The final velocity of the rocket is Vf = Vi < 5/4, -1/2 >. Hence, Option E is the correct answer.
We have a mass of the rocket = m
The velocity of the rocket = vi
The rocket is traveling in the x-direction and the fuel is ejected in the y-direction.
mass of the fuel= m/5
the speed at which the fuel is ejected= 2vi
Now, let us find the final velocity along the x-direction i.e. vx
[tex]m_{rocket}[/tex] * vi = [tex](m_{rocket} -m_{fuel})[/tex] * vx
m*vi = (m-m/5)vx
m*vi = (4/5)m*vx
hence, we have vx = (5/4) vi
Similarly, along the y- direction,
0 = [tex]m_{fuel}[/tex] * 2vi + [tex](m_{rocket} -m_{fuel})[/tex]vy
0 = m/5 * 2vi + (m-m/5)vy
0 = m/5 * 2vi + (4/5)m * vy
(4/5)m * vy = - m/5 * 2vi
(4/5)m * vy = - m/5 * 2vi
vy = -(1/2)vi
Hence, the final velocity is vf = vi <5/4, -1/2>.
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The complete question is-
Rocket final velocity | Problem A rocket with total mass m-is in deep space, traveling with velocity vi in the x-direction. The rocket suddenly shoots some of its fuel out in the y-direction at the speed 2vi. The mass of the fuel is 1/5 the total mass of the rocket. Which of the following could be the final velocity of the rocket?
O V = V; <-1/2,5/4> ما O Ve = V; <1/2, -5/4> O V+ = V; <4/5, -1/2> O V1 = V; <-4/5, 1/2> O V = V; <5/4, -1/2> O V+ = V; <-5/4, 1/2>
a horizontal force of 330 n is exerted on a 2.5-kg ball as it rotates (at arm's length) uniformly in a horizontal circle of radius 0.90 m. Calculate the speed of the ball!
According to given question by applying the centripetal force, the speed of the ball is 12.18 m/s.
What does force, in brief, mean?The definition of force in physics is: This push or draw on a massed object changes its velocity. An unseen factor is an agency that has the power to alter the resting or movement condition of a body. It has both a trajectory and a size.
What are examples of force?There are several instances of energies in daily life, including: heft and drive (i.e. the weight of something) is force a swing applies to a ball. the pressure that a hair applies to hairs when stroking it. the pressure your foot applies to the pedal whenever you're riding your bike.
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calculate the amount of charge incoloumbs that flows through an electric heater in 20 mins when the ucrrent is 8 amps
Q is the energy in coloumbs that passes through with an current heater in 20 minutes at an 8 amp current.
What's current?Charge moves across a point on the a circuit at a rate known as current. When numerous coulombs of charge pass over a wire's cross section in a circuit, a large current is the result. if the wire is tightly packed with charge carriers.
What is the current recipe?The electric current equation is I=V/R, and it can be used to determine electric current. This equation, which is based on Ohm's Law, is also referred to as the "current equation." The variables "I" and "V" stand for current, voltage, and resistance, respectively.
Briefing:I=8Amph,
T=1hr=3600sec,
Charge flow Q=it
=8*3600
Q=28800C
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The capacitors in each circuit are fully charged before the switch is closed. Rank, from longest to shortest, the length of time the bulbs (resistors) stay lit in each circuit.
(picture)
The idea here is to simplify circuit analysis by using resistors and capacitors. Using the time constant for every circuit, rank the circuits from longest to shortest. The circuit's time constant is ranked as follows: C > A = E > B > DC > A = E > B > D.
A capacitor is a device that stores electrical energy in an electric field by building up electric charges on two nearby surfaces that are isolated from one another. It has two terminals and is a passive electronic part.
Capacitance is the name for a capacitor's effect. While there is some capacitance between any two electrical conductors that are close to one another in a circuit, a capacitor is a component made to increase capacitance. Condenser is still used in a few compound names for the capacitor, like condenser microphone. Capacitors are made from a wide range of materials and come in a wide variety of shapes, sizes, and designs. They all have at least two electrical conductors, known as plates, separated by an insulating layer (dielectric).
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The angular speed of a motor is 262 rad/s. The back emf generated by the motor is 89.4 V. Assuming all other factors remain the same, determine the back emf if the angular speed of the motor is reduced to 131 rad/s.
1) 32.3 V
2) 44.7 V
3) 52.5 V
4) 89.4 V
5) 152 V
The back EMF of the motor is 44.7 m.
We know that EMF is directly proportional to angular velocity, thus if angular velocity becomes half then the EMF also becomes half.
Number of field poles = p
Flux per pole = Ф
Number of armature conductor = Z
Number of parallel paths = A
Rotational Speed in rpm = n
Now,
Average EMF generated per conductor = dФ/dt
Flux cut by one conductor in one revolution = dФ = pФ Weber
Number of revolutions per second = N/60
Time required for one revolution = t
= t = dФ/dt = ( pФN ) /60 sec
EMF generated per conductor = dФ/dt = ( pФN ) /60 Volts
The EMF generated in one conductor of the generator. The conductors are connected in series per parallel path, and the emf across the generator terminals is equal to the generated emf across any parallel path.
Thus,
= E = ( pФNZ ) /60 Ampere
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Light is emitted when an electron:
makes a transition to a lower energy level.
The electron in an atom is boosted to a higher orbit and excited. When the electron returns to its original state, it de-excites and emits a photon of light.
When the electron changes levels, it decreases energy and the atom emits photons. The photon is emitted with the electron moving from a higher energy level to a lower energy level.
The electron absorbs the energy and jumps to a higher energy level. In the reverse process, emission, the electron returns to the ground state by releasing the extra energy it absorbed. Recall that the electrons must occupy one of the energy levels.
The electrons in an atom exist in various energy levels. When an electron moves from a lower energy level to a higher energy level, energy is absorbed by the atom. When an electron moves from a higher to a lower energy level, energy is released.
When an electron falls from a higher energy to a lower energy level, it accelerates. We know accelerating charged particle radiates energy in the form of electromagnetic radiation.
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what is currently the most used trajectory strategy to maximize efficiency for modern space probe interplanetary travel?
The typical goal is to maximize the portion of the spacecraft not used for propellant or, alternatively, to minimize the amount of propellant needed.
What is interplanetary travel?
Crewed or uncrewed interplanetary spaceflight, often known as "interplanetary travel," is the movement between stars and planets, typically within a single planetary system. In actuality, these kinds of spaceflights are limited to interplanetary travel only.
What is the trajectory?
A moving object that follows a path through space as a function of time is said to be following a trajectory. A "trajectory" is a description of an object's position over a specific period of time in mathematics.
The typical goal is to maximize the portion of the spacecraft not used for propellant or, alternatively, to minimize the amount of propellant needed. Of course, as is frequently the case in continuous dynamical system optimization, it is typically necessary to provide some reasonable upper bound for the final time; otherwise, the optimizer will substitute time for fuel.
Therefore, The typical goal is to maximize the portion of the spacecraft not used for propellant or, alternatively, to minimize the amount of propellant needed.
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assuming the crate weighs 100 lbs, calculate the tension in each example and explain if a directional advantage exists or not.
Tensions in each examples are, T=222.264 N, T=0 T=148.176 N, T=111.132 N.
Given,
m=100lbs,=45.46 kg
(a) 2T= mg
T=mg/2
=(45.46×9.8)/2
T=222.264 N
(b) For pulley
2T= mg
T=mg/2
T=222.264 N
For pulley 2:
2T=[tex]W_p_u_l_l_e_y[/tex]=0
T=0
(c) Here 3T=mg
T=mg/3
T=148.176 N
(d) Pulley 1:
3T=mg
T=148.176 N
Pulley 2:
T-(-T)=0
2T=0
T=0
(e) Pulley:
4T=mg
T=mg/4
T=111.132 N
From the above cases we can say that the directional advantages exist as the tension get divided to those string which are connected to that weight only.
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Particle 0 experiences a repulsion from particle 1 and an attraction toward particle 2. For certain values of d_1 and d_2, the repulsion and attraction should balance each other, resulting in no net force. For what ratio d_1/d_2 is there no net force on particle 0?
Express your answer in terms of any or all of the following variables: k, q0, q1, q2.
d1/d2 =
I need help with this please. I will rate expert. I only have one try left. I get that p1 has a weaker effect on p0 than p2 because it is further away. Here are the answers I tried:
When there is no net force on the particle 0, the value of d₁/d₂ is √(q₂/q₁).
The distance of the particle 0 from the particle 1 is d₁ and the distance of the particle o from the particle 2 is d₂.
The particle 0 is experiences attraction from particle 2 and repulsion from particle 1.
The charges on the particle 1 and particle 2 are q₁ and q₂ respectively.
So, to experience no net force, the electrostatic forces on the particle 0 from both the particles should be equal, so we can write,
F₁ = F₂
Kq₁q₂/d₁² = Kq₁q₂/d₂²
Now, rearranging the equation,
d₁/d₂ = √(q₂/q₁)
So, the ratio of the distances is given as √(q₂/q₁).
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Compared to an electron in the first electron shell of an atom an electron in the third shell.
They have more energy. One 1s orbital and two electrons are contained within the first shell. 8 electrons are located in the second shell, with 2 in a 2s orbital and 6 in three 2p orbitals.
What is a electron in an atom?The elementary electric charge of the electron is a negative one, making it a subatomic particle. Due to their lack of components or substructure, electrons, which are part of the lepton particle family's first generation, are typically regarded to be elementary particles.Electrons are fundamental to many physical processes, including gravity, electromagnetic interactions, weak interactions, electricity, magnetism, chemistry, and thermal conductivity.For neutrally charged species, the number of electrons in an atom is equal to the atomic number of an element. This indicates that an element has an equal amount of protons and electrons. Consequently, there are 8 electrons in oxygen.Three basic characteristics of an electron in an atom are charge, spin, and orbital angular momentum, the latter of which describes the electron's orbital motion around the nucleus.To learn more about electron refer :
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We usually think about friction as a force that opposes motion, but under some circumstances it can be the force responsible for making an object accelerate. For example, consider hauling a log in the back of a flatbed truck. If there were no friction between the log and the truck, then when the truck accelerates the log would have no force acting on it to make it accelerate also, so it would just stay at rest and the truck would 'drive out from under it'! However, in reality there is friction between the log and the truck and so, providing the log does not slip, we rely on the static frictional force to make the log accelerate at the same rate as the truck.
The frictional pressure opposes the movement of an item relative to its floor in contact unto which the force act upon.
However, the course of frictional pressure can be similar to the course of movement of the item. For example, at some point of on foot we observe a pressure withinside the backward course with our foot. When we carried out brake to the auto friction acts in contrary course of movement like if the auto circulate in east course the friction will act in west course.
We can say that friction act in contrary course hence,it continually opposes relative movement. Friction continually acts in contrary course to motion i.e it opposes the movement of an item. Air resistance is a frictional pressure which opposes movement thru air.
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A large pendulum with a 200-lb gold-plated bob 12 inches in diameter is on display in the lobby of the United Nations building. The pendulum has a length of 75 ft. It is used to show the rotation of the Earth-for this reason it is referred to as a Foucault pendulum.What is the least amount of time it takes for the bob to swing from a position of maximum displacement to the equilibrium position of the pendulum? (Assume that the acceleration due to gravity is g=9.81m/s2 at the UN building.)t=________s
The bob swings from a position of greatest displacement to the pendulum's equilibrium position in the least period of time possible is 2.4 seconds.
How does the time period change when the bob's displacement increases?As a result, the mass of the bob has no effect on the basic pendulum's time period. As a result, the pendulum's period is unaffected if the bob's mass rises.
when the mean position of a simple pendulum's bob is altered?A simple pendulum's bob is moved from its equilibrium position O to a position Q that is h heights above O, and then it is let go. assuming the bob's mass to be m and time period of oscillations to be 2 s, the tension in the string, when the bob passes through O
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Constants Periodic Table Learning Goal: First, let us consider an object launched vertically upward with an initial speed v. Neglect air resistance. To apply the law of conservation of energy to an object launched upward in Earth's gravitational field. In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is one particular case of the law of conservation of energy. Part A As the projectile goes upward, what energy changes take place? Both kinetic and potential energy decrease. In this problem, you will apply the law of conservation of energy to different objects launched from Earth. The energy transformations that take place involve the object's kinetic energy K = (1/2)mv2 and its gravitational potential energy U = mgh. The law of conservation of energy for such cases implies that the sum of the object's kinetic energy and potential energy does not change with time. This idea can be expressed by the equation Both kinetic and potential energy increase. Kinetic energy decreases; potential energy increases. O Kinetic energy increases; potential energy decreases. K+Ui = K+Uf Submit Request Answer where "i" denotes the "initial" moment and "f" denotes the "final" moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem. Part B Complete previous part(s) Part C Complete previous part(s)
A As the projectile goes upward, what energy changes take place the energy is gravitational energy.
At the beginning, the projectile can have kinetic electricity because of the preliminary velocity, and we know, via way of means of conservation of electricity, that if there may be no friction withinside the air, the kinetic electricity of the item could be converted into gravitational capability electricity because the peak increases.
In Part A As the projectile goes upward, what energy changes take place then the energy change is gravitational energy change.
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on a rainy day the coefficient of friction between a car's tires and a certain level road surface is reduced to half its usual value. the maximum safe speed for rounding the curve is
The Maximum safest speed to travel at when navigating a curve is 71% of the normal speed.
What impact does rain have on friction coefficient?In comparison to friction on a dry road, the friction coefficient of tyres sliding at 60 km/h on roads will rise during times of heavy rain and reduce on a wet road after a period of rainfall.
How does friction change on a wet surface?Water can change the amount of friction between two surfaces. Rubber tyres and paved roads have less friction when there is water present. Drivers must therefore take extra precautions to avoid sliding on slick roads. Water can make contact between your fingers and a plastic sheet more abrasive.
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imagine that a car drives from the bottom to the top of a hill. if the initial and final values of each property below remain constant, which of the following represent state functions in this scenario? that is, which properties do not depend on the path taken to reach that specific value. select all that apply.
State function is the property do not depend on the path taken to reach that specific value.
As, we know the property or a feature which does not rely upon the course is known as a state characteristic. Work-achieved in adiabatic processes is equal to the bad of trade in inner power from the primary regulation of thermodynamics. So, it is a state function.
Path functions are houses or portions whose values rely on the transition of a machine from the preliminary kingdom to the final state. the two most common path functions are warmth and paintings.
From all of the above given thermodynamic quantities, work is the best property which depends at the course accompanied by using the system i.e. on the preliminary and the final states of the system. on the opposite, the rest all others i.e. internal energy, enthalpy and entropy are path independent.
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if you see a lightning bolt in the distance and 15 seconds elapse before you hear the corresponding thunder, how far away was the lightning bolt?
The distance of the lightning bolt from the point is 850m
What is speed of sound in air?The speed of sound is defined as the distance through which a sound wave’s point, such as a compression travels per unit of time. The speed of sound remains the same for all frequencies in a given medium under the same physical conditions.
We can use echo formula to calculate the distance at which the sound in air travels. it is given by v= 2x/t
where v is the speed of sound in air which is 340m/s and x is the distance traveled and t is the time.
therefore,
340= 2x/5
2x= 1700
x= 1700/2
x= 850m.
Therefore the distance of the lightning bolt to the point of staying is 850m.
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Compare the probabilities for an oscillating particle in its ground state to be found in a small interval of width dx at the center of the well and at the classical turning points.
Pturning points
----------------------
Pcenter=?
I don't even know where to begin. Show work please.
the probabilities for an oscillating particle in its ground state to be found in a small interval of width dx at the center of the well and at the classical turning points is as the Pturning points is e times smaller than Pcenter.
The probability of finding the particle in a small interval of width dx around the point x (at the center of the well) is---
P (x) = |(x)|²dx
P (x) = (mωo/hπ)½ e^[(-mωo/h) *x²] dx
Putting in the values of x=0 and x=+_xo , we can compare the probabilities of the particle being in the center and of it being at the turning point, respectively
P (x=0) =(mωo/hπ)½ dx.........at center
P (x=+_xo) =(mωo/hπ)½ e-¹ dx.........at turning points
From this, we can see that the probability for the particle to be found at the turning point s is e times smaller than at the center.
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Compare that speed with the Sun's orbital speed around our galaxy. Based on your comparison, do you think the galaxy's gravity would be strong enough to retain the supernova debris if there were no interstellar medium to slow it down?
Supernova debris moves about 100 times faster than the Sun. The gravity of galaxy alone would not retain the supernova debris.
Supernova debris moves about 100 times faster than the Sun. The gravity of galaxy alone would not retain the supernova debris.
A planet's orbital velocity modifications, depending on how far it's far from the solar. The closer a planet is to the solar, the more potent the sun's gravitational pull on it, and the quicker the planet actions. The farther it's far from the sun, the weaker the Solar's gravitational pull, and the slower it moves in its orbit.
Hubble's law, which says certainly that a galaxy's speed is directly proportional to its distance, additionally tells us some thing important approximately the country of the universe. If the universe is static and unchanging, there should be no correlation among distance and pace.
They must come to be greater turbulent. It produces so much visible light that it is opaque and blocks our view of anything beyond it. It reflects most light from far distances of the galaxy away from our line of sight. A star starts offevolved its time on the principle sequence with 10 solar loads.
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draw a phasor diagram, showing v1 , v2 , and vs . state the phase relationships between each pair of these phasors.
The least interference when (A1 - A2)2 is the phase difference between adjacent slits.
What do you understand the term phasor?A phasor is a complex number that represents a sinusoidal function in physics and engineering whose amplitude, angular frequency, & beginning phase are all time-invariant. Phasors are revolving vectors with an angular rate similar to a angular frequency of a oscillations and a length equal to a peak value of the oscillations. When illustrating the phase relationship between the two or more oscillations, they are useful. They can be used to add or eliminate oscillations.
What's a phasor diagram?Phasor diagrams show an oscillating quantity as a rotating vector in phase space with an angular velocity equal to the original trigonometric function's angular frequency. The value of the quantity at a given moment can be determined by projecting the phasor onto an axis at that time.
Briefing:Let A1 represent the first wave's amplitude and A2 represent the second wave's amplitude.
Let the resultant amplitude be A. Using the interference formula, we obtain,
A= (A1)²+(A2)²+ 2×A₁× A₂ (cos theta)
When theta = 180 degrees = π radian, cos π= -1
When we plug the cos theta value into the equation, we get,
A= (A1)² +(A2)² - 2×A1×A2
A= ( A1 -A2)²
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the drill used by most dentists today is powered by a small air-turbine that can operate at angular speeds of 350000 rpm. these drills, along with ultrasonic dental drills, are the fastest turbines in the world-far exceeding the angular speeds of jet engines. suppose a drill starts at rest and comes up to operating speed in 2.2 s . you may want to review (pages 305 - 307) .
The angular acceleration of the drill is 2651.5 rotation/s².
We need to know about angular acceleration to solve this problem. The angular acceleration can be defined as the change in angular speed per interval of time. It can be written as
α = dώ / dt
where α is angular acceleration, dώ is change in angular speed and dt is interval of time.
From the question above, the given parameters are
ώ = 350000 rpm
t = 2.2 s
Change the angular speed unit to rotation per second
ώ = 350000 rpm
ώ = 350000 / 60 rps
ώ = 5833.33 rps
Find the angular acceleration
α = dώ / dt
α = 5833.33 / 2.2
α = 2651.5 rotation/s²
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find the frequency of revolution of an electron with an energy of 100 ev in a uniform magnetic field of magnitude 35.0 mt.
The frequency of revolution of an electron with an energy of 100 ev in a uniform magnetic field of magnitude 35.0 mt is 9.78 x 10^5 Hz
What is cyclotron frequency?
A charged particle travelling perpendicular to the direction of an even magnetic field has a frequency that is known as the cyclotron frequency or gyrofrequency (constant magnitude and direction). The cyclotron frequency is determined by the centripetal force and magnetic Lorentz force being equal because that motion is always circular.
Kinetic Energy of the electron = 100 ev
= 100×(1.60×10^−19 J)
= 1.60×10 ^−17 J
The expression of kinetic energy of the electron in terms of the velocity-
E = mv^2/2
v = (2E/m)^1/2
Putting the values in the above expression we obtain the value of v,
v = ( 2 x 1.60 x 10 ^−17/ 9.1 x 10^-31)^1/2
= 5.92 x 10^6 m/s
The radius of the circular path the electron moves inside a magnetic field is given as-
r = mv / eB
Putting the values we find,
r = (9.11×10^−31 kg)(5.92×10^6m/s)/ (1.6 x 10^-19 C)(35 x 10^-6 T)
= 0.963 m
The orbital frequency is same as the velocity of the electron when it moves over the circular path, which is given as-
f = v / 2πr
= (5.92×10^6 m/s)/2π(0.963 m)
= 9.78 x 10^5 Hz
Hence, the required frequency is 9.78 x 10^5 Hz
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what height does a frictionless playground slide need so that a 35 kg child reaches the bottom at a speed of 6.3 m/s ?
The height of the frictionless playground slide is 2.155 meters
What is kinetic and potential energy ?An object possesses kinetic energy when it is in motion. A force needs to be applied if we want to accelerate an object. We must use effort to apply a force. The object will be moving at a new constant speed once the operation is finished and energy has been transferred to it.
Potential energy is a form of stored energy that is dependent on the arrangement of a system's components. When stretched or squeezed, a spring has higher potential energy. When lifted above the ground, a steel ball has more potential energy than when it is brought to rest on the ground.
Kinetic energy = Potential energy
K. E = 0.5m v² ; P.E = mgh
0.5mv² = mgh
Dividing both sides by m, we get ;
gh = 0.5v²
h = [(0.5v²) ÷ g]
h = (0.5 × 6.5²) ÷ 9.8
height = 2.155 m
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find the critical angle for a water-air boundary. predict the path of a beam of light moving from underwater towards the surface at the critical angle.
The critical angle at the air-water boundary [tex]\theta _{c}=sin-1(1/1.33) =48.6 degree[/tex].
The critical angle can be calculated from Snell's law by setting the refraction angle For each angle of incidence less than the critical angle some of the incident light is transmitted and some are reflected. Total internal reflection occurs when the angle of incidence at the water-air boundary exceeds 48.8 degrees.
The critical angle in optics is the maximum angle at which a ray of light traveling in a transparent medium can strike the boundary between that medium and a second medium with a lower refractive index without undergoing total internal reflection in the first medium angle.
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a container has the mass of 125g when a liquid is added the mass becomes 163g what is the mass of the liquid
A person pulls a block across a rough horizontal surface at a constant speed by applying a force F The arrows in the diagram correctly indicate the directions, but not necessarily the magnitudes of the various forces on the block: Which of the following relations among the force magnitudes Wk, N and F must be true? (a) F = k and N = W. (b) F = k and N > W, (c) F < k and N = W. (d) F > k and N < W. (e) None of the above:
The relations among the force magnitudes Work, k, N and F is none of the above.
What is force?
Force is the push or pull on any given object that can change the velocity of the object. It has both magnitude and direction which has the formula F = ma, where F is force, m is mass and a is acceleration.
Let the force be at angle θ to be horizontal. The block is in equilibrium, so
∑Fx = 0
F cosθ - k = 0
F = k secθ (> k)
∑Fy = 0
F sinθ + N -W = 0
N = W - F sinθ (<W)
Therefore, the relation of force magnitudes can be written as F>k and N<W, the correct answer is e).
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suppose that hiring one, two, three, or four workers at a glass factory generates total outputs of 200, 350, 450, or 500 fancy glasses, respectively. the marginal product of the fourth worker is fancy glasses.
If hiring one, two, three, or four workers at a glass factory generates total outputs of 200, 350, 450, or 500 fancy glasses, respectively. The marginal product of the fourth worker is 50 fancy glasses
Marginal product = ( Qn - Qn-1 ) / ( Ln - Ln-1 )
Qn = Output at n
Qn-1 = Output at n - 1
Ln = Number of workers at n
Ln-1 = Number of workers at n - 1
For the fourth worker,
Qn = 500
Qn-1 = 450
Ln = 4
Ln-1 = 3
Marginal product = ( 500 - 450 ) / ( 4 - 3 )
Marginal product = 50 / 1
Marginal product = 50
Therefore, the marginal product of the fourth worker is 50 fancy glasses
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Two speakers are placed side by side and driven by the same frequency of 0.50 kHz. If the distance from a person to one speaker is 5.0 m and the person detects little or no sound, which of the following is a possible the distance from the person to the other speaker? The sound speed in the room is 340 m/s
The possible distance from the person to the other speaker is c) 8.1m
To determine the possible distance we first convert the frequency from kHz to Hz as follows;
As 1 kHz = 1000 Hz
Therefore; 0.50 kHz = 0.50 × 1000 = 500 Hz
Now we determine the wavelength as follows;
wavelength = v ÷ f
wavelength = 340 ÷ 500
wavelength = 0.68 meters
Half wavelength = 0.5 × wavelength = 0.5 × 0.68 = 0.34 meters
For the sound interference to be destructive, the second source must be an odd multiple of 1/2 wavelength away from the first, therefore we calculate the possible distance from the person to the other speaker as follows;
distance between the person and speaker + odd multiple of wavelength = possible distance from other speaker
5 m + 0.34 m = 5.34 m
5 m + 3 × 0.34 m = 6.02 m
5 m + 5 × 0.34 m = 6.7 m
5 m + 7 × 0.34 m = 7.38 m
5 m + 9 × 0.34 m = 8.06 m
5 m + 11 × 0.34 m = 8.74 m
The value closest to any options provided above is 8.06 m therefore the correct option is 8.1 m.
Although a part of your question is missing, you might be referring to this question:
Two speakers are placed side by side and driven by the same frequency of 0.50 kHz. If the distance from a person to one speaker is 5.0 m and the person detects little or no sound, which of the following is a possible distance from the person to the other speaker? The sound speed in the room is 340 m/s
a) 8.4 m
b) 9.1 m
c) 8.1 m
d) 7.7 m
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an ethernet cable is 3.90 m long and has a mass of 0.190 kg. a transverse pulse is produced by plucking one end of the taut cable. the pulse makes four trips down and back along the cable in 0.835 s. what is the tension in the cable?
One end of the taut cable is pulled, causing a transverse pulse to be created. In 0.835 seconds, the pulse travels four times down the cable and four times back then the tension in the ethernet cable is determined as 67 N.
It is given to us that -
Ethernet cable is 3.90 m long => l = 3.90 m
and has a mass of 0.190 kg => m = 0.190 kg
It is also given that the transverse pulse makes four trips down and back along the cable in 0.835 s.
=> time taken, t = 0.835 s
We have to find out the tension in the cable.
We know that
Speed = Distance/Time ----- (1)
Since the transverse pulse applied on the ethernet cable makes four trips down and back along the cable, the total distance travelled by the pulse = 4 * (2l)
Now, using equation (1) we can find out the speed of the pulse by -
[tex]v = \frac{4*2*3.90}{0.835} \\= > v = 37.36[/tex] m/s ---- (2)
We also know that the mass density of the pulse can be determined by the formula -
μ = [tex]\frac{m}{l}[/tex] ------ (3)
where,
m = mass of the cable
l = length of the cable
Substituting the given values of mass and length of the cable in equation (3), we can find out the mass density of the pulse as -
μ = [tex]\frac{m}{l} = \frac{0.190}{3.90} = 0.048[/tex] kg/m ------ (4)
We also know that the tension in the cable can be represented by the formula -
T = μ[tex]v^{2}[/tex] ----- (5)
Substituting the values of v and μ from equations (2) and (4) respectively, we can find out the tension in the cable as -
T = μ[tex]v^{2}[/tex]
=> T = 0.048 * [tex](37.36)^{2}[/tex]
=> T = 67 N
Thus, the tension in the ethernet cable is determined as 67 N.
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The block moves up an incline with constant speed. What is the total work W. Total done on the block by all forces as the block moves a distance L = 3.40 m up the incline? Include only the work done after the block has started moving at constant speed, not the work needed to start the block moving from rest.
Since the block is moving at a constant speed there is no change in kinetic energy. Since work is the change in kinetic energy and there is no change, the net work on the block is zero.
There is no change in kinetic energy because the block is travelling at a steady pace. The net work on the block is 0 since work is the change in kinetic energy, and there is none.
.kinetic energy. is the ONE of the energy. that an object has as a result of motion. It is defined as the effort necessary to move a mass-based body from rest to the given velocity. In the absence of a change in speed, the body retains the kinetic energy it acquired during acceleration. Kinetic energy is the energy that is present in a moving object. You strolling down the street, molecules moving in space, and the planet rotating around the sun all have kinetic energy. The relationship between an object's kinetic energy and mass and square of its velocity is direct. A particle, an object, or a collection of particles can move because of kinetic energy, which is the force that drives motion.
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A 1.0kg block is placed on a 6.0kg wedge as shown. The block slides down the wedge and then to the right on the frictionless surface. The wedge moves to the left (without friction).If the speed of the wedge when the block reaches the flat surface is 0.28ms , what is the height of the wedge?
The wedge moves to the left (without friction) If the speed of the wedge when the block reaches the flat surface is 0.28ms, the height of the wedge is 5m
A wedge is a simple machine that uses a small force P to lift a heavy weight W. To calculate the force required to push the wedge in or out, draw FBDs of the wedge and the object on top of it. = 0 to the wedge and the object, as well as the frictional equation for impending motion, F = S N. The desired angle of correction () and the actual tibial width () are used to calculate the actual wedge height (y) (x). Actual tibial width should be measured at 2.02.5 cm distal to the joint line and normalized based on magnification. Wedge Volume = Cross Sectional Area x Tank Breadth.
Distance needs to be calculated in meters
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suppose we want a satellite to revolve around the earth 7 times a day. what should the radius of its orbit be?
The radius of its orbit is 102.22 km
What is gravitational constant ?The proportionality constant utilized in Newton's Law of Gravitation is the gravitational constant. The universal gravitational constant, abbreviated G and measured in Nm2/kg2, is the gravitational force that attracts any two unit masses separated by a unit distance.
Earth's acceleration caused by gravity, or the magnitude of g, is 9.8 m/s2. According to this, an item falling freely on Earth would accelerate by 9.8 meters per second. The gravity of the Earth is to blame for this acceleration.
For this question, force caused by the satellite from the planet must be round about equal to the Centrifugal force :
[tex]F_{g} = F_{c[/tex]
[tex]\frac{GMm}{r^2}[/tex] = [tex]mw^2r[/tex]
where ;
G = gravitational constant and this value is constant = 6.67 × [tex]10^-^1^1[/tex]
m = mass of the earth and
r = distance
Using the concept of period through the angular velocity, we have
[tex]\frac{GM}{w^2}[/tex] = [tex]r^3[/tex]
Substitute the value and we will get
[tex]r^3[/tex] = 1068193.154
r = 102.22 km
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