Consider the schematic of the molecule shown, with two hydrogen atoms, H, bonded to an oxygen atom, O. The angle between the two bonds is 106°. If the bond length r = 0.103 nm long, locate the center of mass of the molecule. The mass mH of the hydrogen atom is 1.008 u, and the mass mO of the oxygen atom is 15.9999 u. (Use a coordinate system centered in the oxygen atom, with the x-axis to the right and the y-axis upward. Give the coordinates of the center of mass in nm.)
Answers
The definition of the center of mass allows to find the result for the position of the mass center of more than the H₂O molecule is;
[tex]x_{cm} = 0 \ and \ y_{cm} = 6.9 10^{-3 } nm[/tex]
the concept of center of mass of a system is the point where external forces are applied, it is given by the expression
[tex]\frac{x}{y} =\frac{1}{M_{total}} \sum m_i r_i[/tex]
Where M is the total mass of the systemr_i and m_i sums the position and masses of the element i of the system
In the attachment we have a diagram of the system where the axis and coordinates of the molecules are shown, in this case it is indicated that the origin is in the oxygen atom, so its distance is zero.
[tex]r_{cm} = \frac{1}{2 m + M} \ (2 m r )[/tex] )
They indicate the mass of the hydrogen atom m = 1.008 amu, the bond length r = 0.103 nm and there is an angle 106º between the two hydrogens, therefore the angle from the vertical is:
θ = 106/2 = 53º
Let's find the position of the center of mass for each axis.
x-axis
[tex]x_{cm} = \frac{1}{2m+ M} \ ( m x_1 - m x_2)[/tex]
y-axis
[tex]y_{cm} = \frac{1}{2m + M} \ ( m y_1 + m_2)[/tex]
Let's use trigonometry to find the components of the bond length.
cos θ = [tex]\frac{y}{L}[/tex]
sin θ = [tex]\frac{x}{L}[/tex]
y = L cos θ
x = L sin θ
We substitute.
[tex]x_{cm} = \frac{1}{2m+M} \ (mL (sin 53 + sin (-53)) \\y_{cm} = \frac{1}{2m + M} \ ( mL cos 53 + mL sin 53)[/tex]
we use.
sin θ = - sin -θ
cos θ = cos -θ
Let's calculate.
[tex]x_{cm} = 0 \\y_{cm} = \frac{1}{2 \ 1.008 + 15.9999} \ ( 2 \ 1.008 \ 0.103 cos 53)[/tex]
We see that the center of mass is on the x axis and at a distance from the y-axis of 6.9 10-3 nm
In conclusion using the definition of the center of mass we can find the result for the position of the center of mass of the H₂O molecule is;
[tex]x_{cm}=0[/tex] and [tex]y_{cm}[/tex]cm = 6.9 10⁻³ nm
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Related Questions
Block 1, of mass m1, moves across a frictionless surface with speed ui. It collides elastically with block 2, of mass m2, which is at rest (vi=0). (Figure 1)After the collision, block 1 moves with speed uf, while block 2 moves with speed vf. Assume that m1>m2, so that after the collision, the two objects move off in the direction of the first object before the collision. What is the final speed vf of block 2?
Answers
The conservation of the momentum allows to find the velocity of the second body after the elastic collision is:
[tex]v_f = \frac{2u_o}{1- \frac{m_2}{m_1} }[/tex]
the momentum is defined by the product of the mass and the velocity of the body.
p = mv
The bold letters indicate vectors, p is the moment, m the mass and v the velocity of the body.
If the system is isolated, the forces during the collision are internal and the it is conserved. Let's find the momentum is two instants.
Initial instant. Before crash.
p₀ = m₁ u₀ + 0
Final moment. After crash.
[tex]p_f = m_1 u_f + m_2 v_f[/tex]
The momentum is preserved.
p₀ = [tex]p_f[/tex]
[tex]m_1 u_o = m_1 u_f + m_2 v_f[/tex]
Since the collision is elastic, the kinetic energy is conserved.
K₀ = [tex]K_f[/tex]
½ m₁ u₀² = ½ m₁ [tex]u_f^2[/tex] + ½ m₂ [tex]v_f^2[/tex]
Let's write our system of equations.
[tex]m_1 u_o = m_1 u_f + m_2 v_f \\m_1 u_o^2 = m_1 u_f^2 + m_2 v_f^2[/tex]
Let's solve
[tex]u_f = u_o - \frac{m_2}{m_2} \ v_f \\u_f^2 = u_o^2 - \frac{m_2}{m_1} \ v_f^2[/tex]
[tex]( u_o - \frac{m_2}{m_1} v_f)^2 = u_o - \frac{m_2}{m_1} \ v_f^2 \\u_o^2 - 2 \frac{m_2}{m_1} \ u_o v_f + (\frac{m_2}{m_1} )^2 v_f^2 = u_o^2 - \frac{m_2 }{m_1} \ v_f^2[/tex]
[tex]2 \frac{m_2}{m_1} \ u_o = \frac{m_2}{m_1} v_f \ ( 1 - \frac{m_2}{m_1}) \\v_f = \frac{2u_o}{1-\frac{m_2}{m_1} }[/tex]
In conclusion, using the conservation of momentum, we can find the velocity of the second body after the elastic collision is:
[tex]v_f = \frac{2u_o}{1-\frac{m_2}{m_1} }[/tex]
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8.
Linda thinks that her home is dirty and she will become
contaminated if she does not clean her kitchen. This daily cleaning takes hours to complete. Her hands
are rubbed raw, she has not been able to maintain friendships, and she is struggling to keep up with
work.
Answers
Answer:
she just have to maintain her daily work routin to kepp up with work .she can use glovs than her hand will be protected .and for mantain friendship she have to franky with other and allways talk to you'r friends no matter how bg you are talking with friends can be verry helpfull
on average, astronauts grow ________ percent in space.
Answers
Answer:
3
Explanation:
Astronauts in space can grow up to 3 percent taller during the time spent living in microgravity, NASA scientists say. That means that a 6-foot-tall (1.8 meters) person could gain as many as 2 inches (5 centimeters) while in orbit.
A wave moving with a speed of 0.5 m/s has a frequency of 50 Hz. What is the
wavelength of the wave?
A. 0.10 m
B. 0.01 m
C. 100 m
D, 25 m
Answers
Answer:
0.01 mExplanation:
The wavelength of the wave given it's velocity and frequency can be found by using the formula
[tex] \lambda = \frac{c}{f} \\[/tex]
where
c is the speed of the wave
f is the frequency
From the question we have
[tex] \lambda = \frac{0.5}{50} = 0.01 \\ [/tex]
We have the final answer as
0.01 mHope this helps you
RIGHT ANSWER I WILL GIVE BRAINLYSIT
Which statement best describes the role of carbon dioxide in photosynthesis?
O A. Plants break down molecules of carbon dioxide to make oxygen
molecules.
B. Plants make carbon dioxide molecules as they break down
chlorophyll.
C. Plants release carbon dioxide molecules when sunlight shines on
their leaves.
D. Plants use molecules of carbon dioxide to make sugar molecules.
Answers
Answer:
The answer is...
D ( Plants use molecules of carbon dioxide to make sugar molecules.)
Explanation:
During photosynthesis, plants take in carbon dioxide (CO2) and water (H2O) from the air and soil. This transforms the water into oxygen and the carbon dioxide into glucose. The plant then releases the oxygen back into the air, and stores energy within the glucose molecules. During the process of photosynthesis, cells use carbon dioxide and energy from the Sun to make sugar molecules and oxygen. These sugar molecules are the basis for more complex molecules made by the photosynthetic cell, such as glucose.
Have an awesome day friend! <3
Please help!
What is momentum?
Answers
Answer:
a property of a moving body that the body has by virtue of its mass and motion and that is equal to the product of the body's mass and velocity
Explanation:
Formula:
Momentum: Mass x Velocity
Hope it helps!
Find the gravitational potential energy of a body of mass 25kg,kept at a height of 4m If g=10m/s'.
Answers
Answer:
1000 JExplanation:
The gravitational potential energy of a body can be found by using the formula
GPE = mgh
where
m is the mass
h is the height
g is the acceleration due to gravity which is 10 m/s²
From the question we have
GPE = 25 × 10 × 4 = 1000
We have the final answer as
1000 JHope this helps you
How much potential energy did the the milkshake have after it fell off of the counter, just before it hit the ground (at the bottom)? Make sure to write the correct units with
your answer!
Answers
Answer:
The formula for potential energy depends on the force acting on the two objects. For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m / s2 at the surface of the earth) and h is the height in meters.
waht is pascal law?
Answers
Answer:
P=\frac{F}{A}
P = pressure
{F} = force
{A} = area
Explanation:
The spark plugs are threaded into the top of each cylinder and provide a place for the spark to jump within the ________.
Answers
Answer:
"the spark plug gap"
The plug provides a gap between the input voltage and the ground supplied by the car chassis.
d) A 2-kg book is held 1 m above the floor is for 10s. The work done on the book is zero and its potential energy is 20 J. Is it true or false?
Answers
Ep=2x9.8x1 = 19.6J
what is the relationship of physics and technology
Answers
Answer:
Physics explains and describes natural phenomena. It tells us how different parts of nature work and react to different situations. Technology helps us solve problems and complete tasks by using the world around us.
It is observed that technology gives rise to new physics and at other times physics generates new technology. Physics Generating New Technology: Newton's law of motion helped in the development of rockets.
Explanation:
Hope this helps you! :)
A car goes from 60 m/s to 75 m/s in 10 seconds.calculate the car’s acceleration?
Answers
Explanation:
Uhhhh here is an example
a=vt. =27 m/s10 s. =2.7 m/s2.
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Acceleration of the car is ~
[tex] \boxed{1.5 \: \: m/s}[/tex]
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
We know that,
Acceleration = rate of change in velocity ~
that is ~
[tex]a = \dfrac{v - u}{t} [/tex]where,
v = final velocityu = initial velocity t = time taken ~now, let's solve ~
[tex]a = \dfrac{75 - 60}{10} [/tex][tex]a = \dfrac{15}{10} [/tex][tex]a = 1.5 \: \: m/s[/tex]PLz help--- What's happening here?
This object is not moving
This object is not changing speeds.
This object is changing speeds; it's getting faster.
This object is changing speeds; it's getting slower.
Answers
Answer:
getting faster
Explanation:
the curve gets more steeper, and steeper line shows more distance for less time, meaning faster.
A block with initial velocity of 3 m/s slides 9 m across a rough horizontal surface before coming to rest. What is the coefficient of kinetic
friction?
Answers
The coefficient of kinetic friction between the block and the horizontal surface is 0.051.
The given parameters;
initial velocity, u = 3 m/sdistance traveled by the block, s = 9 mThe acceleration of the block is calculated as follows;
[tex]v^2 = u^2 + 2(-a)s\\\\v^2 = u^2 - 2as\\\\a = \frac{u^2 - v^2}{2s} \\\\a = \frac{3^2 - 0^2}{2\times 9} \\\\a =0.5 \ m/s^2[/tex]
The coefficient of kinetic friction between the block and the horizontal surface is calculated as follows;
[tex]\mu_k mg = ma\\\\\mu_k = \frac{a}{g} \\\\\mu_k = \frac{0.5}{9.8} \\\\\mu_k = 0.051[/tex]
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Fuses of ________________________
a. same kind are used for different purposes
b. different kind are used for different purposes
c. both of the above are correct
d. none of these
Answers
Answer:
C
Explanation:
fuses of same kind can be used for different things, and of different kinds could be used for different things as well.
A. Read these sentences carefully. Choose the correct form of adjectives.
1. Solomon is the
king of all.
a wise
b. wiser
c. wisest
2. Yogurt is
than candies.
a delicious b. more delicious c. most delicious
3. Mayon Volcano is the
volcano for me.
a most majestic b. more majestic
c. majestic
4 My father is an
man
a industrious b. more industrious c. most industrious
5. I was the
when my friend graduated with honors.
a happy b. happier
c. happiest
Answers
Answer:
1. wisest
2. more delicious
3. majestic (not sure about this one)
4. industrious
5. happiest
this planet has a very toxic atmosphere that traps heat, making it the hottest planet in the solar system.
Answers
Answer:
Venus
Explanation:
basic 2nd grade smarts "no offense"
HELPPPPPPPPPPPPPPPPPPP
Answers
Answer:
directly proportional
Explanation:
3. What happens if an object has a negative acceleration?
Answers
Answer:
They will go backwards?
Explanation:
If positive they go forward but is negative they go backwards.
Image credit: The Hubble Heritage Team (AURASTSCI/NASA)
To which category does galaxy #2 belong? Why does it belong in this category?
WRITER
Answers
Can i ask u a question
how to do the next ques for moreBrainliest me please
Which is the BEST example of physics in the body?
A. a single beat of the heart
B. how the circulatory system works
с. balance when the body is standing still
D. the movement of an arm throwing a ball
Answers
The best example of physics in the body is the movement of an arm throwing a ball. The correct option is D.
What is physics?Physics is the branch of science that studies the structure of matter and how the universe's fundamental constituents interact.
It investigates objects ranging from the very small to the entire universe using quantum mechanics and general relativity.
Physics is the natural science that investigates matter, its fundamental constituents, its motion and behavior in space and time, as well as the related entities of energy and force.
Physics is one of the most fundamental scientific disciplines, with the primary goal of understanding how the universe functions.
The movement of an arm throwing a ball is the best example of physics in the body.
Thus, the correct option is D.
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Compare and contrast instantaneous and average speed.
Answers
Answer:
instantaneous velocity is a velocity covered at an instant while average velocity is the change in distance/ the change in time taken
if 20 boys can sweep the school compound in 8 minutes, how many boys can sweep it in 10minutes
Answers
Answer:
So this is just a ratio/proportion problem
so lets say its in boys:minutes
so in the first scenario
20:8
and we want to find
x:10
So proportion really
20/8=x/10
cross multiply
25
25 boys can sweep it in 10 minutes
At the exact same instant that a
ball is thrown horizontally (in a
projectile) another identical ball
is dropped straight down from
the same height. Which ball hits
the ground first?
Answers
Answer:
The ball being thrown straight down.
Explanation:
The downforce and gravitational pull of the ball going down will give it
a higher velocity compared to the one trown horizontially it will take some time for it to catch downforce speed and reach the same velocity.
I need to know how to draw the diagram of the last two questions
Answers
Answer
In the parallel circuit, you have to position the switch on only one of the loops.
Mercury’s natural state is where the atoms are close to each other but are still free to pass by each other. In which state(s) could mercury naturally exist?
Answers
Answer:
Mercury's natural state is where the atoms are close to each other but are still free to pass by each other. In which state(s) could mercury naturally exist?
Liquid is the answer
Explanation:
A bowling ball and a ping-pong ball are each tied to a string and hung from the ceiling. The distance from the ceiling to the CM of each object is the same. Which object would have a longer period of motion if they were set swinging
Answers
what noncontact forces act on an object that are balanced
Answers
Answer:
I can give you a list of noncontact forces off of my head, if that is what you need.
Explanation:
First, gravity. It acts everywhere and pulls down every object that is in the air towards the ground, unless they have an equal and opposite force that counters it.
Second, wind. I don't think this will count because wind is a physical thing, but it can be used in the same way as we did with gravity. If the force counteracting it is larger, equal, and opposite of the force it is countering, then it will move forward, through the wind.
You are walking back toward the back of a bus that is moving forward with a constant velocity. Describe your motion relative to the bus and relative to a point on the ground.
Answers
Answer: Relative to the bus, you are stationary. Relative to a point on the ground, you are walking forward with velocity equal to the velocity of the bus.
As a person walks toward the back of a bus, they are walking towards a stationary object according to their own perspective. However, from an outside perspective, the bus is moving forward with a constant velocity and so relative to that point in motion, you are actually walking backwards with respect to it. This difference in motion means you would not be able have the same experience as the person on the bus when getting off because when you get off you would stop while they continue going forward. The last sentence could be considered a footnote because it only applies if this was an actual situation rather than just an analogy question in a physics test.
Relative to the bus, you move at walking speed. The motion relative to the ground is in the direction same as the bus and equal to the difference between the speed of the bus and walking speed.
What is relative motion?When an object has a certain velocity, then this velocity is w.r.t. some frame that is called the reference frame. When we measure the velocity of an object, the ground or the earth is taken as the reference frame.
The motion of an object observed by the observer depends on the frame of the observer and this type of motion is known as relative motion.
For example, if you are traveling in a train and the train is moving at a speed of 80 km/hr, then your speed according to another passenger sitting on the same train is equal to zero.
Similarly, if you are walking toward the back of a bus, then your motion relative to the bus is walking speed. Relative to the ground, it is the difference between the speed of the bus and walking speed.
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