Answer:
We can use Hooke's Law to find the spring constant k:
F = kx
where F is the force applied to the spring, x is the displacement of the spring from its equilibrium length, and k is the spring constant.
We can find the force applied to the spring by using the weight of the 4.0 kg fish:
F = mg = (4.0 kg)(9.81 m/s^2) = 39.24 N
The displacement of the spring is the difference between its length with the fish and its equilibrium length:
x = 12.0 cm - 10.0 cm = 2.0 cm = 0.02 m
Now we can solve for k:
k = F/x = 39.24 N / 0.02 m = 1962 N/m
To find the length of the spring with an 8.0 kg fish suspended from it, we can use the same formula with the new weight:
F = mg = (8.0 kg)(9.81 m/s^2) = 78.48 N
We can solve for x, which is the new displacement of the spring:
x = F/k = 78.48 N / 1962 N/m = 0.04 m
Therefore, the length of the spring will be:
10.0 cm + 4.0 cm = 14.0 cm
Explanation:
Please help me with this one
formula for calculating a cross sectional area of a cylinder
The formula for calculating the cross-sectional area of a cylinder is:
A = πr^2
The intersection of a cylinder is the area of a shape found if the cylinder is cut perpendicular to its length. This will be a circle for a cylinder. The cross-sectional area of a cylinder is calculated as A = πr^2, where A is the cross-sectional area, is a mathematical constant approximately equal to 3.14, and r is the radius of the cylinder.
This formula computes the volume of a sphere of radius r, which is the cylinder's cross-sectional area. We can calculate various cylinder properties such as thickness, surface area, and so on by knowing the cross-sectional area.
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The formula for calculating the cross-sectional area of a cylinder is Area = πr^2 where 'r' is the radius of the cylinder. An example is provided where the radius is 5 units, yielding a cross-sectional area of 78.5 square units.
Explanation:The cross-sectional area of a cylinder can be calculated using the formula for the area of a circle, because a cross-section of a cylinder is a circle. The formula is Area = πr^2, where 'r' is the radius of the cross-section.
For example, if you have a cylinder with a radius of 5 units, you would calculate the cross-sectional area as follows:
Substitute the radius into the formula: Area = π*5^2.Calculate the square of the radius: Area = π*25.Multiply the result by π (approximately 3.14): Area = 3.14*25 = 78.5 square units.So, the cross-sectional area of this cylinder is 78.5 square units.
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Two charges each 2 x 10-7 C but opposite in sign forms a system. These charges are located at
points A (0,0, -10) cm and B(0,0, +10) cm respectively. What is the total charge and electric dipole
moment of the system?
Answer:
i) Total charge of the
system
= 2 x 10 -7 + (-2 x 10 -7)
= zero P
(ii)
P =q x 2i
P= 2 x 10-7 x 20 x 10-2
P = 4 x 10-8 cm
Direction of Dipole moment – Along negative z-axis.
Explanation:
Food can be eaten in or form
Answer:
from - from the mouth .............
HELPPPPPPPPPP
LATE SCIENCE HOMEWORK
Answer:
motion force
Explanation:
If the catapult throws them then the rocks would be in motions
The fastest recorded pitch in Nippon Professional Baseball, thrown by Shohei Otani in 2016, was clocked at 102.5 mi/h. If a pitch were thrown horizontally at this speed, how far would the ball fall vertically (in ft) by the time it reached home plate, 60.5 ft away?
Answer & Explanation:
we need to calculate how much the ball drops due to the effect of gravity over the 60.5 ft distance from the pitcher's mound to home plate. We can use the formula:
d = 1/2 x g x t^2
where:
d is the distance the ball drops (in ft)
g is the acceleration due to gravity (32.2 ft/s^2)
t is the time it takes for the ball to travel 60.5 ft at a horizontal speed of 102.5 mi/h (which we need to convert to ft/s)
Converting the horizontal speed from miles per hour to feet per second:
102.5 mi/h = 102.5 x 5280 ft / 3600 s = 150.7 ft/s
Now we can find the time it takes for the ball to travel 60.5 ft:
t = d / v
t = 60.5 ft / 150.7 ft/s
t = 0.401 seconds
Finally, we can use the time to calculate how far the ball drops vertically:
d = 1/2 x g x t^2
d = 1/2 x 32.2 ft/s^2 x (0.401 s)^2
d = 0.517 ft
Therefore, the ball drops vertically by approximately 0.517 ft (or 6.2 inches) by the time it reaches home plate, assuming it is thrown horizontally at 102.5 mi/h.
If a baseball is thrown horizontally at a speed of 102.5 mph, it would fall approximately 2.605 feet vertically by time it reaches the home plate 60.5 feet away.
The subject of this problem belongs to the area of projectile motion. First, we need to know the time it takes for the ball to reach the home plate. Given that the distance to the home plate is 60.5 feet and the ball is thrown at 102.5 mph (which is approximately 150 feet per second when converted), the time can be calculated using the formula
time = distance/speed. This gives us approximately 0.403 seconds.
Next, we use the equation for displacement in the vertical direction under the influence of gravity, h = 0.5gt^2, where g is the acceleration due to gravity (32.2 ft/s^2), and t is time. Plugging in the known values, we get
h = 0.5 * 32.2 * (0.403^2) = 2.605 feet.
Therefore, if a baseball were thrown horizontally at a speed of 102.5 mph, it would drop approximately 2.605 feet vertically by the time it reached the home plate, 60.5 feet away.
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2)A three-phase four-pole winding of the double-layer type is to be installed on a 48-slot stator. The pitch of the stator windings is 5/6, and there are 10 turns per coil in the windings. All coils in each phase are connected in series, and the three phases are connected in . The flux per pole in the machine is 0.054 Wb,and the speed of rotation of the magnetic field is 1800 r/min. (a) What is the pitch factor of this winding? (b) What is the distribution factor of this winding? (c) What is the frequency of the voltage produced in this winding? (d) What are the resulting phase and terminal voltages of this stator?
(a) The pitch factor of a three-phase winding is given by Kp = cos(π/6m), where m is the number of slots per pole per phase. Here, m = 48 slots/(4 poles x 3 phases) = 4 slots/pole/phase. Therefore, Kp = cos(π/6 x 4) = cos(π/2) = 0.
(b) The distribution factor of a double-layer winding is given by Kd = sin(π/2p), where p is the number of poles. Here, p = 4, so Kd = sin(π/8) = 0.3827.
(c) The frequency of the voltage produced in the stator winding is given by f = (P/2) × (N/60), where P is the number of poles and N is the speed of rotation in rpm. Here, P = 4 and N = 1800 rpm, so f = (4/2) × (1800/60) = 60 Hz.
(d) The resulting phase voltage of this stator can be calculated using the formula Vφ = 4.44 × f × Φ × Z × K, where Φ is the flux per pole, Z is the total number of conductors in series per phase, and K is the product of the pitch factor and the distribution factor. For this winding, Z = 10 turns/coil x 2 coils/slot x 48 slots/3 phases = 160 conductors/phase, and K = 0 x 0.3827 = 0.
Therefore, Vφ = 4.44 × 60 × 0.054 × 160 × 0 = 0 V.
Since this is a three-phase winding, the resulting terminal voltage will be the line-to-line voltage, which is √3 times the phase voltage. Therefore, the resulting terminal voltage of this stator is 3 × Vφ = 3 × 0 = 0 V.
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2. Dimensions of weight is
a. MLT-¹
b. MLT-2
c. ML²T-2
d. MºLT-2
Answer:
M 1 L 1 T-2
Explanation:
Ariyana is studying sound waves and radio waves for a presentation in class. Which of the following questions would be appropriate to ask for this investigation?
The study of sound generation, regulation, transmission, reception, and effects is known as acoustics. The word comes from the Greek word akoustos, which means "heard."
Why might astronomers use radio waves to study celestial objects? How do radio waves help us understand the cosmos?The advantage of radio astronomy is that it does not interfere with observations due to sunshine, clouds, or rain. Since radio waves travel farther than optical waves, they are constructed differently from visible light telescopes.
What kind of telescopes receive radio waves from celestial objects?They release some energy in the form of radio waves, which have extremely long wavelengths. Radio telescopes are tools used to pick up radio waves from celestial objects.
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A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 23.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 3.67 m/s2 for a distance of 50.0 m to the edge of the cliff, which is 35.0 m above the ocean.
(a) Find the car's position relative to the base of the cliff when the car lands in the ocean.
Incorrect: Your answer is incorrect.
m
(b) Find the length of time the car is in the air.
Incorrect: Your answer is incorrect.
s
Answer:
a) the car lands in the ocean 85.1 meters away from the base of the cliff.
b) the length of time the car is in the air is 2.50 seconds.
Explanation:
Let's start with part (a) of the problem.
First, we need to find the car's velocity at the bottom of the incline using the kinematic equation:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity (which is 0 m/s), a is the acceleration (which is 3.67 m/s^2), and s is the distance traveled down the incline (which is 50.0 m).
Plugging in these values, we get:
v^2 = 0^2 + 2(3.67 m/s^2)(50.0 m)
v^2 = 367 m^2/s^2
v = 19.1 m/s (rounded to one decimal place)
Next, we can use the vertical motion equations to find the time it takes for the car to fall from the cliff to the ocean. We'll use the equation:
h = ut + (1/2)at^2
where h is the height of the cliff (35.0 m), u is the initial vertical velocity (which is 0 m/s), a is the acceleration due to gravity (-9.81 m/s^2), and we're solving for t.
Plugging in these values, we get:
35.0 m = 0 m/s * t + (1/2)(-9.81 m/s^2)t^2
19.9 = t^2
t = 4.46 s (rounded to two decimal places)
Therefore, the car is in the air for 4.46 seconds.
Finally, to find the car's position relative to the base of the cliff when it lands in the ocean, we can use the horizontal motion equation:
s = ut + (1/2)at^2
where s is the horizontal distance the car travels (which is what we're solving for), u is the horizontal velocity (which is the same as the velocity at the bottom of the incline, 19.1 m/s), a is the horizontal acceleration (which is 0 m/s^2), and t is the time the car is in the air (which is 4.46 s).
Plugging in these values, we get:
s = 19.1 m/s * 4.46 s + (1/2)(0 m/s^2)(4.46 s)^2
s = 85.1 m (rounded to one decimal place)
Therefore, the car lands in the ocean 85.1 meters away from the base of the cliff.
Three charged particles are placed at each of three corners of an equilateral triangle whose sides are of length 3.5 cm
. Two of the particles have a negative charge: q1
= -8.3 nC
and q2
= -16.6 nC
. The remaining particle has a positive charge, q3
= 8.0 nC
. What is the net electric force acting on particle 3 due to particle 1 and particle 2?
Find the net force ΣF⃗ 3
acting on particle 3 due to the presence of the other two particles. Report you answer as a magnitude ΣF3
and a direction θ
measured from the positive x axis.
Therefore, the net electric force acting on particle 3 due to particle 1 and particle 2 is -1.38 x 10⁻⁵ N (repulsive).
What is charge?Charge is a fundamental property of matter that describes how strongly an object interacts with electromagnetic fields, such as electric and magnetic fields. There are two types of charge: positive and negative. Like charges repel each other, while opposite charges attract each other. The SI unit of charge is the Coulomb (C). Charge is conserved, meaning that the total amount of charge in a closed system remains constant over time. Charge can be transferred between objects through various mechanisms, such as friction, conduction, and induction. The movement of charged particles, such as electrons or ions, is the basis for electric current and many other electrical phenomena. The study of electric charge and its effects is known as electrostatics.
Here,
To find the net electric force acting on particle 3 due to particle 1 and particle 2, we can use Coulomb's law, which states that the force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them:
F = k * (q1 * q3 / r13²) + k * (q2 * q3 / r23²)
where F is the net electric force on particle 3, k is Coulomb's constant (9.0 x 10⁹ N m²/C²), q1, q2, and q3 are the charges of particles 1, 2, and 3, respectively, r13 and r23 are the distances between particles 1 and 3, and particles 2 and 3, respectively.
To find the distances between the particles, we can use the fact that the triangle is equilateral and has sides of length 3.5 cm. By using trigonometry, we can find that the distances are:
r13 = r23 = 3.5 cm
Substituting the values into the equation, we get:
F = (9.0 x 10⁹ N m²/C²) * [(-8.3 nC) * (8.0 nC) / (0.035 m)² + (-16.6 nC) * (8.0 nC) / (0.035 m)²]
F = -1.38 x 10⁻⁵ N (repulsive)
The direction of this force can be found by considering the angles between the sides of the equilateral triangle and using vector addition. The direction is 120 degrees counterclockwise from the positive x-axis.
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A 6.00v storage battery is connected to
three resistors 6.00, 11.0, and 20.0 respectively
According to the question the equivalent resistance is 37.0 Ω.
What is equivalent resistance?Equivalent resistance is the resistance of a circuit when its individual resistors are replaced with a single resistor that has the same overall effect on the circuit. It is a measure of resistance that is used to simplify calculations of electrical circuits. Equivalent resistance is calculated by taking the sum of the inverse of the individual resistances and then inverting the sum to find the equivalent resistance. This is useful for analyzing complex circuits as it allows for easier calculations.
The equivalent resistance of the three resistors joined in series is equal to the sum of the individual resistances.
Therefore, the equivalent resistance is 6.00 Ω + 11.0 Ω + 20.0 Ω = 37.0 Ω.
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A surface or area that is hardened and does NOT allow water to pass through.
Answer:
Impervious surfaces
Explanation:
Impervious surfaces are paved or hardened surfaces that do not allow water to pass through. Roads, rooftops, sidewalks, pools, patios and parking lots are all impervious surfaces.
Name Label the Parts of the Waves in the Diagram Below. a. b. C. d. e.
The parts of the wave are;
A - CrestB - AmplitudeC - TroughD - WavelengthWhat are the parts of the wave in a wave diagram?A typical wave diagram shows the various parts of a wave. The following are the key parts of a wave:
Crest: The highest point or peak of the wave.
Trough: The lowest point or valley of the wave.
Amplitude: The maximum displacement of the wave from its rest position, which is usually measured from the crest or trough to the equilibrium or rest position.
Wavelength: The distance between two successive crests or two successive troughs of a wave.
Frequency: The number of waves passing through a particular point per unit time, typically measured in hertz (Hz).
Period: The time taken for one complete wave to pass through a particular point, typically measured in seconds.
Velocity: The speed at which the wave propagates, which is usually measured in meters per second.
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A roller skater kept her balance and traveled in a perfect straight line. Her motion slowed down as she cruised along the street. Which of the following statements describes the forces on the skater?
The net force was not 0 on the skater during her motion.
The net force was 0, which is why the skater moved in a straight line.
The forces were unbalanced due to the skater's inertia.
The forces were balanced due to the action-reaction pair required to cruise.
Answer: (A)The net force was not 0 on the skater during her motion.
Explanation:
The net force was not 0 on the skater during her motion. The roller skated slowed down, which indicates that there is another force acting on her roller skates.
The correct statement is "The net force was 0, which is why the skater moved in a straight line." The correct answer is B.
What is Newton's First Law of Motion?Newton's First Law of Motion, states that an object at rest or in motion will remain at rest or in motion with a constant velocity in a straight line unless acted upon by an external force. In this case, the skater is traveling at a constant velocity, which means that the net force acting on her must be zero.
Option A is incorrect because if the net force was not zero, then the skater would not have moved in a straight line. She would have accelerated or changed direction, as per Newton's Second Law of Motion.
Option C is also incorrect because the skater's inertia does not have any effect on the forces acting on her. Inertia is a property of matter that resists changes in motion, but it does not cause any forces to be unbalanced.
Option D is incorrect because the action-reaction pair of forces cancel each other out and do not affect the skater's motion. The action-reaction pair only affects the interaction between two objects, but it does not affect the motion of a single object.
Therefore, The correct option is B i.e. The net force was 0, which is why the skater moved in a straight line.
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You are moving into an apartment and take the elevator to the 6th floor suppose your weigh is 685N and that of your belongings is 915N. Determine the work done by the elevator is lifting you and your belongings up to the 6th floor 15.2m at acontant velocity
If a sunspot has a temperature of 4,360 K and the sunspot can be considered a blackbody, what is the wavelength (in nm) of maximum intensity of the sunspot's radiation?
Given :-
A sunspot has a temperature of 4360 K .Sunspot can be considered as a black body .To find:-
The wavelenght of maximum intensity .Answer :-
Here we are given that the sunspots temperature is 4360K , and considering it as a black body we need to find out the wavelength of its maximum intensity.
So here we can use Wein's displacement Law according to which;
[tex]\qquad\: \underset{\rm\small Wein's \ displacement \ law }{\underbrace{\underline{\underline{ \green{ \quad\quad\lambda_{max}= b/T \quad\quad}}}}} \\[/tex]
where ,
[tex]\lambda_{max}[/tex] is maximum wavelength.[tex] b [/tex] = Wein's displacement constant = 2.89 * 10-³ m K [tex] T[/tex] is temperature in KelvinNow on substituting the respective values, we have;
[tex]\implies \lambda_{max}= \dfrac{2.89\times 10^{-3}m\ K}{4360K}\\[/tex]
[tex]\implies \lambda_{max}= 0.0006628 \times 10^{-3}\ m\\[/tex]
[tex]\implies \lambda_{max}=0.000663 \times 10^{-3}\ m\\[/tex]
[tex]\implies\underline{\underline{\green{ \lambda_{max}= 663 \times 10^{-9} m = 663\ nm }}} \\[/tex]
Hence the maximum wavelength is 663 nm .
and we are done!
HELPPPP MEEE
LATE SCIENCE HOMEWORK
Answer: The answer is C i believe
Please calculate the frequency of the waves in Hz
Answer: 7,6 hz
Explanation:
50/23.4=x+5.5x 18= The equation so its basically 7,6 x 18 to get ur answer in HZ. So yeah thanks and hope this helped !!!!
a 12 kg object has a velocity of 8.0 m/s and is moving in a circle of a radius 16 m
The centripetal force of the object is determined as 48 N.
What is centripetal force?
Centripetal force is the force that acts on an object moving in a circular path, directed towards the center of the circle. It is the force that keeps the object moving in a circle, rather than continuing in a straight line.
The centripetal force required to keep an object moving in a circle is given by the formula:
F = (mv²)/r
where:
m = mass of the objectv = velocity of the objectr = radius of the circleSubstituting the given values, we get:
F = (12 kg)(8.0 m/s)² / 16 m
F = 48 N
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The complete question is below:
A 12 kg object has a velocity of 8.0 m/s and is moving in a circle of a radius 16 m. calculate the centripetal force of the object
It takes 80 pounds of force to
stretch a particular spring 2
inches. How much work is done
in stretching it from its relaxed
state a total of 4 inches?
[?] inch - pounds
How does the size of each push compare with the force of friction on the car? Explain your answer in terms of the net force on the car.
Answer:
Explanation:
The size of each push determines the magnitude of the force applied on the car. The force of friction on the car is the resistance force that opposes the motion of the car and it depends on the nature of the surface in contact and the weight of the car. The force of friction is equal and opposite to the force applied on the car, as per Newton's third law of motion.
If the magnitude of the net force on the car is greater than the force of friction, the car will accelerate in the direction of the net force. If the magnitude of the net force is equal to the force of friction, the car will move at a constant velocity. If the magnitude of the net force is less than the force of friction, the car will decelerate and eventually stop.
Therefore, the size of each push needs to be greater than the force of friction on the car to accelerate it. If the size of each push is equal to the force of friction, the car will not accelerate, and if the size of each push is less than the force of friction, the car will decelerate.
3. (a) Determine the voltages V, and Vx using Nodal Analysis. You must
use the node indicated as your reference (REF) for all other node voltages.
(b) Now happily repeat using Mesh Analysis.
Kirchhoff's current law (KCL) can be written at each node using nodal analysis, and the voltages can be expressed in terms of the node voltages using Ohm's law.
What in nodal analysis is a reference node?The most chosen reference node in the nodal analysis is. a node that is connected to by the most elements. a node that has the greatest amount of voltage sources linked to it, or. a symmetry node.
What does a node's reference mean?An order template data node that references another data node is known as a reference node. The structure and data typing of the reference data node match those of the node it is referencing.
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a person throws a ball upwards into the air with an initial velocity of 15 m.s-1 ignore the effects of air friction. calculate how long the ball is in the air before it comes back to the hand
Answer:
The objective of this study is to determine the duration of time it takes for an object with an initial velocity of 15 m.s-1 to reach its peak height and descend back to its starting point when launched straight upwards, such as when throwing a ball straight up into the air. The study takes into account the effects of gravity, air resistance and Newton's Laws of Motion.
For the purpose of this study, a mathematical investigation is undertaken, taking into consideration the initial velocity (vi = 15 m.s-1) and the gravitational acceleration (g = 9.81 m.s-2). The equation for the Time of Flight (T) is derived by using kinematic equations, as followed:
T = 2vi/g
Where T is the time of flight and vi is the initial velocity of the object.
In this case, the Time of Flight is equal to T = 2∙ 15m/s / 9.81 m/s2 = 3.03 s.
Therefore, when the ball is released into the air the ball was be in the air for 3.03 seconds before descending back to its starting point.
Friction, in this case, does not need to be included in the equations because it's negligible. However, to accurately determine the time the ball reaches its peak, additional equations should be used by considering the forces acting on the object, being drag, air resistance, and gravity
5. The mechanical advantage of a jaw when it is used as a second-class lever is 1.4.
a. If the input force is 100 newtons, what is the output force?
b. How does the input lever arm compare to the output lever arm when the jaw is used as a
second-class lever? Draw a diagram to illustrate your answer.
Answer: a. It would be 140 N
I don’t know, I just got it right
An airplane A flies north with velocity 300 km/h relative to the ground; Another airplane Bhave a velocity of 200 km/h toward a direction 60° west of north. Find the velocity of A relative to B.
Velocity of airplane A relative to B is 200 km/h east and 126.8 km/h north-west.
What is velocity?Rate and direction of an object's movement is known as velocity.
Let velocity of airplane A with respect to the ground be "vA" and velocity of airplane B with respect to the ground be "vB". Velocity of A relative to B, denoted as vAB, is calculated:
vBx = vB cos(60°) = 200 km/h x cos(60°) = 100 km/h
vBy = vB sin(60°) = 200 km/h x sin(60°) = 173.2 km/h
Direction of vBy is north-west.
Velocity of A with respect to the ground is given as 300 km/h north.
vAB = vA - vB
vABx = vAx - vBx = 300 km/h - 100 km/h = 200 km/h
vABy = vAy - vBy = 300 km/h - 173.2 km/h = 126.8 km/h
So, the velocity of airplane A relative to B is 200 km/h east and 126.8 km/h north-west.
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How might form and function of a structure influence
each other?
Answer:
Explanation:
Form must follow function, otherwise the design of a structure is a failure. For example, the function (purpose) of a bridge is to provide a means of crossing an obstacle, such as a body of water, a valley, another road, etc. The form of the bridge must serve the purpose of providing safe and reliable passage of pedestrians, vehicles, trains, etc. A most basic form of a bridge is a beam design: simple, efficient, cost-effective, functional. If budget and public sentiment allow, additions to the design can be incorporated to make the bridge more aesthetically pleasing, but such additions do not add to the basic function.
The United States consumes about 2.5 ✕ 1019 J of energy in all forms in a year. How many years could we run the United States on the energy released by a 1023 J solar flare?
Answer:
Explanation:
To find out how many years the United States could run on the energy released by a 10²³ J solar flare, we need to divide the energy of the solar flare by the energy consumed by the United States in one year:
Number of years = Energy of solar flare / Energy consumed by the United States per year
Number of years = 10²³ J / 2.5 x 10¹⁹ J/year
Number of years = 4 x 10³ years
Therefore, the United States could run for approximately 4,000 years on the energy released by a 10²³ J solar flare.
Place the following descriptions, formulas, and terms in the correct category for Newton's Laws.
For every action, there is an equal and opposite reaction. Action-reaction pairs
Explain in detail about the following categories of the newtons laws ?
Category 1: Newton's First Law
An object at rest stays at rest and an object in motion stays in motion with a constant velocity, unless acted upon by an unbalanced force.
ΣF = 0 (the sum of all forces acting on an object is zero)
Law of Inertia
Category 2: Newton's Second Law
F = m*a (the force applied on an object is equal to the mass of the object multiplied by its acceleration)
Force
Mass
Acceleration
Category 3: Newton's Third Law
For every action, there is an equal and opposite reaction.
Action-reaction pairs
Reaction force
Action force
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A turntable must spin at 33.3 rev/min (3.49 rad/s) to play an old fashion vinyl record . How much torque must the motor deliver if the turntable is to reach its angular speed in 2.20 revolutions starting from rest ? The turntable is an uniform disk of diameter 30.5 cm and mass 0.240kg
Answer……. N-m
0.002355 N-m torque must the motor deliver if the turntable is to reach its angular speed in 2.20 revolutions starting from rest
What is torque and how is it related to rotational motion?Torque is a measure of the twisting force that causes rotational motion. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation at which the force is applied.
Given:
Angular speed, ω = 3.49 rad/s
Number of revolutions, N = 2.20 rev
Diameter of disk, D = 30.5 cm = 0.305 m
Mass of disk, m = 0.240 kg
The moment of inertia of a uniform disk about its center is (1/2) * m * r^2, where r is the radius of the disk. Here, r = D/2 = 0.1525 m.
Moment of inertia, I = (1/2) * m * r^2 = (1/2) * 0.240 kg * (0.1525 m)^2 = 0.002198 J-s^2/rad
The torque required to bring the disk to its angular speed can be found using the formula:
τ = I * α
where α is the angular acceleration of the disk. Since the disk starts from rest, we have:
α = ω^2 / (2 * π * N)
where π is the constant pi. Substituting the given values, we get:
α = (3.49 rad/s)^2 / (2 * π * 2.20 rev) = 1.071 rad/s^2
Therefore, the torque required is:
τ = I * α = 0.002198 J-s^2/rad * 1.071 rad/s^2 = 0.002355 N-m
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