The amount of work performed on the blade by the motor in one minute is 960 J if the blade rotates at a constant angular velocity of 20 rad/s.
A force that generates rotation is known as a torque. demonstrates how well a force can rotate or twist an object.
We are know that,
Torque = F = 0.80N
Angular velocity = ω = 20rad/s
To calculate the value of work done we can use the equation,
work = torque x angular displacement
θ = ωt
θ = 20rad/s x 60s
θ = 1200rad
Then , from the above value we can calculate,
work = 0.80N x 1200rad
W = 960J
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A 20-N crate starting at rest slides down a rough 3 m long ramp, inclined at 30 degree with the horizontal. The force of friction between crate and ramp is 6 N. What is the kinetic energy of the crate at the bottom of the ramp? Zero 2 J 8 J 12 J 32 J
The velocity of the crate is 12 m/s and kinetic energy of the crate at the bottom of the ramp is 144.06 J.
Given that,
Weight of the crate = 20 N
Length of the ramp = 3 m
Inclination of the ramp with horizontal = 30°
The friction between the ramp and the crate = 6 N
Potential energy of the crate at the top = 20 * 3 sin 30° = 30 J
Energy lost due to friction = 6 N* 3 m = 18 J
Let the speed of the crate at the bottom be v.
Applying the law of conservation of energy,
30 - 18 = 1/2* (20/9.8)* v²
(12* 24)/2.04 = v²
v² = 141.18
v = 11.88 m/s ≈ 12 m/s
The kinetic energy of the crate at the bottom of the ramp = 1/2* m* v²
⇒ 1/2* (20/9.8)* 141.18 = 144.06 J
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Your car speeds around the 80-m-radius curved exit ramp of a freeway. A 70-kg student holds the armrest of the car door, exerting a 220-N force on it in order to prevent him self from sliding across the vinyl-covered back seat of the car and slamming into his friend. How fast is the car moving in meters per second and miles per hour? What assumptions did you make?
The speed of the car in miles per hour and meters per second is 2.2369
Explain about the speed?The first person to calculate speed by accounting for both the distance travelled and the amount of time required was the Italian physicist Galileo Galilei. Galileo described speed as the distance travelled in a unit of time.
The speed of anything indicates how quickly it is moving. Miles per hour (mph), kilometres per hour (km/h), and metres per second (m/s) are the three most used speed measurement units (mph).
A speedometer is the most effective tool for demonstrating instantaneous speed. Another method to state the speed of light is as 186,282 miles per second. The speed of sound in dry air is 343.2 metres per second. The term "escape velocity" refers to the speed necessary to escape the gravitational pull of the Earth.
Radius = 80 m
mass of the student m = 70
Force = 220
F/M =220 / 70
=3.14 m
3.14 = v2/80
=15.85m/s
1 m/s = 2.2369 miles per hour
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Joe pushes a 50 kg box for 3 meters.
What is Joe's speed?
Explanation:
It is not possible to determine Joe's speed based on the information provided. Speed is a measure of how quickly an object moves over a given distance and is calculated by dividing the distance traveled by the time it took to travel that distance. In order to determine Joe's speed, we would need to know how long it took him to push the box 3 meters.
water flows through the pipe contraction shown. for the given 0.2-m difference in the manometer level, determine the flowrate as a function of the diameter of the small pipe, d.
The flow rate as a function of diameter is Q^2 = 2.24 × 10^-4×D^4 / 10^-4 - D^4 when 0.2 m difference in the manometer level.
Given: The pipe's diameter at point 1 isD1=0.1 m D1=0.1 m
D2=D at point 2 dia. of pipe
And the pipe's flow rate is Q.
Velocity at point 1, where V1=Q/D12/4.
V1= Q/π×(0.1) (0.1)
^2/ 4
Speed at point 2; V2=Q/D2
^2/ 4
As atmospheric pressure causes pipes 1 and 2 to both open, both are 0; 1 and Bernoulli equation application at point 2
P1/pg+v12/2g+ h1= P2/pg+ v22/2g+ H2, where v12 / 2g+ h1= v2 / 2g+ H2.
Put the velocity and height values in the equation above.
Q^ 2/( π/4)^2×(1/D^4-l/(0.1)^4)= 2×g×(h1-h2) (h1-h2)
Q^2 = 2.24 × 10^-4×D^4 / 10^-4 - D^4
This represents the flow rate as a function of diameter.
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you are standing at the top of a cliff that has a stairstep configuration. there is a vertical drop of 6 m at your feet, then a horizontal shelf of 6 m , then another drop of 4 m to the bottom of the canyon, which has a horizontal floor. you kick a 0.16 kg rock, giving it an initial horizontal velocity that barely clears the shelf below.1. What initial horizontal velocity v will be required to barely clear the edge of the shelf below you? The acceleration of gravity is 9.8 m/s2 . Consider air friction to be negligible. Answer in units of m/s.
2. How far from the bottom of the second cliff will the projectile land? Answer in units of m.
1. The initial velocity required to barely reach the edge of the shell below you is 6.67 m/s.
2. The projectile will land at 9.54 m of the second cliff d = 9.54 m
1. To find the horizontal velocity of the rock we need to use the following equation:
d = v * t
Where:
d: is the distance traveled by the rock
t: is the time
The time can be calculated as follows:
t = √2d/g
g: is gravity = 9.8 m/s²
t = √2d/g = 1.20s
Now, the horizontal velocity of the rock is:
v = d/t = 6.67m/s
Hence, the initial velocity required to barely reach the edge of the shell below you is 6.67 m/s.
To calculate the distance at which the projectile will land, first, we need to find the time:
t = √2d/g = 1.43s
the distance is:
d = v * t = 9.54m
Therefore, the projectile will land at 9.54 m of the second cliff.
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A 50.0 g block of copper whose temperature is 400 K is placed in an insulating box with a 100 g block of lead whose temperature is 200 K. (a) What is the equilibrium temperature of the twoblock system? (b) What is the change in the internal energy of the system between the initial state and the equilibrium state? (c) What is the change in the entropy of the system?
a) The equilibrium temperature of the two block system is 320k
b) The change in the internal energy of the system is zero.
c) The change in entropy is +1.72kj
a) We refer. to the copper. block as block. 1 and the lead block. as block 2. The equilibrium temperature T satisfies
m1c1 (T - Ti) + m2c2 (T - TI2) = 0
T = m1C1Ti1 + m2C2Ti2 / m1C1 + m2C2 = 50 × 386×400 + 100×128×200/50×386 + 100×128 = 320K
T = 320K
b)The internal energy of the two-block system does not change because it is thermally isolated from the outside environment.
C)The change in entropy is ΔS = ΔS1 + ΔS2 = m1c1ln(T /Ti) + m2c2ln(T/Ti)
Δs = +1.72kj
A state of disorder, randomness, or uncertainty is most frequently connected with the scientific notion of entropy, which is also a quantifiable physical attribute. The notion and the phrase are employed in a variety of disciplines, including classical thermodynamics, where they were initially identified, statistical physics, which describes nature at the molecular level, and information theory. It has wide-ranging uses in physics and chemistry, biological systems and how they relate to life, cosmology, economics, sociology, weather science, and information systems, particularly the transfer of information through telecommunication.
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two possible geometric shapes for the clf3 molecule are trigonal planar and t-shaped. the student does some research and learns that the molecule has a dipole moment. which of the shapes is consistent with the fact that the clf3 molecule has a dipole moment? justify in terms of bond polarity and molecular structure.
The trigonal planar shape is consistent with the fact that the CLF3 molecule has a dipole moment.
This shape is formed by three identical polar bonds that are arranged in a flat plane. Each of the three bonds has a slightly negative charge on the chlorine atom and a slightly positive charge on the fluorine atoms. This arrangement of charge creates a permanent dipole moment across the molecule, which is a result of the arrangement of the polar bonds and the molecular structure.
The t-shaped structure, on the other hand, has a single polar bond and two non-polar bonds, which would lead to a net dipole moment of zero, since the charges would cancel out. Therefore, the trigonal planar shape is the most consistent with the fact that the CLF3 molecule has a dipole moment.
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A special type of electro-
magnetic wave that has a
frequency which we can see:
T
To understand the basic principles underlying interference.
One of the most important properties of waves is the principle of superposition. The principle of superposition for waves states that when two waves occupy the same point, their effect on the medium adds algebraically. So, if two waves would individually have the effect "+1" on a specific point in the medium, then when they are both at that point the effect on the medium is "+2." If a third wave with effect "-2" happens also to be at that point, then the total effect on the medium is zero. This idea of waves adding their effects, or canceling each other's effects, is the source of interference.
Part C
In talking about interference, particularly with light, you will most likely speak in terms of phase differences, as well as wavelength differences. In the mathematical description of a sine wave, the phase corresponds to the argument of the sine function. For example, in the function y=Asin(kx), the value of kx at a particular point is the phase of the wave at that point. Recall that in radians a full cycle (or a full circle) corresponds to 2? radians. How many radians would the shift of half a wavelength from the previous part correspond to?
Express your answer in terms of ?.
Shift of half a wavelength from the previous part correspond to π radian.
What is the principle of interference?Interference is a phenomenon in which two waves combine by adding displacement together at every single point in the space and time, to form a resultant wave of greater, lower, or same amplitude.
The superposition principle explains that when two or more waves overlap in space, then the resultant disturbance is equal to the algebraic sum of individual disturbances
Given, Wavelength= λ
We have to find the phase difference when wavelength is half of the initial wavelength.
So, the path difference= Δx = λ/2
As, phase difference= 2π/λ * Δx
So, phase difference= 2π/λ * λ/2
Thus, phase difference= π radian
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g assuming that 200 mev of energy is released per fission of u235 , the mass of that undergoes fission reactor of power 1MW will be approximatelya. 10^-2gb. 1gc. 100gd. 10.000g
Assuming that 200 Mev of energy is released per fission of u235 , the mass of that undergoes fission reactor of power 1MW will be approximately will be the correct option is a i.e. 10^-2g.
The mass of the material that undergoes fission in a reactor with a power of 1 MW, you need to know the number of fissions that occur per second in the fission reactor. The power of a reactor is the rate at which energy is released by the fission reactions taking place inside it. The energy released per fission of uranium-235 is 200 MeV.
The relationship between power, energy, and time is given by the equation:
Power = Energy / Time
Rearranging this equation to solve for the number of fissions per second gives:
Number of fissions/second = Power / (Energy/fission)
Putting the values from the problem gives:
Number of fissions/second = 1 MW / (200 MeV/fission) = 5 x 10^22 fissions/second
Since the mass of uranium-235 is approximately 235.04 g/mol, the mass of the material that undergoes fission in the reactor is approximately:
Mass = (Number of fissions/second) x (235.04 g/mol) / (6.022 x 10^23 fissions/mol) = 3.93 x 10^-2 g
So, the mass of the material that undergoes fission in the reactor is approximately 3.93 x 10^-2 g, which corresponds to the answer choice "a. 10^-2g".
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A newly discovered planet has twice the mass and three times the radius of the earth. What is the free-fall acceleration at its surface, in terms of the free-fall acceleration g at the surface of the earth?
A. 2/9 g
B. 2/3 g
C. 3/4 g
D. 4/3 g
A newly discovered planet has twice the mass and three times the radius of the earth. The free-fall acceleration at its surface, in terms of the free-fall acceleration g at the surface of the earth is 2/9 g
What is Gravitational Acceleration?The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity. M/s² is its SI unit. Its vector nature—which includes both magnitude and direction—makes it a quantity. The unit g stands for gravitational acceleration or free-fall acceleration . At sea level, the standard value of g on earth's surface is 9.8 m/s².
The free fall aceleration can be calculate as follows:
The acceleration due to gravity on Earth is
g= GM
R²
The acceleration due to gravity on the new planet is
gₙ= G2M
(3 R)²
gₙ= G2M
(3 R)²
Dividing the two equations we get
G2M
gₙ = 9 R² = 2 g
g GM 9
R²
Therefore, the free-fall acceleration at its surface, in terms of the free-fall acceleration g at the surface of the earth is 2/9 g.
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In the situation below, ring is stationary in space and initially sits perpendicular to large magnetic field B1 0.59 T. After mT The area of the ring is A 0,61 m2: (a) What the Initial flux, Di when the ring sits In; (b) What the flnal flux, Bi When the ring slt; (c) What is the change flux between the Initial and fina scenarios
When the ring is stationary, the initial flux, Di, is 0.3713. Final flux, Bi, 2.107*10-3Tm If the ring is there and the difference in flux between the initial and final scenarios is 0.3692 Tm2,
The total number of magnetic field lines passing through a coil or other given area is referred to as initial flux. It is the area's typical magnetic field component that travels through. Flux is modelled mathematically as the surface integral of a vector field, where F is the vector field and d A is the vector area of surface A, directed as the surface normal.
The initial flow is 0.97*0.49, which is 0.371 Tm2.
9.3*10-3T*0.49m2 = 2.107*10-3Tm2 is the final flux.
The flux change is calculated as (0.3713 - 2.107*10-3Tm2 = 0.3692Tm2).
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shows a particle of mass m at distance x along the axis of a very thin ring of mass m and radius r. calculate the gravitational potential energy of these two masses. Use what you know about the relationship between force and potential energy to find the magnitude of the gravitational force on when it is at position .
When a very thin ring is at position x>0 and at distance x along its axis, the gravitational force acting on it is 4GMm/4x2-L2.
With a gravitational pull that diminishes with distance as 1/r2, every body in the cosmos is attracted to every other body. The gravitational force of attraction a body experiences must be proportionate to its mass if two bodies of different masses accelerate at the same rate (i.e., a body twice as heavy experiences twice the gravitational force).
The gravitational force experienced by a minuscule unit mass placed at any point P in space is known as the gravitational field at that point.
Using the equation gravitational potential = GMm/r and further integrating on a short dx length at x from the rod's origin, we may determine this relationship.
U equals GMm/Lln2x-2/2x+2.
separating now with regard to dx, we obtain
F equals 4GMm/4x2L2.
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g an intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of t
a) Radius's general expression is R = ∛T²GM/4π².
b) The mass of the planet in kilograms if T = 26 hours and R = 2.1 × 108 m is 4.9 ×10²⁵kg.
a) The general definition of the radius is R = ∛T²GM/4π²
b) The mass of the planet throughout its geosynchronous orbit is 4.9 × 10²⁵ kg.
T = period of the orbit = 26hours
r = radius of the orbit = = 2.1 × 10⁸ m.
G = gravitational constant = 6.674×10⁻¹¹ m³⋅kg⁻¹⋅s⁻²
M = mass of the planet
Putting the value in the radius equation we get,
R = ∛T²GM/4π²
8.98 ×10⁷ m = ∛ (26 × 60 × 60)² ×( 6.67 ×10⁻¹¹) M/ 4×(3.142)²
M = (8.98 ×10⁷ m ×39.49 )/ (∛2.86 × 10¹⁸)
M = 4.9 ×10²⁵
As a result, the planet has a mass of 4.9 ×10²⁵kg throughout its geosynchronous orbital period.
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The question is -
An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T. The spaceship enters a geosynchronous orbit at a distance of R. a) From the given information, write a general expression for the mass of the planet in terms of G and the variables from the problem statement. b) Calculate the mass of the planet in kilograms if T = 26 hours and R = 2.1 × 108 m.
At which latitude on the Earth is the speed of Earth's rotation the slowest?
Answer:
North and South poles
Explanation:
compare and constrast bragg's law of diffraction with the grating diffraction equation and the thin-film interference equation. here, we mean the equations that relate spacing and wavelength to the locations of maxima in the diffraction or interference pattern
Laue diffraction, which establishes the angles of coherent and incoherent scattering from a crystal lattice, is a specific example of Laue's law known as Bragg's law. An electronic cloud moves like an electromagnetic wave when X-rays strike a certain atom.
How does Bragg's law work?In physics, the Bragg law describes the relationship between the distances between atomic planes in crystals and the angles of incidence at which these planes generate the strongest reflections of X-rays, gamma rays, and particle waves like those linked to electrons and neutrons.
Waves from two independent sources that produce different wavefronts are said to be causing interference. On the other hand, diffraction is a word for secondary waves that result from the various components.
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through a refinery, fuel ethanol is flowing in a pipe at a velocity of 1 m/s and a pressure of 101300 pa. the refinery needs the ethanol to be at a pressure of 2 atm (202600 pa) on a lower level. how far must the pipe drop in height in order to achieve this pressure? assume the velocity does not change. (hint: use the bernoulli equation. the density of ethanol is 789 kg/m3 and gravity g is 9.8 m/s2. pay attention to units!)
Δh = -13.101 m Far must the pipe drop in height in order to achieve this pressure.
13,101 m must be removed from the height.
Bernoulli went on to say that at whatever point along the fluid flow, the total amount of pressure, kinetic energy, and potential energy per volume is the same.
P+ 1/2 ρv² + ρgh = constant
Given
v = 1 m/s ⇒ constant
P₁ = 101300 Pa (1 atm)
P₂ = 202600 Pa (2 atm)
ρ ethanol = 789 kg/m3
g = 9.8 m/s2
Required
The height(lower level)
Solution
The Bernoulli equation becomes when v₁=v₂ constant
ρgh₁+P₁=ρgh₂+P₂
Solve for the value (height difference):
P₁-P₂=ρgh₂-ρgh₁
P₁-P₂=ρg(h₂-h₁)
(P₁-P₂)/(ρg) = Δh
- 101300 kg/ms² / 789 kg/m³ × 9.8 m/s² = Δh
Δh = -13.101 m
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a block of mass 5kg starts from rest at point a and is accelerated by a force of 5 n over a total distance from point a to c as shown. the distance measured from point a to b is exactly 10 meters and is frictionless. the distance from b to c is rough and its length is unknown. the block finally comes to rest at point c. if the coefficient of kinetic friction between the rough surface and the mass is 0.5, determine the total distance the mass slides (from a to c).
The total distance when the mass slides of 5kg starts from rest at point a and is accelerated by a force of 5N is 50 m.
F=μ.d
ma=μ.d
d=ma/μ
d=5×5/0.5
d=50 m
Distance, which is independent of direction, is the length between two points or things. Distance only considers the total magnitude and disregards the start and finish positions because it is a scalar property. Distance can only have a positive or zero value because it is a scalar attribute; it cannot be negative. The meter (m) is the most widely used unit of measurement for distance, though kilometers (km) can also be used to express longer distances and centimeters (cm) or millimeters can be used to express shorter distances (mm). The distance traveled is frequently represented by the letter D when calculating distance.
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A sphere of mass mis dropped from the top of a building and reaches the ground before achieving terminal velocity. The force of air resistance that acts on the sphere as it falls is given by F, where is a positive constant and is the velocity of the sphere. What happens to the magnitude of the sphere's velocity and acceleration, and to the distance it falls during each second, as the sphere approaches the ground? Magnitude of Yelocity Magnitude of Acecloration Distance of all Each Second (A) Increases Increases Increases Increases Decreases Increases (C) Increases Decreases Decreases Decreases Increases Decreases (1) Decreases Decreases Increases
The magnitude of the sphere's velocity, acceleration, and to the distance it falls during each second is A)Increases Increases Increases .So, correct option is A.
We know that when an object is coming from a large height towards the surface of earth, due to air resistance it feels huge amount of opposition force which basically tries to decrease its velocity. The equation of force will be given by
F=mg + air resistance force
Since acceleration due to gravity is also responsible for acting of force, therefore, F will increase as when object comes closer to the surface air resistance is very high and due to that value of F is very large.
Same because of the high resistance force, velocity and distance will be also increases.
Hence, correct option is A.
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a full moon appears larger on the horizon than it does overhead not because of the refraction of the atmosphere but because of an optical illusion. objects in the foreground influence the perceived size of objects in the background, and when the moon is on the horizon amid trees and houses the brain interprets it as being larger than when it appears overhead in the absence of those objects.
Moon Illusion is an Optical Phenomenon. This occurs because when the moon is near the horizon, Earthly things that resemble the moon on your retina generate a misunderstanding or inaccurate perception of distance and size.
The brain interprets the low moon as being bigger since it is lower in the sky than the higher moon. The mechanism behind size-distance perception in everyday life, which transforms planar pictures that fall on the retina into a perception of hard objects moving in space, is related to the moon illusion.
What happens when the mechanism acts in an uncommon circumstance is what causes the moon illusion. In typical perception, the angular size of the light image stimulating our eyes expands or shrinks as rigid objects move in depth (distance).
The sense of hard objects with shifting depth perception is produced naturally by the brain in response to these changing stimuli. The ground and horizon make the moon appear comparatively close when it is close to the horizon.
Due to the moon's shifting apparent position in depth while the light stimulus stays constant, the moon appears extraordinarily huge due to the brain's size-distance mechanism.
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an object is intiially hanging in equilibrium froma vertical spring. the object is pulled down 15 cm
The item is lowered 15 cm from its equilibrium point shown above before being let go at time t = 0. The item subsequently begins to oscillate with a 2.0 s period. Assuming that x = 0 represents equilibrium, upward motion is the positive direction.
What does a "object response" mean?A sentence's object is the portion on which the verb performs its action. In conventional English, a sentence is usually written with the object coming first. The verb, or what performs the action, is the subject.
What functions do things have?Things may be done to objects as well as done to them. A function or method object, for instance, may be coded to change the contents of a data structure or variable.
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match the items on the left with the correct definition on the right. 1 . radiant the top of a light wave 2 . speed of sound 1,100 feet per second 3 . speed of light the frequency of sound 4 . vibrations the bottom of a light wave 5 . pitch the cause of sound 6 . photons the loudness of a sound 7 . amplitude 186,000 miles per second 8 . trough longer wavelength than visible light 9 . crest particles of light energy 10 . microwaves energy of light
The sound speed Pitch at 1,100 feet per second, light speed at 1,860 miles per second, radiant sound frequency, top and bottom vibrations of a light wave, and pitch at 1,100 feet per second.
What exactly are wavelengths and frequencies?The wavelength is the separation between two wave crests, while troughs have the same wavelength. The frequency is the quantity of vibrations that cross a specific area in a second.
How do you calculate wavelength?The distance between any two identical locations on adjacent waves may always be used to calculate the wavelength. A longitudinal wave's wavelength is determined by counting the distance between each compression and the one after that, or from a rarefaction.
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iuf the angle between the horizintaon lad tje direction of the 5.0 meters per second vecpol;tiy decreases from 30 degrees to 30 degrees, the horitzontal distance the ball travels will
The horizontal distance the ball travels is 2.209 meters ,if it has velocity of 4 m/s
Given,
velocity (v) = 5 m/s
angle (Θ) = 30+30 = 60
gravitational constant (g) = 9.8 m/s
We know that the distanced travelled by a ball can be find using the below formulae
distance (D) = v² sin2Θ / g
D = 5²×sin 120 / 9.8
D = 2.209 meters
Aerial distance is the distance between two points or locations that is calculated in the air, as opposed to the ground or a road, which is the route that an aeroplane takes to get from one location to another.
Distance in the air must be measured when flying since it is crucial information for the aviation industry. The nautical mile is a measurement that is widely used to compute distances in space.
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Part A In addition to their remarkable top speeds, cheetahs have impressive cornering abilities. In one study, the sideways force on the feet of a 45 kg cheetah, with its claws dug into the ground, was found to be 960 N What was the cheetah's centripetal acceleration? Express your answer with the appropriate units. HÃ… ? a = Value Units Submit Request Answer Part B What was the radius of the turn if the cheetah was running at 20 m/s? Express your answer with the appropriate units. HA ?
Centripetal acceleration of cheetah is 21.3 m/s^2. the radius of the turn was approximately 18.9 meters.
To find the centripetal acceleration, we can use the formula a = v^2/r, where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the turn.
In this case, we are given the mass of the cheetah (45 kg) and the sideways force on its feet (960 N), so we can use the formula F = ma to find the acceleration.
F = ma 960 N = (45 kg)(a) a = 960 N / 45 kg a = 21.3 m/s^2
Now that we have the acceleration, we can use the formula a = v^2/r to find the radius of the turn if the cheetah was running at 20 m/s.
a = v^2/r 21.3 m/s^2 = (20 m/s)^2/r r = (20 m/s)^2 / 21.3 m/s^2 r = 18.9 m
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A flat uniform circular disk has a mass of 3.00 kilogram and a radius of 70.0 \text{~cm}70.0 cm. It is suspended in a horizontal plane by a vertical wire attached to its center. If the disk is rotated 2.50 \text{~rad}2.50 rad about the wire, a torque of 0.0600 \text{~N}\cdot \text{m}0.0600 Nâ‹…m is required to maintain that orientation. Calculate the rotational inertia of the disk about the wire.
The rotational inertia of the disk about the wire is 243 kilograms*meters^2.
The rotational inertia of a body about a given axis is a measure of the body's resistance to changes in its rotational motion. It is given by the formula I = ∑m*r^2, where m is the mass of each particle in the body, r is the distance of each particle from the axis of rotation, and the sum is taken over all particles in the body.
In this case, the body is a flat circular disk with a mass of 3.00 kilograms and a radius of 70.0 centimeters. The axis of rotation is the vertical wire attached to the center of the disk. To find the rotational inertia of the disk about the wire, we need to calculate the sum of m*r^2 for all the particles in the disk.
Since the disk is uniform, all the particles in the disk have the same mass. Therefore, we can simplify the formula for rotational inertia to I = mR^2, where m is the mass of the disk and R is the radius of the disk. Plugging in the values for m and R, we get
I = 3.00 kilograms * (70.0 centimeters)^2 = 24300 kilograms centimeters^2.To convert this value to the units of rotational inertia (kilogrammeters^2), we can use the conversion factor 1 meter = 100 centimeters. This gives us
I = 24300 kilogramscentimeters^2 * (1 meter / 100 centimeters)^2 = 243 kilograms*meters^2.Learn more about Rotational inertial here:
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A uniform30 cmruler of mass50 gis attached to a friction-less vertical wall by a nail through one end. A horizontal force F=0.545 Nis applied to the end of the rod. If the rod is tilted at 40∘ from the vertical, what is the angular acceleration of the rod (around the nail) at this instant? Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g.0.23,−2,1e6, 5.23e-8
The value of the angular acceleration of the rod is approximately equal to 0.0055 rad/s².
To find the angular acceleration of the rod, we need to first determine the torque acting on the rod around the nail. The torque is given by the formula:
torque = force * distance * sin(angle)
Where: 'force' is the applied force F, 'distance' is the distance between the point where the force is applied and the point around which the torque is calculated (in this case, the nail) and 'angle' is the angle between the force and the distance vector
Plugging in the values, we get:
torque = 0.545 N * 30 cm * sin(40°) = 4.14 N cm
We can then use the formula for torque to calculate the angular acceleration:
torque = moment of inertia * angular acceleration
The moment of inertia of a rod about an end is given by:
moment of inertia = mass * length² / 12
Plugging in the values, we get:
moment of inertia = 50 g * (30 cm)² / 12 = 750 g*cm^2
Solving for angular acceleration, we get:
angular acceleration = torque / moment of inertia = 4.14 N cm / 750 gcm² = 0.0055 rad/s².
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the reason that buoyant force acts upward on a submerged object is that question 12 options: if it acted downward, nothing would float. it acts in a direction to oppose gravity. the weight of fluid displaced reacts with an upward force. upward pressure against the bottom is greater than downward pressure against the topof the submerged object.
Upward pressure against the bottom is greater than downward pressure against the top of the submerged object.
Buoyant Force:
The upward force applied to an object that is fully or partially submerged in a fluid is known as the buoyant force. Upthrust is another name for this upward thrust. A body submerged partially or completely in a fluid appears to shed weight or to be lighter, due to the buoyant force.
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a block of mass 2.57 kg lies on a frictionless horizontal surface. the block is connected by a cord passing over a pulley to another block of mass 5.2 kg which hangs in the air, as shown. assume the cord to be light (massless and weightless) and unstretchable and the pulley to have no friction and no rotational inertia. The acceleration of gravity is 9.8 m/s2 Calculate the acceleration of the first block. Answer in units of m/s .
The acceleration of the two blocks are the same and it is 6.56 m/s².
The free-body diagram is in the attached picture.
Applying the Newton's second law of motion,
First block:
T = m₁a ....... (equation 1)
Second block:
m₂g - T = m₂a .... (equation 2)
Where:
m₁ = mass of the 1st block = 2.57 kg
m₁ = mass of the 2nd block = 5.2 kg
T = chord tension
a = acceleration
g = acceleration of gravity = 9.8 m/s²
Substitute equation 1 to equation 2
m₂g - m₁a = m₂a
( m₁ + m₂) a = m₂g
a = [m₂/( m₁ + m₂)] x g
= [5.2 / (2.57+5.2)] x 9.8
= 6.56 m/s²
Hence, the acceleration is 6.56 m/s²
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A 570 N physics student stands on a bathroom scale in an 900 kg (including the student) elevator that is supported by a cable. As the elevator starts moving, the scale reads 400 N.Find the magnitude of the acceleration of the elevator.
Part B
Find the direction of the acceleration of the elevator.
up or down
Part C
What is the acceleration if the scale reads 610 ?
Part D
If the scale reads zero, should the student worry? Explain.
Essay answers are limited to about 500 words (3800 characters maximum, including spaces).
part E
What is the tension in the cable in part A?
Part F
What is the tension in the cable in part D?
The acceleration of the elevator when the scale reads 400 N is 0.18m/[tex]s^{2}[/tex] downwards.
The acceleration of the elevator when the scale reads 610 N is 0.04m/[tex]s^{2}[/tex] upwards.
Yes, the student should worry because the elevator is in free fall, that is, there are no supporting cables on the elevator.
The tension in the cable for part A is 450 N.
The tension on the cable for part D is 0.
The given parameters;
weight of the student, W = 570 Nmass of the student and the elevator, m = 900 kgWhen the scale of the elevator reads 400 N, is moving downwards since the apparent weight is less than the real weight
R = mg + ma
400 = 570 + ma
400 - 570 = ma
- 170 = ma
a = [tex]\frac{-170}{m}[/tex] = [tex]\frac{-170}{900}[/tex] = 0.18m/[tex]s^{2}[/tex] , downwards
so, The acceleration of the elevator when the scale reads 400 N is 0.18m/[tex]s^{2}[/tex] downwards.
The scale of the elevator will read more when it is moving upwards;
610 = mg + ma
610 = 570 + ma
610 - 570 = ma
ma =40
a = [tex]\frac{40}{m}[/tex] = [tex]\frac{40}{900}[/tex] = 0.04m/[tex]s^{2}[/tex] , upwards
So, the acceleration of the elevator when the scale reads 610 N is 0.04m/[tex]s^{2}[/tex] upwards.
When the scale reads, the upward acceleration is equal to the acceleration due to gravity and the student will be in free fall.
R = m(g - a)
g = a
R = m(0)
R = 0
Thus, the student should worry because the elevator is in free fall, that is, there are no supporting cables on the elevator.
The tension in the cable for part A is 400 N.
The tension in the cable for part D is 0.
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compare the frequency of an electromagnetic wave with the frequency of the vubrating charge that produces the wave
An electromagnetic wave's frequency is the same as the frequency of the vibrating charge that causes it. The amount of vibrations, or back and forth motions, that occur in a charge in a second, is known as its frequency.
What is meant by electromagnetic waves?Electromagnetic waves, often known as EM waves, are waves that are produced when an electric field and a magnetic field vibrate together. In other words, the oscillation of the magnetic and electric fields results in electromagnetic (EM) waves. In contrast to mechanical waves, electromagnetic waves can move through voids. This suggests that electromagnetic waves can travel into empty space in addition to through solid materials like air and rock.
What is the significance of electromagnetic?Food-borne microorganisms can be eliminated by the widespread use of electromagnetic radiation in food preparation. Recent research on the microwave or radio wave portion of the electromagnetic spectrum has found promising results for the inactivation of germs in food preparation.
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