The required torque is 25386 N.m. to accelerate the merry-go-round.
To calculate the net torque required to accelerate the merry-go-round, we need to use the rotational equivalent of Newton's second law, which states that the net torque applied to an object is equal to its moment of inertia times its angular acceleration.
The moment of inertia of a uniform disk can be calculated as [tex]$I = \frac{1}{2}mr^2$[/tex], where [tex]$m$[/tex] is the mass of the disk and [tex]$r$[/tex] is its radius. Substituting the given values, we get
I = (31000kg)(7m)²/2 = 897250 kg.m²
The angular acceleration can be calculated by dividing the final angular velocity by the time taken for acceleration. Therefore,
[tex]\alpha = \frac{\omega_f - \omega_i}{t} = \frac{0.68 \text{ rad/s}}{24 \text{ s}} =[/tex] 0.0283 rad/s²
Now, we can use the rotational equivalent of Newton's second law to find the net torque required. The equation is [tex]$\tau = I\alpha$[/tex], where [tex]$\tau$[/tex] is the net torque. Substituting the values we get
[tex]$\tau[/tex] = (897250 kg.m²)(0.0283 rad/s²) = 25386 N.m
Therefore, the net torque required to accelerate the merry-go-round from rest to 0.68 rad/s in 24 s is 25386 N[tex]$\cdot$[/tex]m.
In conclusion, the net torque required to accelerate the uniform disk merry-go-round can be calculated by using the rotational equivalent of Newton's second law, which relates torque, moment of inertia, and angular acceleration. The moment of inertia of a uniform disk can be calculated as [tex]$\frac{1}{2}mr^2$[/tex].
In this case, the net torque required to accelerate the merry-go-round was found to be 25386 [tex]N$\cdot$m.[/tex]
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The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of 2.00 103 N with an effective perpendicular lever arm of 3.40 cm, producing an angular acceleration of the forearm of 165 rad/s2. What is the moment of inertia of the boxer's forearm
Answer: The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of 2.00 103 N with an effective perpendicular lever arm of 3.40 cm, producing an angular acceleration of the forearm of 165 rad/s2. Then, the moment of inertia of the boxer's forearm will be 0.412Nm/rad/sec2.
Explanation: To find the correct answer, we have to know more about the moment of force or torque.
What is Torque?Torque is the measure of turning effect of a force.If the object rotates about an axis, then the perpendicular distance from the axis to the line of action of the force is called the lever arm.Torque is measured by the product of force and the lever arm.If r is the position vector of the point of application of force, then torque T is,[tex]T=rFsin\alpha[/tex], where, [tex]\alpha[/tex] will be the angle between r and F.
Torque in terms of moment of inertia [tex]I[/tex] and the angular acceleration [tex]\beta[/tex] will be,[tex]T=I\beta[/tex]
Where, [tex]I=r[/tex]×m
How to solve the problem?Given that,[tex]F=2*10^3N\\r=3.40*10^-2m\\\beta =165 rad/sec^2[/tex]
From the above equation of T, we can produce the equation of moment of inertia as,[tex]I=\frac{T}{\beta } =\frac{rFsin\alpha }{\beta } \\where, sin\alpha =1.\\Thus,\\T=\frac{rF}{\beta } =\frac{68}{165} =0.412Nm/rad/s^2.[/tex]
Thus, we can conclude that, moment of inertia of the boxer's forearm will be, 0.412Nm/rad/sec².
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Noah drops a rock with a density of 1.73 g/cm° into a
pond. Will the rock float or sink? Explain your answer.
Answer:
the rock will probably sink in water because density of rock heavier than the density of water.
Density of water=1g/cm
density of rock=1.73g/cm
1g/cm< 1.73g/cm
Find the work done when a constant force f = 13 lbs moves a chair from x = 2.4 to x = 4.1 ft. along the x -axis.
The work done in moving the chair from x = 2.4 to x = 4.1 ft using a force of F = 13 lbs is 29.98 J
What is work done?This is simply defined as the product of force and distance moved in the direction of the force. Mathematically, it can be expressed as
Workdone (Wd) = force (F) × distance (d)
Wd = Fd
How to convert lb to N1 lb = 4.45 N
Therefore,
13 lbs = 13 × 4.45
13 lbs = 57.85 N
How to determine the distance in mInitial distance = 2.4 ftFinal distance = 4.1 ftChange in distance = 4.1 -2.4 = 1.7 ft1 ft = 0.3048 m
Therefore,
1.7 ft = 1.7 × 0.3048
1.7 ft = 0.51816 m
How to determine the workdoneForce (F) = 57.85 NDistance (d) = 0.51816 mWorkdone (Wd) =?Wd = Fd
Wd = 57.85 × 0.51816
Workdone = 29.98 J
Thus, the workdone in moving the chair is 29.98 J
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A sound wave traveling through dry air has a frequency of 16 hz, a
wavelength of 22 m, and a speed of 350 m/s. when the sound wave passes
through a cloud of methane, its wavelength changes to 28 m, while its
frequency remains the same. what is its new speed? (the equation for the
speed of a wave is v= f * 1.)
Answer:
[tex]\huge\boxed{\sf v = 448\ m/s}[/tex]
Explanation:
Given data:Frequency = f = 16 Hz
Wavelength = λ = 28 m
Required:Speed = v = ?
Formula:v = fλ
Solution:Put the givens.
v = (16)(28)
v = 448 m/s
[tex]\rule[225]{225}{2}[/tex]
Assignment 1.4
VOLUME OF SPHERE
The radius of sphere 'r' is measured with vernier callipers as
(r+Ar)= (2.25 +0.01) cm. Calculate the volume of sphere. (47.7+0.6) cm³.
PHYSICS
you can use the graph to estimate the value of x when y is required to start a doubles match with the sun and the sky very well from her childhood and a kind young women who lives with her wearing a black and a veil and shows to be in that position or they have a bad past or bad life that they want to take revenge on every one by murder goes on by them in the streets of St and St Mary's Church and its followers are known as Sikhs and the other children claim she
a charged partocle produces an electric field with a magnitude of 2.0 N/C at a point that is 50cm away from the particle
The charge on the particle is 5.6 × 10⁻¹¹ C.
Calculation:The magnitude of an electric field produced by a charge is given by:
E = q/ 4πε₀r²
where,
E = electric field
q = charge
r = distance
1/4πε₀ = 8.99 × 10⁹ Nm²/C²
Given,
E = 2.0 N/C
r = 50 cm = 0.5 m
To find,
q =?
Put the values in the above equation:
E = q/ 4πε₀r²
q = E (4πε₀r²)
q = 2.0 × (0.50²)/ 8.99 × 10⁹
q = 5.6 × 10⁻¹¹ C
Therefore, the particle has a charge of 5.6 × 10⁻¹¹ C.
What is an electric field?The physical field that surrounds each electric charge and acts to either attract or repel all other charges in the field is known as an electric field. Electric charges or magnetic fields with different amplitudes are the sources of electric fields.
I understand the question you are looking for is this:
A charged particle produces an electric field with a magnitude of 2.0 N/C at a point that is 50 cm away from the particle. What is the magnitude of the particle's charge?
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Water flows through a pipe with a cross-sectional area of 0.002 m^2 at a mass flow rate of 4 kg/s. the density of water is 1 000 kg/m^3. Determine its average velocity
Water flows through a pipe with a cross-sectional area of 0.002 m^2 at a mass flow rate of 4 kg/s. The density of water is 1 000 kg/m^3 . The average velocity will be 2m/s
The flow rate of a liquid is how much fluid passes through an area in a particular time. Flow rate can be articulated in either in terms of velocity and cross-sectional area, or time and volume.
Flow rate = Volume of fluid / time
= (Area * distance) / time
= Area * average velocity (distance / time = average velocity)
Given
Cross-sectional area = 0.002 [tex]m^{2}[/tex]
Flow rate = 4 kg/s
Average velocity = Flow rate / (Area * density)
= 4 / (0.002 * 1000)
= 2m/s
hence , the average velocity will be 2 m/s
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According to max weber, flaunting of one’s wealth to show one’s status is called?
Status refers to a person's prestige, social honor, or reputation in society. Weber stated that political strength become now not rooted entirely in capital fees, but additionally in a single's individual popularity. Poets or saints, for example, can own a massive impact on society, often with little monetary worth.
The German sociologist Max Weber formulated a three-component theory of stratification that defines a status group (additionally status class and status estate) as a group of humans within a society who can be differentiated by means of non-financial characteristics along with honor, prestige, ethnicity, race, and religion.
Social stratification entails society as a system of hierarchical categories. Max Weber defined stratification because the division of a society into distinct communities, that have varying assignments of “status honor” or status.
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Two boys with masses of 40 kg and 60 kg stand on a horizontal frictionless surface holding the ends of a light 10-m long rod. The boys pull themselves together along the rod. When they meet the 40-kg boy will have moved what distance?.
When they meet the 40-kg boy would have moved a distance of 6 m.
Distance moved by the 40 kg boyApply the principle of center mass;
Take the 40 kg mass as the reference point;
X(40 kg) = (40kg x 0 + 60kg x 10 m)/(40 kg + 60 kg)
X(40 kg) = (600)/(100)
X(40 kg) = 6 m
Thus, when they meet the 40-kg boy would have moved a distance of 6 m.
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A speed is a scalar physical quantity. Why?
Answer:
A speed is a scalar quantity because it only has magnitude.
Answer:
what is electronic configuration
Plane-polarized light is incident on a single polarizing disk with the direction of E0 parallel to the direction of the transmission axis. Through what angle should the disk be rotated so that the intensity in the transmitted beam is reduced by a factor of:
Answer: Plane-polarized light is incident on a single polarizing disk with the direction of E0 parallel to the direction of the transmission axis. Through angle [tex]\alpha=cos^-1(\sqrt{\frac{1}{n} })[/tex] should the disk be rotated so that the intensity in the transmitted beam is reduced by a factor of n .
Explanation: To find the correct answer, we need more clarifications about the Malu's law.
What is Malu's law?When a beam of plane polarized light is passed through an analyzer, the intensity I of the transmitted light varies directly as the square of the angle between the direction of polarizer and the analyzer.[tex]I=I_0cos^2\alpha[/tex]
where, [tex]I_0[/tex] is the maximum intensity of transmitted light.
Intensity of the light transmitted through the polarizer is half of the incident intensity.How to solve the problem?Here in the question ,let's take the factor at which the intensity of transmitted light is reduced by as n.we have the expression[tex]I=I_0cos^2\alpha[/tex]
we have to find the value of angle alpha, so that the intensity in the transmitted beam is reduced by a factor of n.[tex]\alpha =cos^-1\sqrt{(\frac{I}{I_0}} )=cos^-1\sqrt{\frac{I}{nI} } \\\alpha =cos^-1\sqrt{\frac{1}{n} }[/tex]
If we know the value of n, then we can easily find the angle.Thus, we can conclude that, the value of angle alpha, so that the intensity in the transmitted beam is reduced by a factor of n will be,
[tex]\alpha=cos^-1(\sqrt{\frac{1}{n} })[/tex] .
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When the Sun runs out of hydrogen in its core, it will become larger and more luminous because Choose one: A. energy balance no longer holds, and the star just drifts apart. B. infalling material rebounds off the core and puffs up the star. C. it starts fusing hydrogen in a shell around a helium core. D. it starts fusing helium in a shell and hydrogen in the core.
It starts fusing hydrogen in a shell around a helium core
Eventually, a star will run out of hydrogen fuel in its core, nuclear fusion will stop, and the star will enter a new stage of its lifetime.
What happen to the Sun when it runs out of hydrogen ?Faster hydrogen burning means the star will grow larger and more luminous to allow the extra energy created to escape but since the temperature of the core remains constant the star's surface temperature will drop.
When our Sun runs out of hydrogen fuel in the core, it will contract and heat up to a sufficient degree that helium fusion can beginOnce that mass/temperature threshold is crossed, the star begins fusing hydrogen into helium, and will encounter one of three different fates.Learn more about Sun here:.
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Provided following are four different ranges of stellar masses. Rank the stellar mass ranges based on how many stars in each range you would expect to be born in a star cluster, from highest number to lowest number.
Highest to lowest number:
-less than 1 solar mass
-between 1 and 10 solar masses
-between 10 and 30 solar masses
-between 30 and 60 solar masses
What is Stellar masses ?Stellar mass is a phrase that is used by astronomers to describe the mass of a star. It is usually enumerated in terms of the Sun's mass as a proportion of a solar mass (M☉).
Hence, the bright star Sirius has around 2.02 M☉.A star's mass will vary over its lifetime as mass is lost with the stellar wind or ejected via pulsational behavior, or if additional mass is accreted, such as from a companion star.Learn more about Stellar masses here:
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When the absolute value of the price elasticity of demand falls in the range 0 to 1, demand is said to be _____.
When the absolute value of the price elasticity of demand falls in the range 0 to 1, demand is said to be inelastic.
A good or service that has an income elasticity of demand between zero and 1 is considered a normal good and income inelastic. If a good or service has an income elasticity of demand below zero, it is considered an inferior good and has negative income elasticity.
Inelastic is an economic term referring to the static quantity of a good or service when its price changes. Inelastic means that when the price goes up, consumers' buying habits stay about the same, and when the price goes down, consumers' buying habits also remain unchanged.
Price elasticity of demand is a measurement of the change in consumption of a product in relation to a change in its price. A good is elastic if a price change causes a substantial change in demand or supply.
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Which types of decay will cause the mass number a of a nucleus to change?.
Nuclear decay results in the change in the mass number of a nucleus. In precise it is alpha decay.
What is nuclear decay?The process through which an unstable atomic nucleus loses energy through radiation is known as radioactive decay, also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration.
What is alpha decay?A nuclear process known as "alpha decay" releases a particle made up of two protons and two neutrons when an unstable nucleus transforms to another element. The helium nucleus that is being ejected is known as an alpha particle. Positive charge and a sizable mass characterize alpha particles.How is mass number of nucleus is changed by alpha decay?
When a nucleus emits an alpha particle, these changes happen:
the mass number decreases by 4. the atomic number decreases by 2.To learn more about Radioactive decay visit:
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The kinetic friction force that a horizontal surface exerts on a 60.0-kg object is 50.0 n. if the initial speed of the object is 25.0 m/s, what distance will it slide before coming to a stop?
Answer:
KE = 1/2 M v^2
KE = 60/2 * 25^2 = 18750 Joules initial Kinetic Energy
W = Fs * d distance thru which friction acts
d = W / Fs = 18750 J / 50 N = 375 m
You are looking down on a 20 kg beam resting on a horizontal, frictionless surface. The beam is 2 m long and can pivot about one end. A small 0.1 kg rock slides across the surface at 400 m/s and hits the middle of the beam, embedding itself inside. What is the angular speed of the rod after the impact (in rad/s)
The angular speed of the rod after the impact is 1.49 rad/s
What is angular speed?
The rate of change of angular displacements is known as angular speed.
Angular speed is a scalar measure of the rotating object.
What is Angular momentum?
It is the property of a rotating body given by the product of the moment of inertia and the angular velocity of the rotating object.
Angular momentum is expressed as follows:
L=m*v*r
Here,
mass of beam, M =20 kg
mass of rock, m =0.1 kg
length of the beam, L =2 m
length where rock slides, l = (L / 2), l = 1 m
velocity of rock, v =400 m/s
As here the Torque on which the system is zero implies that the angular momentum is conserved.
Initial angular momentum for rock: I(ri) = m*v*r
Final angular momentum for rock: I(rf) = m*w*r^2
Final angular momentum for beam: I(bf) = 1/3 (M*L^2w)
Now, According to the conservation of momentum:
m*v*r = m*w*r^2 + 1/3 (ML^2w)
w = m*v*r / ( mr^2 + 1/3 ML^2 )
w = 0.1 *400*1 / ( (0.1 * 1) + 1/3 20* 2^2 )
w = 1.49 rad / s
The angular speed of the rod after the impact is 1.49 rad/s
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What occurs when a temperate glacier meets its pressure-melting point?
Answer:
a whole new glacier will start because the other one is melting
Compared with a car moving at some original speed, how much work must the brakes of a car supply to stop a car that is moving twice as fast? how will the stopping distances compare?.
It takes four times the work and four times the stopping distance.
Given:
original speed of car = x
brakes applied so final speed = 0
moving speed of another car = 2x
To Find:
work done to stop the car
Solution: Work is done whenever a force moves something over a distance. You can calculate the energy transferred, or work done, by multiplying the force by the distance moved in the direction of the force.
Work done is given by
W = KE(final) - KE(initial)
W = 1/2m(v)^2 - 1/2m(u)^2
W = 1/2m(0 - (x)^2)
W = 1/2m(4x^2)
W = 4(1/2mx^2)
W = 4W
So, work done will be 4 times initial work
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How do astronomers explain the energetic jets that come out of quasars and active galactic nuclei in opposite directions
Astronomers explain the energetic jets that come out of quasars and active galactic nuclei(AGN) in opposite directions in a way that the supermassive black holes' chaotic accretion discs "spit out" jets in directions perpendicular to the disc.
Quasar : A supermassive black hole with a mass between millions and tens of billions of solar masses that is fueled by an extraordinarily bright active galactic nucleus (AGN) and encircled by a gaseous accretion disc is known as a quasar.
An active galactic nucleus (AGN) is a compact area at the Centre of a galaxy that exhibits features that indicate the luminosity is not coming from stars and is substantially brighter than usual over at least some of the electromagnetic spectrum.
Hence, astronomers propose that the chaotic accretion discs of supermassive black holes "spit out" jets in directions perpendicular to the disc, explaining the intense jets that emerge from quasars and active galactic nuclei in different directions.
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A mass m is attached to an ideal massless spring. When this system is set in motion with amplitude a, it has a period t. What is the period if the amplitude of the motion is increased to 2a?.
The period will be the same if the amplitude of the motion is increased to 2a
What is an Amplitude?
Amplitude refers to the maximum extent of a vibration or oscillation, measured from the position of equilibrium.
Here,
mass m is attached to the spring.
mass attached = m
time period = t
We know that,
The time period for the spring is calculated with the equation:
[tex]T = 2\pi \sqrt{\frac{m}{k} }[/tex]
Where k is the spring constant
Now if the amplitude is doubled, it means that the distance from the equilibrium position to the displacement is doubled.
From the equation, we can say,
Time period of the spring is independent of the amplitude.
Hence,
Increasing the amplitude does not affect the period of the mass and spring system.
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What is the safest method to determine electrical current
What is the total energy that the ball has when the launcher is in the ""ready to launch"" position with the spring fully compressed?
A piece of copper of mass 150g at temperature of mass 70g containing 60g of water at temperature of 20°C. Ignoring heat losses, what would be the final steady temperature of the mixture? [Specific of heat capacity of copper = 4.0× 10²J/kg-1/K ^-1. Please any Physics student can help or if you have any idea, you can help me out. Thanks.✨✨
Answer:
The final temperature is [tex]29.6^oC[/tex].
Explanation:
When the two masses come in contact, one releases heat and the other absorbs it. The former can be modelled with the equation [tex]HeatLost = (Mass1 (kg))(c1)(T1-T)[/tex], and the latter by [tex]HeatGained=(Mass2(kg))(c2)(T-T2)[/tex]
m1=0.15 kg
m2=0.06 kg
T1 = 70 degrees Celsius = 343 K
T2 = 20 degrees Celsius = 293 K
T= Final temperature
c1 = Specific heat capacity of copper
c2 = Specific heat capacity of water
Because there is no heat lost into the surroundings, the heat removed from one substance is the same as the heat gained in the other. Therefore:
[tex](Mass1)(c1)(T1-T)=(Mass2)(c2)(T-T2)[/tex]
[tex](0.150)(400)(343-T)=(0.06)(4184)(T-293)[/tex]
[tex](60)(343-T)=(251.04)(T-293)[/tex]
[tex]20580-60T=251.04T-73554.72[/tex]
[tex]-311.04T=-94134.72[/tex]
[tex]T=302.6 K[/tex]
[tex]T=29.6^oC[/tex]
Hope this helps! (My apologies if the answer is wrong, it has been a while since I've done this)
the question is down below
The speed of the airplane, v is 144.2 m/s
The height, H of the roof above the head of the man is 66.4 m.
What is the speed of the airplane?The speed of the airplane is determined using the Pythagoras theorem.
The speed of the airplane, v is calculated as follows:
v = √(80² + 120²0
v = 144.2 m/s
The height, H of the roof above the head of the man is calculated as follows:
tan 38° = H/85
H = tan 38° * 85 m
H = 66.4 m
In conclusion, the tangent ratio is used to find the height of the roof above the head of the man.
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An object of mass 1.00 kg is attached to a vertical spring with spring constant 100 N/m. The object is held at rest in a position such that the spring is stretched upward a distance 1.00 cm beyond its undisturbed length. If the object is released, how far will it drop before coming to rest
The object will drop 5 cm if released before coming to rest.
How far will the object fall?We know from Hooke's law that the work that is done when the spring is stretched is given by the formula;
W = 1/2 kx^2
k= 100 N/m
x = 1.00 cm or 0.01 m
W = 0.5 * 100 * 0.01
W = 0.5 J
Now;
W = mgh
h = W/mg
m = 1.00 kg
g = 9.8 m/s^2
h = 0.5 J/1.00 kg * 9.8 m/s^2
h = 0.05 m or 5 cm
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Which of these is most likely to create a boating hazard around river bridges?
a) boats slowing as they approach the bridge
b) cars crossing the bridge
c) debris collecting around pilings
d) bridges swaying due to wind and waves
Debris collecting around pilings is most likely to create a boating hazard around river bridges.
The option (c) is the correct option.
Boating Hazards:
Dams, submerged items, freezing water, rapidly changing weather, sunstroke, and current are just a few of the dangers that boaters may encounter. It's not always easy to see these risks. These risks must be recognized by boaters, and they must always be prepared to prevent hazards.
Operator negligence is the most frequent reason for boating accidents, according to US Coast Guard (USCG) recreational boating statistics from 2019. Inattentiveness on the part of the operator can result in crashes, people falling overboard, and slip-and-fall incidents on board, all of which can result in life-threatening injuries.
The greatest places to find more about any potential local risks are marinas and local boaters. Check any nearby marine charts as well to learn about potential dangers and how to avoid them.
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An object falls from the top of a building that is 25 m high. Air resistance is negligible.
What is the speed of the object when it hits the ground?
The velocity of the object s calculated as 22.1 m/s.
What is the speed of the object?Given that we can write that;
v^2 = u^2 + 2gh
Now u = 0 m/s because the object was dropped from a height
v^2 = 2gh
v = √2 * 9.8 * 25
v = 22.1 m/s
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In the NEC Code, what does 210.8 indicate
A. Article 210, Section 8
B. Chapter 210, Paragraph 8
C. Page 210, Chapter 8
D. That Article 210 contains 8 paragraphs
In the NEC Code, 210.8 indicates article 210, section 8 and is denoted as option A.
What is NEC code?This is referred to the standards which are required for the safe installation of electric wires and equipment in USA.
This comprises of several articles covering different topics and sections which gives it a more elaborate meaning and understanding.
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question is down below need rply fast
The X and Y components are as follows;
1. X = 35 * cos 57 = 19. 1m/s; Y = 35 * sin 57 = 29.4 m/s
2. X = 12 * -cos 34 = -10 m/s; Y = 12 * -sin 34 = -6.7 m/s
3. X = 8 * -cos 90 = 0 m/s; Y = 12 -sin 90 = -8 m/s
4. X = 20 * cos 75 = 5. 2m/s; Y = 20 * (-sin 75) = -19.3 m/s
What are the horizontal and vertical components of the vectors?The horizontal and vertical components of the velocities are given as follows:
Horizontal component, X = x cos θVertical component, Y = y sin θ1. 35 m/s at 57° from x-axis
X = 35 * cos 57 = 19. 1m/s
Y = 35 * sin 57 = 29.4 m/s
2. 12m/s at 34° S of W
X = 12 * -cos 34 = -10 m/s
Y = 12 * -sin 34 = -6.7 m/s
3. 8 m/s at South
X = 8 * -cos 90 = 0 m/s
Y = 12 -sin 90 = -8 m/s
4. 20 m/s at 275° from x-axis
X = 20 * cos 75 = 5. 2m/s
Y = 20 * (-sin 75) = -19.3 m/s
In conclusion, the X and Y components are found by taking cosines and sine of the angles.
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