Answer:
A. We have that radius r = 4.00m intensity I = 8.00 W/m^
total power = power/ Area ( 4πr2)= 8.00 w/m^2( 4π ( 4.00 m)2=1607.68 W
b) I = total power/ 4πr2= 8.00 W/m2 ( 4.00 m/ 9.5 m)2= 1.418 W/m2
c) E = total power x time= 1607 . 68 W x 1s= 1607.68 J
If you were to come back to our solar system in 6 billion years, what might you expect to find?
A) a red giant star
B) a rapidly spinning pulsar
C) a white dwarf
D) a black hole
E) Everything will be essentially the same as it is now
Answer:
A)a red giant star
In an adiabatic process:
a. the energy absorbed as heat equals the work done by the systemon its environment
b. the energy absorbed as heat equals the work done by theenvironment on the system
c. the work done by the environment on the system equals the changein internal energy
Answer:
c. the work done by the environment on the system equals the changein internal energy.
Explanation:
Adiabatic process:
When the boundary of a system is perfectly insulated, it means that the energy can not flow from the system and into the system ,these system is known as adiabatic system.
When the energy transfer in the system is zero ,then these type of process is known as adiabatic process.
From the first law of thermodynamics
Q= ΔU + W
Q=Heat transfer
ΔU=Change in internal energy
W=Work transfer
In adiabatic process , Q= 0
Therefore
0=ΔU +W
W=- ΔU
Negative sign indicates that ,the work done by the environment.
Therefore the correct option will be (c).
All household circuits are wired in parallel. A 1140-W toaster, a 270-W blender, and a 80-W lamp are plugged into the same outlet. (The three devices are in parallel when plugged into the same outlet.) Assume that this is the standard household 120-V circuit with a 15-A fuse.
a. What current is drawn by each device?
b. To see if this combination will blow the 15-A fuse, find the total current used when all three appliances are on.
Answer:
total current = 12.417 A
so it will not fuse as current is less than 15 A
Explanation:
given data
toaster = 1140-W
blender = 270-W
lamp = 80-W
voltage = 120 V
solution
we know that current is express as
current = power ÷ voltage ......................1
here voltage is same in all three device
so
current by toaster is
I = [tex]\frac{1140}{120}[/tex]
I = 9.5 A
and
current by blender
I = [tex]\frac{270}{120}[/tex]
I = 2.25 A
and
current by lamp is
I = [tex]\frac{80}{120}[/tex]
I = 0.667 A
so here device in parallel so
total current is = 9.5 A + 2.25 A + 0.667 A
total current = 12.417 A
so it will not fuse as current is less than 15 A
according to the big bang theory, what did protons and neutrons form from?
Answer:
Explanation:
In the first moments after the Big Bang, the universe was extremely hot and dense. As the universe cooled, conditions became just right to give rise to the building blocks of matter – the quarks and electrons of which we are all made. A few millionths of a second later, quarks aggregated to produce protons and neutrons. Within minutes, these protons and neutrons combined into nuclei. As the universe continued to expand and cool, things began to happen more slowly. It took 380,000 years for electrons to be trapped in orbits around nuclei, forming the first atoms. These were mainly helium and hydrogen, which are still by far the most abundant elements in the universe. Present observations suggest that the first stars formed from clouds of gas around 150–200 million years after the Big Bang. Heavier atoms such as carbon, oxygen and iron, have since been continuously produced in the hearts of stars and catapulted throughout the universe in spectacular stellar explosions called supernovae.
But stars and galaxies do not tell the whole story. Astronomical and physical calculations suggest that the visible universe is only a tiny amount (4%) of what the universe is actually made of. A very large fraction of the universe, in fact 26%, is made of an unknown type of matter called "dark matter". Unlike stars and galaxies, dark matter does not emit any light or electromagnetic radiation of any kind, so that we can detect it only through its gravitational effects.
An even more mysterious form of energy called “dark energy” accounts for about 70% of the mass-energy content of the universe. Even less is known about it than dark matter. This idea stems from the observation that all galaxies seems to be receding from each other at an accelerating pace, implying that some invisible extra energy is at work.
Protons and neutrons formed from quarks in the early universe, a process driven by extremely high temperatures and energies.
In the early cosmos, quarks generated protons and neutrons, which form atomic nuclei, according to the Big Bang hypothesis. Quarks and gluons, which bond quarks, existed freely in a quark-gluon plasma state in the early cosmos due to extreme heat and energy.
Hadronization formed protons and neutrons from quarks as the cosmos cooled and expanded. Eventually, protons and neutrons formed atomic nuclei as the cosmos evolved. This key stage in the early universe's existence formed the basic particles that make up matter today.
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According to the conservation of mechanical energy, the kinetic energy before plus the kinetic energy after equals the
potential energy before plus the potential energy after.
True
False
Answer:
False
Explanation:
The conservation of mechanical energy says that the kinetic energy before plus the potential energy before equals the kinetic energy after plus the potential energy after.
why do we go to hospital
Answer:
bcz we want to have fun there lolol
Answer:
for emergency, treatment, medicines,etc.....
The place you get your hair cut has two nearly parallel mirrors 6.5 m apart. As you sit in the chair, your head is
Complete question is;
The place you get your hair cut has two nearly parallel mirrors 6.50 m apart. As you sit in the chair, your head is 3.00 m from the nearer mirror. Looking toward this mirror, you first see your face and then, farther away, the back of your head. (The mirrors need to be slightly nonparallel for you to be able to see the back of your head, but you can treat them as parallel in this problem.) How far away does the back of your head appear to be?
Answer:
13 m
Explanation:
We are given;
Distance between two nearly parallel mirrors; d = 6.5 m
Distance between the face and the nearer mirror; x = 3 m
Thus, the distance between the back-head and the mirror = 6.5 - 3 = 3.5m
Now, From the given values above and using the law of reflection, we can find the distance of the first reflection of the back of the head of the person in the rear mirror.
Thus;
Distance of the first reflection of the back of the head in the rear mirror from the object head is;
y' = 2y
y' = 2 × 3.5
y' = 7
The total distance of this image from the front mirror would be calculated as;
z = y' + x
z = 7 + 3
z = 10
Finally, the second reflection of this image will be 10 meters inside in the front mirror.
Thus, the total distance of the image of the back of the head in the front mirror from the person will be:
T.D = x + z
T.D = 3 + 10
T.D = 13m
Four friends push on the same block in different directions. Allie pushes on the block to the north with a force of 18 N. Bill pushes on the block to the east with a force of 14 N. Chris pushes on the block to south with a force of 23 N. Debra pushes on the block to the west with a force of 20 N. Assuming it does not move vertically, in which directions will the block move? north and west south and east south and west north and east
Answer:
South and West
Explanation:
Those people are pushing the hardest. It will move south faster than it moves west.
A 1.2-m length of wire centered on the origin carries a 20-A current directed in the positive y direction. Determine the magnetic field at the point x= 5.0m on x-axis.
a. 1.6 nt in the negative z direction
b. 1.6 nt in the positive z direction
c. 2.4 T in the positive z direction
d. 2.4 nt in the negative z direction
e. None of the above
Answer:
None of the above
Explanation:
The formula of the magnetic field of a point next to a wire with current is:
B = 2×10^(-7) × ( I /d)
I is the intensity of the current.
d is the distance between the wire and the point.
● B = 2*10^(-7) × (20/5) = 8 ×10^(-7) T
You plan to take your hair blower to Europe, where the electrical outlets put out 240 V instead of the 120 V seen in the United States. The blower puts out 1700 W at 120 V.Required:a. What could you do to operate your blower via the 240V line in Europe? which one is it?b. What current will your blower draw from a European outlet?c. What resistance will your blower appear to have when operated at 240 ?
Answer:
a) Connect a series resistance of 8,47 ohms
b)14,16 [A]
c) r = 10,96 ohms
Explanation:
My blower requires 120 (v) then, I have to connect a series resistor to make the nominal 240 (v) of the European voltage outlet drop to 120 (V) but at the same time keep the level of current to operate my blower
In America
P = V*I
1700 (w) = 120*I
I = 1700/120 [A]
I = 14,16 [A] current needed for the blower
In Europe
120 (v) (the drop of voltage I need) when a current of 14,16 passes through to series resistor is
V = I*R 120 = 14,16* R R = 8,47 ohms
c) P = I*r²
1700 (w) = 14,16 (A) * r²
r² = 120,06
r = 10,96 ohms
At what speed, as a fraction of c, will a moving rod have a length 65% that of an identical rod at rest
Answer:
v/c = 0.76
Explanation:
Formula for Length contraction is given by;
L = L_o(√(1 - (v²/c²))
Where;
L is the length of the object at a moving speed v
L_o is the length of the object at rest
v is the speed of the object
c is speed of light
Now, we are given; L = 65%L_o = 0.65L_o, since L_o is the length at rest.
Thus;
0.65L_o = L_o[√(1 - (v²/c²))]
Dividing both sides by L_o gives;
0.65 = √(1 - (v²/c²))
Squaring both sides, we have;
0.65² = (1 - (v²/c²))
v²/c² = 1 - 0.65²
v²/c² = 0.5775
Taking square root of both sides gives;
v/c = 0.76
If a sample emits 2000 counts per second when the detector is 1 meter from the sample, how many counts per second would be observed when the detector is 3 meters from the sample?
Using the sample in above question how many counts per second would be observed when the detector is 10 meters away from the sample?
Answer:
At 3 meter distance, the per-second count is 222.22 and at a 10 meter distance, the per-second count is 20.
Explanation:
The number of particles (N) counts are inversely proportional to the distance between the source and the detector.
By using the below formula we can find the number of counts.
[tex]N2 = \frac{(D1)^2}{(D2)^2} \times N1 \\N1 = 2000 \\D 1 = 1 \ meter \\D2 = 3 \\[/tex]
The number of count per second, when the distance is 3 meters.
[tex]= \frac{1}{3^2} \times 2000 \\= 222.22[/tex]
Number of count per second when the distance is 10 meters.
[tex]= \frac{1}{10^2} \times 2000 \\= 20[/tex]
A wheel of radius 25cm has eight spokes. It is mounted on a fixed axle and is rotating at a constant angular speed w. You shoot a 20cm long arrow parallel to the axle through the wheel at a speed of 6m/s. The arrow and the spokes are supposed to be thin. Calculate the maximum value of w ( in rad/second and in rev/second) so that the arrow just goes through without hitting any of the spokes. Does it matter where between the axle and the rim of the wheel you aim? If so, what is the best location?
Explanation:
We will assume that the rim of the wheel is also very thin, like the spokes. The distance s between the spokes along the rim is
[tex]s = \frac{1}{8}C = \frac{1}{8}(2\pi)(0.25\:\text{m}) = 0.196\:\text{m}[/tex]
The 20-cm arrow, traveling at 6 m/s, will travel its length in
[tex]t = \dfrac{0.2\:\text{m}}{6\:\text{m/s}} = \dfrac{1}{30}\:\text{s}[/tex]
The fastest speed that the wheel can spin without clipping the arrow is
[tex]v = \dfrac{s}{t} = \dfrac{0.196\:\text{m}}{\left(\dfrac{1}{30\:\text{s}}\right)} = 5.9\:\text{m/s}[/tex]
The angular velocity [tex]\omega[/tex] of the wheel is given by
[tex]\omega = \dfrac{v}{r} = \dfrac{5.9\:\text{m/s}}{0.25\:\text{m}} = 23.6\:\text{rad/s}[/tex]
In terms of rev/s, we can convert the answer above as follows:
[tex]23.6\:\dfrac{\text{rad}}{\text{s}}×\dfrac{1\:\text{rev}}{2\pi\:\text{rad}} = 3.8\:\text{rev/s}[/tex]
As you probably noticed, I did the calculations based on the assumption that I'm aiming for the edge of the wheel because this is the part of the wheel where a point travels a longer linear distance compared to ones closer to the axle, thus giving the arrow a better chance to pass through the wheel without getting clipped by the spokes. If you aim closer to the axle, then the wheel needs to spin slower to allow the arrow to get through without hitting the spokes.
Answer:omega=23.56... rad/s
Explanation:for the arrow to pass without hitting the 8 spokes
taking the spokes thickness to be a point along the spokes linear motion path
lets calculate the time athe arrow pass point length of the wire 0.25m and it's speed(6m/s)
t=0.25m÷6m/s=0.0333...s
so every spoke around the wheel must move replacing each other's position so distribution of eight spokes=2π÷8=0.78... rad so using as angular displacement and t=0.033s then omega=∅/t=0.78/0.033=23.56rad/s
*yes
*space between spokes
g A smart phone charger delivers charge to the phone, in the form of electrons, at a rate of -0.75 C/s . Part A How many electrons are delivered to the
Answer:
Approximately 5 x 10^18 electrons are delivered to the smart phone charger.
Explanation:
The electric current in a circuit is the flow of charges through a circuit with time.
The charges through the circuit are due to the electrons that flow through the circuit.
An individual electrons has a charge of -1.60 x 10^-19 C on it.
If the current through the circuit is -0.75 C/s, then the number of electrons that are delivered is gotten by dividing the charge per second by the charge on an electron.
==> -0.75/(-1.60 x 10^-19) = 4.67 x 10^18 electrons ≅ 5 x 10^18 electrons are delivered to the smart phone charger.
Physical properties of a mineral are a result of the arrangement of the atoms in the mineral. Use this fact to explain the following:_________
A. One mineral has a density of 2.7 g/ml while another has a density of 5.1 g/ml
B. The mineral mica cleaves into thin flat sheets while olivine does not show cleavage
Explanations:
a) The physical properties of a mineral is as a result of the arrangement of the atoms in the minerals. The reason behind one mineral having a density of 2.1 g/ml which is lower than that of another mineral with density of 5.1 g/ml is the packing density of the minerals. Minerals with high density have their atoms more closely packed together, leaving less space between the atoms. This characteristics means that they have more atomic mass per unit volume for a given molecular space, when compared to another mineral with its atoms less closely packed.
b) The property of cleavage is due to the crystalline structure of a mineral species. Cleavage is used to describe the ease with which minerals cleaves. Cleavage is due to a weak bonding strength between the molecules of the mineral, or a due to a greater lattice spacing across the the cleavage plane than in other planes within the crystal. The greater the lattice spacing, the weaker the strength of the bond across a plane.
From these, we can clearly see that the property of cleavage is due to the physical properties of the crystalline structure of the mineral species.
Design a voltage divider to provide the following approximate voltages with respect to ground using a 30 V source: 8.18 V, 14.7 V, and 24.6 V. The current drain on the source must be limited to no more than 1 mA. The number of resistors, their values, and their wattage ratings must be specified. A schematic showing the circuit arrangement and resistor placement must be provided
Answer:
R₁ = 14.7 10³ Ω , R₂ = 8.18 10³ Ω , R₃ = 1.72 10³ Ω , R₄ = 5.4 10³ Ω 1/8 W resistor
Explanation:
For this exercise we must use a series circuit since the sum of the voltage on each resin is equal to the source voltage (V = 30 V)
Therefore we build a circuit with 4 resistors in series, in such a way that
V = i R
let the voltage
1st resistance
V = i R
R₁ = V / i
R₁ = 14.7 / 1 10⁻³
R₁ = 14.7 10³ Ω
power is
P = V i
P = 14.7 1 10⁻³
P = 14.7 10⁻³ W = 0.0147 W
a resistance of ⅛ W is indicated
2nd resistance
R₂ = 8.18 / 1 10⁻³
R₂ = 8.18 10³ Ω
Power
P = 8.18 1 10⁻³
P = 0.00818W
a 1/8 W resistor
3rd resistance
this resistance is calculated in such a way that
V₁ + V₂ + V₃ = 24.6
V₃ = 24.6 - V₁ -V₂
V₃ = 24.6 - 14.7 - 8.18
V₃ = 1.72 V
R₃ = 1.72 / 1 10⁻³
R₃ = 1.72 10³ Ω
power
P = Vi
P = 1.72 10⁻³
P = 0.00172 W
a resistance of ⅛ W
To obtain the voltage of 24.6 we use this three resistors together
4th resistance
The value of this resistance is calculated so that the sum of all the voltages reaches the source voltage
30 = V₁ + V₂ + V₃ + V₄
V₄ = 30 - V₁ -V₂ -V₃
V₄ = 30 -14.7 - 8.18 - 1.72
V₄ = 5.4 V
R₄ = 5.4 / 1 10⁻³
R₄ = 5.4 10³ Ω
Power
P = V i
P = 5.4 10⁻³
P = 0.0054 W
⅛ W resistance
The values of these resistance are commercially
Let's check the consumption of the circuit
R_total = R₁ + R₂ + R₃ + R₄
R_total = (14.7 + 8.18 + 1.72 + 5.4) 10³
R_total = 30 10³
the current circulating in the circuit is
i = V / R_total
i = 30/30 10³
i = 1 10⁻³ A
therefore it is within the order requirement.
for connections see attached diagram
A wire along the z axis carries a current of 4.9 A in the z direction Find the magnitude and direction of the force exerted on a 3.3 cm long length of this wire by a uniform magnetic field pointing in the x direction having a magnitude 0.43T
Answer:
0.069 N, in the X directionExplanation:
According to Flemming's left hand rule, it sates that if the first three fingers of the left hand are held mutually at right angles to one another, the fore finger will point in the direction of magnetic field, the middle finger will point in direction of current, while the thumb will point to the direction of force.
Mathematically the law is stated as
F= BIL
given data
Magnetic field B= 0.43T
Current I= 4.9 A
length of conductor L= 3.3cm to meter , 3.3/100= 0.033 m
Applying the formula the force is calculated as
F= 0.43*4.9* 0.033= 0.069 N
According to Flemming's rule the direction of all parameters are mutually perpendicular to one another, then the Force is in the X direction
M
A boy of mass 60 kg and a girl of mass 40 kg are
together and at rest on a frozen pond and push
each other apart. The girl moves in a negative
direction with a speed of 3 m/s. What must be the
total final momentum of the boy AND girl
combined?
A. -120 kgm/s
B. 0 kgm/s
C. -100 kgm/s
D. 120 kgm/s
Answer:
option D thinking so
Explanation:
okay na your whish
When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 55m wide tub is 0.80 Hz.
Required:
What is the speed of the water wave?
Answer:
The speed of the water wave is [tex]v = 88 \ m/s[/tex]
Explanation:
From the question we are told that
The width of the tube is [tex]L = 55 \ m[/tex]
The fundamental frequency is [tex]f = 0.80 \ Hz[/tex]
Generally the fundamental frequency is mathematically represented as
[tex]f = \frac{v}{2 * L }[/tex]
=> [tex]v = f * 2 * L[/tex]
substituting values
[tex]v = 0.8 * 2 * 55[/tex]
[tex]v = 88 \ m/s[/tex]
The speed of the water wave will be 88 m/s.
Given information:
When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center.
The frequency of the standing wave is [tex]f=0.8[/tex] Hz.
The width of the tub is [tex]w=55[/tex] m.
Let v be the speed of the standing wave.
The speed of the wave can be calculated as,
[tex]v=2wf\\v=2\times 55\times 0.8\\v=88\rm\; m/s[/tex]
Therefore, the speed of the water wave will be 88 m/s.
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In a physics lab, Asha is given a 11.5 kg uniform rectangular plate with edge lengths 62.9 cm by 46.9 cm . Her lab instructor requires her to rotate the plate about an axis perpendicular to its plane and passing through one of its corners, and then prepare a report on the project. For her report, Asha needs the plate's moment of inertia ???? with respect to given rotation axis. Calculate ???? .
Answer:
6.9kgm²
Explanation:
For an axis through the center of the rectangle, I = m[(w²+L²)/12
Using the parallel axis theorem, the added value of I = mR² = m[(w²/4 + L²/4]
Adding the 2 expressions,
I = (m/3)*(w²+L²)
I =6.95 kg∙m²
A red card is illuminated by red light. Part A What color will the card appear? What color will the card appear? a. Red b. Black c. White d. Green
The color that is reflected when a red card is illuminated by red light is white.
The color an object is perceived to have, depends on the frequency of light it reflects.
If white light incidents on a red filter, red is transmitted while blue and green are absorbed.
Consequently, when a red card is illuminated by red light, the red card will reflect back almost all the incident light on it, causing it to appear brighter which creates an illusion of white color to the eyes.
Thus, we can conclude the color that is reflected when a red card is illuminated by red light is white.
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3. Is it possible for a scientific theory to become a law? Why or why not?
A theory does not change into a scientific law with the accumulation of new or better evidence. A theory will always remain a theory; a law will always remain a law. Both theories and laws could potentially be falsified by countervailing evidence. Theories and laws are also distinct from hypotheses.
Which of the units of the following physical quantities are derived
Answer:
where is the attachment
Explanation:
When using a crowbar to remove a nail, the person should hold it at which of the following spots to increase the IMA of the lever? nearest the end prying out the nail furthest from the end prying out the nail right in the middle the location where the person holds it will not affect the IMA
Answer: the furthest from the end prying out the nail
Answer:
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Explanation:
Using this information...
Determine the velocity of the pebble as it passes over the top of the tree.
[tex]19.2\:\text{m/s}[/tex]
Explanation:
At the top of the tree, the velocity of the pebble is purely horizontal so we can calculate it as
[tex]v_{y} = v_{0y} = v_0\cos 40° = (25\:\text{m/s})(0.766)[/tex]
[tex]\:\:\:\:\:= 19.2\:\text{m/s}[/tex]
The height of the tree is approximately 12.5 meters when velocity of the pebble as it passes over the top of the tree.
Let's calculate the height of the tree step by step:
Given:
Initial velocity (v0) = 25 m/s
Launch angle (θ) = 40° above the horizontal
Time after launch (t) = 2 seconds
Acceleration due to gravity (g) = -9.8 m/s² (negative because it acts downward)
Step 1: Calculate the vertical component of the initial velocity (Vy):
Vy = v0 * sin(θ)
Vy = 25 m/s * sin(40°)
Vy ≈ 25 m/s * 0.6428 ≈ 16.07 m/s (rounded off to two decimal places)
Step 2: Calculate the vertical displacement (change in height) of the pebble after 2 seconds:
d = vot + (1/2)at²
d = (16.07 m/s) * (2 s) + (1/2) * (-9.8 m/s²) * (2 s)²
d ≈ 32.14 m - 19.6 m
d ≈ 12.54 m (rounded off to two decimal places)
Step 3: The height of the tree is equal to the vertical displacement of the pebble:
Height of the tree ≈ 12.54 m ≈ 12.5 m (rounded off to one decimal place)
The height of the tree is approximately 12.5 meters.
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Calculate the work performed by an ideal Carnot engine as a cold brick warms from 150 K to the temperature of the environment, which is 300 K. (Use 300 K as the temperature of the hot reservoir of the engine). The heat capacity of the brick is C
Answer
Work done is 57.9KJ
Explanation
First solve the problem according to work done due to variation in temperature
So W= intergral Cu( 1-Tu/T). at Tu and T
So Given that
C = Heat capacity of the Brick
TEPc= Cold Temperature
TEPh = Hot Temperature
W = C ( TEPh-TEP) - TEPhCln ( TEPh/TEPc)
So
W= (1)-(300-150)-300 (1) ln 2
W= -57.9KJ
A high school physics student claims her muscle car can achieve a constant acceleration of 10 ft/s/s. Her friend develops an accelerometer to confirm the feat. The accelerometer consists of a 1 ft long rod (mass=4 kg) with one end attached to the ceiling of the car, but free to rotate. During acceleration, the rod rotates. What will be the angle of rotation of the rod during this acceleration? Assume the road is flat and straight.
Answer: Ф = 17.2657 ≈ 17°
Explanation:
we simply apply ET =0 about the ending of the rod
so In.g.L/2sinФ - In.a.L/2cosФ = 0
g.sinФ - a.cosФ = 0
g.sinФ = a.cosФ
∴ tanФ = a/g
Ф = tan⁻¹ a / g
Ф = tan⁻¹ ( 10 / 32.17405)
Ф = tan⁻¹ 0.31080948777
Ф = 17.2657 ≈ 17°
Therefore the angle of rotation of the rod during this acceleration is 17.2657 ≈ 17°
Three children are riding on the edge of a merry-go-round that is a solid disk with a mass of 102 kg and a radius of 1.53 m. The merry-go-round is initially spinning at 9.71 revolutions/minute. The children have masses of 31.7 kg, 29.0 kg and 31.9 kg. If the child who has a mass of 29.0 kg moves to the center of the merry-go-round, what is the new angular velocity in revolutions/minute
Three children of masses and their position on the merry go round
M1 = 22kg
M2 = 28kg
M3 = 33kg
They are all initially riding at the edge of the merry go round
Then, R1 = R2 = R3 = R = 1.7m
Mass of Merry go round is
M =105kg
Radius of Merry go round.
R = 1.7m
Angular velocity of Merry go round
ωi = 22 rpm
If M2 = 28 is moves to center of the merry go round then R2 = 0, what is the new angular velocity ωf
Using conservation of angular momentum
Initial angular momentum when all the children are at the edge of the merry go round is equal to the final angular momentum when the second child moves to the center of the merry go round Then,
L(initial) = L(final)
Ii•ωi = If•ωf
So we need to find the initial and final moment of inertia
NOTE: merry go round is treated as a solid disk then I= ½MR²
I(initial)=½MR²+M1•R²+M2•R²+M3•R²
I(initial) = ½MR² + R²(M1 + M2 + M3)
I(initial) = ½ × 105 × 1.7² + 1.7²(22 + 28 + 33)
I(initial) = 151.725 + 1.7²(83)
I(initial) = 391.595 kgm²
Final moment of inertial when R2 =0
I(final)=½MR²+M1•R²+M2•R2²+M3•R²
Since R2 = 0
I(final) = ½MR²+ M1•R² + M3•R²
I(final) = ½MR² + (M1 + M3)• R²
I(final)=½ × 105 × 1.7² + ( 22 +33)•1.7²
I(final) = 151.725 + 158.95
I(final) = 310.675 kgm²
Now, applying the conservation of angular momentum
L(initial) = L(final)
Ii•ωi = If•ωf
391.595 × 22 = 310.675 × ωf
Then,
ωf = 391.595 × 22 / 310.675
ωf = 27.73 rpm
Answer: So, the final angular momentum is 27.73 revolution per minute
A wire is carrying current vertically downward. What is the direction of the force due to Earth's magnetic field on the wire
Answer:
The direction of the force is towards the East.
Explanation:
Using the right hand rule, the force on the current carrying conductor is east.
In the right hand rule, if the hand is held with the fingers pointed parallel to the palm representing the magnetic field, and the thumb held at right angle to the rest of the fingers representing the direction of the current, then the palm will push in the direction of the force.
In this case, the thumb is pointing downwards, with the fingers pointing north away from the body in the direction of the earth's magnetic field, the palm will push east.
Mention the importance of writing the physical quantities as vectors.
Answer:
Knowledge of vectors is important because many quantities used in physics are vectors. If you try to add together vector quantities without taking into account their direction you'll get results that are incorrect.
Explanation:
An example of the importance of vector addition could be the following:
Two cars are involved in a collision. At the time of the collision car A was travelling at 40 mph, car B was travelling at 60 mph. Until I tell you in which directions the cars were travelling you don't know how serious the collision was.
The cars could have been travelling in the same direction, in which case car B crashed into the back of car A, and the relative velocity between them was 20 mph. Or the cars could have been travelling in opposite directions, in which case it was a head on collision with a relative velocity between the cars of 100 mph!