Answer:
15mm
Explanation:
We know that for circular holes first dark spot is given by
sin စ = 1.22 λ/D
Also we know that at the same time
tan စ = r/L
So
r = L tanစ = 6 x tan( arcsin(1.22x 500 x10^9/0.50 x 10^ 3))
= 0.0073 m = 7.3 mm
However since the size is twice that so 14.6 mm which is approx 15mm
A billiard ball moves with 3 kg⋅m/s of momentum and strikes three other billiard balls. What is the total momentum of the balls after the collision? A. less than 3 kg⋅m/s B. It depends on the mass of each ball. C. 3 kg⋅m/s D. more than 3 kg⋅m/s
Answer:
It should be C
Explanation:
It depends on the mass of each ball
Remember the formula for momentum, mass X velocity
Momentum depends on the mass of the object
The momentum of the billiard balls after the collision is 3 Kgm/s.
Let the billiard ball be B.Given the following data:
Momentum B = 3 Kgm/sTo find the momentum of the balls after the collision:
Momentum is simply a multiplication (product) of the mass of an object with its velocity. Also, momentum is a vector quantity because it has both magnitude and direction.
Mathematically, momentum is given by the formula;
[tex]Momentum = Mass[/tex] × [tex]Velocity[/tex]
[tex]Total \; momentum = Momentum \; B + Momentum \;of \;the \;other\; balls.[/tex]
Since the other billiard balls were at rest (not experience any motion), there velocities would be zero (0) m/s.
Substituting the values, we have:
[tex]Total \; Momentum = 3 + 0[/tex]
Total momentum = 3 Kgm/s.
Therefore, the momentum of the billiard balls after the collision is 3 Kgm/s.
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State two precautions each that you will take while performing refractive index of a glass box experiment
Answer:
light should be direct
glass should not be cracked
pins should be pointed carefully
Explanation:
What are the magnitude and direction of the net force on the third spider (S3) when it is resting at the origin
Complete Question
The complete question is shown on the first uploaded image
Answer:
The magnitude is [tex]F_3 =0.62\ N[/tex]
Explanation:
From the question we are told that
The distance between the spiders is [tex]a =0.59\ m[/tex]
The charge on the [tex]S_1\ and\ S_3[/tex] is [tex]q_{1}=q_{3}=q =+4.9\mu \ C[/tex]
The charge on [tex]S_2[/tex] is [tex]q_2 = 4.9\mu \ C[/tex]
Given that the charge are arranged in an equilateral triangle, it implies that the angle at each vertices of the triangle is 60°
Generally the magnitude of net force on [tex]S_3[/tex] is mathematically represented as
[tex]F_3= F_{13} cos(60)+ F_{21} cos(60)[/tex]
So
[tex]F_{13} =\frac{k* q^2 }{a^2}[/tex]
Here k is the columns constant with value [tex]k = 9*10^9 \ kg\cdot m^3\cdot s^{-4} \cdot A^{-2}.[/tex]
So
[tex]F_{13}=\frac{9*10^9*((4.9*10^{-6})^2)}{0.59^2}[/tex]
=> [tex]F_{13} = 0.62 \ N[/tex]
From the diagram we see that [tex]F_{13}= F_{23} = 0.62\ N[/tex]
So
[tex]F_3=0.62cos(60)+0.62cos(60)[/tex]
[tex]F_3 =0.62\ N[/tex]
Now from the diagram the ls [tex]270^o[\tex] counterclockwise from x-axis
Two long wires hang vertically. Wire 1 carries an upward current of 1.20 A. Wire 2, 20.0 cm to the right of wire 1, carries a downward current of 4.20 A. A third wire, wire 3, is to be hung vertically and located such that when it carries a certain current, each wire experiences no net force.
(a) Is this situation possible?
A. Yes
B. No
Is it possible in more than one way?
A. Yes
B. No
(b) Describe the position of wire 3.
distance ________ cm
direction: left of wire 1
(c) Describe the magnitude and direction of the current in wire 3.
magnitude
direction
down
Answer:
Explanation:
A, yes
b,
The force(per unit length) on wire 1 by 2 is to the left and
= μo*I1*I2/2πr
= 2*10^-7 * 1.2 * 4.2/0.20
= 5.04*10^-6N/m
From third law we have the force on wire2 by wire 1 is 5.04*10^-6N/m and to the right
So the magnitude of the force on each wire by wire 3 must be 4.2*10^-6N/m
Since the current in wire 2 is > wire 1 then wire 3 must be closer to wire 1 than 2
and wire 3 must be to the left of wire 1
Let x be the distance from wire 3 to wire 1 so x + 0.20 = distance from wire 3 to wire 2
Now μo*I1*I3/2πx = μo*I3*I2/2π(x + 0.20)
so solving for x we get
I1/x = I2/(x+0.20)
or x +0.20 = 4x
so x = 0.20/3 = 0.0667m
Now μo*I1*I3/2πx = 4.2*10^-6
so I3 = 4.2x10^-6 * 0.0667/(2.0x10^-7 * 1.2) = 1.167 A and its direction is down
Approximately how long will it take light to travel to 1.7 AU in minutes? Use 3 × 108 m/s for the speed of light. unanswered
Answer:
14.1mins
Explanation:
We know that
Time =Distance/Speed
So
= 1.7 au/ (3 E8 m /s )
= 1.7 x 1.496 x 10^11 m /(3 x 10^8 m /s
Converting Au to meters (1.7 x 1.496 x 10^11 m)
= 847.7 s
=14.1 mins
Answer:
Time = 847.73 s = 14.12 min
Explanation:
The distance traveled by an object travelling at a constant speed is given by the following formula:
Distance = (Speed)(Time)
Time = Distance/Speed
where,
Distance = 1.7 AU
converting it into meters:
Distance = (1.7 AU)(1.496 x 10¹¹ m/1 AU) = 2.543 x 10¹¹ m
Speed = 3 x 10⁸ m/s
Therefore, using these values in the equation we get:
Time = (2.543 x 10¹¹ m)/(3 x 10⁸ m/s)
Time = 847.73 s = 14.12 min
Light of wavelength 3500Å is incident on two metals A and B whose work functions are 3.2 eV and 1.9 eV respectively. Which metal will emit photoelectrons?
(a) A
(b) B
(c) Both A and B
(d) Neither A nor B
Answer:
(c) Both A and B
Explanation:
Given;
wavelength of the incident light, λ = 3500 Å = 3500 x 10⁻¹⁰ m
The energy of the incident light is given by;
E = hf
where;
h is Planck's constant = 6.626 x 10⁻³⁴ J/s
f is frequency = c / λ
[tex]E = \frac{hc}{\lambda} \\\\E = \frac{(6.626*10^{-34})(3*10^8)}{3500*10^{-10}}\\\\E = 5.68 *10^{-19} \ J\\\\E = 5.68 \ eV[/tex]
Work function is the minimum amount of energy required to liberate electrons from a metal surface.
The work function of metal A is 3.2 eV and
Th e work function of metal B is 1.9 eV
Both work functions are less than the incident energy of the light calculated as 5.68eV.
Thus, both metals will emit photoelectrons.
(c) Both A and B
Calculate the kinetic energy of an 88-kg scooter moving at 12 m/s .
Answer:
kinetic energy = 1/2 X m(v)^2
= 1/2 X 88 X 12
= 528 j
Your question has been heard loud and clear.
Kinetic energy formula= 1/2mv^2
Mass = 88kg (convert to grams because velocity is in m/s)
Mass in grams = 88000g or 88*10^3 g
Velocity= 12m/s
Now kinetic energy = 1/2 * 88000*12*12= 6336 joules
Kinetic energy = 6336 Joules or 6.336 Kilo joules
Thank you.
The electric flux through a spherical surface is 1.4 ✕ 105 N · m2/C. What is the net charge (in C) enclosed by the surface?
Answer:
The value is [tex]Q_{net} = 1.239 *10^{-6} \ C[/tex]
Explanation:
From the question we are told that
The electric flux is [tex]\Phi = 1.4*10^{5} \ N\cdot m^2/C[/tex]
Generally the net charge is mathematically represented as
[tex]Q_{net} = \Phi * \epsilon_o[/tex]
Here [tex]\epsilon_o[/tex] is the permetivity of free space with value
[tex]\epsilon_o = 8.85*10^{-12} \ \ m^{-3} \cdot kg^{-1}\cdot s^4 \cdot A^2[/tex]
So
[tex]Q_{net} = 1.4*10^5 * 8.85*10^{-12}[/tex]
=> [tex]Q_{net} = 1.239 *10^{-6} \ C[/tex]
In a particular wire in a circuit, conventional current flows in the z direction. What is the direction of electron current in the wire
Answer:
Electron current will flow in the negative z axis
Explanation:
This is because flow of conventional current is opposite that if electron current so since conventional is in +z axis electron will be -z axis
What is the power in D of the eyes of a woman who can see an object clearly at a distance of only 9.5 cm
Answer:
Explanation:
It is the far point an myopic person . For it she uses concave lens . For her ,
object distance u = infinity
image v = - 9.5 cm
f = ?
form the lens formula
[tex]\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \\[/tex]
[tex]\frac{1}{f} = \frac{1}{-9.5} - 0 \\[/tex]
f = - 9.5 cm = - 9.5 / 100 m
P = 1 /f = - 100 / 9.5 = - 10.52 D .
Which of these equations is dimensionally correct?
I. mv/ t= F
II. xv^2= Fx^3/ x^2
III. xt= vt^2+at^3
Answer: first and third.
Explanation:
An equation is dimensionally correct if the units are the same in both sides of the equation.
first, let's define the units used:
{m} = kg
{v} = m/s
{F} = kg*m/s^2
{x} = m
{t} = s
{a} = m/s^2
Now, let's analyze each option:
1) m*v/t = F
in the left side the units are:
{m}*{v}/{t} = kg*(m/s)*(1/s) = kg*m/s^2
And as is written above, these are the units of F, so this is correct.
2) x*v^2 = F*(x^3/x^2)
This is more trivial, in the right side we can see an F, that has mass units (kg) and in the left side we have x and v, and we know that none of these have mass units, so this expression is not correct.
3) xt= vt^2+at^3
the units in the right side are:
{x}*{t] = m*s
in the right side are:
{v}*{t}^2 + {a}*{t}^2 = (m/s)*s^2 + (m/s^2)*s^3 = m*s + m*s
So in both sides of the equation we have the same units, then this equation is dimensionally correct.
According to Newton's Third Law, if someone jumps off a skateboard, the
skateboard will roll backwards because
Answer:
every action has a same an equal reaction
If someone jumps off a skateboard, the skateboard will roll backwards because action and reaction are equal and opposite.
Newton's third law states that action and reaction are equal and opposite. That is, for every action there is a resulting reaction equal in magnitude to the action but opposite in direction.
If someone jumps off a skateboard, he will exert an action force downwards while the skate board exerts a reaction force upwards on him. This causes the skateboard to move backwards while he moves upwards.
Thus, if someone jumps off a skateboard, the skateboard will roll backwards because action and reaction are equal and opposite.
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A stretched string is 2.11 m long and has a mass of 19.5 g. When the string oscillates at 440 Hz , which is the frequency of the standard A pitch, transverse waves with a wavelength of 15.3 cm travel along the string. Calculate the tension T in the string.
Answer:
The tension of the string is 41.876 N
Explanation:
Given;
length of the string, L = 2.11 m
mass of the string, m = 19.5 g = 0.0195 kg
frequency of the wave, f = 440 Hz
wavelength, λ = 15.3 cm = 0.153 m
The velocity of the wave is given by;
v = fλ
v = 440 x 0.153
v = 67.32 m/s
Also the velocity of the wave is given by
[tex]v = \sqrt{\frac{T}{\mu} }[/tex]
where;
μ is mass per unit length = 0.0195 / 2.11 = 0.00924 kg/m
T is the tension of the string
T = v²μ
T = (67.32)²(0.00924)
T = 41.876 N
Therefore, the tension of the string is 41.876 N
In the absence of government, what would determine the way people act towards each other?
Answer:
In the absence of government, what would determine the way people act towards each other is the need to acquire means of survival such as food or shelter.
Thus, since the government regulates the rights and obligations of citizens to guarantee equal access to essential services and goods for life, in the event of the disappearance of the state as a form of social organization, people would tend to act selfishly. to provide itself with those goods and services.
Society would then return to a state of nature, where man competes with his peers for access to resources. So the need for those resources would ultimately determine the way humans relate to each other.
Throughout the absence of regulation, the necessity to gain means of subsistence, which includes extra help, would decide how individuals interact with one another.
Absence of Government:
As a consequence, while the organization governs individuals' rights and duties purpose of providing equitable access to vital services and products for life, if the community as more than just a form of social organization disappears, individuals might likely behave selfishly to offer such commodities.
The community would therefore revert to its natural condition, with man competing with equal fellows for distribution of wealth. As a result, the necessity for such resources would eventually decide how humans interact with one another.Thus the response above is right.
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To whom does the vha provide care for today ?
Answer:
The Veterans Health Administration (VHA) is the largest integrated health
care system in the United States, providing care at 1,255 health care
facilities, including 170 VA Medical Centers and 1,074 outpatient sites of care
of varying complexity ( VHA outpatient clinics) to over 9 million Veterans
enrolled in the VA .
"If we increase the amplitude of transverse waves on a string, what happens to the speed of a wave along the string?"
Answer:
It is increased
Explanation:
If the amplitude of a transverse wave in a string is increased, then also, the speed of that wave along the string also increases.
In transverse waves, the particles of the medium does move vertically, m either up or down and also moves at right angles to the direction of the wave. It should be noted also, that the wave amplitude of a transverse wave is defined as the difference in height between the crest(high) and the resting position(low).
The highest point particles of the medium reach is often tagged as the crest, while the lowest point is tagged as the resting position. The higher the height of the crests are, the greater the amplitude of the wave will be.
Why are experimental investigations the best type of scientific investigation o demonstrat cause-and-effect relationships?
Answer:
Isolation of Variables.
Explanation:
I am just taking a guess but Experimental investigations allow you to isolate variables (making most variables constant, allowing only the independent variable to have an impact on the dependent variable). With other scientific investigations, if they don't isolate the variables it is very possible that an unknown third variable could be skewing the results (which will result in correlation but not causation).
Answer:
Experimental investigations are the best type of scientific investigation to demonstrate cause-and-effect relationships because they allow the investigator to actively manipulate variables and control conditions. The independent variable can be isolated and manipulated, producing a change (or no change) in the dependent variable. This change can be measured to gather evidence to support or refute the cause-and-effect relationship. Experimental investigations also use a control group (a group that does not receive the factor being tested) for comparison.
Explanation:
Automated-response....it's right
what do u mean by the activity series of metals ??
Answer:
An activity series is a list of substances ranked in order of relative reactivity. For example, magnesium metal can knock hydrogen ions out of solution, so it is considered more reactive than elemental hydrogen. The activity series is a useful guide for predicting the products of metal displacement reactions.
A graph of x vs. t2 is linear, and intercepts the vertical axis at 12 m and the horizontal axis at 4 s2. What is the function?
Answer:
x = -3t² + 12
Explanation:
x vs t² is a line.
x = at² + b
The y intercept is 12.
x = at² + 12
At t² = 4s², x = 0.
0 = a(4) + 12
a = -3
Therefore, the function is:
x = -3t² + 12
A bus took 8 hours to travel 639 km. For the first 5 hours, it
travelled at an average speed of 72 km/h. What was the
average speed for the remaining time of the journey?
Answer:
93
Explanation:
If a proton and an electron are released when they are 7.00×10−10 m apart (typical atomic distances), find the initial acceleration of each of them. aelectron = nothing m/s2
Answer:
The acceleration of the proton is 2.823 x 10¹⁷ m/s²
The acceleration of the electron is 5.175 x 10²⁰ m/s²
Explanation:
Given;
distance between the electron and proton, r = 7 x 10⁻¹⁰ m
mass of proton, [tex]m_p[/tex] = 1.67 x 10⁻²⁷ kg
mass of electron, [tex]m_e[/tex] = 9.11 x 10⁻³¹ kg
The attractive force between the two charges is given by Coulomb's law;
[tex]F = \frac{k(q_p)(q_e)}{r^2}[/tex]
where;
k is Coulomb's constant = 9 x 10⁹ Nm²/c²
[tex]F = \frac{k(q_p)(q_e)}{r^2} \\\\F = \frac{(9*10^9)(1.602*10^{-19})(1.602*10^{-19})}{(7*10^{-10})^2} \\\\F = 4.714 *10^{-10} \ N[/tex]
Acceleration of proton is given by;
F = ma
[tex]F = m_pa_p\\\\a_p = \frac{F}{m_p}\\\\a_p = \frac{4.714*10^{-10}}{1.67*10^{-27}}\\\\a_p = 2.823 *10^{17} \ m/s^2[/tex]
Acceleration of the electron is given by;
[tex]F = m_ea_e\\\\a_e = \frac{F}{m_e}\\\\a_e = \frac{4.714*10^{-10}}{9.11*10^{-31}}\\\\a_e = 5.175 *10^{20} \ m/s^2[/tex]
Given:
Mass of proton, [tex]m_p = 1.67\times 10^{-27} \ kg[/tex]Mass of electron, [tex]m_e = 9.11\times 10^{-31 } \ kg[/tex]Distance between electron & proton, [tex]r = 7\times 10^{-10} \ m[/tex]By using Coulomb's law, the attractive force will be:
→ [tex]F = \frac{k(q_p) (q_e)}{r^2}[/tex]
By substituting the values, we get
[tex]= \frac{(9\times 10^9)(1.602\times 10^{-19}) (1.602\times 10^{-19})}{(7\times 10^{-10})^2}[/tex]
[tex]= 4.714\times 10^{-10} \ N[/tex]
Now,
The acceleration of proton will be:
→ [tex]F = ma[/tex]
[tex]= m_p a_p[/tex]
or,
→ [tex]a_p = \frac{F}{m_p}[/tex]
[tex]= \frac{4.714\times 10^{-10}}{1.67\times 10^{-27}}[/tex]
[tex]= 2.823\times 10^{17} \ m/s^2[/tex]
and,
The acceleration of electron will be:
→ [tex]F = m_c a_c[/tex]
or,
→ [tex]a_e = \frac{F}{m_e}[/tex]
[tex]= \frac{4.714\times 10^{-10}}{9.11\times 10^{-31}}[/tex]
[tex]= 5.175\times 10^{20} \ m/s^2[/tex]
Thus the above answer is correct.
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A spaceship is traveling through deep space to a space station and needs to make a course correction to go around a nebula. The captain orders the ship to travel 2.3 106 kilometers before turning 70° and traveling 1.5 106 kilometers to reach the space station. If the captain had not ordered a course correction, what would have been the magnitude and direction of the path of the spaceship if it had traveled to the space station through the nebula?
Answer:
Explanation:
Using the given values
Let
Px= 2.3 x 10^6, Py=0, Qx=1.5x10^6cos(70),
Qy= 1.5x10^6sin(70)
So let
Hx= Px+Qx=2.813 x 10^6, Hy=Py+Qy=1.401 x 10^6
Magnitude = √ ((2.813 x 10^6)^2+(1.401 x 10^6)^2)= 3.14 x 10^6
To find direction
tan စ = Hy/Hx = 1.401/2.813= 0.4980
စ = 26.5°
The magnitude and direction of the path of the spaceship if it had traveled to the space station through the nebula are 3.14 x 10⁶ m and 26.5°.
What is nebula?A nebula is a huge cloud consisting of dust and gas in space. Some nebula come from the gas and dust thrown out by the explosion of a dying star known as a supernova.
The captain orders the ship to travel in horizontal direction, Px= 2.3 x 10⁶ m, Py=0,
After turning 70° and it travels to reach the space station, Qx = 1.5x10⁶ x cos70° in horizontal direction.
and Qy= 1.5x10⁶sin70°
So, total horizontal distance moved is
Hx= Px+Qx = 2.813 x 10⁶
Total vertical distance moved is
Hy=Py+Qy = 1.401 x10⁶
Magnitude of the path = sq rt [(2.813 x 10⁶)²+(1.401 x 10⁶)²]
Path = 3.14 x 10⁶ m
Direction of the path,
tan α = Hy/Hx
tan α = 1.401/2.813
tan α = 0.4980
α = 26.5°
Thus, the magnitude and direction of the path of spaceship is 3.14 x 10⁶ m and 26.5°.
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To conduct a study on depression, you ask people to rate their depression on
a scale of 1 to 10. Their responses are a(n) ___ in your study.
A. discrete variable
B. hidden variable
C. variable
D. observation
Answer:
The answer is C variable. Just took the quiz.
Explanation:
Answer:
C. variable
Explanation:
A car travels in a straight line with an average velocity of 80 km/h for 2.5 h and then with an average velocity of 40 km/h for 1.Sh. What is the total displacement for the 4h trip and what is the average velocity for the total trip
Answer:
260 km
65 km/hr
Explanation:
The displacement of an object is the distance moved by that object in a particular direction.
velocity = displacement / time, therefore,
Displacement = velocity * time.
Total displacement for the 4 HR trip = displacement for 2.5 hr + displacement for 1.5 hr
total displacement = (80 * 2.5) + (40 * 1.5)
Total displacement = 200 + 60
Total displacement = 260 Km
average velocity for the total trip = total displacement / total time taken
average velocity = 260 km/ 4 hr
average velocity = 65 km/hr
If one has twice the length of the other, what is the ratio of the diameter of the longer wire to the diameter of the shorter wire
Explanation:
The resistance of a wire is given by the formula as follows :
[tex]R=\rho \dfrac{l}{A}[/tex]
l is length of wire
A is area of cross section, [tex]A=\pi r^2[/tex]
Since, r=d/2, d = diameter
[tex]A=\pi \dfrac{d^2}{4}[/tex]
It is given in the problem that the resistance of two aluminum wires is same.
[tex]R_1=R_2\\\\\rho\dfrac{L_1}{\pi d_1^2/4}=\rho\dfrac{L_2}{\pi d_2^2/4}\\\\\dfrac{L_1}{L_2}=\dfrac{d_1^2}{d_2^2}[/tex]
We have, L₁=2L₂
So,
[tex]\dfrac{2L_2}{L_2}=\dfrac{d_1^2}{d_2^2}\\\\\dfrac{d_1^2}{d_2^2}=2\\\\\dfrac{d_1}{d_2}=\sqrt{2}[/tex]
So, the ratio of the diameter of the longer wire to the diameter of the shorter wire is [tex]\sqrt2:1[/tex]
Help me please !!!!!
Answer:
confounding cause they had exposure to many programmes
Answer:
Confounding should be your answer please mark brainliest
URGENT!!!!!! Assume that a wire has 1.5 ohms of resistance. If the wire is connected to two batteries with a total voltage of 3.0 V, how much current will flow through the wire? 3.0 amps 2.3 amps 2.0 amps 1.0 amps
Answer:
2.0 amps
Explanation:
Current is the ratio of voltage to resistance:
I = V/R = (3.0)/(1.5) = 2.0
The current in the wire is 2.0 amps.
The horizontal and vertical components of the initial velocity of a projectile are 50 m/s and 120 m/s respectively. What is the magnitude of the initial velocity
Answer:
50 m/s
Explanation:
In a projectile motion, acceleration is only on the vertical plane, that is, the vertical velocity is the only velocity component that undergoes acceleration under gravitational force. The horizontal component of velocity dos not change with time, and hence is the same as the initial velocity of the projectile.
Two students measure the speed of light. One obtains (3.001 0.001)10^8 m/s; the other obtains (2.999 0.006)10^8 m/s.Required:Which is more precise?
Answer:
(30010001) 10^8 m/s
Explanation:
An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.200 rev/s . The magnitude of the angular acceleration is 0.883 rev/s2 . Both the the angular velocity and angular accleration are directed counterclockwise. The electric ceiling fan blades form a circle of diameter 0.760 m .A. Compute the fan's angular velocity magnitude after time 0.204 s has passed.Express your answer numerically in revolutions per second.B. Through how many revolutions has the blade turned in the time interval 0.204 s from Part A?Express the number of revolutions numerically.C. What is the tangential speed vt of a point on the tip of the blade at time t = 0.204 s?Express your answer numerically in meters per second.D. Calculate the magnitude atat of the tangential acceleration of a point on the tip of the blade at time t = 0.204 s.Express the acceleration numerically in meters per second squared.
Answer:
(A). the angular velocity of fan is 0.380 rev/s.
(B). The number of revolution is 0.059 rad.
(C). The tangential speed of the blade is 0.907 m/s.
(D). The tangential acceleration of the blade is 2.10 m/s²
Explanation:
Given that,
Initial angular velocity = 0.200 rev/s
Angular acceleration = 0.883 rev/s²
Diameter = 0.760 m
Time = 0.204 s
(A). We need to calculate the angular velocity of fan
Using equation of angular motion
[tex]\omega_{f}=\omega_{i}+\alpha t[/tex]
Put the value into the formula
[tex]\omega_{f}=0.200+0.883\times0.204[/tex]
[tex]\omega_{f}=0.380\ rev/s[/tex]
(B). We need to calculate the number of revolution
Using formula of angular displacement
[tex]\theta=\omega_{i}t+\dfrac{1}{2}\alpha t^2[/tex]
Put the value into the formula
[tex]\theta=0.200\times0.204+\dfrac{1}{2}\times0.883\times(0.204)^2[/tex]
[tex]\theta=0.059\ rad[/tex]
(C). We need to calculate the tangential speed of the blade
Using formula of speed
[tex]v=\dfrac{d}{2}\omega_{f}[/tex]
Put the value into the formula
[tex]v=\dfrac{0.760}{2}\times0.380\times2\pi[/tex]
[tex]v=0.907\ m/s[/tex]
(D). We need to calculate the tangential acceleration of the blade
Using formula of tangential acceleration
[tex]a_{t}=\alpha r[/tex]
Put the value into the formula
[tex]a_{t}=0.883\times0.38\times2\pi[/tex]
[tex]a_{t}=2.10\ m/s^2[/tex]
Hence, (A). the angular velocity of fan is 0.380 rev/s.
(B). The number of revolution is 0.059 rad.
(C). The tangential speed of the blade is 0.907 m/s.
(D). The tangential acceleration of the blade is 2.10 m/s²