The angle of total acceleration with centripetal acceleration is 13.14 degree.
What is acceleration?
The rate at which an object's velocity with regard to time changes is referred to as acceleration in mechanics. It is a vector quantity to accelerate. The direction of an object's acceleration is determined by the net force that is acting on it. the quantity of acceleration a body undergoes in accordance with Newton's Second Law. For instance, when a vehicle moves from the a standstill (nil velocity, inside of an inertial frame of reference to the a straight line at increasing speeds, it accelerates inside the direction of travel.
Here ,
radius , r = 0.380 m
angular velocity , w = 1.50 rad/s
angular acceleration ,alpha = 2 rad/s^2
after the time 0.5 s
for the final angular velocity
wf = wi + alpha * t
wf = 1.50 + 2 * 1
wf = 2.5 rad/s
Centripetal Acceleration: wf2 * r
ac = 2.5^2 * 0.380 m/s^2
ac = 2.375 m/s^2
for tangential acceleration
at = alpha * r
at = 1.5 * 0.380
at = 0.57 m/s^2
a) for the total acceleration = sqrt(at^2 + ac^2)
total acceleration = sqrt(2.375^2 + 0.57^2)
total acceleration = 2.44 m/s^2
b)
angle =arctan(at/acceleration)
angle = arctan(0.57/2.44)
angle = 13.14 degree
The angle of total acceleration with centripetal acceleration is 13.14 degree
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a 0.29 kg harmonic oscillator has a total mechanical energy of 3.6 j. if the oscillation amplitude is 0.22 meters, what is the oscillation frequency f?
If the oscillation amplitude is 0.22m, from a 0.29kg harmonic oscillator which has a total of mechanical energy 3.6j, the oscillation frequency is 4.141Hz.
What is oscillation frequency?It is a number of oscillations in the one-time unit, says per second. For example, a pendulum that takes 0.5s to make one full oscillation has a frequency of 1 oscillation per 0.5s or 2 oscillations / second.
How to calculate the oscillation frequency?
mass (m) = 0.29kg
Total energy (E) = 3.6j
amplitude (x) = 0.22m
E = 1/2 k*x^2
k = 2*E / x^2
= 2 * 3.6 / 0.22^2
= 148.76 N/m
Frequency (v) = 1/2π √k/m
= 1/2*3.14 * √148.76 / 0.22
= 4.141Hz
Therefore, the oscillation frequency is 4.141Hz.
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17. Astronomers estimate that the plains of venus are only about 500 to 600 million years old. How do they estimate dates like this?
They estimate dates by counting the number of craters visible on the surface and comparing crater counts to other worlds.
Crater counting is a technique for determining the age of a planet's surface based on the suppositions that impact craters are absent from freshly formed planetary surfaces and that they collect through time at a known pace.
The density of craters on a planet's surface can be used to estimate the relative ages of various regions; the older the surface, the more craters it has accumulated.
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if the collision is elastic, what are the final velocities v1 and v2 of particles 1 and 2? give the velocity v1 of particle 1 followed by the velocity v2 of particle 2, separated by a comma. express each velocity in terms of v.
Velocities V1 and V2 will exchange in general. Velocity may increase or decrease. If V1 decreases, then V2 increases. The angle between velocities also gets changed.
For a head-on elastic collision for two equal masses, the velocities gets exchanged. For a non-head-on elastic collision for two equal masses, the angle between the velocities is always 90 degrees.
Where the projectile is much heavier than the target, the velocity of the given target particle changes to about twice that of the projectile after the collision. And the projectile velocity will remain unchanged. In this case, the angle between the projectile and the target remains less than 90 degrees.
In the case of a head-on elastic collision, when there is a small projectile and a much more heavy target, the projectile will bounce back with the same speed, and the massive target will gain a very small velocity. In this case, the angle of the path of the projectile will be more than 90 degrees.
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Determine the magnitude and direction of the force between two parallel wires 35 m long and 7.0 cm apart, each carrying 35 A in the same direction. O The force on each wire will be attractive. O The force on each wire will be repulsive. O The wires will not interact.
3.5*10^-5 N/m is the magnitude of the force between two parallel wires 35 m long and 7.0 cm apart, each carrying 35 A current and the force on each wire will be repulsive.
What is Magnitude of force means?The number which shows or represents the strength of the force is termed as the magnitude of that force.
Data given :
Two parallel wires
35 m long and 7.0 cm apart,
each carrying 35 A current .
To find the magnitude and direction of current.
f=μ/4π*2[tex]I_{1}[/tex][tex]I_{2}[/tex]/d
f=[tex]10^{-7}[/tex]*2*35*35/7
f=3.5*10^-5
Hence, 3.5*10^-5 N is the magnitude of the force between two parallel wires 35 m long and 7.0 cm apart, each carrying 35 A current.
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(c) a cylindrical rod of uniform density is located with its center at the origin, and its axis along the z axis. its radius is 0.06 m, its length is 0.7 m, and its mass is 4 kg. it makes one revolution every 0.05 s. if you stand on the x axis and look toward the origin at the rod, the rod spins clockwise. what is the rotational angular momentum of the rod? what is the rotational kinetic energy of the rod?
Angular momentum is given by L=Iω.becomes part of their thermal energy.
In physics, angular momentum is the rotational analog of linear momentum. Its miles are an essential physical amount due to the fact it's miles a conserved amount the overall angular momentum of a closed machine stays steady. Angular momentum has a route and significance, and each is conserved.
Angular momentum is described as The assets of any rotating object given by using second of inertia instances angular speed. it's miles the property of a rotating body given via the product of the instant of inertia and the angular velocity of the rotating object.
The method for angular momentum is written as L = Iω, where L is angular momentum, I is rotational inertia and ω the Greek letter omega is angular speed. To simplify this, you can say that an item's angular momentum is the product of its mass, speed, and distance from the point of rotation.
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According to the principle of continuity, the velocity of a fluid multiplied by the cross section through which it flows at one point will equal the product ofA) velocity and cross section at another point.B) velocity and pressure at another point.C) a constraint factor.D) none of the above
According to the principle of continuity, the velocity of a fluid multiplied by the cross-section through which it flows at one point will equal the product of velocity and cross-section at another point.
The principle of continuity, also known as the continuity equation, is the fluid mechanic's principle. Simply put, what flows into a defined volume over a specified period of time minus what flows out of that volume over that specified period of time must accumulate in that volume. The substance in that volume is depleted if the accumulation's sign is negative.
This is so that our eyes, once they start to follow anything, will keep moving in that direction until they come across another thing or object. A line with an arrow at the end of it, for instance, is a great illustration of the continuity concept.
Note that three conditions must be met for a function to be continuous at a point: At that time, the limit must exist.
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mass of blood. the human body typically contains 5.1 l of blood of density 1060 kg/m3 . how many kilograms of blood are in the body?
If the human body typically contains 5.1 L of blood of density 1060 kg/m³, there are 5 kilograms 406 ounce of blood in the body.
The density of blood plаsmа is аpproximаtely 1025 kg/m³ аnd the density of blood cells circulаting in the blood is аpproximаtely 1125 kg/m³. Blood plаsmа аnd its contents are known аs whole blood. The аverаge density of whole blood for а humаn is аbout 1060 kg/m³.
e = 1.060 kg/liter ⇒ change to m³
e = 1.060 × [tex]10^{-3}[/tex]
Blood is in the body (m):
m = e × v
m = 1.060 × 5.1 × [tex]10^{-3}[/tex]
m = 5.406 × [tex]10^{-3}[/tex] kg
m = 5 kg 406 ounce
The аverаge density of whole blood for а humаn is 1.060 kg/liter. So, 5.1 liters of аverаge blood will weigh 5 kg 406 ounce.
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in comparing two unequal forces on a rigid body, is it possible to have the larger force produce less torque than the smaller force?
Different torques can be generated by the same force. When the force and lever arm are both large, greater torques are generated.
Explain about the torques?A torque is a linear force's reciprocating rotating counterpart. Distance travelled over a predetermined period of time is referred to as speed. Torque and speed are related to one another inversely in proportion. Numerically describing the torque of a rotating object is done by dividing power by angular velocity.
Torque is the unit of measurement for the force that may rotate an item around an axis. The acceleration of an item in linear kinematics is caused by force. An angular acceleration is caused by torque in a manner similar to this. It follows that torque might be viewed as the rotational counterpart to force.
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) what are the possible reasons we discussed for the existence of different types of galaxies in the universe?
There are many different sizes and shapes of galaxies. Low-angular-momentum protogalactic clouds may have generated spheroidal star systems, whereas clouds with larger angular
what is angular momentum?The characteristic of just about any rotating object determined by the product of the moment of inertia and the angular velocity is known as angular momentum. It is a characteristic of rotating bodies determined by the sum of their moment of inertia + angular velocity.
Why is angular momentum important? What is it?The rotational equivalent of linear momentum in physics is called angular momentum, also known as moment of momentum , rotational momentum. Because this is a constant number total angular momentum of such a closed environment stays constant—it is a significant physical quantity.
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A 45. 0 kg woman stands up in a 60. 0 kg canoe 5. 00 m long. She walks from a point 1. 00 m from one end to a point 1. 00 m from the other end (fig. P8. 92). If you ignore resistance to motion of the canoe in the water, how far does the canoe move during this process?.
The distance that the canoe moves in this process is 1.29 meters.
We first have to find the center of mass
X = MsXs + McXc/ Mw+Mc
Where
Ms = Woman's mass = 45
Mc = Canoe's mass = 60kg
Xs = position from left= 1 cm
Xc = position from left end of canoe's mass = 2.5cm
When we put these values into the equation we have:
X= 1.857
The center of gravity lies at the center of this boat. Therefore,
3.14 metres
To get the distance that is moved by this canoe distance = 3.143-1.857
= 1.286
≈ 1.29 meters
Thus, The distance that the canoe moves in this process is 1.29 meters.
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Hand warmers and instant cold packs use _____________________ that release or absorb thermal energy.
Answer: Endothermic and Exothermic reactions
An infinitely long wire carrying a current of 3.10 A is bent at a right angle as shown in the figure. Determine the magnitude and direction of the magnetic field at the point P a distance
a = 23.9 cm
from each leg of the right angle bend.
magnitude ? T
direction ?
The direction of the magnetic field depends on the direction of the current in the wire.
What is magnetic field?
A magnetic field is indeed a vector field which explains the magnetic influence on moving electrical charges, electric currents, as well as magnetic materials. A force perpendicular to the charge's own motion and the magnetic field acts on it when the charge is moving through a magnetic field. The magnetic field of a permanent magnet pulls on magnetic material like iron and attracts as well as repels other magnets. The three other magnetic effects of paramagnetism, diamagnetism, as well as antiferromagnetism also exert minute forces on "nonmagnetic" materials in a nonuniform magnetic field, though these forces are typically so minute that they can only be discovered by laboratory equipment. Electric currents, like those used in electromagnets, as well as electric fields that change over time produce magnetic fields that surround magnetised materials.
The magnitude of the magnetic field at P can be determined using the equation B = μ0I/2πr, where μ0 is the permeability of free space, I is the current, and r is the distance from the wire. Thus, the magnetic field at P is:
B = (4π x 10-7 T•m/A) x (3.10 A) / (2π x 0.239 m) = 0.817 T
The direction of the magnetic field depends on the direction of the current in the wire. If the current is flowing in the clockwise direction, then the magnetic field will be directed out of the plane of the paper at P. If the current is flowing in the counterclockwise direction, then the magnetic field will be directed into the plane of the paper at P.
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a 185 g185 g object is attached to a spring that has a force constant of 78.5 n/m.78.5 n/m. the object is pulled 8.25 cm8.25 cm to the right of equilibrium and released from rest to slide on a horizontal, frictionless table. calculate the maximum speed ????maxvmax of the object.
The maximum speed of the object is 1.28 m/s.
What is Speed?
Speed is described as the rate at which an object's position changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it only has a direction and no magnitude.
One meter per second is the speed of an object, for instance, if it starts at the origin and moves three meters in three seconds. Simple math can be used to calculate speed. time-distance ratio.
According to the given information:
Force constant K:78.5 n/m
Mass: 0.185 kg
The maximum speed of the object is,
[tex]$$\begin{aligned}v_{\mathbf{n} E} & =A \omega \\& =A \sqrt{\frac{k}{m}}\end{aligned}$$[/tex]
Here A is the amplitude, k is force constant, m is mass.
[tex]$$\begin{aligned}v_{\mathrm{ne:}} & =\left(6.25 \times 10^{-2} \mathrm{~m}\right) \sqrt{\frac{78.5 \mathrm{~N} / \mathrm{m}}{0.185 \mathrm{~kg}}} \\& =1.28 \mathrm{~m} / \mathrm{s}\end{aligned}$$[/tex]
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which of the following provides evidence that a warming planet is related to human behavior (select all that apply; there are one to four possible correct answers)? scientists showing that increasing levels of carbon dioxide cannot impact our climate scientific research showing that temperatures have risen along with carbon dioxide emissions from the nineteenth century scientists agreeing that the earth can only sustain an atmospheric concentration of carbon of about 39,000 parts per million scientific discoveries that burning coal changes the climate by increasing the levels of carbon in the atmosphere
Discoveries that burning coal changes the climate by increasing the levels of carbon in the atmosphere provide evidence that a warming planet is related to human behavior, which causes global warming.
What is Global Warming?
The heating of the earth's surface is due to an increase in carbon content and another pollutant in the atmosphere that, traps the heat being radiated back by the earth's surface, which in turn increases the temperature.
What are pollutants?
Pollutants are a substance that increases the toxicity of something, such as air, water, land, etc., and thus contributes to pollution.
what is pollution?
Pollution is the contamination of the environment by toxic substances, such as nitrogen oxide, carbon monoxide, Ground level ozone, etc. that increase the toxicity of the environment and are hazardous for living organisms.
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at what rate will a pendulum clock run on the moon, where the acceleration due to gravity is 1.631.63 m/s2, if it keeps time accurately on earth? that is, find the time (in hours) it takes the clock's minute hand to make one revolution on the moon.
The time it takes the clock's minute hand to make one revolution on the moon is (1.631.63/9.8)^2 * 60 minutes, or roughly 1.4 hours.
What is revolution?
When the populace rebels against the government, usually because of perceived oppression (ideological, social, or economic), or political incompetence, a revolution is defined in political science as a fundamental and comparatively unexpected change in political politics and influence organisation.
The period of a pendulum is determined by the equation T = 2π√(L/g), where T is the time it takes for the pendulum to make one complete oscillation, L is the length of the pendulum, and g is the acceleration due to gravity. Thus, on the moon, the period of the pendulum is T = 2π√(L/1.631.63 m/s2).
On Earth, the period of a pendulum is T = 2π√(L/9.8 m/s2). Thus, the ratio between the period on the moon and the period on Earth is T_moon/T_Earth = (2π√(L/1.631.63 m/s2))/(2π√(L/9.8 m/s2)) = sqrt(1.631.63/9.8).
Since the period of the pendulum is related to the time it takes for the clock's minute hand to make one revolution, the ratio between the time it takes the clock's minute hand to make one revolution on the moon and the time it takes the clock's minute hand to make one revolution on Earth is (T_moon/T_Earth)^2 = (1.631.63/9.8)^2.
Therefore, the time it takes the clock's minute hand to make one revolution on the moon is (1.631.63/9.8)^2 * 60 minutes, or roughly 1.4 hours.
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a student finds the mass of a pure sample of a metal chloride hydrate. the student heats the sample several times, reaching a constant mass that contains 0.100 mole of anhydrous metal chloride. which of the following questions about the hydrated metal chloride substance is most likely to be answered by the results of the experiment?
Answer:How many moles of water are in one mole of the substance?
Explanation:
Mole measure the number of elementary entities of a given substance that are present in a given sample. Therefore, "How many moles of water are in one mole of the substance".
What is mole?The SI unit of amount of substance in chemistry is mole. The mole is used to measure the quantity or amount of substance. We know one mole of any element contains 6.022×10²³ atoms which is also called Avogadro number.
Mathematically,
mole =given mass ÷ molar mass
A student finds the mass of a pure sample of a metal chloride hydrate. the student heats the sample several times, reaching a constant mass that contains 0.100 mole of anhydrous metal chloride. The most important question that can be asked from this experiment is "How many moles of water are in one mole of the substance".
Therefore, "How many moles of water are in one mole of the substance".
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A solenoidal coil with 30 turns of wire is wound tightly around another coil with 310 turns. The inner solenoid is 20.0 cm long and has a diameter of 2.50 cm. At a certain time, the current in the inner solenoid is 0.150 A and is increasing at a rate of 1700 A/s.
Part A For this time, calculate the average magnetic flux through each turn of the inner solenoid.
Part B For this time, calculate the mutual inductance of the two solenoids.
Part C For this time, calculate the emf induced in the outer solenoid by the changing current in the inner solenoid.
The emf induced in the outer solenoid by the changing current in the inner solenoid is: 3.93 x [tex]10^{-2}[/tex] Volt .
Given that -
Number of turns in inner solenoid = N1 = 300
Number of turns in outer solenoid = N2 = 30
Length of inner solenoid = L= 24.0 cm = 0.24 m
Radius of inner solenoid = r = diameter/2 = 2.5/2=1.25 cm = 0.0125 m
The current in the inner solenoid = i = 0.140 A
Rate of increasing of current =di/dt = 1700 A/s.
(A) The average magnetic flux through each turn of the inner solenoid. =B.A
Put the values,
The average magnetic flux through each turn of the inner solenoid:
= 1.08 x [tex]10^{-7}[/tex] Wb
(B) Mutual inductance of the two solenoids, M = N2 x (average flux) / current= = 2.314 x [tex]10^{-5}[/tex]H
(C) The emf induced in the outer solenoid by the changing current in the inner solenoid.= M×di/dt
= 3.93 x [tex]10^{-2}[/tex] Volt
What is a solenoid?
A solenoid is a type of electromagnet consisting of a helical coil of wire whose length is much greater than its diameter, creating a controlled magnetic field. A uniform magnetic field can be generated in a certain space by passing an electric current through the coil. The term solenoid was coined by André-Marie Ampère in 1823.
The electromagnet's coil does not necessarily have to rotate about a linear axis. For example, William Sturgeon's his 1824 electromagnet consisted of a solenoid bent into a horseshoe shape (similar to an arc spring).
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the evil team of ms. moonstruck and mr. luny intend to deflect the moon from its orbit around earth by pulling it with a force of 3530 n . they plan to accomplish this by placing a mini black hole 7.33×106 m from the center of the moon and letting gravitation do what gravitation does. what must the mass of the mini black hole be for the evil duo's evil scheme to succeed? the mass of the moon is 7.36×1022 kg .
In order for the wicked duo's plot to work, a small black hole with a mass of 38634.83 kg must exist.
How does science define force?Science has a specific definition for the term "force." At this point, describing a force as being pushed or pulled is quite acceptable. A strength is not something that something "contains" or "has in it." A force is applied to one thing by another. The idea of such a force encompasses either living and non-living things.
Briefing:To overcome this issue, you should be aware of Isaac Newton discovered an equation that expresses the gravitational effect of two mass-bearing things at a distance r. The formula is as follows:
where,
G = It is the universal gravitational constant = 6.67 x 10⁻¹¹ Nm²/kg²
m₁ = mass of the moon=7.36 × 10²² kg
m₂ = mass of the mini black hole
r = distance=7.33 × 10⁶ m
F = force=3530N
solving for m;
(F)(r²)/m₁(G) = m₂
3530*[(7.33 × 10⁶)²]/(7.36 × 10²²) (6.67 x 10⁻¹¹) = m₂
m₂ = 38634.83 kg
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a novelty clock has a 0.014-kg mass object bouncing on a spring that has a force constant of 1.6 n/m. (a) what is the maximum velocity of the object if the object bounces 3.45 cm above and below its equilibrium position?
Answer: The maximum velocity of the object if the object bounces 3.45 cm above and below its equilibrium position is 4.62 m/s.
Reason:
The maximum velocity of the object is 4.62 m/s. This can be calculated by using the equation v = sqrt(2 * g * x), where g is the acceleration due to gravity (9.8 m/s2) and x is the displacement from the equilibrium position (3.45 cm), or 0.0345 m.
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a bicycle and ridder together have a momentum of 318 kg*m/s and are moving at 8 m/s l. what is their combined mass?
Answer: 39.75 kg
Explanation:
p = mv where,
p = momentum
m = mass
v = velocity
Given p=318 kg*m/s
v=8 m/s
therefore, 318=8*m
or, m= 318/8= 39.75
how big does the sun appear to be from plutos surface from the neighborhood of pluto, new horizons took this photo showing the disk of pluto with the sun shining to the upper left
The solar seems to be 1/39th, or zero.026 times as large as visible from Earth. when considered from the floor of Pluto.
Pluto is so far away from the sun (common distance to her is three,670,050,000 miles) that the solar seems much darker and smaller than it does from Earth.
From Pluto, the solar seems as a very brilliant star, illuminating Pluto at some point of the day approximately as a great deal as the whole Moon illuminates the Earth at night.
Nearest (perihelion) 2.seventy six billion miles from our megastar. at the furthest point (Aphelion) it's miles four.58 billion miles away. that is approximately zero.000456308 light years from sun.
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At a construction site, a 22.0 kg bucket of concrete is connected over a very light frictionless pulley to a 375 N box on the roof of a building. There is no appreciable friction on the box, since it is on roller bearings. The box starts from rest.
A. Find the acceleration of the bucket.
B. How fast is the bucket moving after it has fallen 1.50 m (assuming that the box has not yet reached the edge of the roof)?
A. The acceleration of the bucket is 3.58 m/[tex]s^{2}[/tex].
B. bucket is moving with a velocity of 3.28 m/s.
What is acceleration?
If an object's velocity changes, it is said to have been accelerated. An object's velocity can alter depending on whether it moves faster or slower or in a different direction. A falling apple, the moon orbiting the earth, and a car stopped at a stop sign are a few instances of acceleration. Through these illustrations, we can see that acceleration happens whenever a moving object changes its direction or speed, or both.
What is Velocity?
The direction in which a body or an object is moving.
What are the calculations?
Given that the mass of bucket m = 22.0 kg
Weight of the box W = 375 N
Then the mass of box M = W / g
= 375 / 9.8 m/[tex]s^{2}[/tex]
= 38.27 N
Let T be the tension in the string
Let a be the acceleration of the bucket
Apply Newton's second law to the bucket
mg - T = ma
T = m (g - a) ....... (1)
Apply Newton's second law to the box
T = Ma ....... (2)
From equations (1) and (2) we get
Ma = m (g-a)
( m+ M )a = m g
a = m g / (M + m)
= (22.0 kg) (9.8 m/[tex]s^{2}[/tex]) / (22.0 kg + 38.27 kg )
= 3.58 m/[tex]s^{2}[/tex]
Initial velocity of the bucket u = 0
Let v be the final velocity of the bucket after displacement s = 1.5 m
From equation of motion
v2 - u2 = 2as
v2 - 0 = 2as
v = √2as
v = √2(3.58 m/[tex]s^{2}[/tex])(1.5 m)
v = 3.28 m/s
Hence, the acceleration of the bucket is 3.58 m/[tex]s^{2}[/tex] and the bucket is moving with a velocity of 3.28 m/s.
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What is shepherding? (it involves space)
Answer:
What is a Shepherd planet?
Image result for What is shepherding? (it involves space)
An international team of astronomers exploring the disk of gas and dust around a nearby star have uncovered a compact cloud of poisonous gas formed by ongoing rapid-fire collisions among a swarm of icy, comet-like bodies.
Explanation:
(a) find the work done by f in moving an object from a point p1 along a path to a point p2 in terms of the distances d1 and d2 from these points to the origin. (b) an example of an inverse square field is the gravitational field f
The strength of gravitational or electrostatic fields is frequently determined using the inverse square law as an illustration, the Earth's surface has a gravitational field strength of about 9.8 N/kg.
Take note that the field F(r) is a vector along the ray passing through each point in space with the coordinates r=(x, y, z) and coming from the coordinate center. So you can visualize the entire field as a blast from a single central point. Picture two points A and B on a sphere with radius |A| that are both located at the same distance from 0 and a path that connects them. You would expend no energy to move a particle along this path because you are always orthogonal to the force's direction. Work accounted for is the work along the path from distance |P2| to distance |P1| along this ray. For all intents and purposes, the points P1 and P2 can be located on the same ray emanating from the origin (while preserving only their distances from it). This is conservative as per physics forums.To understand about gravitational field strength-
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a ferris wheel starts from rest and builds up to a final angular speed of 1.9 rad/s while rotating through an angular displacement of 4.9 rad. what is its average angular acceleration?
The average angular acceleration of a Ferris wheel with final angular speed 1.9 rad/s and angular displacement 4.9 rad is 0.37 radians per square second.
What is angular displacement ?
The angle at which a point revolves around a particular axis or centre defines the angular displacement of a body. Because a body rotates about its axis, its motion cannot simply be analysed as a particle because it is constantly altering its speed and acceleration.
According to the given information
Angular speed = 1.9 rad/s
Angular displacement= 4.9 rad
Let the Ferris wheel accelerates at constant rate,then
[tex]w^{2} = w{o} ^2 + 2.\alpha .[/tex] (θ - θo)
given that
[tex]w_{0 }[/tex] = 0 rad/s
[tex]w[/tex] = 1,.9 rad/s
θ - θo = 4.9 rad
α = [tex](1.9 rad/s)^{2} - (0 rad/s)^{2} / 2. (4.9 rad )[/tex]
α = 0.37 [tex]rad/s^{2}[/tex]
The time needed to accelerate the Ferris wheel uniformly is given by-
[tex]w = w_{0} + \alpha .t[/tex]
t = [tex]1.9 - 0 / 0.37[/tex]
t = 5.13 sec
now average angular velocity = [tex]\frac{w - w_{0} }{t}[/tex]
[tex]\alpha _{avg}[/tex] = 1.9- 0/ 5.13
= 0.37 [tex]rad/s^{2}[/tex]
The average angular acceleration of the ferris wheel is = 0.37 [tex]rad/s^{2}[/tex].
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Sam is racing her soapbox racer on a straight downhill track. Suppose that the track is 1000 feet long and her distance down the track in feet is given by the function S (t) = t 2 + 30t, where t is in seconds. Assume that S ′(t) = 2t + 30. Sam is trying to break the soapbox racer speed record of 65 feet per second. Does she do it as she races down the 1000 foot track?
Yes, she breaks the record.
Given
distance of track = 1000 feet = 304.8 m
S(t) = t² + 30t
After differentiating we get,
S'(t) = 2t + 30
S''(t) = 2
The time taken by racer = 65 feet per second.
Time taken to for 1000 feet,
1000/65 = 15 second.
Time taken by Sam = S''(t) = 2 by which we can know that the time taken by Sam is less than that of the racer.
Therefore, with differentiating equation, she can surpass the racer and break the record.
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A Private jet flies the same distance in 10 hours That it commercial jet Flies in 6 hours. If the speed of the commercial jet was 200 mph less than 3 times the speed of a private jet. Find the speed of each jet.answer:Speed of private jet:Speed of commercial jet:
The speed of the private jet and the commercial jet were 200mph and 400mph respectively.
The private jet flies the same distance in 10 hour that the commercial jet cover in 6 hours.
The speed of the commercial jet is 200mph less than 3 time of the speed of private jet.
Now, if we assume the speed of Private jet to be X mph then the speed of the commercial jet will be (3X - 200) mph.
If the distance cover is D, then, for the private jet,
D = 10X
For commercial jet,
D = (3X-200)6
Now, we can write,
10X = 18X - 1200
6X = 1200
X = 200 mph.
So, the speed of the private jet was 200mph and the speed of the commercial jet was 400mph.
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which message travels faster - the one that travels along the surface of the axon or the one that jumps from node to node? group of answer choices
In case of node to node, the message travels faster. Our brain can exchange signals with our toes in a few thousandths of a second by jumping signals hundreds of times quicker than signals that travel along the surface of the axon.
Which axon conducts impulses most quickly ?The speed of nerve impulse conduction is accelerated by the presence of a myelin sheath. Similar unmyelinated axons conduct impulses about ten times slower than myelinated ones do.
Action potentials "jump" from node to node as they move down the axon. The term saltatory conduction, which means "to leap," describes this. Moving in an axon with myelin is slower than traveling along an axon through saltatory conduction.
E. myelinated neurons conduct impulses at the quickest speeds. A fatty layer called myelin surrounds the neuronal axon. When compared to continuous conduction on unmyelinated axons, saltatory conduction on myelinated axons is a faster and more energy-efficient type of impulse conduction.
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A block of iron has the dimensions of 3. 00 cm x 3. 00 cm x 3. 00 cm. It has a mass of 213 g. What is its density? 0. 0773 g/cm 3 638 g/cm 3 7. 89 g/cm 3 6240 g/cm 3.
Density of iron block is 7. 89 g/cm 3
Define density.
The substance's mass per unit of volume is its density (also known as specific mass or volumetric mass density). The Latin letter D can also be used to represent density, however the most common symbol is ρ (the lower case Greek letter rho). The mathematical definition of density is mass divided by volume.
Density, ρ = Mass (m)/ Volume(V)
Volume = 3 cm × 3cm × 3cm
= 27 cm ³
Mass = 213 g
Density = m/V
= 213/27
= 7.89 g / cm³
The word "specific volume," which is infrequently used in thermodynamics, refers to the reciprocal of a substance's density. A substance's density is an intense attribute in that its mass grows rather than its density when its amount is increased.
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a large metal ball is at rest, and a small rubber ball is moving at a high velocity. when they collide, the large metal ball begins to roll slowly. what must have happened to the momentum of the small rubber ball?(1 point)
The small rubber ball was moving quickly as well as a huge metal ball is now at rest. The massive metal ball starts to roll more slowly once they meet, slowing the small rubber ball's speed.
What is a momentum in physics?Momentum is characterized as the intensity of a body's motion. As momentum depends on both velocity as well as the direction of a body's motion, it is quantified by "mass velocity". Because velocity is just a vector and mass is a scalar, momentum is a vector.
What is momentum and example?Momentum can be viewed as a body's "power" while it is moving, or the amount of force it can exert on another body.
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