In a series resonant LCR circuit, the voltage across R is 100 volts and R= 1Ω with C = 2μF. The resonant frequency ω is 200 rad/s. At resonance, the voltage across L is D) 2.5 × 10⁵ volt.
given that :
V = 100 v
R = 1Ω
ω = 200 rad/s
C = 2μF
ω² = 1 / LC
(200)² = 1/ L × 2 × 10⁶
L = 12.5 H
current = 100 A
now, at resonance ,
voltage across the L is equals to voltage across C
voltage across L = 100 × ( 1 / 200 × 2 × 10⁶)
voltage across L = 2.5 × 10⁵ volt.
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which of the following vectors best describes the path of the airplane? question 6 options: none of these
The following vectors best describes the path of the airplane Aniseed of the as plan is 528 [tex]\mathrm{mi} / \mathrm{hr}[/tex]
What is airplane?
A fixed-wing aircraft that is pushed forward by the thrust of a jet engine, propeller, or rocket engine is known as an aeroplane or aeroplane. There are many different sizes, forms, and wing arrangements for airplanes.
[tex]\text { bearing } 25^{\circ} \text { west of north }[/tex]
[tex]\text { Since } \quad 90^{\circ}+25^{\circ}=115^{\circ}[/tex]
[tex]\text { so path of the airplane is }[/tex]
[tex]\left.v=528 \cos \left(i 15^{\circ}\right) i+528 \sin \left(115^{\circ}\right)\right][/tex]
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in 1.8 hours a sailboat sailed 81 kilometers east across the sea at a constant velocity. what was the sailboats velocity?
The velocity of the sailboats at sailed a distance of 81 km is 12.5 m/s.
What is velocity?
Velocity is the rate of change of displacement.
To calculate the velocity of the sailboats, we use the formula below.
Formula:
v = d/t................. Equation 1Where:
v = Velocity of the sailboatsd = Distancet = TimeFrom the question,
Given:
d = 81 km = 81000 mt = 1.8 hours = 1.8×60×60 = 6480 sSubstitute these values into equation 1
v = 81000/6480v = 12.5 m/sHence, the velocity is 12.5 m/s.
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Which of the following is/are accurate? (select any that apply)
a muscle cell has many nuclei
the muscle cell membrane is called the sarcolemma
muscle cells have multiple mitochondria
a muscle cells has one myofibril
The accurate statements about muscle cells are:
the muscle cell membrane is called the sarcolemmamuscle cells have multiple mitochondriaWhat are the features of a muscle cell?A muscle cell also known as a myocyte is a cell that has differentiated with contractility ability.
The muscles differ according to the type of muscle.
There are two types of muscles; smooth muscles and skeletal muscles.
The features of skeletal muscle cells include:
they are long, cylindrical, multi-nucleated, and striatedThe features of smooth muscle cells include:
they contain thick and thin filaments and are non-striated.Muscles cells contain many mitochondria and myofibrils.
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Using the loop rule and deriving the differential equation for an LC circuit find the current (sign included) through the inductor at the instant t = 2.2 s if L = 3.7 H, C = 5.0 F. The initial charge at the capacitor is Qo = 3.2 C and the initial current through the inductor is lo = 0. = Number i Units
Initial current via the inductor is lo = 0, and initial charge at the capacitor is Q-o = 3.2 C. The only two devices allowed by the loop rule.
Find the current (sign included) flowing through the inductor at the point t = 2.2 seconds using the loop rule and the differential equation derived for an LC circuit. Derive the differential equation for an LC circuit using the loop rule. To improve comprehension of complex concepts in electrical circuit analysis, such as inductance, capacitance, and reactance, By building up electric charges on two nearby surfaces, a capacitor is a device that stores electrical energy in an electric field. An RL circuit is one with resistance and self-inductance, and an RL circuit with a resistor.
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(a) Find the amplitude, frequency, and period of motion for an object vibrating at the end of a horizontal spring if the equation for its position as a function of time is the following. x = (0.225 m) cos ???? 8.00 t A = m f = Hz T = s (b) Find the maximum magnitude of the velocity and acceleration. vmax = m/s amax = m/s2 (c) What are the position, velocity, and acceleration of the object after 1.45 s has elapsed? x = m v = m/s a = m/s2
When a function p(x) determines location, the velocity and acceleration are its first and second derivatives, respectively.
The equation a = v/t denotes acceleration (a), which is the change in velocity (v) over the change in time (t). This enables you to calculate the change in velocity in meters per second squared (m/s2). Since acceleration is a vector quantity, both its magnitude and its direction are included. The speed and direction of an object's motion are its velocity. Alternatively put, velocity is the pace at which an object's position changes (where position incorporates direction by specifying whether the object is moving backwards or forwards on a line, or moving sideways or up and down in two or three dimensions).
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Scientists are now targeting Europa, one of Jupiter's moon, as a likely site for searching elementary life-forms because
Jupiter's moon Europa is regarded as one of the solar system's most promising locations to look for indications of modern life.
The geophysical characteristics of Europa, particularly the potential existence of an ocean of subglacial water, raise the prospect that human life could exist on or below the surface. The solar system's frozen moon Europa of Jupiter may provide the greatest promise for discovering modern settings conducive to life outside of Earth. Scientists have made progress in their quest to determine whether extraterrestrial life actually does exist. The best contender for alien habitability in our solar system is Jupiter's moon Europa. The hypothesis that life could exist in the inner ocean of Jupiter's moon Europa is supported by a new model created by NASA scientists.
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What is the weight of an 11 kg crate?
When completely filled with apples, the crate weighs 15 kg; when only 2/3 full, it weighs 11 kg; and when only 1/3 full (with only 1/3 of the crate's apples), it weighs 15-11=4 kg.
What does it mean to weigh?Definition of WEIGH in the Britannica Dictionary. She measures herself every morning in order to determine how heavy she is. 1. a [+ object]: to determine (someone or something's) weight. The bananas were weighed using a scale.
what are they Weight scales?To quantify weight or mass, one uses a scale or balance. These are also referred to as weight balances, mass balances, and scales of both mass and weight.
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Light of 650 nm wavelength illuminates a single slit of width 0.20 mm. (Figure 1) shows the intensity pattern seen on a screen behind the slit. You may want to review (Pages 941 - 943) . Figure1 of 1The graph shows intensity as a function of distance. Distance is measured from 0 to 3 centimeters on the x-axis. No values or units are given for the intensity on the y-axis. A large central peak is positioned at 1.5 centimeters with much smaller secondary and tertiary peaks flanking it. The width of the central peak is 1 centimeter. The secondary peaks are positioned at approximately 0.67 centimeters and 2.3 centimeters. The graph shows intensity as a function of distance. Distance is measured from 0 to 3 centimeters on the x-axis. No values or units are given for the intensity on the y-axis. A large central peak is positioned at 1.5 centimeters with much smaller secondary and tertiary peaks flanking it. The width of the central peak is 1 centimeter. The secondary peaks are positioned at approximately 0.67 centimeters and 2.3 centimeters.
Part A What is the distance to the screen? Express your answer to two significant figures and include the appropriate units.
The intensity pattern visible on a screen behind the slits can be stated to depend on the screen's distance (d=1.168m).
How to solve ?From the question we are told,
Two slits that are 0.20 mm apart are illuminated by 650 nm light. The intensity pattern shown on a screen behind the slits is depicted in (Figure 1).
Typically, the mathematical formula for the distance is as follows:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
d=0.33x10^-2x0.23x10^-3/650x10^-9
d=1.168m
What purpose does the distance formula serve?The distance formula is a formula used to determine how far apart two places are from one another. The dimensions of these points are unlimited. For instance, you could need to determine the separation between two points in space, a plane, or a line (1, 2, or 3 dimensions) (3d).
How far is that?Distance is the overall, directionless movement of an object. Distance can be characterized as the amount of space an object has covered, regardless of the starting or ending location.
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a 1.0kg block and a 2.0 kg block are pressed together and both are on a horizontal fricitionless surface with a compressed light spring between them concerning the states of the two blocks after they are released and detached from the spring which of the following statements is correct
The spring and pan have very little mass. The mass executes a SHM when it is lightly squeezed and then released.
Forces, location, velocity, and energy—both kinetic and potential energy—are some examples of these quantities. Hoare's Rule. Energy conservation: When the compressed spring returns to its natural length, all of the energy that was stored in it is transformed into kinetic energy. The block is propelled along a horizontal surface as the spring is let go. Friction and the spring's bulk can be disregarded. Between two blocks with masses of 1 kg and 2 kg that are lying on a smooth horizontal surface is a compressed elastic spring. The block is freed from rest once the spring has been compressed by 2.0 cm.
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A 20 kg crate is placed on a horizontal conveyor belt. The materials are such that μs = 0.41 and μk = 0.21. Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up to the right What is the maximum acceleration the belt can have without the crate slipping? If acceleration of the belt exceeds the value determined in part C, what is the acceleration of the crate?
The maximum acceleration for the belt that the slipping of the crate does not appear is 2 m/s².
what is a belt?
Each rotating pulley is supported on a shaft by a belt drive, which transfers motion from one to the next.Pulley belts are often manufactured from a soft, flexible material such as rubber, although shafts and pulley wheels can be made of any material. The pulleys and belts' grooves aid in their ability to grasp and turn.The frictional force between the two surfaces increases with the amount of wrap around the curved surface, and only a portion of that force (or the resulting belt tension) is transmitted to the other end of the belt or rope when a force applies tension to one end of a belt or rope wrapped around a curved surface. The Belt friction equation can be used to model belt friction.To learn more about belt refer to
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If two metal blocks of different masses slide freely down the same frictionless incline,
which one of the following is true?
A) They have equal accelerations
B) They have unequal accelerations, but the forces acting on them are equal.
C) The more massive block reaches the bottom first.
D) The less massive block reaches the bottom first.
E) None of these is correct.
If two metal blocks of different masses slide freely down the same frictionless incline, option a is correct.
Objects accelerate due to imbalanced forces. However, not every item accelerates at the same rate in the presence of the same imbalanced force. As a result, the speed and net force in the direction perpendicular to the plane must both be zero. Since the plane is assumed to be "frictionless," no force is applied to the block that is perpendicular to the surface by the plane. The acceleration is determined by multiplying the acceleration of gravity by the sine of the angle for a frictionless incline of angle degrees. The force of gravity is not parallel to the surface when there is an inclination. The normal force diminishes as the angle of the incline increases, which reduces the frictional force. You can increase the inclination until the thing barely starts to slip.
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a 1.8-cmcm-tall object is 22 cmcm to the left of a lens with a focal length of 11 cmcm . a second lens with a focal length of -5 cmcm is 37 cmcm to the right of the first lens.
A lens with an 11 cm focal length is 22 cm to the left of a 1.8 cm tall object. The image's height has decreased by 0.25 pixels when a second lens with a focal length of -5cm is placed 37cm to the right of the first lens.
Let's determine the distance at which the image is formed from the first lens since the image of the first lens serves as a virtual object for the second lens. Use the lens manufacturer's formula:
1/o + 1/i = 1/f, where I am the image distance and o is the object distance,
1/i = 1/f - 1/o = 1/(11cm) - 1/(22cm) = 0.045 1/cm, so
i = 22cm
the virtual object for the second lens is left at a distance of 37 cm - 22 cm, or 15 cm, from the second lens. Utilize the lens manufacturer's formula once more:
1/i = 1/f - 1/o (This time, the object distance is the separation between the second lens and the virtual object.)
1/i = 1/(-5cm) - 1/(15cm) = -0.26 1/cm, so
i = -15/4cm away from the second lens.
The sum of the two magnifications from the two lenses is the total magnification: m = m1m2, where m = -i/o, so
m = (-22 cm/22 cm)( 15/4cm/15cm) = -0.25, Consequently, the image's height is 0.25 pixels shorter than it was before.
It is the inverse of the system's optical power that determines how strongly an optical system diverges or converges light: the focal length. The convergence or divergence of light is indicated by a positive focal length, whilst the opposite is true for a negative focal length.
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the rod has a diameter of 40 mm. if it is subjected to the force system shown, determine the stress components that act at point a, and show the results on a volume element located at this point
In this case, we are given that the rod is subjected to the force system shown in the figure. There is a vertical force F acting on the rod at point A, as well as a horizontal force P. The rod is also subjected to a moment M about the z-axis.
To determine the stress components that act at point A, we need to consider the forces that are acting on a small volume element located at this point.
The stress on a volume element is defined as the force acting on the element per unit area. The stress components at a point can be represented by a stress tensor, which is a 3x3 matrix with nine elements. The diagonal elements of the stress tensor represent the normal stress components, while the off-diagonal elements represent the shear stress components.
To determine the stress components at point A, we need to consider how these forces are distributed over the surface of the volume element. The normal stress components can be found by considering the forces acting perpendicular to the surface of the element. The shear stress components can be found by considering the forces acting tangent to the surface of the element.
For example, the normal stress component in the x-direction at point A can be found by considering the force F acting perpendicular to the surface of the element in the y-direction. The normal stress component in the y-direction at point A can be found by considering the force P acting perpendicular to the surface of the element in the x-direction. The shear stress component in the XY-plane at point A can be found by considering the moment M acting tangent to the surface of the element.
To determine the specific values of the stress components, we would need to know the dimensions of the volume element, as well as the magnitudes of the forces and moments acting on the rod. With this information, we can use the equations of statics to solve for the stress components at point A.
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In a mass spectrometer, a specific velocity can be selected from a distribution by injecting charged particles between a set of plates with a constant electric field between them and a magnetic field across them (perpendicular to the direction of particle travel). If the fields are tuned exactly right, only particles of a specific velocity will pass through this region undeflected. Consider such a velocity selector in a mass spectrometer with a 0.105 T magnetic field. 50% Part (a) What electric field strength, in volts per meter, is needed to select a speed of 3.9 x 10 m/s? Grade Summary Deductions 090 Potential 100% sino cos tan) cotan asino acos atan) acotan sinho cosho tanho) cotanho Degrees Radians 7 8 9 E4 5 6 1 2 3 0. VOCAL Submissions Attempts remaining 20 per attempt) detailed view Submit Hint French I give up! Hints: O deduction per hint. Hints remaining 2 Feedback: deduction per feedback 50% Part (b) What is the voltage, in kilovolts, between the plates if they are separated by 0.95 cm?
The electric field strength in volts per meter is calculated to be 4.095 V/m.
Given that, speed v = 3.9 * 10 m/s
Magnetic field B = 0.105 T
Using the mass spectrometer velocity selector relationship between the electric field and magnetic field is,
v = E/B
Where,
v is the speed selector
B is magnetic field
E is electric field
Therefore, E = vB
E = 3.9 × 10 × 0.105
E = 4.095 V/m
Thus, electric field E is 4.095 V/m.
The question is incomplete. The complete question is 'What is the electric field strength in volts per meter?'
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find the amplitude, frequency, and period of motion for an object vibrating at the end of a horizontal spring if the equation for its position as a function of time is the following.
The amplitude is 0.25s.
Calculation:
Amplitude = A = 0.225 m
Angular frequency = w = 8π rad/s.
Frequency = f = w/2π = 8π/2πHZ = 4 HZ
Time period = T = 1/f = (1/4)s = 0.25s.
The maximum displacement or distance traveled by a point on an oscillating body or shaft, measured from the equilibrium position. This corresponds to half the length of the vibration path. Amplitude difference between a rest position and maximum shaft deflection.
Frequency The number of waves passing a particular point per second. Duration How long it takes for a wave cycle to complete. Sound wave amplitude is a measure of wave height. The amplitude of a sound wave can be defined as the magnitude or loudness of the maximum displacement from the average position of the vibrating particles in the medium when the sound was produced.
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A diffraction grating is illuminated simultaneously with red light of wavelength 690 nm and light of an unknown wavelength. The fifth-order maximum of the unknown wavelength exactly overlaps the fourth-order maximum of the red light. What is the unknown wavelength?
According to the given statement 414 nm is the value of the unknown wavelength.
What is wavelengths and frequency?The distance between two wave crests, which also applies to troughs, is known as the wavelength. Cycles per second (Hz), the number of vibrations that pass across a certain region in a second, is used to measure frequency (Hertz). The link between wavelength and frequency is discussed in this article.
Briefing:For third order maxima,
asinθ = mλ
asinθ = 3 * 690
The slit width in this instance is a, and the angular spacing is.
The fifth order maximum, meanwhile
asinθ = mλ
asinθ = 5λ
Solving as,
5λ = 3 * 690
λ = 414 nm
Therefore, 414 nm is the value of the unknown wavelength.
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What type of timer would you use to measure
the period of a simple pendulum? How many
oscillations would you time?
It is easy to measure the period using the photogate timer.
What is photogate timer?Photogate timer is used to study free fall, rolling objects, collisions, and pendulums. Photogates allow for extremely accurate timing of events within physics experiments, for studying free fall, air track collisions, pendulum periods, the speed of a rolling object, among other things.
To measure the period of a simple pendulum, we set the simple pendulum into oscillation. Let's say 10 oscillations. The time to complete this oscillation is recorded. This time is divided by the no of oscillation to get the period. Period is also measured in second.
This means that period of a simple pendulum is given as T = t/n
where T is the period and t is the time to complete a given oscillation.
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A sinusoidal transverse wave of wavelength 20 cm travels along a string in the positive direction of an x axis. The displacement y of the string particle at x=0 is given in Fig. 16-34 as a function of time t. The scale of the vertical axis is set by y s =4.0 cm. The wave equation is to be in the form y(x,t)=y msin(kx±ωt+ϕ). (a) At t=0, is a plot of y versus x in the shape of a positive sine function or a negative sine function? What are (b) y m(c) k (d) ω (e) ϕ (f) the sign in front of ω and (g) the speed of the wave? (h) What is the transverse velocity of the particle at x=0 when t=5.0 s?
The transverse velocity of the particle at x=0 when t=5.0 s is 2.5 cm/s.
y(x,t) = ymsin(kx +- wt + Ф)
(a). At t =0 , y verses x is positive sine function
(b). Ym = y5 = 4 cm
(c). k = 2Π/λ = (2*3.14)/20 = 0.314 rad cm⁻¹
(d). w = 2Πf = 2Π/T = (2*3.14)/10 = 0.628 rad/sec
(e). since at t =0 , x= 0
y = Ym sinΦ
but y = 0 from graph
sinΦ = 0 Φ=0
(f). sin in front of w is 't'
(g) . speed = v= w/k = 0.628/0.314 = 2cm/s
(h) . at x = 0
y = ym sinwt
vy = dy/dt= wym constant
= 0.628*4*cos(0.628*5)
vy = 2.5 cm/s
Wavelength is the spatial period of a periodic wave, i.e. the distance over which the wave shape repeats. [1][2] This is the distance between successive corresponding points of the same phase in the wave. B. Two adjacent peaks, valleys, or zero crossings, characteristic of both traveling and standing waves and other spatial wave patterns.
The reciprocal of wavelength is called spatial frequency. Wavelength is usually represented by the Greek letter lambda (λ). The term wavelength is also sometimes applied to the sinusoidal envelope of modulated waves and waves formed by interference of modulated waves or multiple sinusoids.
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a) Calculate the ratios of longitudinal modulus of the composite to the matrix modulus for glass/epoxy and carbon /epoxy composites with 10% and 50% fibers by volume. Elastic modules of glass fibers, carbon fibers and epoxy resin are 70, 350, and 3.5 GPa, respectively.
b) Discuss what is the effect of the fibers in the elastic modulus of the composite in the longitudinal direction (2-3 phrases.)
carbon fibers and epoxy resin have respective tensile strengths of 70, 350, and 3.5 GPa. According to these estimates, fibers are particularly effective at increasing the composite modulus in the longitudinal direction.
(a) [tex]V_{f}[/tex]=[tex]A_{f} /A_{c}[/tex] ,[tex]V_{m} =A_{m}/A_{c}[/tex]
The elastic modulus of the composite is given by
E[tex]_{c}[/tex]=[tex]E_{f} V_{f} +E_{m} V_{m}[/tex]
E[tex]_{c}[/tex]/E[tex]_{m}[/tex]=([tex]E_{f} /E_{m}[/tex] - 1) [tex]V_{f}[/tex]+1
the calculation will give the following result
System([tex]E_{f} /E_{m}[/tex]) [tex]V_{f}[/tex]=10% [tex]V_{f}[/tex]=50%
Glass – epoxy(20) 2.9 10.5
Carbon epoxy (100) 10.9 50.5
(b) 50 It has been found that as the volume fraction of fiber grows by a factor of 5, the ratio (E[tex]_{c}[/tex]/E[tex]_{m}[/tex]) similarly increases by a corresponding amount (3.62 for glass epoxy and 4:63 for carbon epoxy )
Additionally, as the fiber modulus increases by a factor of 5, the ratio of (E[tex]_{c}[/tex]/E[tex]_{m}[/tex]) increases by a comparable factor (3.7 at [tex]V_{f}[/tex]=10% and 4.81 at [tex]V_{f}[/tex] =50%). These calculations demonstrate that fibers are particularly successful in raising the composite modulus in the longitudinal direction.
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The bullet strikes a block of wood which exerts, on average, a force of 50,000 N opposing the motion of the bullet. How far does the bullet penetrate?
The distance that the bullet penetrates is 0.03m.
How to solve?Given data:
The mass of the bullet is
m = 25 g = 0.025 kg
The bullet's initial velocity is
u = 350 m/s
The final velocity of the bullet is
v = 0
The average force opposing the motion is
F = 50000N
From Newton's second law, the acceleration derived as,
F = m. a.
a = F. m..........(1)
Substituting values in equation (1), we get:
a = 50000 N / 0.025 kg = 2×106 m/s 2
The equation of motion is,
v 2=u 2−2 a S
2 a S=u 2−v 2
S = u 2−v 2/2 a.......(2)
Substituting values in equation (2), we get:
S = (350 m/s)2−0/2(2×106 m/s 2)
=12.25×104 m/s 4×106 m/s 2=0.03m
here, the distance that bullet penetrates is 0.03m.
What is the kinetic energy equation?Kinetic energy has the following formula: K.E. = 1/2 m v 2, where m is the object's mass and v is its square velocity. The kinetic energy is measured in kg/m per second squared if the mass is measured in kg and the velocity is measured in meters per second.
Which 4 forms of kinetic energy are there?Radiant, thermal, electrical, and mechanical kinetic energies are the basic categories.
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Approximately, ___ municipal solid waste landfills in the United States combust landfill gas to generate heat and electricity
400
Approximately, 400 tons of municipal solid waste landfills in the United States combust landfill gas to generate heat and electricity
What is municipal waste?We know that municipal waste has to do with the waste products that can be obtained from the activities that go on in the city. the magnitude of the municipal waste that is generated in a place would have a lot to do with the population of the area as well as the industrial saturation of the area.
This is the reason why the areas that have less population and the industries that are there are not so much do not expirience a lot of pollution and do not have a large amount of waste water that goes out as sewage.
The solid wastes that are generated in the United States is just as large as the sewage that is generated in the united states and calls for a very urgent attention.
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The principle of connectedness would most likely lead you to perceive all the ________ as parts of a single unit.
A) words in a sentence
B) clouds in the sky
C) rungs in a ladder
The principle of connectedness would most likely lead you to perceive all the (c) rugs in a ladder as part of a single unit.
The law of unified connectedness states that elements that are connected to each other using colours, lines, frames, or other shapes are perceived as a single unit when compared with other elements that are not linked in the same manner.
In quantum mechanics, there's a phenomenon called entanglement. Entanglement really does connect things in different places for a very specific definition of “connect”. And there’s a real (but complicated) sense in which these connections end up connecting everything.
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what is the amplitude and period of this wave? I WILL MARK BRAINLIEST!
Answer:
amplitude:1m
period:10s
Explanation:
dr. bronfman has administered her new 100-item test of abstract reasoning to a large sample of students. she is presently comparing their scores on the odd-numbered questions with those on the even-numbered questions in an effort to
Determine the test's reliability. Test-retest reliability is a metric of dependability that is acquired by giving the same test to a set of people twice over time.
How long should reliability tests be repeated?Although the ideal testing interval will vary depending on the construct being assessed, its stability over time, and the target population, several research have demonstrated that the target time of 2 weeks is the most frequently advised interval [15].
Interrater reliability between tests is it?The degree to which various raters and observers provide consistent estimates of the same occurrence is measured by inter-rater or inter-observer reliability. Test-Retest Reliability: Used to evaluate a measure's consistency across time.
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The elevator descends with an acceleration of 0.9 m/s². Find how much a 95 kg person weighs in it at the moment of descent.
Two blocks on a surface of negligible friction are attached together by a spring, as shown in the figure above. The mass of block 1 is MM, and the mass of block 2 is 2M. Block 1 is initially moving toward block 2, which is at rest. The spring compresses and decompresses in a repeated motion as the two blocks slide to the right. Which of the following statements best describes the speed of the center of mass of the two-block system?
In the absence of an external force, the total linear momentum of the system maintains conservation, indicating that the speed of the system's center of mass is constant.
This is because the spring force between the masses acts as an internal force between the two masses.
The product of an object's mass, m, and velocity, v, is known as linear momentum, and it is a vector quantity. In order to express it and refer to momentum informally, the letter "p" is utilized. You should be aware that a body's momentum always points in the same direction as its velocity vector. Because it is a conserved quantity, the overall momentum of a system is always constant. Linear momentum is measured in kg/s.
The total linear momentum prior to an object's interaction and the total linear momentum following that interaction is identical. Any system of objects that is subject to no net external force has a constant total linear momentum.
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A penguin slides on ice.
A. Newton's First Law of Motion
B. Newton's Second Law of Motion
C. Newton's Third Law of Motion
Answer:
Newton's first law: An object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force.
In the figure; two point sources S1 and S2, Which are in phase and emit identical sound waves of wavelength 2.0 m: The length L1 = 21 m. A listener stands at point P: Assume the amplitude of individual sound reaching at point P does not change, the sound that the listener hears willl be least intense if the L2 is
The length L₂ for destructive interference is L₂ = 22 m
What is a sound wave?A sound wave is a mechanical wave which carries sound energy from one point to another.
How to find the point L2?Since two point sources S₁ and S₂, Which are in phase and emit identical sound waves of wavelength 2.0 m: The length L₁ = 21 m. A listener stands at point P: Assume the amplitude of individual sound reaching at point P does not change, to find L₂, we need to know the path difference for destructive interference.
What is path difference for destructive interference?The path difference for destructive interference is given by ΔL = (n + 1)λ/2
where
ΔL = path difference = L₂ - L₁, λ = wavelength and n is an integer.Since we require the least intensity, we have the minimum interference. So, n = 0.
So, ΔL = (n + 1)λ/2
ΔL = (0 + 1)λ/2
L₂ - L₁ = λ/2
So, making L₂ subject of the formula, we have
L₂ = L₁ + λ/2
Given that
L₁ = 21 mλ = 2.0 mSubstituting the values of the variables into the equation, we have that
L₂ = L₁ + λ/2
L₂ = 21 m + 2.0 m/2
L₂ = 21 m + 1 m
L₂ = 22 m
So, the length L₂ = 22 m
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one of the strongest emission lines observed from distant galaxies comes from hydrogen and has a wavelength of 122 nm (in the ultraviolet region).
(a) The galaxy moves with a velocity of 0.8 c away from us.
(b) When the galaxy moves towards us we observed that the wavelength of the line is 40.67 nm.
We know that,
The relativistic Doppler effect when the galaxy is moving away from us
In this case, when the source moves away from the observer its frequency ([tex]f[/tex]) is lower than the emitted frequency ([tex]f_{0}[/tex]) and the preceding wavelength ([tex]\lambda[/tex]) is higher than the emitted wavelength ([tex]\lambda_{0}[/tex]).
[tex]f=f_{0} \sqrt{\frac{1-\frac{u}{c} }{1+\frac{u}{c} } }[/tex]
[tex](\frac{\lambda_{0} }{\lambda})^{2} = \sqrt{\frac{c-u}{c+u} }[/tex]
Given that
[tex]\lambda_{0} =122 nm\lambda=366nm[/tex]
So
[tex](\frac{122}{366} )^{2} =\frac{c-u}{c+u} \frac{1}{9} = 8cu=0.8c[/tex]
Where c is the velocity of light it is equal to [tex]3*10^{8} m/s[/tex].
So when the galaxy moves towards us we observed that the wavelength of the line is 40.67nm.
(b) When the galaxy moves towards us its wavelength is shorter than the emitted wavelength.
The expression of the wavelength in this case is given by
[tex]\frac{\lambda _{0} }{\lambda } =\sqrt{\frac{c-u}{c+u} }[/tex]
= 40.67 nm
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A triathlon athlete swims at an average rate 2.4 miles per hour, and bikes at an average rate of 16.1 miles per hour. At the end of one training session, she has swum and biked more than 20 miles in total.
The inequality and this graph represent the relationship between the hours of swimming, , the hours of biking, , and the total distance the athlete could have traveled in miles. Graph of an inequality. Hours of biking. Hours of swimming.
Mai said, "I'm not sure the graph is right. For example, the point is in the shaded region, but it's not realistic for an athlete to swim for 10 hours and bike for 3 hours in a training session! I think triathlon athletes generally train for no more than 2 hours a day."
Write an inequality to represent Mai's last statement. Graph the solution set to your inequality. Determine a possible combination of swimming and biking times that meet both the distance and the time constraints in this situation.
Elena is considering buying bracelets and necklaces as gifts for her friends. Bracelets cost $3, and necklaces cost $5. She can spend no more than $30 on the gifts. Elena needs at least 7 gift items.
This graph represents the inequality , which describes the cost constraint in this situation.
Let represent the number of bracelets and the number of necklaces.
Graph of inequality. Number of necklaces. Number of bracelets.
Write an inequality that represents the number of gift items that Elena needs.
On the same coordinate plane, graph the solution set to the inequality you wrote.
Use the graphs to find at least two possible combinations of bracelets and necklaces Elena could buy.
Explain how the graphs show that the combination of 2 bracelets and 5 necklaces meet one constraint in the situation but not the other constraint.
Combination of swimming and biking times that meets distance and the time constraints in this situation is s + b ≤ 2. An inequality that represents number of gift items that Elena needs is : 3b+5n≤30.
How is the inequality equation written?If athletes train for not more than 2 hours a day, then the sum of the hours training swimming 'a' and biking 'b' should be less than or equal to 2. Hence, we can write the following inequality:
s + b ≤ 2
Inequality that represents Mai's statement is:
s + b ≤ 2
Part 2:
It is given that , bracelets cost $3, necklaces cost $5 and she can spend not more than $30
Then the inequality that represents the number of gift items that Elena needs : 3b+5n≤30
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