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ F 1_x & F 1_y & F 1_z \\ r_x & r_y & r_z\end{array}\right]$[/tex]
[tex]\begin{aligned}& \vec{r} \times \vec{F}=-\left(\left(F 1_y r_z-F 1_z r_y\right) \hat{i}-\left(F 1_x r_z-F 1_z r_x\right) \hat{j}+\left(F 1_x r_y-F 1_y r_x\right) \hat{k}\right) \\& \vec{r} \times \vec{F}=-((0(2.0 m)-0(-3.0 m)) \hat{i}-((4.0 N)(2.0 m)-(0)(0)) \hat{j}+((4.0 N)(-3.0 m)- \\& 0(0) \hat{k}) \\& \vec{r} \times \vec{F}=-2.0 N m \hat{i}+8.0 N m \hat{j}+12.0 N m \hat{k}=\vec{\tau}\end{aligned}[/tex]
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In a period of 1.00 s, 5.00×1023 nitrogen molecules strike a wall with an area of 8.00cm2. Assume the molecules move with a speed of 300 m/s and strike the wall head-on in elastic collisions. What is the pressure exerted on the wall? Note: The mass of one N2 molecule is 4.65×10−26kg.
A wall with an area of 8 cm² is struck by 5.00 x 10²³ nitrogen molecules over the course of 1 s. Assume that the molecules are moving at a speed of 300 m/s and colliding with the wall in an elastic manner. The pressure acting on the wall is 17.43 kPa.
Mass in motion is a definition of momentum. Mass and velocity are multiplied to determine momentum. That is, p = mv where p,m, and v denotes momentum, mass, and velocity.
Given the change in the time period, Δt is 1 second, the number of nitrogen molecules is 5.00×10²³ molecules, the change in velocity Δv is 300 m/s, and the area is 8×10⁻⁴ m².
The momentum of one molecule is given as 2mΔv. Then, the momentum of N molecules is 2NmΔv.
The force exerted on the wall by nitrogen molecule is written as,
[tex]\begin{aligned}\text{Force F}&=\frac{\Delta\text {momentum}}{\Delta t}\\&=\frac{2Nm\Delta v}{\Delta t}\end{aligned}[/tex]
Then, the pressure exerted by nitrogen molecule on the wall is,
[tex]\begin{aligned}P&=\frac{F}{A}\\&=\frac{2Nm\Delta v}{\Delta t\times A}\\&=\frac{2\times 5\times10^{23}\times4.65\times10^{-26}\times300}{8\times 10^{-4}\times 1.00}\\&=\mathrm{17.43\;kPa}\end{aligned}[/tex]
Therefore, the required answer is 17.43 kPa.
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Consider a pendulum swinging. Which type(s) of energy is/are associated with the pendulum in the following instances: i. the moment at which it completes one cycle, just before it begins to fall back towards the other end, ii. the moment that it is in the middle between the two ends, iii. just before it reaches the end of one cycle (just before instant i.).
i. potential, ii. kinetic, iii. potential and kinetic
In the following situations, the type(s) the energy is/are related to the pendulum: potential kinetic potential,kinetic
When someone is kinetic, what does that mean?When an organism moves as a result of a stimulation like light, this is known as kinesis. Being able to use one's own internal kinesis power is what it means to be kinetic. Kinetics have such a supernatural ability, just like Telekinetics, Psychokinetics, and those who have Extra Sensory Perception.
What is it that makes kinetic energy move?Kinetic energy is the energy that any item has with a result of motion. An item can only be accelerated through the application of a force. Applying force requires effort on our part. Following completion of the work, energy is transmitted to the object, which then moves at the a new, consistent rate.
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the surface of the water in the rotating tank is perpendicular to the effective gravitational force. the surface force on the mass element due to the rest of the fluid is perpendicular to the surface. the fluid is in static equilibrium in the rotating frame: (part a) use newton's second law in the rotating frame to find an equation for , the angle of the water's surface from the horizontal.
Angular momentum and effective gravitational force about the mass center. For a rigid body rotating on a fixed axis with respect to its center of mass.
How does effective gravity become calculated?The gravitational acceleration g = F / m can also be used to express gravity. Since the acceleration is constant for all masses m, m need not be included in the expression when using the gravitational acceleration instead of the gravitational force.
In fluid mechanics, what does g Effective mean?It should be noted that a brand-new "effective gravity" vector, G, has been established as the vector sum of gravity and the opposite of the acceleration vector. With a little trigonometry, we can calculate the new effective gravity vector, which is the resultant vector of adding g and -a.
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an electron in a cathode-ray tube is accelerated through a potential difference of 10 kv, then passes through the d
The field strength that will deflect the electrons is 2.93*10^-3 T or 2.93mT.
Calculation:
from figure
sin(o) =d/r
r =d/sin(o) =1.6/sin8 =11.5 cm
from conservation of energy
qV =(1/2)mv^2
[tex](1.6*10^-19)(10*10^3)=(1/2)(9.11*10^-31)*v^2[/tex]
[tex]v=5.93*10^7 m/s[/tex]
and
r = mv/qB
= [tex]B =mv/qr =(9.11*10^-31)*(5.93*10^7)/(1.6*10^-19)(11.5*10^-2)[/tex]
B = 2.93*10^-3 T or 2.93mT.
An electron is a subatomic particle with a negative elementary charge. Electrons belong to the first generation of the leptonic particle family and are generally considered elementary particles because they have no known composition or substructure. In the standard model of particle physics.
Electrons are the smallest particles that make up an atom and have a negative charge. In neutral atoms, the number of protons and electrons is the same, and are considered elementary or elementary particles. electrons belong to a group of elementary particles called leptons.
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in the instant of fig. 11-41, two particles move in an xy plane. particle p1 has mass 6.5 kg and speed v1 2.2 m/s, and it is at dis- tance d1 1.5 m from point o. particle p2 has mass 3.1 kg and speed v2 3.6 m/s, and it is at distance d2 2.8 m from point o. what are the (a) magnitude and (b) direction of the
The magnitude and direction of net angular momentum of particles is [tex]52.7kg.m^2/s[/tex] out of the page.
Given,
particle 1:-
Mass ,m1 = 6.5 kg
speed , v1 = 2.2 m/s
distance from point O, d1 = 1.5 m
Particle 2:-
Mass ,m2 = 3.1 kg
speed, v2 = 3.6 m/s
distance from point O, d2 = 2.8 m
Angular momentum can be determined by formula,
p=mvd
angular momentum of particle-1, [tex]\rho_1=6.5*2.2*1.5=21.45 kg.m^2/s[/tex]
angular momentum of particle-2, [tex]\rho_2=3.1*3.6*2.8=31.248 kg.m^2/s[/tex]
Then, the net angular momentum is
[tex]\rho=\rho_1+\rho_2=21.45+31.248=52.69kg.m^2/s[/tex]
The direction of angular momentum of particle is always perpendicular to the motion of particle, as the particles are moving on xy-plane then the their direction will be perpendicular to xy-plane i.e. z-plane, it means out of the page.
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Your question is incomplete, here is the complete question.
In the instant shown in the diagram, two particles move in an xy-plane. Particle P1 has mass 6.5 kg and speed v1 = 2.2 m/s, and it is at distance d1 = 1.5 m from point O. Particle P2 has mass 3.1 kg and speed v2 = 3.6 m/s, and it is at distance d2 = 2.8 m from point O. What is the magnitude and direction of net angular momentum of the two particles about O?
A) 52.7 kg · m2/s out of the page B) 52.7 kg · m2/s into the page C) 21.5 kg · m2/s into the page D) 9.8 kg · m2/s into the page E) 9.8 kg · m2/s out of the page
❧ What are the uses of mirrors and other reflecting surfaces?
Mirrors and other reflecting surfaces can be used in the following way; used in kaleidoscopes, periscopes which are widely used in submarines, used in headlights to reflect parallel rays of light in a straight line etc.
What is a mirror?A mirror is a reflecting surface that reflects light almost totally and does not allow it to refract, producing a clear image. It produces either real or virtual images.
Types of MirrorsPlane Mirror - These are made by putting some reflective substance like silver nitrate onto a piece of glass. When we place an object in front of a plane mirror, an image is formed by reflection.
Concave - It is a mirror that is bent inside at its center. The law of reflection also holds for the concave mirror, but the angle of incidence is not equal to the angle of reflection. A concave mirror can produce a real or virtual image in front of it at its point of focus.
Convex - is also called a diverging mirror. The reflective surface of the convex mirror is slightly extended towards the source of light. A convex mirror can reflect all rays falling on it in the outward direction. It produces a virtual image. The size of the image produced by this kind of mirror is smaller than the actual object.
Uses of mirrorsA plane mirror is used in kaleidoscopes. Plane mirrors are also used in periscopes which are widely used in submarines.They are used in headlights to reflect parallel rays of light in a straight line. Convex mirrors are used as side mirrors in vehicles because they form erect images and cover wider views. Plane mirrors are also used in flashlights and torches to give the source light a straight path. They are also used in microscopes to reflect the beam of light. Plane mirrors are used in solar cookers because they excellently reflect solar rays.Learn more about mirrors:https://brainly.com/question/20331340
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An object is undergoing simple harmonic motion along the x-axis. Its position is described as a function of time by x(t) = 1.6 cos(3.5t - 1.4), where x is in meters, the time, t, is in seconds, and the argument of the cosine is in radians.
a) Find the amplitude of the simple harmonic motion, in meters.
b) What is the value of the angular frequency, in radians per second?
c) Determine the position of the object, in meters, at the time t = 0.
d) What is the object s velocity, in meters per second, at time t = 0?
e) Calculate the object s acceleration, in meters per second squared, at time t = 0.
f) What is the magnitude of the object s maximum acceleration, in meters per second squared?
The amplitude of the object is 1.6m, the angular speed, position, velocity and acceleration of the object at t = 0 ate 3.5rad/s, 0.256m, 4.459m/s and 3.136m/s² and the maximum acceleration is 19.6m/s².
The object is undergoing Simple Harmonic Motion along x-axis and its position is described by,
x(t) = 1.6cos(3.5t-1.4)
t is the time.
(a) The standard equation of simple harmonic motion is,
X = Acos(wt)
So, comparing the given equation with the standard equation, we get,
Amplitude = 1.6m.
(b) Again comparing the given equation with standard equation, we get the angular velocity as,
W = 3.5rad/s.
(c) To find the position of the object at t=0,
Putting t=0 in x(t) = 1.6cos(3.5t-1.4).
x = 1.6cos(-1.4)
x = 1.6 × 0.16
x = 0.256m.
(d) To find the speed of the object,
Differentiating x(t) = 1.6cos(3.5t-1.4) with respect to x,
v(t) = 1.6sin(3.5t-1.4)3.5
Putting t = 0
v(t) = 1.6 x -0.98 x 3.5
v(t) = 4.459m/s.
(e) To find the acceleration of the object,
Double Differentiating x(t) = 1.6cos(3.5t-1.4) with respect to x,
a(t) = -1.6(3.5)²cos(3.5t-1.4)
Putting t = 0,
a(t) = -1.6 x (3.5)² x 0.16
a(t) = 3.136m/s².
(f) For maximum acceleration,
cos(3.5t-1.4) = 1
a(t) = -19.6m/s².
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Use Eq. (9.20) to calculate the moment of inertia of a uniform, solid disk with mass M and radius R for an axis per- pendicular to the plane of the disk and passing through its center
Circular disc's moment of inertia around axis passing through mass and parallel to disc Icm=MR22
Explain about the moment of inertia?The phrase "moment of inertia" in physics refers to the precise calculation of a body's inertia with respect to rotation, or the resistance a body exhibits when a torque is applied to alter its rate of rotation around an axis (turning force).
It is a broad (additive) property: the moment of inertia for a point mass is equal to the mass squared by the perpendicular distance from the axis of rotation. Because it resists rotational motion, the moment of inertia is referred to as such and not as a moment of force.
Moment of inertia is the propensity of an object to continue rotating at a constant speed or in a condition of rest. More torque is needed to shift this state the higher the moment of inertia.
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find the tension in each cord in the following figure, if the weight of the suspended object is 100 n. (make a free body diagram).
T a = 573.77 N and T b = 702.7 N are the tensions in the system's cords A and B, respectively.
What is meant by tension?A rope, string, or cable that is stretched under an applied force develops a force known as a tension force in physics. In the opposite direction of the force imparted to the rope or cable, tension is exerted along its whole length. Other names for tension include stress, tensity, and tautness.
The force transferred through a rope, string, or wire when pushed by forces acting from opposite sides is referred to as tension. The tension force is applied along the entire length of the wire and exerts an equal amount of strain on the bodies at each end.
Something can stretch under tension. Something gets squeezed together through compression. Only materials having the ability to resist forces are useful. Similar to how water moves through a pipe, force moves through a material.
We have to solve the system of equations:
- T a × cos 60° + T b × sin 45° - 210 N = 0
- T a × sin 60° + Tb cos 45° = 0
------------------------------------------------------
- 1/2 T a + √2 / 2 T b = 210 N
- √3 / 2 T a + √ 2 / 2 T b = 0 / * ( - 1 )
---------------------------------------------------
- 1/2 T a + √2 / 2 T b = 210 N
√ 3 / 2 T a - √2 / 2 T b = 0
----------------------------------------
T a ( √3 / 2 - 1 / 2 ) = 210 N
0.366 T a = 210 N
T a = 210 N : 0.366
1 ) T a = 573.77 N
Ta × √3 / 2 = T b × √ 2 / 2
T b = ( 573.77 × 1.732 ) : 1.4142
2 ) T b = 702.7 N
The complete question is:
Find the tension in each cord in the figure if the weight of the suspended object is w = 210N
A) Find the tension in the cord A for system (b).
B) Find the tension in the cord B for system (b).
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If the speed of every atom in a monatomic ideal gas were doubled, by what factor would the Kelvin temperature of the gas be multiplied?
a) 4
b)2
c)1
d) 1/2
e) 1/4
If the given speed of any atom in a monatomic state of an ideal gas were doubled, then by using four factor we would multiplied the Kelvin present temperature of the gas. Option (a) is correct.
We recollect a monatomic best fueloline having debris of mass m that don't engage and whose middle of mass stays at rest. For a monatomic best fueloline (which include helium, neon, or argon), the most effective contribution to the strength comes from translational kinetic strength. The common translational kinetic strength of a unmarried atom relies upon most effective at the fueloline temperature and is given through the equation: Kavg = 3/2 kt.
These are helium, neon, argon, krypton, xenon, and radon. Noble gases have a complete outer valence shell making them as an alternative non-reactive species. Many gases which include nitrogen, oxygen, hydrogen, noble gases, a few heavier gases like carbon dioxide and combinations which include air, may be dealt with as best gases inside affordable tolerances over a significant parameter variety round widespread temperature and pressure.
We know that,
K.E = (1/2) m*[tex]V^{2}[/tex]
If we doubled the speed then 2*2=4 times its affect the temperature.
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1. There is a spacecraft in the form of a ball of radius R and mass M, uniformly distributed over the volume. We investigate the rotation around an axis passing through the center of the spacecraft such that a set of engines with masses m1, m2, m3 lies in the plane of rotation. Each engine can give angular acceleration eps_i. The initial rotation speed w is given.
a) Investigate different variants of angular accelerations for one motor (constant, variable). Solve the basic equation of rigid body dynamics, see if the rotational velocity can be zeroed out.
(b) Investigate different arrangements of orientation control motors (one, two, three, different angles between them). Investigate the issue of the fastest settling of rotation - just parametrically set the angular accelerations and see if the time in which the velocity is zeroed out decreases.
2. There is a spacecraft in the form of a cylinder of length L and radius R, combined with a cone of base radius R and height h (similar to Apollo). The mass of the cylinder is M1, the mass of the cone is M2, each mass is evenly distributed over the volume. The rotation occurs around the axis passing through the longitudinal axes of the cylinder and cone. The initial velocity of rotation w is set. Similarly to point 1, calm the rotation. The location of the orientation control motors and the form of angular accelerations are at the student's discretion. It will be necessary to independently write out the moment of inertia of the spacecraft relative to the longitudinal axis. It is desirable to give as much as possible the opportunity to adjust the parameters of the problem.
p.s.
You may write program in Python or use Mathcad/Matlab.
a) The basic equation of rigid body dynamics for angular motion is I * alpha = Sum(T), where I is the moment of inertia of the spacecraft, alpha is the angular acceleration, and T is the sum of the torque applied by the motors.
For constant angular acceleration, the equation becomes I * eps = Sum(T), where eps is a constant value. If we assume that all the motors have the same constant angular acceleration, the equation becomes I * eps = m1eps1 + m2eps2 + m3*eps3.
For variable angular acceleration, we need to integrate the equation of torque with respect to time, to get the angular velocity. The equation becomes I * dw/dt = Sum(T)
To zero out the rotational velocity, we need to apply a torque that is equal and opposite to the initial angular momentum of the spacecraft. The torque can be achieved by adjusting the angular accelerations of the motors in such a way that the angular momentum is cancelled out.
b) Different arrangements of orientation control motors (one, two, three, different angles between them) can affect the speed of settling the rotation. For example, having three motors at 120 degrees apart will provide a more stable and efficient way of canceling out the angular momentum, compared to having only one motor.
The fastest settling of rotation can be achieved by parametrically setting the angular accelerations of the motors in such a way that the angular momentum is cancelled out as quickly as possible. This can be achieved by adjusting the torque applied by each motor, the direction of the torque, and the location of the motors relative to the center of mass of the spacecraft.
To calm the rotation of the spacecraft in the form of a cylinder and cone, we need to find the moment of inertia of the spacecraft relative to the longitudinal axis. The moment of inertia of a cylinder is given by I = 1/2 * M1 * R^2 + 1/12 * M1 * L^2 and the moment of inertia of a cone is given by I = 1/10 * M2 * R^2 + 1/3 * M2 * h^2.
The location of the orientation control motors and the form of angular accelerations are at the student's discretion. To achieve the fastest settling of rotation, the student needs to adjust the torque applied by each motor, the direction of the torque, and the location of the motors relative to the center of mass of the spacecraft. The student can also adjust the parameters of the problem such as the mass, length, radius and height of the spacecraft, the initial rotation speed, and the angular acceleration of the motors.
What is rotation around an axis?Rotation around an axis refers to the movement of an object in which it spins around a fixed point or axis. In physics, rotation is defined as a change in the orientation of an object in space with respect to a fixed reference point. The fixed point or axis around which the object is rotating is known as the axis of rotation.
Rotation can be characterized by several properties, such as angular velocity, which describes the rate of rotation, and angular displacement, which describes the total angle through which the object has rotated. The rotational motion of an object can be described by the equations of rotational dynamics, which include the moment of inertia and torque, which describe the forces and energy involved in the rotation.
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what happens when light passes from air into water? does it slow down; when light travels from glass to air; when light travels from air to glass the ray of light bends; when light travels from air to glass what happens to the speed; when light travels from air to water does wavelength change; what happens when light travels from air to water; light refraction; what happens to a light ray when it travels from water into air?
When light passes from air into water, it slows down and bend towards the normal.
When light travels from glass to air its speed increases and bend away from the normal.
When light travels from air to glass, speed decreases.
When light travels from air to water wavelength increase as refractive index of air is less than the water.
When light travels from water into air, its speed increases and it bend away from the normal.
Refraction is defined as the bending of light at the surface of two media when it changes medium of propagation.
When light passes from an optically rarer medium to optically denser medium. its speed decreases and it bend towards the normal. When light passes from the denser medium to a rarer medium, its speed increases and it bends away from the normal.
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Scientists have been able to develop a nuclear fusion plant to generate energy.
True or False
Answer: true
Explanation:
A proton accelerates from rest in a uniform electric field of 640 N/C. At some later time, its speed is 1.20 x 10% m/s (nonrelativistic, because v is much less than the speed of light).
(a) Find the acceleration of the proton.
(b) How long does it take the proton to reach this speed?
(c) How far has it moved in this time?
(d) What is its kinetic energy at this time?
a) The acceleration of the proton is 6.4×10¹⁰ m/s².
b) Time taken is 1.875×10⁻⁵ second .
c) It moved in this time is 11.25 meter.
d) its kinetic energy is 1.15×10⁻¹⁵ Joule.
What is electric field?The force per unit charge exerted on a positive test charge that is at rest at a given position is the force per unit charge that is used to define the electric field analytically.
uniform electric field: E = 640 N/C.
its speed is: v= 1.20 x 10⁶ m/s
a) the acceleration of the proton = qE/m
= (1.6×10⁻¹⁹×641)/(1.6×10⁻²⁷) m/s²
= 6.4×10¹⁰ m/s²
b) Time taken = (1.20 x 10⁶ / 6.4×10¹⁰)second = 1.875×10⁻⁵ second .
c) it moved in this time = ( 1.20 x 10⁶×1.875×10⁻⁵ )/2 meter = 11.25 meter.
d) its kinetic energy = mv²/2 = (1.6×10⁻²⁷)(1.20 x 10⁶)²/2 joule = 1.15×10⁻¹⁵ Joule.
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what is the sound intensity level of a sound with an intensity of 2.4ร10โ6 w/m2 ?; what is the sound intensity level of a sound with an intensity of 4.0ร10โ6 w/m2 ?; what is the sound intensity level of a sound with an intensity of 3.2ร10โ6 w/m2 ?; what is the sound intensity level of a sound with an intensity of 3.6ร10โ6 w/m2 ?; from a distance of 4.0 m, a bystander listens to a jackhammer breaking concrete.; an opera singer in a convertible sings a note at 600 hz while cruising down the highway at 90km hr
The sound intensity level of a sound with an intensity of 3.6 is 63.8 dB.
Calculation:-
[tex]10 log(\frac{2.4 * 10^{-6} }{1*10^{-12} }) = 63.8dB.[/tex]
Power per unit area carried by the shaft. Sound intensity level A unitless quantity that indicates the sound level relative to a fixed reference. Sound pressure level ratio of pressure amplitude to reference pressure. which has a higher sound intensity than the sine wave.
Intensity refers to the speed at which a task is performed or the amount of effort required to perform an activity or exercise. A square wave consists of an infinite number of odd harmonics, while a sawtooth wave consists of odd and even harmonics. As a result of the experiment, it was found that the square wave has a higher sound intensity than the sawtooth wave.
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students attach a force probe in the middle of string a to measure ta and then use a different force probe to provide the applied force f to the box of mass m1. with the box of mass m3 held in place by one student, a second student pulls to the left on the force probe that provides the applied force f. as the second student pulls with a steady force, and with the boxes remaining at rest, the following pairs of readings from the two force probes are recorded at different times. Time F(N) TA (N) ti 10.6 11 10 10.4 10.2 10.8 10 11 t5 10.6 11 Based on the measurements above, how do the magnitudes of the two force quantities compare? The two quantities exactly agree numerically. The two quantities agree within experimental uncertainty but do not exactly agree numerically. The two quantities disagree by an amount that is larger than the experimental uncertainty. The two quantities cannot be compared because the two force probes have different levels of precision.
The magnitudes of the two force quantities after comparing the two quantities agree within experimental uncertainty but do not agree numerically.
What is applied force?One of the most prevalent forms of force is applied force, which is the force we exert on objects with our hands, legs, or any other item. As an illustration, push a chair with some force to move it in a certain direction.
According to Newton's second equation of motion, an object's force is equal to its mass times its acceleration, or F = m × a.
Use Newtons for force, kilograms for mass, and meters per second squared for acceleration when applying this formula.
Given that, time F(N) TA(N)
t₁ 10.6 11
t₂ 10.4 10
t₃ 10.2 10
t₄ 10.8 11
t₅ 10.6 11
Thus, The mean value of F is: 10.52 N
The mean value of TA is: 10.6 N
So, the two quantities agree within experimental uncertainty but do not agree numerically.
Thus, the two quantities cannot be compared because the two force probes have different levels of precision.
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If the mass of a satellite is doubled while the radius of its orbit remains constant, the speed of the satellite is a increased by a factor of 2 b. reduced by a factor of 2. c. 8 reduced by a factor of 8. d. increased by a factor of 8. e. not changed.
If the mass of the satellite is doubled and the radius of orbit is remains same then the speed of the satellite is constant.
The speed at which a body orbits the system's center, which is typically a planet or a natural satellite, is known as its orbital speed. Typically, this system is centred on a large body. The earth orbits the sun at a speed of 108,000 kilometres per hour.
Through the provided formula, it is linking the mass of a specific planet to the gravitational constant and radius. The "universal gravitational constant," G, is a constant that appears in the orbital speed formula. It is worth 6.673 10 11 Nm2 kg2. The radius of the Earth is 6.38 x 106 metres.
we know that the orbital speed is
Vo = sqrt(G*M/R)
wher M is mass of the Earth not the mass of the satellite
and R is radius of the orbit
so the speed will be same not changed
Hence, the correct option is e.
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Cardiopulmonary resuscitation is a procedure used to deliver oxygenated blood to the brain when the heart is no longer beating.
Responses
False
False
True
Answer: True
Explanation:
Cardiopulmonary resuscitation (CPR) is a medical procedure involving repeated compression of a patient's chest in an attempt to restore the blood circulation and breathing of a person who has suffered cardiac arrest.
the average late afternoon temperature in downtown areas is approximately ____ warmer than rural areas.
Late afternoon temperatures in metropolitan areas are typically 5°F higher than those in rural areas.
Urban areas are often flat and devoid of greenery. Most renewable energy is used to warm surfaces because there is often not much water available for evaporation.
In comparison to plants, buildings and other structures may retain more heat throughout the day. At night, they release some of this heat, which helps to increase the temperatures when it becomes dark outside. Cities could also reflect less sunlight, allowing them to receive more of the Sun's heat.
If you live there, the surface of a town or city will absorb more insulation than a forest or the damp soil surface of a hamlet.
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The gravitational force between two bodies varies inversely as the square of the distance between them. If the force between two bodies is 18 N when the distance between them is 10 km, find the fource between the bodies when the distance between them is 7.5 km.
The statement states that the force between both the bodies at a distance of 7.5 km equals F = 32 N.
What is gravitational force?This force that earth applies to a body is referred to as gravitational force. Its down motion of water in the river, the downwards motion if water in a stream, or an upwards motion of a ball being thrown are examples of motion brought on by gravitational influence.
Briefing:F = k/d² where k is the inverse variation's constant.
18 N = k / (10 km)²
18 N = k / 100 km²
k = (18 N) (100 km²)
k = 1800 (N)(km²)
F = ?
d = 7.5 km
k = 1800 (N) (km²)
F = 1800 (N)(km²) / (7.5 km)²
F = 1800 (N) (km²) / (55.25 km²)
F = 32 N
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the distances to the nearest 100,000 or so stars can be measured by which of the following techniques? group of answer choices redshift triangulation brightness-distance techniques radar ranging measuring tape
Triangulation can be used to calculate the separations between the closest 100,000 or so stars.
What is the triangulation method of measuring distance?A surveying technique called triangulation measures the angles of a triangle made up of three survey control sites. The additional dimensions there in triangle are determined using geometry and the reported length of always one side.
Why is the procedure of triangulation used?A process of analyzing study results using many data collection methods is known as triangulation. It serves three key functions: to improve validity, to paint a clearer image of a study problem, and to examine various approaches to problem-solving.
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what activates a convection current, starting the flow of a fluid?
Temperature differences in the mantle activate a convection current, starting the flow of a fluid.
What is convection current?Convection currents are a natural process of heat transfer that involves the movement of energy and heat from one location to another. We can see this in action by placing our hands above a campfire and feeling hotter. This is caused by convection currents.Convection currents transfer heat from one location to another by utilizing the mass motion of a fluid such as water, air, or molten rock. The heat transfer function of convection currents drives ocean currents, atmospheric weather, and geology.When a liquid is heated, it expands, becoming less dense or lighter and rising. As lighter hot liquid rises, cooler liquid from the top takes its place at the bottom. Therefore in the liquids convection currents are formed.To learn more about convection current refer to :
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