Answer:
w = - 197.5 rad / s
The negative sign indicates that the rotations are clockwise
Explanation:
To solve this exercise, let's use the concept of conservation of the angular number.
We create a system formed by the two discs, in this case the forces last the shock are internal
initial instant .. just before shock
L₀ = I₀ w₀ + I₁ w₁
instnte final. Right after crash
L_f = (I₀ + I1) w
angular momentum is conserved
I₀ w₀ + I₁ w₁ = (I₀ + I₁) w
w = I₀ w₀ + I₁ w₁ / Io + I1
The moment of inertia of a disk with an axis passing through its thermometric center
I₀ = ½ m² r₀²
I₁ = ½ m₁ r₁²
we substitute
I₀ = ½ 2.0 0.70²
I₀ = 0.49 kg m
I₁ = ½ 2.0 0.5²
I₁ = 0.25
₁
let's reduce the magnitudes the SI system
w₀ = -50 rev / (2pi rad / 1rev) = -314.15 rad / s
w₁ = 70 rev (2pi rad / 1rev) = 439.82 rad / s
we will assume that the counterclockwise turns are positive
w = -0.49 314.15 + 0.25 439.82 / (0.49 + 0.25)
w = (- 4.696 + 1.0995) 102) / 0.74
w = -197.75 + 0.25
w = - 197.5 rad / s
The negative sign indicates that the rotations are clockwise
Help please is for today
Answer:
All of the above.
Explanation:
A person is said to be at rest when he or she is not performing any action. The heartbeat stays normal in this condition.
A person is said to perform a moderate activity when his heart beats faster than the normal rest condition. It requires extra effort within the limit. For example, walking and dancing are examples of moderate activity.
A person is said to perform a vigorous activity when his heart beats much than in moderate activity. It requires a lot of effort over the limit. Running is an example of vigorous activity.
In view of the above information, all the options given in the question are true. Hence, the correct answer will be:
All of the above.
a student starts his lawnmower by applying a constant tangential force of 150 N to the 0.3 kg disk-shaped flywheel. the radius of the flywheel is 18 cm. what is the flywheels angular acceleration? b. what is the angular speed of the wheel after it has turned through one revolution,( neglect friction and motor compression.) c. what is the tangent speed of a point on the rim of the flywheel?
Answer:
okay
Explanation:
please I don't know
does altitude has an effect on weight? HELP
Answer: lose weight at high altitudes.
Explanation:
Answer:
Just a week at high altitudes can cause sustained weight loss, suggesting that a mountain retreat could be a viable strategy for slimming down. Overweight, sedentary people who spent a week at an elevation of 8,700 feet lost weight while eating as much as they wanted and doing no exercise
What do meteorologists call the lines
that join places with the same
temperature?
A. isobars
B. isotherms
C. anisobars
D. anisotherms
On a perfect fall day, you are hovering at low altitude in a hot-air balloon, accelerated neither upward nor downward. The total weight of the balloon, including its load and the hot air in it, is 20,000 N. a. Show that the weight of the displaced air is 20,000 N. b. Show that the volume of the displaced air is 1700 m3 .
Explanation:
Since the balloon is not accelerating means that the net force on the balloon is zero. This implies that the weight of balloon must be equal to the buoyant force on balloon.
Hence, the buoyant force equals the weight of air displaced by the balloon, also 20,000 N.
Weight of the air displaced = density of air × volume
The density of air at 1 atm pressure and 20º C is 1.2 kg/m³
the volume V = 20,000/(1.2×9.8) = 1700 m³
Which of the following is an example of heat transfer by conduction?
A. Heat is transferred to the air above a candle flame.
B. Heat is transferred to the soil on a sunny day.
c. Heat is transferred to your hand from a warm cup.
D. Heat is transferred to the air from a warm lightbulb.
Answer:
option c
Heat is transferred to your hand from a warm cup
conduction is the process of transferring of heat from one material to another when they are in contact
hope it helps
Calculate the velocity of a wave that has a frequency of 60 Hz and wavelength of 2.0 m/s
Answer:We have , a relation in frequency f and wavelength λ of a wave having the velocity v as ,
v=fλ ,
given f=60Hz , λ=20m ,
therefore velocity of wave , v=60×20=1200m/s
Determiner l'interfrange i sur le plan d'observation π distant de L de D:
Determine the interfringe i on the observation plane π distant from L from D:
1) pour D=f
if D=f
2)pour D=2f
if D=2f
Answer:
can you explain in Hindi language
because i learn hindi
A mass of slug, when attached to a spring, stretches it feet and then comes to rest in the equilibrium position. Starting at , an external force equal to is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to times the instantaneous velocity.
Answer:
Equation of motion is x(t) = [tex]-te^{-4t}[/tex] + [tex]\frac{1}{4}[/tex] sin(4t)
Explanation:
P.S - The exact question is -
Given - A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t = 0, an external force equal to [tex]f(t) = 8 cos(4t)[/tex] is applied to the system.
To find - Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity.
Proof -
Given that,
Mass = 1 slug
We know that, 1 slug = 32 lb
Now,
Force, f = kx
⇒32 = k(2)
⇒k = 16
Now,
Given that, C = 8 ( 8 times the instantaneous velocity)
Now,
The differential equation of motion is equals to
mx'' + Cx' + kx = 8 cos(4t)
⇒x'' + 8x' + 16x = 8 cos(4t) ...........(1)
Let the General solution of equation (1) be
x(t) = x(c) + x(p)
Now,
The auxiliary equation is
m² + 8m + 16 = 0
m² + 4m + 4m + 16 = 0
m (m+4) + 4 (m+4) = 0
⇒(m+4)(m+4) = 0
⇒m = -4, -4
So,
The Complimentary equation becomes
x(c) = [tex]Ae^{-4t} + Bte^{-4t}[/tex] ...........(2)
Now,
Let the particular solution be
x(p) = C cos(4t) + D sin(4t)
x'(p) = -4C sin(4t) + 4D cos(4t)
x''(p) = -16C cos(4t) - 16D sin(4t)
It also satisfy equation (1)
Equation (1) becomes
-16C cos(4t) - 16D sin(4t) + 8 [ -4C sin(4t) + 4D cos(4t) ] + 16 [ C cos(4t) + D sin(4t) ] = 8 cos(4t)
⇒-16C cos(4t) - 16D sin(4t) - 32C sin(4t) + 32D cos(4t) ] + 16C cos(4t) + 16D sin(4t) ] = 8 cos(4t)
⇒-4C sin(4t) + 4B cos(4t) = cos(4t)
By comparing, we get
4B = 1 , A = 0
⇒ B = [tex]\frac{1}{4}[/tex] , A = 0
So, The particular solution becomes
x(p) = [tex]\frac{1}{4}[/tex] sin(4t)
Now,
The General solution becomes
x(t) = [tex]Ae^{-4t} + Bte^{-4t}[/tex] + [tex]\frac{1}{4}[/tex] sin(4t) .......(3)
Now,
Given that, At t = 0, initial velocity is zero and the system starts equilibrium
⇒x(0) = 0, x'(0) = 0
By putting t = 0 in equation (3) , we get
A = 0
Now,
Differentiate equation (3), we get
x'(t) = [tex]-4Ae^{-4t} + Be^{-4t} - 4Bte^{-4t}[/tex] + [tex]\frac{1}{4}[/tex] *4 cos(4t)
Put t = 0, we get
0 = -4A + B + 1
⇒B = -1
∴ we get
The general solution becomes
x(t) = [tex]-te^{-4t}[/tex] + [tex]\frac{1}{4}[/tex] sin(4t)
Equation of motion is x(t) = [tex]-te^{-4t}[/tex] + [tex]\frac{1}{4}[/tex] sin(4t)
Coherent light with wavelength of 580 nm passes through two very narrow slits, and the interference pattern is observed on a screen a distance of 3.00 m from the slits. The first-order bright fringe is at 4.81 mm from the center of the central bright fringe. For what wavelength of light will the first-order dark fringe be observed at this same point on the screen?
Answer:
the required wavelength is 1.15815 μm
Explanation:
Given the data in the question;
The position of bright fringes [tex]y_m[/tex] on screen in double slit experiment is expressed as follows;
[tex]y_m[/tex] = mλD / d
solving for d, we substitute 1 for m
y₁ = (1)λD / d
d = λD / y₁
given that λ = 580 nm = 5.8 × 10⁻⁷ m, D = 3.00 m and y₁= y₀ = 4.81 mm = 0.00481 m
so we substitute
d = λD / y₁
d = ( 5.8 × 10⁻⁷ m × 3.00 m ) / 0.00481 m
d = 0.00000174 m² / 0.00481 m
d = 3.6117 × 10⁻⁴ m
Now, position of dark fringe [tex]y_m[/tex] on screen in double slit experiment is expressed as;
[tex]y_m[/tex] = ( m + 1/2 )λD / d
we substitute 0 for m
y₀ = ( 0 + 1/2 )λD / d
y₀ = λD / 2d
2y₀d = λD
λ = 2y₀d / D
we substitute
λ = ( 2(0.00481 m) ( 3.6117 × 10⁻⁴ m) ) / 3.0 m
λ = 1.15815 × 10⁻⁶ m
λ = 1.15815 μm
Therefore, the required wavelength is 1.15815 μm
In many places on Earth, humans are responsible for the removal of grasses, shrubs, trees, and other plants with roots that hold soil in place. This activity is best described by which of the following? *
A) deforestation
B) urbanization
C) air pollution
D) rise in sea level
A ball with a weight of 70 N hangs from a string that is coiled around a 3 kg pulley with a radius of 0.4 m. Both the ball and the pulley are initially at rest. The rotational inertia of the pulley is 0.5mr2 and the ball is released from rest. Calculate the ball's velocity after it falls a distance of 2 meters.
Answer:
v = 6.195 m / s
Explanation:
For this exercise we can use the conservation of energy, for the system formed by the ball and the pulley
starting point. Higher before releasing the system
Em₀ = U = M g h
final point. When the ball has lowered h = 2
Em_f = K = ½ M v² + ½ I w²
the energy is preserved
Em₀ = Em_f
M g h = ½ M v² + ½ I w²
angular and linear velocity are related
v = w r
w = v / r
indicate that the moment of inertia is
I = ½ m r²
we substitute
M g h = ½ M v² + ½ (½ m r²) (v/r) ²
½ v² (M + [tex]\frac{1}{2}[/tex] m) = M g h
v² = [tex]2gh \ \frac{M}{M + \frac{m}{2} }[/tex]
let's calculate
v = [tex]\sqrt{ 2 \ 9.8 \ 2 \ \frac{70}{70 + 1.5} }[/tex]
v = 6.195 m / s
Consider a pulley of mass mp and radius R that has a moment of inertia 1/2mpR2. The pulley is free to rotate about a frictionless pivot at its center. A massless string is wound around the pulley and the other end of the rope is attached to a block of mass m that is initially held at rest on frictionless inclined plane that is inclined at an angle β with respect to the horizontal. The downward acceleration of gravity is g. The block is released from rest .
How long does it take the block to move a distance d down the inclined plane?
Write your answer using some or all of the following: R, m, g, d, mp,
Answer:
a = [tex]\frac{m}{m+ \frac{1}{2} m_p} \ g \ sin \beta[/tex] , t = [tex]\sqrt{ \frac{2d}{a} }[/tex]
Explanation:
To solve this exercise we must use Newton's second law
For the block
let's set a reference system with the x axis parallel to the plane
X axis
Wₓ - T = m a
Y axis
N- W_y = 0
N = W_y
for pulley
∑τ = I α
T R = (½ m_p R²) α
let's use trigonometry for the weight components
sin β = Wₓ / W
cos β = W_y / W
Wx = W sin β
angular and linear variables are related
a = α R
α = a / R
we substitute and group our equations
W sin β - T = m a
T R = ½ m_p R² (a / R)
W sin β - T = m a
T = ½ m_p a
we solve the system of equations
W sin β = (m + ½ m_p) a
a = [tex]\frac{m}{m+ \frac{1}{2} m_p} \ g \ sin \beta[/tex]
let's find the time to travel the distance (d) through the block
x = v₀ t + ½ a t²
d = 0 + ½ a t²
t = [tex]\sqrt{ \frac{2d}{a} }[/tex]
un
A block of 48kg 18
is resting
a slope of a 23° angle.
khat is the normal reachion Force?
Hydrocarbons are by-products of which of the following:
a. Fossil oils, mines and fossil fuels
b. Burning fires, water treatment plants and fossil oils
C. Combustion in fossil, lighting and exhaust fumes
d. Petrol, sea waves and combustion in vehicles
e. Burning fires and combustion in factories and vehicles
Answer:
A
Explanation:
Look at the attached photo:
Answer:
C) Mass of the ball
Explanation:
Independent variable is the variable the researcher changes.
Since Martin is testing the mass of the ball, he'll be using different balls and that is the only thing he changes.
The distance traveled by the ball is the dependent variable since it depends on the mass of the ball.
The height and length of the ramp are the constant variables since that's the only ones that remain the same throughout this experiment.
Medical devices implanted inside the body are often powered using transcutaneous energy transfer (TET), a type of wireless charging using a pair of closely spaced coils. And emf is generated around a coil inside the body by varying the current through a nearby coil outside the body, producing a changing magnetic flux. Calculate the average induced emf, of each 10-turn coil has a radius of 1.50 cm and the current in the external coil varies from its maximum value of 10.0 A to zero in 6.25 x10-6s.
Answer:
[tex]0.475\ \text{V}[/tex]
Explanation:
n = Number of turns = 10
r = Radius = 1.5 cm
I = Current = 10 A
t = Time = [tex]6.25\times 10^{-6}\ \text{s}[/tex]
[tex]\mu_0[/tex] = Vacuum permeability = [tex]4\pi\times 10^{-7}\ \text{H/m}[/tex]
Magnetic field is given by
[tex]B=\dfrac{\mu_0I}{2r}\\\Rightarrow B=\dfrac{4\pi 10^{-7}\times 10}{2\times 1.5\times 10^{-2}}\\\Rightarrow B=0.00042\ \text{T}[/tex]
EMF is given by
[tex]\varepsilon=\dfrac{nBA}{t}\\\Rightarrow \varepsilon=\dfrac{10\times 0.00042\times \pi (1.5\times 10^{-2})^2}{6.25\times 10^{-6}}\\\Rightarrow \varepsilon=0.475\ \text{V}[/tex]
The average induced emf is [tex]0.475\ \text{V}[/tex].
What is being despited in this picture
Answer:
i am guessing for reflection but not so sure
does altitude has an effect on weight, yes or no
Answer: yes
Explanation:
Weight is the gravitational force experienced on a body. If you move up to higher altitudes, the distance between you and earth increases. ... Yes, weight drops as you go up in altitude (because of diminishing gravity), though your mass remains the same. However, the effect is not huge.
Three 5 Ohm resistors are connected in series to a 10 Volt power supply. What is the current through each resistor?
Answer74.3
:
Explanation:
In which direction does the magnetic field in the center of the coil point?
Answer:
Right
Explanation:
Coil move right yes
The diagram shows two bowling balls, A and B, each having a
mass of 7 kilograms, placed 2 meters apart.
А
B
7.00 kg
(7.00 kg
-2.00 m
What is the magnitude of the gravitational force exerted by ball
A on ball B?
(A) 8.17x10-9 N
(B) 1.63x10-9N
(C) 8.17x10-10 N
(D) 1.17 x 10-10 N
Answer:
b) 1.63x10-9N
Explanation:
i dont think this is right answer
Answer:
C or 8.17x10^-10 N
Explanation:
I was looking for the explanation but the answer is correct.
2. What does SCA stand for? (1 Point) Student Conservation Association h Securities Class Action Sudden Cardiac Arrest Solar Cell Array:',)
Answer:
sudden cardiac arrest
Explanation:
All EM waves (light waves) travel at the same speed through the vacuum of space. If the different types of waves are distinguished by their frequency, what basic characteristic of the waves determines their difference
Answer:
Their different wavelengths.
Explanation:
trust me
All EM waves (light waves) travel at the same speed through the vacuum of space. If the different types of waves are distinguished by their frequency, the basic characteristic of the waves that determine their difference is the wavelength of the electromagnetic waves.
What is Wavelength?It can be understood in terms of the distance between any two similar successive points across any wave for example wavelength can be calculated by measuring the distance between any two successive crests.
It is the total length of the wave for which it completes one cycle.
The wavelength is inversely proportional to the frequency of the wave as from the following relation.
C = νλ
where c is the speed of light
ν is the frequency of the wave
λ is the wavelength of the wave
As we know electromagnetic waves (light waves) travel at the same speed through the vacuum of space which is the speed of light which is 3×10⁸ meter/second
All EM waves (light waves) travel at the same speed through the vacuum of space. If the different types of waves are distinguished by their frequency, the basic characteristic of the waves that determine their difference is the wavelength of the electromagnetic waves.
Learn more about wavelength from here
brainly.com/question/7143261
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Assignment: Calculating Speed Investigation
Data Analysis:
Note: Please submit your data table with this assignment.
1. Write your original hypothesis here.
2. Calculate the average time for vehicle 1 from the information in your data table. Show all work.
3. Calculate the average time for vehicle 2 from the information in your data table. Show all work.
4. Calculate the average speed for vehicle 1 from the information in your data table. Show all work, including the formula used.
5. Calculate the average speed for vehicle 2 from the information in your data table. Show all work, including the formula used.
Conclusion:
Think about this information and then write a conclusion based on the data of this experiment. Don’t forget to connect the conclusion to the original hypothesis.
Were you able to support your hypothesis or not? Be sure to base your answer on the data you collected. Consider whether your conclusion is the only explanation for the data you collected or if there could be alternate explanations. Don’t forget to mention any scientific laws or theories you have studied that would apply to this experiment.
Follow-up Questions:
1. If your experiment did not seem to match the expected results, what did you learn from the experience?
2. Instantaneous speed is the rate of motion of an object at a particular moment in time. What change(s) to the experimental procedure would be necessary if you wanted to gather data on instantaneous speed?
and as for the data can you please make your own
Answer:
Assignment: Calculating Speed Investigation
Data Analysis:
Note: Please submit your data table with this assignment.
1. Write your original hypothesis here.
2. Calculate the average time for vehicle 1 from the information in your data table. Show all work.
3. Calculate the average time for vehicle 2 from the information in your data table. Show all work.
4. Calculate the average speed for vehicle 1 from the information in your data table. Show all work, including the formula used.
5. Calculate the average speed for vehicle 2 from the information in your data table. Show all work, including the formula used.
Conclusion:
Think about this information and then write a conclusion based on the data of this experiment. Don’t forget to connect the conclusion to the original hypothesis.
Were you able to support your hypothesis or not? Be sure to base your answer on the data you collected. Consider whether your conclusion is the only explanation for the data you collected or if there could be alternate explanations. Don’t forget to mention any scientific laws or theories you have studied that would apply to this experiment.
Follow-up Questions:
1. If your experiment did not seem to match the expected results, what did you learn from the experience?
2. Instantaneous speed is the rate of motion of an object at a particular moment in time. What change(s) to the experimental procedure would be necessary if you wanted to gather data on instantaneous speed?
and as for the data can you please make your own
Explanation:
Assignment: Calculating Speed Investigation
Data Analysis:
Note: Please submit your data table with this assignment.
1. Write your original hypothesis here.
2. Calculate the average time for vehicle 1 from the information in your data table. Show all work.
3. Calculate the average time for vehicle 2 from the information in your data table. Show all work.
4. Calculate the average speed for vehicle 1 from the information in your data table. Show all work, including the formula used.
5. Calculate the average speed for vehicle 2 from the information in your data table. Show all work, including the formula used.
Conclusion:
Think about this information and then write a conclusion based on the data of this experiment. Don’t forget to connect the conclusion to the original hypothesis.
Were you able to support your hypothesis or not? Be sure to base your answer on the data you collected. Consider whether your conclusion is the only explanation for the data you collected or if there could be alternate explanations. Don’t forget to mention any scientific laws or theories you have studied that would apply to this experiment.
Follow-up Questions:
1. If your experiment did not seem to match the expected results, what did you learn from the experience?
2. Instantaneous speed is the rate of motion of an object at a particular moment in time. What change(s) to the experimental procedure would be necessary if you wanted to gather data on instantaneous speed?
and as for the data can you please make your ownWhich sentence uses a superlative adjective correctly?
Anthony is running more quickly than anyone else on the field.
Shalon is a very talented pianist.
That is the best chocolate cake I have ever tasted.
Ani is the better gymnast of the two.
Which statement best compares and contrasts the purpose of "PROSERPINE" to that of "How Old Man Winter Was Driven Back"?
The Greek myth explains the creation of the earth, while the Iroquois myth also explains why there is evil in the world.
The Greek myth explains the creation of the earth, while the Iroquois myth also explains the creation of the moon.
The Greek myth explains the changing of the seasons as well as the existence of the underworld, while the Iroquois myth also explains the changing of the seasons.
The Greek myth explains the creation of the moon, while the Iroquois myth explains the creation of the sun.
Read the passages:
from "How Old Man Winter Was Driven Back"
"I, too, am powerful, and I am young! I do not fear you. When I touch the earth, it grows soft and warm. Every living thing stirs in its sleep,—birds and bees, flowers and trees, animals and men. When I speak, the sleeping sun awakes. See! Already he begins to send down his arrows. Hasten! that they may not find you, on the trail to the North Sky."
from "How the World Was Made"
Even some of the trees went to sleep. Only the cedar, the pine, the spruce, the holly, and the laurel were awake all seven nights. Therefore they are always green. They are also sacred trees. But to the other trees it was said, “Because you did not stay awake, therefore you shall lose your hair every winter.”
Which best uses textual evidence to compare and contrast these two myths?
Both myths show the change in seasons as a violent battle.
In "How Old Man Winter Was Driven Back," the change in
Calculate the induced electric field (in V/m) in a 52-turn coil with a diameter of 17 cm that is placed in a spatially uniform magnetic field of magnitude 0.45 T so that the face of the coil and the magnetic field are perpendicular. This magnetic field is reduced to zero in 0.10 seconds. Assume that the magnetic field is cylindrically symmetric with respect to the central axis of the coil. (Enter the magnitude.)
Answer:
the induced electric field is 9.95 V/m
Explanation:
Given the data in the question;
Number of turns N = 52
Diameter of coil D = 17 cm = 0.17 m
Radius r = D/2 = 0.17/2 = 0.085 m
Now,
cross-section area A of the coil = πr²
A = π × ( 0.085 m )²
A = 0.0227 m²
Also given that;
Initial magnetic field B₁ = 0.45 T
Final magnetic field B₂ = 0
∴ change in magnetic field ΔB = B₁ - B₂ = 0.45 T - 0 = 0.45 T
Time taken dT = 0.10 seconds
Now, we know that;
Induced emf ∈ = N[tex](\frac{d\eta }{dt} )[/tex]
where η = BAcosθ
We know that, magnetic field is cylindrically symmetric, coil is also perpendicular to magnetic field.
Hence, the angle between B & A is 0°
∴ θ = 0°
Induced emf ε = N[tex](\frac{d }{dt} )BAcos\theta[/tex]
we substitute
ε = N[tex](\frac{d }{dt} )[/tex] (BAcos0°)
A is constant and cos0° = 1
so
ε = NA[tex](\frac{dB }{dt} )[/tex]
We now substitute in our values;
ε = 52 × 0.0227 m² × [tex](\frac{0.45T }{0.10s} )[/tex]
ε = 5.3118 V
we know that, from the relation between electric and emf
ε = ∫∈.dl or ε = ∈∫dl { for coil; ∫dl = πD }
so we have;
ε = ∈πD
solve for ∈
∈ = ε/πD
we substitute
∈ = 5.3118 V / ( π × 0.17 m )
∈ = 9.95 V/m
Therefore, the induced electric field is 9.95 V/m
It is almost as if each outer planet is a solar system in its own right.
True or False
Please help The position of masses 4kg, 6kg, 7kg, 10kg, 2kg, and 12kg are (-1,1), (4,2), (-3,-2), (5,-4), (-2,4) and (3,-5) respectively. Determine the position of the center of mass of this system?
Answer:
(1.9756, -2.1951)
Explanation:
The center of mass equation is: [tex]x_{cm}[/tex] = [tex]\frac{m_{1}x_{1} + m_{2}x_{2} + m_{3}x_{3} + m_{4}x_{4} + m_{5}x_{5} + m_{6}x_{6}}{m_{1} + m_{2} + m_{3} + m_{4} + m_{5} + m_{6}}[/tex], where m represents the masses and x represents the position.
In order to find the coordinates of the center of mass, we need to use this equation for both the x-values and the y-values.
x-values:
[tex]x_{cm}[/tex] = [tex]\frac{m_{1}x_{1} + m_{2}x_{2} + m_{3}x_{3} + m_{4}x_{4} + m_{5}x_{5} + m_{6}x_{6}}{m_{1} + m_{2} + m_{3} + m_{4} + m_{5} + m_{6}}[/tex] = [tex]\frac{4(-1)+6(4)+7(-3)+10(5)+2(-2)+12(3)}{4+6+7+10+2+12}[/tex] = [tex]\frac{(-4)+(24)+(-21)+(50)+(-4)+(36)}{41}[/tex] = [tex]\frac{81}{41}[/tex] = 1.9756
y-values:
[tex]y_{cm}[/tex] = [tex]\frac{m_{1}y_{1} + m_{2}y_{2} + m_{3}y_{3} + m_{4}y_{4} + m_{5}y_{5} + m_{6}y_{6}}{m_{1} + m_{2} + m_{3} + m_{4} + m_{5} + m_{6}}[/tex] = [tex]\frac{4(1)+6(2)+7(-2)+10(-4)+2(4)+12(-5)}{4+6+7+10+2+12}[/tex] = [tex]\frac{(4)+(12)+(-14)+(-40)+(8)+(-60)}{41}[/tex] = [tex]\frac{-90}{41}[/tex] = -2.1951
center of mass:
(1.9756, -2.1951)
What is the mass of a mallard duck whose speed is 9.1 m/s and whose momentum has a magnitude of 12 kg⋅m/s?
Answer:
m = 1.31 kg
Explanation:
Given that,
The speed of duck, v = 9.1 m/s
The magnitude of momentum, p = 12 kg-m/s
We need to find the mass of the duck. We know that the momentum of an object is given by :
p = mv
Where
m is the mass of the duck
[tex]m=\dfrac{p}{v}\\\\m=\dfrac{12\ kg-m/s}{9.1\ m/s}\\\\m=1.31 kg[/tex]
So, the mass of the duck is equal to 1.31 kg.
32. Assume the helium-neon lasers commonly used in student physics laboratories have power outputs of 0.500 mW. (a) If such a laser beam is projected onto a circular spot 1.00 mm in diameter, what is its intensity
Answer:
636.6 W/m²
Explanation:
From the given information:
The area of the circular spot can be calculated as:
A = πr²
A = π(0.5 × 10⁻³ m)²
A = 7.85 × 10⁻⁷ m²
The intensity can be determined by using the formula:
[tex]I = \dfrac{P}{A}[/tex]
[tex]I = \Big ( \dfrac{0.500 \ mW}{\pi (0.5 \times 10^{-3} \ m )^2} \Big) \Big( \dfrac{10^{-3} \ W}{1\ mW} \Big)[/tex]
[tex]I = \dfrac{0.500 \times 10^{-3} }{\pi(0.25 \times 10^{-6} )}[/tex]
I = 636.6 W/m²