Answer:
It is toward the center
Explanation:
A certain amusement park ride consists of a large rotating cylinder of radius R=3.05 m.R=3.05 m. As the cylinder spins, riders inside feel themselves pressed against the wall. If the cylinder rotates fast enough, the frictional force between the riders and the wall can be great enough to hold the riders in place as the floor drops out from under them. If the cylinder makes f=0.450 rotations/s,f=0.450 rotations/s, what is the magnitude of the normal force FNFN between a rider and the wall, expressed in terms of the rider's weight W?W? FN=FN= WW What is the minimum coefficient of static friction µsμs required between the rider and the wall in order for the rider to be held in place without sliding down?
Answer:
a. N = 2.49W b. 0.40
Explanation:
a. What is the magnitude of the normal force FNFN between a rider and the wall, expressed in terms of the rider's weight W?
Since the normal force equals the centripetal force on the rider, N = mrω² where r = radius of cylinder = 3.05 m and ω = angular speed of cylinder = 0.450 rotations/s = 0.450 × 2π rad/s = 2.83 rad/s
Now N = mrω² = m(3.05 m) × (2.83 rad/s)² = 24.43m
The rider's weight W = mg = 9.8m
The ratio of the normal force to the rider's weight is
N/W = 24.43m/9.8m = 2.49
So the normal force expressed in term's of the rider's weight is
N = 2.49W
b. What is the minimum coefficient of static friction µsμs required between the rider and the wall in order for the rider to be held in place without sliding down?
The frictional force, F on the rider by the wall of the cylinder equals the weight, W of the rider. F = W.
Since the frictional force F = μN, where μ = coefficient of static friction between rider and wall of cylinder and N = normal force between rider and wall of cylinder.
So, the normal force equals
N = F/μ = W/μ = mg/μ = mrω²
μ = mg/mrω²
= W/N
= 9.8m/24.43m
= 0.40
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If you know that your average speed on road trips in 47 mph, how much time should you plan for a road trip to Atlanta, which is 715 miles away?
Answer:
about 15 hours and 13 minutes
Explanation:
If the average speed on road trips is 47 mph, then we use the formula for speed to estimate the time it would take to cover a distance of 715 miles:
speed = distance / time
solve for "time" by cross-multiplication:
time = distance / speed
time = 715 / 47 = 15.212 hours
Which is about 15 hours and 13 minutes
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In this graphical representation of a vector, which direction is designated as positive?
a) horizontal
b) vertical
c) downward
d) upward
Answer:
D
Explanation:
when you try to find out if it is positive, the line goes from left to right, and in this question the line is going upward.
this is a Physical Education question
What is the most dangerous electromagnetic wave?
Answer:
Gamma Rays
Explanation:
Because it has the most energetic radiation and could penetrate through six feet of concrete. It is so strong it can damage your dna.
A scientist just learned that she will not receive enough money to complete her year-long study about the
relationship between certain diseases and the foods that people eat.
How can she best overcome this limitation?
conduct smaller studies for more than a one-year period
study only a very small group of people
conduct a study about something else
use data from a similar study and adjust it to fit her study
Please answer I need help
When faced with limited funding to complete a year-long study on the relationship between certain diseases and people's diets she can best overcome this by conduct smaller studies for more than a one-year period, study only a very small group of people, conduct a study about something else, use data from a similar study and adjust it to fit her study.
The correct answer would be all of the above.
There are several strategies the scientist can consider to overcome this limitation. Each option has its own advantages and potential drawbacks, so the scientist should carefully evaluate which approach aligns best with her research goals and available resources.
1. Conduct smaller studies for more than a one-year period: Instead of one large-scale study, the scientist can break down the research into smaller, more manageable studies. This approach allows for incremental progress, and findings from each smaller study can contribute to the overall understanding of the topic. By conducting multiple studies over an extended period, the scientist can still gather valuable data and draw meaningful conclusions.
2. Study only a very small group of people: Focusing on a small group of participants can reduce costs and streamline data collection and analysis. While the sample size may be limited, the scientist can still gain insights into the relationship between diseases and diet within this specific group. However, generalizing the findings to a larger population may be challenging due to the limited sample size.
3. Conduct a study about something else: If funding limitations prevent the scientist from conducting the intended study, she could consider redirecting her research efforts towards a related but more feasible topic. This allows her to leverage her expertise and resources while still generating valuable scientific knowledge.
4. Use data from a similar study and adjust it to fit her study: The scientist could explore existing datasets or previous studies that are relevant to her research question. By analyzing and adapting this data to fit her study's context, she can gain insights without incurring the costs and time associated with primary data collection. However, it is crucial to ensure that the adjusted data aligns with the specific objectives and parameters of her study.
Ultimately, the scientist should carefully assess the feasibility, potential impact, and trade-offs associated with each option. It may also be beneficial to seek guidance from peers, mentors, or funding agencies to explore alternative funding sources or collaborative opportunities that could support her research goals.
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A 60kg woman on skates throws a 3.9kg ball with a velocity of
37m.s west. What is the velocity of the woman?
Answer:
2.405 m/s
Explanation:
Given that,
Mass of a women, m₁ = 60 kg
Mass of a ball, m₂ = 3.9 kg
Velocity of the ball, v₂ = 37 m/s
We need to find the velocity of the woman. It is a concept based on the conservation of linear momentum. Let v₁ is the velocity of the woman. So,
[tex]m_1v_1=m_2v_2\\\\v_1=\dfrac{m_2v_2}{m_1}\\\\v_1=\dfrac{3.9\times 37}{60}\\\\v_1=2.405\ m/s[/tex]
So, the velocity of the woman is 2.405 m/s.
PLS HELP THIS IS FOR AN EXAM!!!
How many exercises encompass stretching in the human body
A) eight
B) too many to count
C) that depends on each individual
D) none
Answer: (B) Too many to count
Explanation: Have a wonderful day everyone! :D
The exercises that encompasses stretching in the human body is : B) too many to count
Meaning of exerciseexercises can be defined as any activity that puts your muscle to work and helps burn calories in your body.
exercises are one of the keys to staying and living healthy.
exercises are of different types and forms and some encompasses stretching in the human body.
In conclusion, The exercises that encompasses stretching in the human body is too many to count
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When jumping straight down, you can be seriously injured if you land stiff-legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. A 60.0-kg man just before contact with the ground has a speed of 4.18 m/s. (a) In a stiff-legged landing he comes to a halt in 1.00 ms. Find the magnitude of the average net force that acts on him during this time. (b) When he bends his knees, he comes to a halt in 0.245 s. Find the magnitude of the average net force now. (c) During the landing, the force of the ground on the man points upward, while the force due to gravity points downward. The average net force acting on the man includes both of these forces. Taking into account the directions of the forces, find the magnitude of the force applied by the ground on the man in part (b).
Answer:
a) The average force that acts on the man is [tex]2.508\times 10^{8}[/tex] newtons.
b) The average force that acts on the man is 1023.673 newtons.
c) The force of the ground on the man is 1612.093 newtons upwards.
Explanation:
a) After a careful reading of the statement we construct the following model by applying Impact Theorem, that is:
[tex]m\cdot \vec v_{A} + \vec F \cdot \Delta t = m\cdot \vec v_{B}[/tex] (Eq. 1)
Where:
[tex]m[/tex] - Mass of the man, measured in kilograms.
[tex]\vec v_{A}[/tex] - Initial velocity of the man, measured in meters per second.
[tex]\vec v_{B}[/tex] - Final velocity of the man, measured in meters per second.
[tex]\Delta t[/tex] - Impact time, measured in seconds.
[tex]\vec F[/tex] - Average net force, measured in newtons.
Now we proceed to clear average net force within expression:
[tex]\vec F \cdot \Delta t = m\cdot (\vec v_{B}-\vec v_{A})[/tex]
[tex]\vec F = \frac{m}{\Delta t}\cdot (\vec v_{B}-\vec v_{A})[/tex] (Eq. 2)
If we know that [tex]m = 60\,kg[/tex], [tex]\vec v_{A} = -4.18\,\hat{j}\,\,\,\left[\frac{m}{s} \right][/tex], [tex]\vec v_{B} = 0\,\hat{j}\,\,\,\left[\frac{m}{s} \right][/tex] and [tex]\Delta t = 1\times 10^{-6}\,s[/tex], we obtain the following vector:
[tex]\vec F = \frac{60\,kg}{1\times 10^{-6}\,s} \cdot (4.18\,\hat{j})\,\,\,\left[\frac{m}{s} \right][/tex]
[tex]\vec F = 2.508\times 10^{8}\,\hat{j}\,\,\,[N][/tex]
The average force that acts on the man is [tex]2.508\times 10^{8}[/tex] newtons.
(b) If we know that [tex]m = 60\,kg[/tex], [tex]\vec v_{A} = -4.18\,\hat{j}\,\,\,\left[\frac{m}{s} \right][/tex], [tex]\vec v_{B} = 0\,\hat{j}\,\,\,\left[\frac{m}{s} \right][/tex] and [tex]\Delta t = 0.245\,s[/tex], we obtain the following vector:
[tex]\vec F = \frac{60\,kg}{0.245\,s} \cdot (4.18\,\hat{j})\,\,\,\left[\frac{m}{s} \right][/tex]
[tex]\vec F = 1023.673\,\hat{j}\,\,\,\left[N\right][/tex]
The average force that acts on the man is 1023.673 newtons.
(c) From Second Newton's Law we find the following equation of equilibrium:
[tex]\vec F = \vec N -\vec W[/tex] (Eq. 3)
Where:
[tex]\vec F[/tex] - Average force that acts on the man, measured in newtons.
[tex]\vec N[/tex] - Force of the ground on the man, measured in newtons.
[tex]\vec W[/tex] - Weight of the man, measured in newtons.
By applying the concept of weight, we expand the previous equation:
[tex]\vec F = \vec N -m\cdot \vec g[/tex] (Eq. 3b)
Where [tex]\vec g[/tex] is the gravitational acceleration, measured in meters per square second.
And then we clear the force of the ground on the man:
[tex]\vec N = \vec F +m\cdot \vec g[/tex] (Eq. 4)
If we get that [tex]\vec F = 1023.673\,\hat{j}\,\,\,\left[N\right][/tex], [tex]m = 60\,kg[/tex] and [tex]\vec g = 9.807\,\hat{j}\,\,\,\left[\frac{m}{s^{2}} \right][/tex], the average force is:
[tex]\vec N = 1023.673\,\hat{j}\,\,\,[N]+(60\,kg)\cdot (9.807\,\hat{j})\,\,\,\left[\frac{m}{s^{2}} \right][/tex]
[tex]\vec N = 1612.093\,\hat{j}\,\,\,\left[N\right][/tex]
The force of the ground on the man is 1612.093 newtons upwards.
3 general relevant psychology related problems at present
Answer:
Explanation:
Scientific research conducted by psychologists, organized by topics here, can inform and guide those seeking help with issues that affect their professional lives, family relationships and emotional wellness.Tips for choosing a psychotherapist and answers to financial questions related to therapy.
When faced with important events (stressors) which are threatening or very hard to, psychological symptoms of stress include anxiety and tension, uncontrollable. In general, this refers to high levels of suspicion and mistrust, usually seen in this psychological condition is associated with acute physical sickness
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What role does the internet play in allowing us to share,inspire, and critique images that have been edited
Answer: However, the Internet takes digital photo manipulation.
Explanation: This discussion is not only limited to digital manipulation, but also includes .However, there was no way to take this image in a single exposure .
Find the force that must be exerted on the rod to maintain a constant current of 0.173 A in the resistor.
Complete Question
Find the force that must be exerted on the rod to maintain a constant current of 0.173 A in the resistor.
The figure below shows a zero-resistance rod sliding to the right on two zero-resistance rails separated by the distance L = 0.451 m . The rails are connected by a [tex]12.6 \Omega \ resistor[/tex], and the entire system is in a uniform magnetic field with a magnitude of 0.751 T .
The diagram illustrating this question is shown on the first uploaded image
Answer:
The value is [tex]F = 0.0586 \ N [/tex]
Explanation:
From the question we are told that
The current is [tex]I = 0.173 \ A[/tex]
The length of separation is [tex]L= 0.451 \ m[/tex]
The resistance is [tex]12.6 \Omega[/tex]
The magnetic field is [tex]B = 0.751\ T[/tex]
Generally the force is mathematically represented as
[tex]F = BIL sin (\theta )[/tex]
Given that the velocity is perpendicular to magnetic field then [tex]\theta = 90[/tex]
=> [tex]sin(90) = 1[/tex]
So
[tex]F = 0.751 *0.173 * 0.451 sin (\theta )[/tex]
[tex]F = 0.751 *0.173 * 0.451 * 1[/tex]
[tex]F = 0.0586 \ N [/tex]
A net force of 500 newtons causes
an object to accelerate at a rate of
5.0 m/s2. What is the mass of the
object?
A - 100 kg
B - .20kg
C - 600 kg
D - 2500 kg
Answer:
The answer is option AExplanation:
To find the mass of an object given it's acceleration and the force acting on it we use the formula
[tex]mass = \frac{force}{acceleration} \\ [/tex]
From the question
force = 500 N
acceleration = 5.0 m/s²
We have
[tex]mass = \frac{500}{5} \\ [/tex]
We have the final answer as
100 kgHope this helps you
A 4kg object is at rest. How much force is required to get the object to a velocity of 20m/s in 2 seconds? (Show work and include units)
Explanation:
Answer:-The Object was at rest. So, Initial Velocity is Zero.
[Initial Velocity]u = 0[Final Velocity]v = 20 m/s[Time]t = 2 seconds Mass = 4kgForce = ?We know that:-
[tex]\sf{Force = Mass \times \dfrac{(v-u)}{t}}[/tex]
Applying it, we get:-
[tex]\sf{Force = 4 \times \dfrac{(20-0)}{2}}[/tex]
[tex]\sf{Force = 2 \times \dfrac{(20)}{2}}[/tex]
[tex]\sf{Force = 2 \times 10}[/tex]
[tex]\sf{Force = 20 \ N \ (Newton)}[/tex]
Hope it helps :)
Why can concave mirror is used in cosmetic mirror
for which pair of objects would adding the same amount of eletrons to each object result in a decrease in a electrical force
Answer:
two positively charged objects
Explanation:
how do Red Ants and squirrels depend on plants
A block of wood mass 0.60kg is balanced on top of a vertical port 2.0m high. A 10gm bullet is fired horizontally into the block and the embedded bullet land at a 4.0m from the base of the port. Find the initial velocity of the bullet.
Answer:
Mass of bullet is m=0.01kg
Mass of the block is M=4kg
Coefficient=0.25,distance=20m
So, let the speed of the block just after the bullet embedded in it be V and v be the speed of bullet before striking the block,
By applying conservation of momentum,
mv=(m+M)V
V=
M+m
mv
Explanation:
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The initial velocity of the bullet is 382 m/s
The given parameters;
mass of the wood, m₁ = 0.6 kgheight of the port, h = 2mass of the bullet, m₂ = 10 g = 0.01 kghorizontal distance traveled by the bullet, x = 4 mApply the principle of conservation of mechanical energy;
The maximum potential energy of the bullet-wood system at the top of the port = maximum kinetic energy of the system at the base of the port.
[tex]K.E_{max} = P.E_{max}\\\\\frac{1}{2} mv_{max}^2 = mgh_{max}\\\\v^2_{max} = 2gh_{max}\\\\v_{max} = \sqrt{2gh_{max}} \\\\v_{max} = \sqrt{2\times 9.8\times 2} \\\\v_{max} = 6.26 \ m/s[/tex]
Apply the principle of conservation of linear momentum to determine the initial velocity of the bullet;
let the initial velocity of the bullet = u₂[tex]m_1u_1 + m_2u_2 = v(m_1 + m_2)\\\\0.6(0) + 0.01(u_2) = 6.26((0.6 + 0.01)\\\\0.01u_2 = 3.819\\\\u_2 = \frac{3.819}{0.01} \\\\u_2 = 381.9 \ \approx 382 \ m/s[/tex]
Thus, the initial velocity of the bullet is 382 m/s
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An airplane is traveling at 250 m/s in level flight. If the airplane is to make a change in direction, it must travel is a horizontal curved path. To fly in the curved path, the pilot banks the airplane at an angle such that the lift has a horizontal component that provides the horizontal centripetal acceleration to move in a horizontal circular path. If the airplane is banked at an angle of 15.0 degrees, then the radius of curvature of the curved path of the airplane is
Answer:
The radius of curvature of the curved path of the airplane is 23784.356 meters (23.784 kilometers).
Explanation:
We assume that airplane can be represented as a particle. The free body diagram of the vehicle is presented below as attachment, whose variables are:
[tex]W[/tex] - Weight of the airplane, measured in newtons.
[tex]F[/tex] - Lift, measured in newtons.
[tex]\theta[/tex] - Banking angle, measured in sexagesimal degrees.
The equations of equilibrium associated with the airplane are, respectively:
[tex]\Sigma F_{r} = F\cdot \sin \theta = m\cdot \frac{v^{2}}{R}[/tex] (Eq. 1)
[tex]\Sigma F_{z} = F\cdot \cos \theta - W = 0[/tex] (Eq. 2)
From (Eq. 2):
[tex]F = \frac{W}{\cos \theta}[/tex]
In (Eq. 1):
[tex]W\cdot \tan \theta = m\cdot \frac{v^{2}}{R}[/tex]
By using the definition of weight, we eliminate the mass of the airplane:
[tex]g\cdot \tan \theta = \frac{v^{2}}{R}[/tex]
Where:
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]v[/tex] - Speed, measured in meters per second.
[tex]R[/tex] - Radius of curvature, measured in meters.
Lastly, we clear the radius of curvature with the expression:
[tex]R = \frac{v^{2}}{g\cdot \tan \theta}[/tex]
If we know that [tex]v = 250\,\frac{m}{s}[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]\theta = 15^{\circ}[/tex], the radius of curvature is:
[tex]R = \frac{\left(250\,\frac{m}{s} \right)^{2}}{\left(9.807\,\frac{m}{s^{2}} \right)\cdot \tan 15^{\circ}}[/tex]
[tex]R = 23784.356\,m[/tex]
The radius of curvature of the curved path of the airplane is 23784.356 meters (23.784 kilometers).
g A person exploring a deep cave system becomes injured and needs to be rescued. The fastest way to get them is to pull them straight up out of the cave through a small opening just overhead, using a motor-driven cable. The lift is performed in three stages, each of them 10 m in height (total of 30 meters to extract the person). In the first stage, the person is accelerated to a speed of 5 m/s. They are then lifted at constant speed of 5 m/s, then in the last stage they are slowly decelerated to zero speed. If the person weighs 80 kg, how much work is done in each stage
Answer:
1. W = 8848 J
2. W = 7848 J
3. W = 6848 J
Explanation:
The work (W) can be found using the following equation:
[tex] W = E_{k} + E_{p} [/tex]
Where: E(k) is the kinetic energy and E(p) is the potential energy
Now let's find the work for every stage.
Stage 1:
[tex] W = E_{k} + E_{p} = \frac{1}{2}mv^{2} + mgh [/tex]
Where: m is the mass, g is the gravity, h is the height, v is the speed
[tex] W = \frac{1}{2}mv^{2} + mgh = \frac{1}{2}80 kg*(5 m/s)^{2} + 80 kg*9.81 m/s^{2}*10 m = 8848 J [/tex]
Stage 2:
[tex] W = E_{k} + E_{p} = 0 + E_{p} [/tex]
The kinetic energy is equal to zero because the acceleration is constant.
[tex] W = E_{p} = mgh = 80 kg*9.81 m/s^{2}*10 m = 7848 J [/tex]
Stage 3:
[tex] W = E_{k} + E_{p} = \frac{1}{2}mv^{2} + mgh = -\frac{1}{2}80 kg*(5 m/s)^{2} + 80 kg*9.81 m/s^{2}*10 m = 6848 J [/tex]
I hope it helps you!
What's the equation with gravity that involves acceleration and time?
Answer:
g = G*M/R^2, where g is the acceleration due to gravity, G is the universal gravitational constant, M is mass, and R is distance.
Explanation:
These two laws lead to the most useful form of the formula for calculating acceleration due to gravity
suppose you put some ice is put into a container of water at room temperature. For faster cooling, the ice should (i) be allowed to float naturally in the water or (ii) be pushed to the bottom of the container with a glass rod and held there. Explain your answer.
Answer:
i am just trying it could be wrong too i am not sure about it but according to me the ans is (1)let ice be allowed to float naturally in the water
Explanation:
if u put water in ice or ice in water the temperature of water decreases and then the process gets slower but if u allow to float it then the temperature of water and surrounding air decreases and the heat is lost from air and water both so here the heat is more than only just water here it allows both to give heat and in 2nd option the heat is only lost by water and gained by icehere it allows only water to give heat so the heat is less in surrounding of ice in water so more heat more faster the process therefore i think the 1st option is correct
What are tides?
O Circulation of water
O Glaciers melting causing rising water
O Wind pushing ocean water
O Rise and fall of the water level on the shore
Answer:
4th
Explanation:
Rise and fall of the water level on the sea shore
Part 2: Vertical Distance
1
do
2.942
d, = vertical distance
g = acceleration due to gravity (10m/s2)
t = time
How high was a brick dropped from if it falls in 2.5 seconds?
2.5 m
Ob
12.5 m
25 m
с
Od
31.25 m
Answer:
31.25m
Explanation:
Given parameters:
Acceleration due to gravity = 10m/s²
Time of drop = 2.5s
Unknown
Height of drop = ?
Solution:
To solve this problem, we must note that the brick was originally at rest. The appropriate motion equation to solve this is shown below;
H = ut + [tex]\frac{1}{2}[/tex]gt²
H is the height
u is the initial velocity
g is the acceleration due to gravity
t is the time taken
Input the parameters and solve;
H = 0 + [tex]\frac{1}{2}[/tex] x 10 x 2.5²
H = 31.25m
Velocity of a car traveling in a straight line increases from 0 m/s to 30 m/s in eight seconds what is the average acceleration of the car
Average acceleration is how much the car increases (on average) per second. So, since it increases by 30 m/s in 8 s, then dividing 30 by 8 will give you an average acceleration of 3.75 m/s^2 (remember that acceleration is ever increasing, so the unit is s^2, not just s)
The speedometer of a car moving east reads 60 mph. It passes another car that travels west at 60 mph do the cars have the same velocity?
Answer:
no but yes at the same time
Explanation:
they are going a different direction but they are the same speed.
A particular car can go from rest to 90 km/h in 10 s. What is its acceleration? (Report your answer in km/h*s)
Answer: 9 km/h
Explanation:i’m pretty sure
Answer:
Well, it depends on the type of car but a regular car like a toyota 4x4 only goes at 5k/h if the car starts when complete rest
In 2.5 s, a car increases its speed from 60 km/h to 65 km/h while a bicycle goes from rest to 5 km/h. Which undergoes the
greater acceleration?
What is the acceleration of each? (Don't forget your units when reporting answers).
Answer:
Same, 2 km/h/s
Explanation:
Acceleration is change in velocity over time.
a = Δv / Δt
The car's acceleration is:
a = (65 km/h − 60 km/h) / 2.5 s
a = 2 km/h/s
The bicycle's acceleration is:
a = (5 km/h − 0 km/h) / 2.5 s
a = 2 km/h/s
In a mass spectrometer chlorine ions of mass 35u and charge 5e are emitted from a source and accelerated through a potential difference of 250 kV. They then enter a region with a magnetic field that is perpendicular to their original direction of motion. The chlorine ions exit the spectrometer after being bent along a path with radius of curvature 3.5 m. What is the speed of the chlorine ions as they enter the magnetic field region
Answer:
Explanation:
From the question we are told that
The mass of chlorine ion is [tex]m_c = 35u = 35 * 1.66*10^{-27} = 5.81*10^{-26}\ kg[/tex]
The charge is [tex]q = 5e = 5 * 1.60 *10^{-19} = 8.0*10^{-19}\ C[/tex]
The potential difference is [tex]V = 250 kV = 250*10^{3} \ V[/tex]
The radius of curvature of the path is [tex]r = 3.5 \ m[/tex]
Gnerally the magnetic force will cause the speed of the chlorine ions to change from 0 m/s to [tex]v_y[/tex] m/s along the y -axis but will not affect the velocity along the x-axis
Generally according the law of energy conservation
[tex]K = PE[/tex]
Here K is the kinetic energy of the of the chlorine ions which is mathematically represented as
[tex]K = \frac{1}{2} mv^2[/tex]
And PE is electric potential energy which is mathematically represented as
[tex]PE = Q * V[/tex]
So
[tex] \frac{1}{2} mv^2 = Q * V [/tex]
=> [tex] \frac{1}{2} * 5.81*10^{-26} * v^2 = 8.0*10^{-19} * 250*10^{3} [/tex]
=> [tex] v = sqrt{6.8847 *10^{12}} [/tex]
=> [tex] v = 2.634 *10^{6} \ m/s [/tex]
1) The equilibrium constant Kc for the reaction N 2(g) + O 2(g) 2NO(g) at 1200 C is 1.00x 10^-5. Calculate the molar concentration of NO, N2 and O2 in equilibrium at 1200 C in a 1.00L container that initially had 0.114 mol of N2 and 0.114 mol of O2
2) A 2.0 mmol sample of Cl2 was closed inside a 2.0 L reaction vessel and heated to 1000k to study its dissociation into Cl atoms, Kc= 1.2x10^- 7 (a) Calculate the composition of the mixture in equilibrium. What is the percentage of decomposition of Cl2? (b) If 2.0 mmol of F2, Kc= 1.2x10^-4, is placed inside the container instead of chlorine, what will be its equilibrium composition at 1000k? Use your results from (a) and (b) to determine which is the most stable with respect to your atoms, Cl2 or F2, at 1000k
Explanation:
1) N₂ + O₂ → 2 NO
Kc = [NO]² / ([N₂] [O₂])
Set up an ICE table:
[tex]\left[\begin{array}{cccc}&Initial&Change&Equilibrium\\N_{2}&0.114&-x&0.114-x\\O_{2}&0.114&-x&0.114-x\\NO&0&+2x&2x\end{array}\right][/tex]
Plug into the equilibrium equation and solve for x.
1.00×10⁻⁵ = (2x)² / ((0.114 − x) (0.114 − x))
1.00×10⁻⁵ = (2x)² / (0.114 − x)²
√(1.00×10⁻⁵) = 2x / (0.114 − x)
0.00316 = 2x / (0.114 − x)
0.00361 − 0.00316x = 2x
0.00361 = 2.00316x
x = 0.00018
The volume is 1.00 L, so the concentrations at equilibrium are:
[N₂] = 0.114 − x = 0.11382
[O₂] = 0.114 − x = 0.11382
[NO] = 2x = 0.00036
2(a) Cl₂ → 2 Cl
Kc = [Cl]² / [Cl₂]
[tex]\left[\begin{array}{cccc}&Initial&Change&Equilibrium\\Cl_{2}&2.0&-x&2.0-x\\Cl&0&+2x&2x\end{array}\right][/tex]
1.2×10⁻⁷ = (2x)² / (2 − x)
1.2×10⁻⁷ (2 − x) = 4x²
2.4×10⁻⁷ − 1.2×10⁻⁷ x = 4x²
2.4×10⁻⁷ ≈ 4x²
x² ≈ 6×10⁻⁸
x ≈ 0.000245
2x ≈ 0.00049
2(b) F₂ → 2 F
Kc = [F]² / [F₂]
[tex]\left[\begin{array}{cccc}&Initial&Change&Equilibrium\\F_{2}&2.0&-x&2.0-x\\F&0&+2x&2x\end{array}\right][/tex]
1.2×10⁻⁴ = (2x)² / (2 − x)
1.2×10⁻⁴ (2 − x) = 4x²
2.4×10⁻⁴ − 1.2×10⁻⁴ x = 4x²
2.4×10⁻⁴ ≈ 4x²
x² ≈ 6×10⁻⁵
x ≈ 0.00775
2x ≈ 0.0155
F₂ dissociates more, so Cl₂ is more stable at 1000 K.
