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
Suppose measure the mass of an orange. Then you peel the orange and separate out the slices. If you measure the orange peel and all the slices, will that mass equal the mass of the whole orange?
Answers
Answer:
Yes
Explanation:
It's still the same orange with the same amount of stuff.
The acceleration of an object is inversely proportional to its mass, so if you decrease its mass while keeping the net force the same, the acceleration will increase.
true or false
Answers
Answer:
True
Explanation:
Since acceleration is inversely proportional to mass, decreasing mass will make the object lighter, and thus easier to speed up. So acceleration increases as mass decreases and vice versa
Answer: TRUE Explanation:Newton's second law of motion can be formally stated as follows: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
what Characteristic of an object is related to both kinetic energy and its potential energy a objects velocity b height c speed d mass
Answers
Answer:
I think it's a. Object velocity
Explanation:
.
Answer:
Object mass
Explanation:
I had answered and thats what it is
What would the kinetic energy of a 20kg person running at a velocity of 2.5m/s?
Answers
Answer:
62.5 JExplanation:
The kinetic energy of an object can be found by using the formula
[tex]k = \frac{1}{2} m {v}^{2} \\ [/tex]
m is the mass in kg
v is the velocity in m/s
From the question
m = 20 kg
v = 2.5 m/s
From the question we have
[tex]k = \frac{1}{2} \times 20 \times {2.5}^{2} \\ = 10 \times 6.25 \\ = 62.5\: \: \: \: \: \: \: \: \: \: [/tex]
We have the final answer as
62.5 JHope this helps you
what is the average power supplied by a 60.0 kg person running up a flight of stairs a vertical distance of 4.0 in 4.2s
Answers
Hi there!
We know that:
[tex]P = \frac{W}{t}\\\\[/tex]
Where:
W = Work done (J)
t = time (s)
We can calculate the work using the equation:
[tex]W = \Delta U = mg\Delta h[/tex]
Plug in the given values:
[tex]W = 60(9.8)(4) = 2352J[/tex]
Now, divide by time:
[tex]P = \frac{W}{t} = \frac{2352}{4.2} = \boxed{560W \text{ (Watts)}}[/tex]
a tube of constant circular cross-section, sealed at on end, contains an ideal gas trapped by a cylinder of mercury of length 0.035m. The whole arrangement is in the Earth's atmosphere. The density of mercury is 1.36*10^4, more details provided in the images.
Answers
Answer:
P V = N R T ideal gas equation
V = .19 * A volume of enclosed gas
.19 P = N R T / A using volume of enclosed gas
P = Po + Phg pressure on gas = atmospheric (Po) + Phg pressure due to column of mercury
.19 (Po + Phg) = N R T / A which is what was asked
Note Phg = density of Hg * height of Hg * acceleration due to gravity
A tube of constant circular cross-section, sealed at on end, contains an ideal gas trapped by a cylinder of mercury of length 0.035m. There will atmospheric pressure and pressure due to mercury column on trapped gas column having length 0.19m which is given by,
(p₀+pm)×0.190 = nRT÷A.
What is Pressure?Pressure is defined as force per unit area. i.e. P = F/A it gives the force on unit area. its SI unit is Pascal (Pa) which is equal to N/m². is a scalar quantity. its dimensions are [M¹ L⁻¹ T⁻²].
Looking at the figure from top to bottom, we can see the top end of the tube is opened. There is 0.035m of mercury column below which we have a air 0.190m of gas column.
We can feel the physics behind this figure what is happening here, top of the tube is open so there is atmospheric pressure acting on the mercury column and mercury column is above the gas column, it means that both atmospheric pressure and mercury pressure will act on gas column.
i.e. (p₀+pm) = pressure on the air column
this (p₀+pm) is downward pressures, hence gas inside the tube gets compressed due to this pressure because bottom end is closed. it means that back pressure will be created inside the gas in upward direction and both pressures becomes equal at equilibrium.
i.e. (p₀+pm) = back pressure inside the gas column......1)
according to ideal gas equation, PV=nRT
pressure inside the air column is P = nRT÷V
where V is volume of gas that is A×0.190.
P = nRT÷(A×0.190).....( back pressure inside the gas column).
equation 1 becomes
(p₀+pm) = nRT÷(A×0.190).
Hence we get
(p₀+pm) ×0.190= nRT÷(A).
Hence proved.
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UV light has ______ wavelengths than visible light waves, and its peak energy is at a wavelength of ______.
Answers
Explanation:
Shorter wavelength since UV light has more energy than visible light
365 nm - What is the peak energy wavelength of UV light? It allows both infrared daylight and ultraviolet night-time communications by being transparent between 320 nm and 400 nm and also the longer infrared and just-barely-visible red wavelengths. Its maximum UV transmission is at 365 nm
Jefferson refers to
_____ rights in the Declaration of Independence.
Explain what these rights are:
Answers
Answer: natural
Explanation:
Answer:
natural i just copy tha answer in there i just explain it(づ￣ 3￣)づ
Explanation:
The meaning of the term “Pursuit of Happiness.” In the Declaration of Independence, Thomas Jefferson announced that every human being has “certain unalienable rights,” among which are those to “life, liberty, and the pursuit of happiness.” What did he mean by “the pursuit of happiness”?
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
A source produces 25 waves every second. The wavelength of the waves is
50 cm. How fast will the waves be travelling?
Answers
Answer:
1 s
Explanation:
The speed of the sound, distance travelled and the time taken relationship is given as follows.
Speedofsound,v=Distancetravelled×Timetaken ----eqn 1
With the given values of wavelength = 50 cm = 0.5 m and frequency =1000 Hz, the speed of the wave is calculated as follows.
Speedofsound,v=Frequency(ν)×Wavelength(λ) -- eqn 2
That is, v=ν×λ=1000Hz×0.5m=500m/s
Substituting the value of the speed of sound in eqn 1 gives the time taken for the sound wave to travel a distance of 500 m.
That is, Timetaken=
Distancetravelled
Speedofsound
=
500m
500m/s
=1second.
Hence, the time taken for the sound wave to travel is 1 second.
The speed with which the waves will be travelling is 12.5m/s.
Given the data in the question;
Frequency; [tex]f = 25\ waves\ per\ second = 25s^{-1}[/tex]Wavelength; [tex]\lambda = 50cm = 0.5m[/tex]Speed of the wave; [tex]v =\ ?[/tex]
To determine how fast the waves will be travelling, we use the expression for the relations between wavelength, frequency and speed of wave.
[tex]\lambda = \frac{v}{f}[/tex]
Where [tex]\lambda[/tex] is wavelength, f is frequency and v is speed of wave
We substitute our values into the equation
[tex]0.5m = \frac{v}{25s^{-1}} \\\\v = 0.5m * 25s^{-1}\\\\v = 12.5ms^{-1}[/tex]
Therefore, the speed with which the waves will be travelling is 12.5m/s.
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How does Earth's magnetic field compare
with that of a bar magnet?
A Their magnetic fields increase with size.
B The attractive force of their magnetic
fields is greatest at the poles.
C The attractive force of their magnetic
fields is greatest at the center.
D Electric current causes them to lose
magnetism
Answers
Answer:
C
Explanation:
The attractive force of their magnetic fields is greatest at the poles. Option B is correct.
Earth's magnetic field is similar to that of a bar magnet in that both have north and south poles. The magnetic field lines of both Earth and a bar magnet originate from the north pole and loop around to the south pole. The magnetic field lines are most concentrated and the attractive force is strongest near the poles of both Earth and a bar magnet.
At the poles, the magnetic field lines are densely packed and closely spaced, leading to a stronger magnetic force. This is why compass needles, which align with Earth's magnetic field, point towards the magnetic north pole.
The statement about electric current causing them to lose magnetism (option D) is not accurate. Electric current can actually create magnetic fields, as seen in electromagnets. Earth's magnetic field is generated by the movement of molten iron in its outer core, not by electric currents in the conventional sense.
In summary, option B is the correct answer as it accurately reflects the similarity in the distribution of magnetic field lines and the strength of the attractive force near the poles for both Earth and a bar magnet.
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as shown in the figure, a 10-kg block on a perfectly smooth horizontal table is connected by a horizontal string to a 63-kg block that is hanging over the edge of the table. what is the magnitude of the acceleration of the 10-kg block when the other block is gently released?
Answers
Newton's second law allows to find the acceleration of the two-body system, where a mass is hanging is:
The acceleration of the system is: a = 8.46 m / s²
Newton's second law states that the net force on a body is equal to the product of the mass and the acceleration.
∑ F = m a
Where the bold letters indicate vectors, F is the force, m the mass and the acceleration of the body.
A free body diagram is that diagram of the system where the forces are shown without the details of the bodies. In the attachment we have a free-body diagram of the system.
Let's write Newton's second law for each axis.
x- axis
T = m₁ a
y-axis
body in the horizontal part
N-W₁ = 0
N = W₁
Body hanging.
W₂ - T = m₂ a
Wwhere the positive direction is down, let's write our system of equations.
T = m₁ a
W₂-T = m₂ a
Let's Resolve.
m₂ g = (m₁ + m₂) a
a = [tex]\frac{m_2}{m_1+m_2} \ g[/tex]
Let's calculate.
a =[tex]\frac{63}{10+63} \ 9.8[/tex]
a = 8.46 m / s²
In conclusion using Newton's second law we can find the acceleration of the two-body system, where a mass is hanging is:
The acceleration of the system is: a = 8.46 m / s²
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Explain in terms of pressure why a boat made of modelling clay floats?
Answers
Answer:
cuz model clay float
Explanation:
yeah
please help me guys please
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Solution is in attachment ~
I hope that you got what you were looking for, and if there's different data then go through the same procedure, using same formula with different values and you will get your answer ~
[tex]\mathrm{✌TeeNForeveR✌}[/tex]
Answer:1.9 × 10³⁰
Explanation:
why does the energy of characteristic x rays tend to increase for heavier elements?
Answers
The energy of characteristic x rays tend to increase for heavier elements
because the charge of the nucleus increases.
X ray is a form of an electromagnetic spectrum and the energy is directly
proportional to the charge of the nucleus. This implies that an increase in
the nucleus charge will lead to a corresponding increase in x ray energy
and vice versa.
X rays energy is also usually more in heavier elements than when
compared to lighter elements
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A cyclist rides 4.7 km east for 17 minutes. He then heads west for 11 minutes, riding 2.9 km. Finally, he rides east for 13 km, which takes 51 minutes.
What is the final displacement of the cyclist from their starting point?
What is the cyclist’s average velocity?
Answers
Answer: Look at Explanation
Explanation:
4.7 east
2.9 west
4.7 - 2.9 = 1.8 to the east
then 13km to the west
-1.8 + 13 = 11.2 to the west left side
Asap
A cyclist needs to spin 100 meters with a velocity of 5 m/s. How long will the cyclist take?
Answers
Answer:
[tex]v = \frac{d}{t} \rightarrow t= \frac{v}{d} \\ = 100m \div 5m. {s}^{ - 1} = \frac{100}{5} \\ \color{green} \boxed{ t = 20s}[/tex]
16g 2g/cm3 what is the Volume
Answers
Answer:
V = 1.25E-7 cubic meter
4. According to Newton's First Law of Motion, an object with a net force acting on it will
Answers
Answer:
a object with net force on it will stay in motion unless acted on by an equal opposite force.
I will give Brainliest answer and 5 stars
Jay decides to walk home from school today. He lives 3 miles from school and can walk home in 45 minutes. At what rate is Jay traveling?
A. 1 mile/10 minutes
B. 1 mile/15 minutes
C. 1 mile/20 minutes
D. 1 mile/30 minutes
Answers
Answer:
James is traveling at 4 miles per hour.
Explanation:
3 miles per 45 minutes
x miles per 60 minutes(1 hour)
___________________
3*60=45*x
180=45x |:45
x=4
Can anyone tell the answer
Answers
When making a left turn, drive into the intersection, make the turn smoothly and without strain on the engine, braking to about ... to .........mph and stay on the brake until approximately half way into the intersection.
Answers
Answer:
whats the question
Explanation:
I'LL MARK YOU BRAINLIST ......By referring to the graph shown below, the acceleration from t = 0 s to t = 25 s is:
positive
negative
zero
increasing
Answers
Answer:
When an object is speeding up, the acceleration is in the same direction as the velocity. Thus, this object has a positive acceleration. In Example B, the object is moving in the negative direction (i.e., has a negative velocity) and is slowing down.
Explanation:
Answer:
It’s zero.
Explanation:
It’s a straight line so its at a rest.
How does air and debris travel within a tornado?
Answers
Answer:
anywhere the tornado goes debri goes except for the more heavier pieces they just go in random places but the lighter pieces stay with the tornado until the tornado is gone or disinegrated
Explanation:
around and around
The ______________ is all the surroundings of a living organism.
genetics
environment
temperature
heredity
Answers
You make a bar graph with the following data. What do you plot on the x-axis?
Answers
A student wants to show the transfer of heat energy without matter. Which investigation design would best help the student
Answers
Answer:
C
Explanation:
Answer:
C) an investigation of conduction through collisions between particles in space
Do we grow taller when we hang on a branch for 1 min?
Answers
Answer:
Temporarily yes, if you are speaking of a skeletally mature person, taking pressure off of joints will allow them to absorb more fluid and thus be a larger diameter. If that expansion is in a vertical direction then you would in fact be taller until the fluid was returned to outside of the joint.
Question 2 (1 point)
Potential energy depends on...
Speed and velocity
Position or shape
Length and color
Density and volume
Answers
Answer:
potential energy depends on position or shape
the pressure inside a latex balloon is nearly the same as the pressure outside. if you let a helium balloon go, and if, as it rises, it stays at a constant temperature, the volume of the balloon will
Answers
Answer: If you let a helium balloon go, and if, as it rises, it stays at a constant temperature, the volume of the balloon will. The magnitude of the buoyant force is equal to the weight of the amount of fluid that has the same total volume as the object.
If you let a helium balloon go, it rises, it stays at a constant temperature, the volume of the balloon will increases.
What is volume?A measurement of three-dimensional space is volume. Several imperial or US customary units, as well as SI-derived units (such the cubic meter and liter), are frequently used to quantify it quantitatively (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship.
The density for helium remains lower than that of air, therefore when the balloon is inflated with that as well, it rises. The atmosphere's pressure continues to drop as it rises, which causes the internal pressure to rise. The balloon's volume of the balloon will increase.
Therefore, the volume of the balloon will increase.
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