Answer:
(a). The maximum stretch during the motion is 20.7 cm
(b). The maximum speed during the motion is 3.84 m/s.
(c). The energy is 0.060 Watt.
Explanation:
Given that,
Spring stiffness = 205 N/m
Mass = 0.6 kg
Compression of spring = 13 cm
Initial speed = 3 m/s
(a). We need to calculate the maximum stretch during the motion
Using conservation of energy
[tex]E_{initial}=E_{final} [/tex]
[tex]\dfrac{1}{2}kx_{c}^2+\dfrac{1}{2}mv^2=\dfrac{1}{2}kx_{m}^2[/tex]
Put the value into the formula
[tex]\dfrac{1}{2}\times205\times(13\times10^{-2})^2+\dfrac{1}{2}\times0.6\times3^2=\dfrac{1}{2}\times205\times x_{m}^2[/tex]
[tex]x_{m}=\sqrt{\dfrac{4.43\times2}{205}}[/tex]
[tex]x_{m}=20.7\ cm[/tex]
(b). Maximum speed comes when stretch is zero.
We need to calculate the maximum speed during the motion
Using conservation of energy
[tex]E_{initial}=E_{final} [/tex]
[tex]\dfrac{1}{2}kx_{c}^2+\dfrac{1}{2}mv^2=\dfrac{1}{2}mv'^2[/tex]
Put the value into the formula
[tex]\dfrac{1}{2}\times205\times(13\times10^{-2})^2+\dfrac{1}{2}\times0.6\times3^2=\dfrac{1}{2}\times0.6\times v'^2[/tex]
[tex]v'=\sqrt{\dfrac{4.43\times2}{0.6}}[/tex]
[tex]v'=3.84\ m/s[/tex]
(c). Now suppose that there is energy dissipation of 0.02 J per cycle of the spring-mass system
We need to calculate the time period
Using formula of time period
[tex]T=2\pi\sqrt{\dfrac{m}{k}}[/tex]
Put the value into the formula
[tex]T=2\pi\sqrt{\dfrac{0.6}{205}}[/tex]
[tex]T=0.33\ sec[/tex]
We need to calculate the energy
Using formula of energy
[tex]E=\dfrac{P}{t}[/tex]
Put the value into the formula
[tex]E=\dfrac{0.02}{0.33}[/tex]
[tex]E=0.060\ Watt[/tex]
Hence, (a). The maximum stretch during the motion is 20.7 cm
(b). The maximum speed during the motion is 3.84 m/s.
(c). The energy is 0.060 Watt.
A pole-vaulter just clears the bar at 5.31 m and falls back to the ground. The change in the vaulter's potential energy during the fall is -3900 J. What is his weight?
Answer:
Weight = 734.46 N
Explanation:
Given:
Initial height of the pole-vaulter is, [tex]h_i=5.31\ m[/tex]
Final height of the pole-vaulter is, [tex]h_f=0\ m[/tex]
Change in the vaulter's potential energy is, [tex]\Delta U=-3900\ J[/tex]
We know that, change in potential energy is given as:
[tex]\Delta U=mg(h_f-h_i)[/tex]
Where, 'm' is the mass of the object, 'g' is acceleration due to gravity and has a value of 9.8 m/s².
Now, weight of the object is given as the product of its mass and acceleration due to gravity. So, replace 'mg' by weight 'w'. So, the equation becomes,
[tex]\Delta U = w(h_f-h_i)[/tex]
Now, rewriting in terms of 'w', we get:
[tex]w=\dfrac{\Delta U}{(h_f-h_i)}[/tex]
Now, plug in all the given values and solve for 'w'. This gives,
[tex]w=\dfrac{-3900\ J}{(0-5.31)\ m}\\\\\\w=\dfrac{3900}{5.31}\ N\\\\\\w=734.46\ N[/tex]
Therefore, weight of the vaulter is 734.46 N.
The weight of the pole-vaulter is calculated using the principle of conservation of mechanical energy and the equation for gravitational potential energy, resulting in a value of approximately 734.46 Newtons.
Explanation:The question asked concerns the calculation of the weight of a pole-vaulter given a change in potential energy as the vaulter falls. The calculation can be made using the principle of conservation of mechanical energy, and the equation for gravitational potential energy: PE = mgh, where PE is potential energy, m is mass, g is the acceleration due to gravity, and h is the change in height.
The change in the vaulter's potential energy is given in the problem as -3900 J, which is negative because potential energy decreases as height decreases. Assuming that the entire change in potential energy is converted into kinetic energy, we can arrange the equation: -PE = mgh = weight * h for the weight of the vaulter, giving: weight = -PE / h.
Substituting the given values into this equation gives weight = (-(-3900 J)) / (5.31 m) = 734.46 N. So, the weight of the pole-vaulter is approximately 734.46 Newtons.
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Some Canadian troops are sent (as part of a U.N. peacekeeping force) to a country located on the Earth's equator. At night, when homesickness makes them gaze sleeplessly at the stars, which of the following will be familiar to them (the same at the equator as in Canada):
a. the celestial poles are on the north and south points of the horizon
b. the celestial equator is overhead and passes through the zenith
c. all stars rise and set (none remain in the sky all night long)
d. all-stars are above the horizon exactly half a day
e. none of the above are the same on the equator as in Canada
Answer:
Option E is correct.
none of the listed options are the same on the equator as at the celestial north pole; the region where Canada is.
Explanation:
Firstly, let's explain some terms.
The earth's rotation is not straight forward as a sphere just rotating. The shape of the earth (better described as geoid; spherical, but a bit flattened at the poles), some gravitational forces on the earth and the existence of seasons mean the earth's rotation is tilted at an angle of 23.5° relative to our orbital plane; the plane of the earth's orbit round the sun.
When the tilted earth is considered, the celestial north and south poles are the north and south poles on the tilted earth's rotational axis.
And the celestial equator is when the equator on the tilted earth, equidistant from the celestial north and south poles is projected into space. A portion of the celestial equator passes through the real equator.
Now, the options one by one,
A) the celestial poles are on the north and south points of the horizon
At the celestial north and south poles, the poles are observable at the north and south points of the horizon.
At the celestial north pole, it is usually located by locating the north star, Polaris, and at the celestial South poles, there are about 4 different methods of locating the poles on the horizon.
But these poles aren't noticeable on the horizon at the equator. The northern one can only be noticed at regions around the celestial north pole.
Hence, the statement A isn't correct.
B) the celestial equator is overhead and passes through the zenith.
Zenith describes the the point in the sky directly above one's head.
At some points on the equator, the celestial equator is truly overhead, but the celestial equator doesn't pass overhead at the north pole, So, this isn't something common to the equator and the north pole.
C) all stars rise and set (none remain in the sky all night long)
Stars remaining in the sky all night long only occurs at the poles (north pole especially). Depending on the seasons, there are times and/or places that have 24 hour sunlight or darkness.
But, this is usually not the case at the equator. At the equator, all stars rise and set all year round. Only small noticeable longer days, shorter nights or longet nights, shorter days are experienced at the equator.
Hence, the statement given isn't true for the north pole and the equator.
D) all-stars are above the horizon exactly half a day.
The paths of the stars are vertical and are cut exactly in half by the horizon at the equator. Each star is up half the time and down half the time.
Unlike at the poles, as explained in the previous statement, they enjoy more varied daytime and night times.
Again, the statement described isn't true for the north pole and the equator.
A basketball with a mass of 0.61 kg falls vertically to the floor where it hits with a velocity of −7 m/s. (We take the positive direction to be upward here.) The ball rebounds, leaving the floor with a velocity of 4.6 m/s. (Indicate the direction with the signs of your answers.)
Answer:
a. What impulse act on the ball during its collision with the floor?
b. If the ball is in contact with the floor for 0.04 s, what is the average force of the ball on he floor?
The answers to the question are
a. The impulse acting on the ball during its collision with the floor is
7.076 kg·m/s
b. The average force of the ball on the floor with contact of 0.04 s is
176.9 N
Explanation:
Mass of the ball = 0.61 kg
Initial velocity = -7 m/s
Final velocity = 4.6 m/s
Impulse = Δp = FΔt = mΔv
Where Δt =change in time
m = mass of Average force of he the ball
Δv = velocity change
Therefore impulse = m×(Final velocity - initial velocity)
= 0.61 × (4.6-(-7)) = 0.61×11.6
= 7.076 kg·m/s
b. Average force of the ball on the floor is given by
[tex]F_{Average}[/tex]×Δt = mΔv = 7.076 kg·m/s
where Δt = change in time = 4.6 m/s
Therefore [tex]F_{Average}[/tex] =mΔv /Δt = 7.076/0.04 = 176.9 kg·m/s²
= 176.9 N
What are the similarities between the operation of a radio telescope and that of an optical reflecting telescope?
Answer:
They both intercept,focus and determine the intensity of an incoming radiation but at different degree.
Explanation:
Radio telescope is much larger than optical telescope because radio wavelengths are much longer than optical wavelengths. The longer the wavelengths implies that the radio waves has a lower energy than optical light waves. So, in order to collect enough radio photons to detect a signal, the radio dishes must be very large.
MIT’s robot cheetah can jump over obstacles 46. cm high and has speed of 12.0 km/h. a) If the robot launches itself at an angle of 60.° at this speed, what is its maximum height? b) What would the launch angle have to be to reach a height of 46. cm?
Answer:
(a) [tex]y_{max}=0.423m[/tex]
(b) [tex]\alpha =64.3^{o}[/tex]
Explanation:
Given data
[tex]v_{i}=12km/h=3.33m/s\\\alpha =60^{o}\\g=9.8m/s^{2}\\Required\\(a)y_{max}\\(b)Angle[/tex]
Solution
For Part (a)
As the velocity component in direction of y is given by:
[tex]v_{yi}=v_{i}Sin\alpha \\v_{yi}=3.33Sin60\\v_{yi}=2.88m/s[/tex]
The maximum displacement is given by:
[tex]v_{yf}^{2}=v_{yi}^{2}-2gy_{max}\\ y_{max}=\frac{(2.88)^{2}}{2(9.8)}\\ y_{max}=0.423m[/tex]
For Part (b)
To reach y=46cm =0.46m apply:
[tex]0=v_{yi}^{2}-2(9.8)(0.46)\\v_{yi}=3m/s\\As\\Sin\alpha =\frac{v_{yi}}{v_{i}}\\\alpha =Sin^{-1}(\frac{v_{yi}}{v_{i}})\\\alpha =Sin^{-1}(\frac{3}{3.33} )\\\alpha =64.3^{o}[/tex]
a) When launched at a 60° angle with a speed of 3.33 m/s, the robot cheetah can reach a maximum height of about 0.715 meters.
b) To reach a height of 0.46 meters, the launch angle needs to be approximately 31.74 degrees.
a) To find the maximum height (h_max) when the robot cheetah launches at a 60-degree angle with a speed of 3.33 m/s, we can use the following formula:
h_max = (u^2 * sin^2(θ)) / (2 * g)
Where:
u is the initial speed (3.33 m/s)
θ is the launch angle (60 degrees)
g is the acceleration due to gravity (9.8 m/s²)
First, calculate sin(60 degrees):
sin(60 degrees) = √3 / 2 ≈ 0.866
Now, plug in the values and calculate h_max:
h_max = (3.33^2 * (0.866)^2) / (2 * 9.8) ≈ 0.715 meters
b) To determine the launch angle (θ) required to reach a height of 0.46 meters (46 cm), we'll rearrange the same formula:
sin^2(θ) = (2 * g * h_desired) / u^2
Plug in the values:
sin^2(θ) = (2 * 9.8 * 0.46) / (3.33^2)
Now, find sin(θ):
sin(θ) ≈ √(0.2794) ≈ 0.5289
Finally, calculate θ:
θ ≈ arcsin(0.5289) ≈ 31.74 degrees
So, the launch angle required to reach a height of 0.46 meters is approximately 31.74 degrees.
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Tech A says that the solenoid on the starter motor switches the high current on and off. Tech B says that the solenoid engages the starter motor with the ring gear. Who is correct
Tech B is correct.
Explanation:
Generally the electromagnet for a coil of wire, which allow the system to transform electric energy into mechanical energy is understood as a solenoid, by generating magnetic field from electric current and induces linear motion by utilizing the magnetic field. Every modern starters depend on the solenoid to use the flywheel ring gear to enable the start drive. When the solenoid is rejuvenated, a plunger or lever is controlled which pushes the ring gear into mesh with the pinion. A standard starter solenoid has one small adapter for the starter control wire and two major terminals: one for the positive battery cable, and another one for the thick wire that drive the starter motor by its own.
The correct answer is that both Tech A and Tech B are correct.
In a vehicle's starting system, the solenoid serves two main functions:
1. Switching High Current: When the ignition key is turned to start the engine, a small current flows through the solenoid coil, creating an electromagnetic field that pulls the solenoid plunger inward. This action closes a pair of heavy contacts, allowing a high current to flow from the battery to the starter motor. This is what Tech A is referring to when they mention that the solenoid switches the high current on and off.
2. Engaging the Starter Motor with the Ring Gear: The movement of the solenoid plunger also pushes a lever that engages the starter motor's pinion gear with the ring gear on the engine's flywheel. This engagement is necessary to turn the engine over during the starting process. This is the function that Tech B is describing.
Therefore, the solenoid is responsible for both switching the high current to the starter motor and engaging the starter motor with the ring gear. Both technicians are correct in their statements about the functions of the solenoid in the starting system.
why the sun emits most of its energy in the form of visible light?
Human eye could perceive this visible light and used it to look at the objects.
Explanation:
There are 3 forms of radiation emitted by the sun. They are Infrared radiation, Ultra Violet radiation as well as visible radiation.
Visible light is the type of light can perceive by the human eye and utilizes to see the objects.
Since the sun is hotter (5800 K) than the earth, it emits mostly the radiation energy in the form of this visible light.
A uniform cylindrical grindstone has a mass of 15.0 kg and a radius of 18.6 cm. The grindstone reaches a rotational velocity of 1.83 rev/min before its motor turns off. After the grindstone motor is turned off, a knife blade is pressed against the outer edge of the grindstone with a perpendicular force of 8.82 N. The coefficient of kinetic friction between the grindstone and the blade is 0.80. Use the work energy theorem to determine how many turns the grindstone makes before it stops.
Answer:
[tex]n \approx 5.778\times 10^{-4}\,rev[/tex]
Explanation:
The Work-Energy Theorem is applied herein:
[tex]-\frac{1}{4}\cdot m_{cyl}\cdot R^{2}\cdot \omega^{2} = - \mu_{k}\cdot N\cdot r \cdot 2\pi \cdot n[/tex]
The number of turns needed to stop the grindstone is:
[tex]n = \frac{m_{cyl}\cdot R^{2}\cdot \omega^{2}}{4\cdot \mu_{k}\cdot N \cdot r\cdot 2\pi}[/tex]
[tex]n = \frac{(15\,kg)\cdot (0.186\,m)^{2}\cdot [(1.83\,\frac{rev}{min} )\cdot (\frac{2\pi\,rad}{1\,rev} )\cdot (\frac{1\,min}{60\,s} )]^{2}}{4\cdot (0.80)\cdot (8.82\,N)\cdot(0.186\,m)\cdot 2\pi}[/tex]
[tex]n \approx 5.778\times 10^{-4}\,rev[/tex]
A good baseball pitcher can throw a baseball toward home plate at 93 mi/h with a spin of 1510 rev/min. How many revolutions does the baseball make on its way to home plate? For simplicity, assume that the 60 ft path is a straight line.
Answer:
[tex]\Delta \theta =11.073\ rev[/tex]
Explanation:
Given,
Speed of baseball = 93 mi/h
spin = 1510 rev/min
[tex]\Delta x = 60\ ft[/tex]
[tex]v =93\times \dfrac{88}{60} = 136.4 ft/s[/tex]
[tex]\omega = 1510\times \dfrac{1}{60}= 25.167\ rad/s[/tex]
[tex]\Delta t = \dfrac{\Delta x}{v}[/tex]
[tex]\Delta t = \dfrac{60}{136.4 }[/tex]
[tex]\Delta t = 0.44\ s[/tex]
Revolutions of ball
[tex]\Delta \theta = \omega t[/tex]
[tex]\Delta \theta = 25.167\times 0.44[/tex]
[tex]\Delta \theta =11.073\ rev[/tex]
Revolution of the ball is equal to [tex]\Delta \theta =11.073\ rev[/tex].
A satellite system that has unique properties is the ____ satellite, which is used by governments for spying and by scientific agencies for observing celestial bodies
Answer: Highly-elliptical-earth-orbit (heo)
Explanation: Highly-elliptical-earth-orbit (heo) satellite system has unique properties
which is used by governments for spying and by scientific agencies for observing celestial bodies. It is an extremely elongated orbit that is useful for communication satellites which creates signals between a source transmitter and a receiver at different locations on earth. They are used by government for spying, scientific agencies for observing celestial bodies, for the internet and telephone communications.
Answer:
Highly elliptical satellite orbit.
Explanation:
Highly elliptical satellite orbit is used to provide coverage over any point on the globe. The HEO is not limited to equatorial orbits like the geostationary orbit and the resulting lack of high latitude and polar coverage.
As a result of its ability to provide high latitude and polar coverage, countries such as Russia which need coverage over polar and near polar areas make significant use of highly elliptical orbits, HEO. With two satellites in any orbit, they are able to provide continuous coverage.
fessor drives off with his car (mass 840 kg), but forgot to take his coffee mug (mass 0.41 kg) off the roof. The coefficient of static friction between the mug and the roof is 1.1, and the coefficient of kinetic friction is 0.4. What is the maximum acceleration of the car, so the mug does not slide off
Answer:
Acceleration =4.42m/s^2
Explanation:
As the mug is not sliding on the car roof ,there must be static friction between the car and the mug. The maximum limit of static friction that can act is given by:
Kmg
Where I is coefficient of static friction between car roof and mug
m = mass of mug
g= acceleration due to gravity
Acceleration of the car= Kmg
Acceleration = 1.1 × 0.41 × 9.8 =4.42m/s
Answer:
10.791 m/s^2
Explanation:
Solution:
- As the mug is not sliding on the car roof , there will be static friction between car and mug.
- The maximum limit of static friction that can act is given by = k*m*g
- Where, k = coefficient of static friction between the mug and the roof
m = mass of mug
g = acc. due to gravity
- So the maximum acc. of car ,
(m*a = k*m*g)
a = k*g
- Therefore max. a = 1.1*g = 1.1*9.81 = 10.791 m/s^2
f we apply an electrical stimulus to a muscle cell to cause it to contract, the magnitude of that stimulus must be strong enough to reach a critical value that is essential to initiate contraction. This critical value is known as __________.
Answer:
critical value is known as threshold
Explanation:
solution
when we apply electrical stimulus to the cell of muscle
then magnitude of stimulus will be strong enough for reaching the critical value
and this critical value is threshold because when the size of an stimulus change in requirement for the detection, this is called the threshold
but if change is done by without stimulation then there threshold stimulus is absolute threshold
so correct answer is threshold
The prominent semicircular space above a doorway in a Romanesque church portal is referred to as a ___________ and was often covered in elaborate carvings
Answer: Tympanum
Explanation: A Tympanum could be described as the semicircular space above the doorway or window or entrance of a building. The space is usually designed using elaborate sculptural designs, Rocky costumes and ornaments. The tympanum could also be triangular-shaped and attributed to classical Greece and Roman architecture. It is usually located between the portals archivolt and the lintel. The tympanum is commonly observed in the churches and temples of ancient Rome and Greece.
The semicircular space above a doorway in a Romanesque church portal is called a tympanum and it was often decorated with intricate carvings relating to religious themes.
Explanation:The prominent semicircular space above a doorway in a Romanesque church portal is referred to as a tympanum. These were often covered in elaborate carvings that represented religious imagery or important biblical stories. The Romanesque style of architecture, prevalent in Europe from the 9th to 12th centuries, was known for its massive quality, thick walls, and robust pillars. This style also romanticized elaborate decorative details, among them the beautifully carved tympanum.
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In 50 words or more, describe the scientific process that led to the development of the big bang theory. Include the key ideas and observations of the various scientists you've learned about.
Answer:
Explanation:
The Big Bang theory is a cosmological model of the observable universe from the earliest known periods through its subsequent large-scale evolution.
These theories were based on the hypothesis that all the matter in the universe was created in one big bang at a particular time in the remote past.
What led to big bang theory was that free electrons would have caused light (photons) to scatter the way sunlight scatters from the water droplets in clouds," NASA stated. Over time, however, the free electrons met up with nuclei and created neutral atoms. This allowed light to shine through about 380,000 years after the Big Bang.
The best-supported theory of our universe's origin centers on an event known as the big bang. This theory was born of the observation that other galaxies are moving away from our own at great speed in all directions, as if they had all been propelled by an ancient explosive force.
Origins of the universe, explained
The most popular theory of our universe's origin centers on a cosmic cataclysm unmatched in all of history—the big bang.
The best-supported theory of our universe's origin centers on an event known as the big bang. This theory was born of the observation that other galaxies are moving away from our own at great speed in all directions, as if they had all been propelled by an ancient explosive force.
A Belgian priest named Georges Lemaître first suggested the big bang theory in the 1920s, when he theorized that the universe began from a single primordial atom. The idea received major boosts from Edwin Hubble's observations that galaxies are speeding away from us in all directions, as well as from the 1960s discovery of cosmic microwave radiation—interpreted as echoes of the big bang—by Arno Penzias and Robert Wilson.
Further work has helped clarify the big bang's tempo. Here’s the theory: In the first 10^-43 seconds of its existence, the universe was very compact, less than a million billion billionth the size of a single atom.
It's thought that at such an incomprehensibly dense, energetic state, the four fundamental forces—gravity, electromagnetism, and the strong and weak nuclear forces—were forged into a single force, but our current theories haven't yet figured out how a single, unified force would work. To pull this off, we'd need to know how gravity works on the subatomic scale, but we currently don't.
What enables humans to see light in the infrared range of the electromagnetic spectrum
Answer: night vision goggles
Explanation: These goggles use technology to enhance all light, including the infrared rays, which aren't normally visible to the naked eye. This way you can see any type of light that is surrounding you.
please give brainliest!
Nothing does. That's why we can't see it without some sort of external imaging device.
Two cylindrical solenoids, A and B, each have lengths that are much greater than their diameters. The two solenoids have the same density of turns in their windings. Solenoid A has a diameter that is twice the diameter of solenoid B, but solenoid B has a length that is twice the length of solenoid A. How do their inductances compare with one another
Answer:
The inductance of solenoid A is twice that of solenoid B
Explanation:
The inductance of a solenoid L is given by
L = μ₀n²Al where n = turns density, A = cross-sectional area of solenoid and l = length of solenoid.
Given that d₁ = 2d₂ and l₂ = 2l₁ and d₁ and d₂ are diameters of solenoids A and B respectively. Also, l₁ and l₂ are lengths of solenoids A and B respectively.
Since we have a cylindrical solenoid, the cross-section is a circle. So, A = πd²/4.
Let L₁ and L₂ be the inductances of solenoids A and B respectively.
So L₁ = μ₀n²A₁l₁ = μ₀n²πd₁²l₁/4
L₂ = μ₀n²A₂l₂ = μ₀n²πd₂²l₂/4
Since d₁ = 2d₂ and l₂ = 2l₁, sub
L₁/L₂ = μ₀n²πd₁²l₁/4 ÷ μ₀n²πd₂²l₂/4 = d₁²/d₂² × l₁/l₂ = (2d₂)²/d₂² × l₁/2l₁ = 4d₂²/d₂² × l₁/2l₁ = 4 × 1/2 = 2
L₁/L₂ = 2
L₁ = 2L₂
So, the inductance of solenoid A is twice that of solenoid B
Consider two uniform solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is:_________.a) 2b) 8c) 4d) 10e) 6
Answer:
The ratio of moment of inertia of larger sphere to that of smaller sphere = 4
Explanation:
The moment of inertia of solid sphere is given by I = 2/5MR² where M = mass of sphere and R = radius of sphere.
Radius of smaller sphere = D/2
Radius of larger sphere = 2D/2 = D.
Moment of inertia of smaller sphere I₁ = 2/5M × D²/4 = MD²/10
Moment of inertia of larger sphere I₂ = 2/5M × D² = 2MD²/5
The ratio of moment of inertia of larger sphere to that of smaller sphere = I₂/I₁ = 2MD²/5 ÷ MD²/10 = 10 × 2/5 = 4
Consider a current carrying a wire coming out of your computer screen towards you. Which statement below correctly describes the magnetic field created by the current in the wire?
1. The magnetic field encircles the wire in a counterclockwise direction
2. The magnetic field encircles the wire in a clockwise direction
Answer:
The magnetic field encircles the wire in a reversal or counterclockwise direction
Explanation:
Lenz's law states that the direction of the current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field which produced it. According to Lenz law, the magnetic field encircles the wire in a reversal or counterclockwise direction.
Therefore, the first option is the correct answer.
In Millikan's experiment, an oil drop of radius 2.342 μm and density 0.816 g/cm3 is suspended in chamber C when a downward-pointing electric field of 1.92 ✕ 105 N/C is applied. Find the charge on the drop, in terms of e. (Include the sign of the value in your answer.)
Answer:
-14 e
Explanation:
Assuming oil drop is spherical then V = 4pi.r^3/3
density = 0.816 g/cm^3= 0.816 x 10^-3kg/cm^3= 0.816 x 10^-3/10^-6 kg/m^3= 0.816 x 10^3 kg/m^3
mass =(4 x 3.142 x (2.342 x 10^-6)^3 x 0.816 x 10^3)/3 kg
mass = (12.568 x 12.85 x 10^-18 x 0.816 x 10^3)/3 kg
m= 4.39 x 10^-14 kg
F=qE…. Eqn. 1
F=mg… Eqn. 2
Compare both eqn.1 and eqn. 2
qE=mg
q=mg/E
q = (4.39 x 10^-14 x 9.81)/1.92 x 10^5
q = 2.24 x 10^-18 C
Number of charges, n = 2.24 x 10^-18/1.62 x 10^-19
n=13.827
Charges come in integer values, nearest is 14
Number of charges is 14.
The direction of the field (downwards) is the direction a positive test charge would move. This means a positive charge would move downwards and repelled by the top plate which must be positive.
Since mg acts downwards then the other force must act up if the oil drop is suspended. This means that the charge is being attracted to the top plate which we have already determined is positive. for the charge to be attracted to the positive top plate then the charge must be negative.
Charge is electron hence the sign is minus.
-14 e
What should be the speed for this to happen? Assume that the radius of the Moon is rMrM = 1.74×106m×106m, and the mass of the Moon is mMmM = 7.35×1022kg.
Answer:
a. v = 1.679 × 10⁹ m/s b. The answer of v = 1.679 × 10⁹ m/s is not reasonable
Explanation:
Here is the complete question
You read in a science magazine that on the Moon, the speed of a shell leaving the barrel of a modern tank is enough to put the shell in a circular orbit above the surface of the Moon (there is no atmosphere to slow the shell).
A.....What should be the speed for this to happen? Assume that the radius of the Moon is rM = 1.74×106m, and the mass of the Moon is mM = 7.35×1022kg.(Express your answer to two significant figures and include the appropriate units.)
B.....Is this number reasonable?
Solution
From the question, the centripetal force in orbit for the shell = gravitational force of moon on shell.
So, mv²/r = GMm/r²
So v = √(GM/r) where v = velocity of shell, G = universal gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg², M = mass of moon = 7.35 × 10²² kg and r = radius of moon = 1.74 × 10⁶ m.
v = √(GM/r) = v = √(6.67 × 10⁻¹¹ Nm²/kg² × 7.35 × 10²² kg/1.74 × 10⁶ m)
v = √(49.0245/1.74 × 10¹⁷) m/s
v = √28.175 × 10¹⁷ m/s
v = √2.8175 × 10¹⁸ m/s
v = 1.679 × 10⁹ m/s
b. The answer of v = 1.679 × 10⁹ m/s is not reasonable because, it is over 1000000 km/s which is greater than the speed of light which is 300000 km/s
Because the block is not moving, the sum of the y components of the forces acting on the block must be zero. Find an expression for the sum of the y components of the forces acting on the block, using coordinate system b.
Answer:
Incomplete questions
Completed question, check attachment for diagram
Because the block is not moving, the sum of the y components of the forces acting on the block must be zero. Find an expression for the sum of the y components of the forces acting on the block, using coordinate system shown. Express your answer in terms of some or all of the variables
Fn, Ff, Fw and θ.
Explanation:
Check attachment for solution
Final answer:
The sum of the y components of forces on a stationary block must be zero due to Newton's second law, which results in the normal force being equal to the weight of the block.
Explanation:
In physics, when analyzing the forces acting on a stationary block, we apply Newton's second law, which implies that the net force in the y-component must be zero because the block is not moving vertically. An expression for the sum of the y components of the forces acting on the block can be deduced by considering all the vertical forces, including the weight of the block (acting downward) and the normal force (acting upward).
For a block on a frictionless surface attached to a spring, we consider the spring force and gravitational force. If the block is in equilibrium, these forces satisfy the equation mg = k Δy, where m is the mass of the block, g is the acceleration due to gravity, k is the spring constant, and Δy is the displacement from the equilibrium position. Therefore, the sum of the y components equates to zero: normal force - weight = 0, which also indicates that the normal force is equal to the weight.
Consider a steam power plant that operates between the pressure limits of 5 MPa and 10 kPa. Steam enters the pump as saturated liquid and leaves the turbine as saturated vapor. Determine the ratio of the work delivered by the turbine to the work consumed by the pump. Assume the entire cycle to be reversible and the heat losses from the pump and the turbine to be negligible
The ratio of the work delivered by the turbine to the work consumed by the pump in the steam power plant is 1.
To determine the ratio of the work delivered by the turbine to the work consumed by the pump in the steam power plant, we need to consider the energy conversions that occur in the cycle. The work done by the turbine is equal to the area under the pressure-volume curve in the turbine phase, while the work consumed by the pump is equal to the area under the pressure-volume curve in the pump phase. Since the process is reversible and heat losses are negligible, the amount of work done in the turbine is equal to the amount of work consumed by the pump. Therefore, the ratio of the work delivered by the turbine to the work consumed by the pump is 1.
Learn more about Steam power plant cycle here:https://brainly.com/question/31731141
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Tito knows that one of the reasons people do not return to his electronics store is because of the slow service. How would a SWOT analysis classify the slow service at Tito's electronic store?
It is classified as Weakness in SWOT analysis.
Explanation:
SWOT analysis is performed to understand the characteristics of any start ups. It is the abbreviation of Strength, Weakness, Opportunities and Threats. It helps in self analyzing and to plan strategically for improvements. So in this different loopholes, advantages, benefits, profits and loss attained by any organized is classified in these four options like Strength, Weakness, Opportunities and Threats.
In the present case, the problem of slow service speed by Tito's company lead to reduction in customers. Also many of the customers are not returning back due to its slow speed in servicing any instrument. So this loophole is placed in the box of weakness in SWOT analysis. So it is classified as Weakness in SWOT analysis.
Assume that a uniform magnetic field is directed into the monitor you are reading this on. If an electron is released with an initial velocity directed from the bottom edge to the top edge of the screen, which of the following describes the direction of the resultant force acting on the electron?a. out of the page
b. to the right
c. to the left
d. into the page
Answer:
b. to the right
Explanation:
In the given condition we have the magnetic field lines perpendicular to the direction of moving charges then here in this case we can apply the Fleming's left-hand rule to determine the force acting on the charges (here electrons).As the direction of magnetic field lines is into the screen and the electrons move form bottom of the screen towards up then we apply the Fleming's left-hand rule and find that the deviation will be towards right.We spread the index finger, thumb and the middle finger of our left hand mutually perpendicular to each other then we align the pointing of the index finger in the direction of the magnetic field and the middle finger in the direction of the current or the direction of the motion of the positive charge and if we have a negative charge then we take the direction to be opposite. Now the direction of the thumb pointing tells us the direction of the force.Final answer:
Using the left-hand rule for a negatively charged particle like an electron, the force on an electron moving upward with the magnetic field directed into the page is to the left. The correct answer is option c, to the left.
Explanation:
To determine the direction of the resultant force acting on an electron as it moves within a magnetic field, one can use the right-hand rule or, in the case of negatively charged particles like an electron, the left-hand rule. Considering that an electron is negatively charged, we apply the left-hand rule, with the thumb in the direction of the electron's velocity (from the bottom to the top edge of the screen), and the index finger in the direction of the magnetic field (into the page). The middle finger then points in the direction of the force experienced by the electron.
By this rule, for a magnetic field directed into the page and an electron moving upward, the resultant force will be to the left of the electron's initial direction of travel. The correct answer to the question is option c, to the left. This force will cause the electron to move in a circular path due to the magnetic Lorentz force.
Although solid matter is mostly empty space, we don't fall through the floor because atoms are constantly vibrating, even at absolute zero. of electrical forces. of gravitational forces. of nuclear forces. none of the above
We don't fall through the floor because of the electrical forces, specifically the electrostatic repulsion between negatively charged electrons surrounding atoms in both our bodies and the floor.
Although solid matter is mostly empty space, we don't fall through the floor because of electrical forces. Atoms consist mostly of empty space, with the volume of protons, neutrons, and electrons comprising less than 1% of an atom's total volume. The reason we perceive matter as solid and do not pass through the floor is that the electrons surrounding atoms are negatively charged, and the same charges repel each other. This repulsive electrostatic force is stronger at the scale we experience than gravitational force, which is comparatively weak.
Two machines, A and B, each working at a constant rate, can complete a certain task working together in 6 days. In how many days, working alone, can machine A complete the task?
your question is missing the given conditions, here is the complete question;
Two machines, A and B, each working at a constant rate, can complete a certain task working together in 6 days. In how many days, working alone, can machine A complete the task?
(1) The average time A and B can complete the task working alone is 12.5 days.
(2) It would take machine A 5 more days to complete the task alone than it would take machine B to complete the task
Answer:
Machine A, working alone, can complete the task in 15 days.
Explanation:
As the average is given as 12.5 so,
A+B=2*12.5
A+ B=25
second condition says machine A takes 5 more days to complete the task alone than B so
A=B+5........Eq1
Now from the question statement we can get that
1/A+1/B=1/6, where A is time needed for A to do the task alone and B is the time needed for B to complete the task alone
thus, simplyfing above equation we get as
AB/A+B=6; \\ putting A+B=25 we get
AB/25=6
AB=6*25
AB=150; \\ putting Eq1 we get
(B+5)B=150
B^2+5B-150=0
simplifying the quadratic equation above we get B=10
putting B=10 in Eq1, we get
A+10=25
A=15
Thus, Machine A, working alone, can complete the task in 15 days.
human beings can typically detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount
Answer: 1.25
Explanation:
The ratio of the amplitude of the sound can be calculated using the wave intensity by squaring the amplitude of the two wave particles.
Let the sound level be S2 and S1 and intensities be I1 and I2
Difference in sound level(S) = S2 - S1 = 2dB
Using the relationship between difference in sound level and Intensity
S2 - S1 = 10log(I2 ÷ I1)
Note : Intensity is the square of the amplitude of sound
Therefore,
I1 = A1^2 and I2 = A2^2
Substituting the values into the equation:
S2 - S1 = 10log (I2 ÷ I1)
2dB = 10log (A2^2 ÷ A1^2)
2dB = 10log(A2 ÷ A1)^2
2 dB= 20log(A2 ÷ A1)
2÷20 = log (A2 ÷ A1)
0.1 = log (A2 ÷ A1)
(A2 ÷ A1) = 10^0.1
A2/A1 = 1.25
The muzzle velocity of a gun is the velocity of the bullet when it leaves the barrel. The muzzle velocity of one rifle with a short barrel is greater than the muzzle velocity of another rifle that has a longer barrel. In which rifle is the acceleration of the bullet larger
Answer:small barrel gun
Explanation:
Given
Muzzle velocity of bullet is greater in short barrel gun as compared to larger barrel gun
acceleration is given by change in velocity with respect to time
[tex]a=\dfrac{\Delta v}{\Delta t}[/tex]
In case of short barrel bullet time taken by bullet to reach its muzzle velocity is less therefore acceleration of small barrel bullet is more compared to long barrel bullet.
Final answer:
The muzzle velocity of a bullet can be calculated using the formula v = u + at. Using the given acceleration of 6.20 x 10⁵ m/s² and time of 8.10 x 10⁻⁴ s, the muzzle velocity is 502 m/s.
Explanation:
To calculate the muzzle velocity of a bullet, which is the velocity of the bullet as it leaves the barrel of a gun, we can use the formula for uniform acceleration: v = u + at, where v is the final velocity, u is the initial velocity (which is 0 m/s in this case, as the bullet starts from rest), a is the acceleration, and t is the time. Here, we are given an acceleration of 6.20 × 10⁵ m/s² and a time of 8.10 × 10⁻⁴ s. Plugging these values into the formula gives us the muzzle velocity.
Using the formula, we have: v = 0 m/s + (6.20 × 10⁵ m/s²)(8.10 × 10⁻⁴ s), which simplifies to v = 502 m/s. Therefore, the muzzle velocity of the bullet is 502 meters per second. This value represents how fast the bullet is traveling when it exits the gun barrel.
An ice cream machine produced 44 ice creams per minute. After reconditioning, its speed increase to 55 ice creams per minute. By what percent did the speed of the machine increase
Answer:
an ice cream machine produced 44 ice cream per minute.
Now, after reconditioning it speeds up to 55 ice cream per minute.
=> 55 - 44 = 11
=> 11 / 44 = 0.25
=> 0.25 * 100% = 25%.
thus it increased it production to 25%.
Explanation:
Answer:
25%
Explanation:
The way to find this answer is to:
Subtract 44 from 55 (11)
Then, you can put 11 over 44
Simplified, this is equal to 1/4.
1/4 as a percentage is 25%.
Good luck with your RSM work!
When Dr. Hewitt immerses an object in water the second time and catches the water that is displaced by the object, how does the weight lost by the object compare to the weight of the water displaced?
Answer:
The weight loss of object is equal to the weight of water displaced.
Explanation:
- When the object is immersed the force of Buoyancy acts against the weight and reducing the scale weight.
- The amount of Buoyancy Force is proportional to the fraction of Volume of object immersed in water; hence, the same amount is spilled/lost.
- The amount of water is proportional to the volume of object of fraction of object immersed in water will lead to the same fraction of water displaced and caught by Dr. Hewitt.