Answer:
A dissipates more power.
Explanation:
In a series circuit, the current is the same at any point in it.The power dissipated in any resistor follows Joule's law, as follows:[tex]P = I^{2} * R[/tex]
So, for a given current, the power is directly proportional to the resistance of the resistor.In this case, as resistor A has twice the resistance of resistor B, A dissipates twice more power than B.An ideal gas increases in temperature from 22°C to 42°C by two different processes. In one process, the temperature increases at constant volume, and in the other process the temperature increases at constant pressure. Which process requires more heat or are the required amount of heat same in both?
Answer:
a- More heat is required for the constant-pressure process than for the constant-volume
Explanation:
we have to solve using the thermodynamic first law. this is the heat applied to the system
dQ = dU + dW
definition of terms:
dU = change in internal energy
dW = work done
we have it that
change in internal energy dU is directly proportional to work done dW
but when we are in constant volume process, work done of the gas is zero
therefore
dQ of constant pressure is > than that of constant volume
so constant pressure process requires more heat
The process that requires more heat is the constant-pressure process than the constant-volume process.
According to the first law of thermodynamics, the heat that's applied to the system will be the addition of the change in internal energy and the work done.
In a constant-volume process, the work done on the gas is equal to zero. More heat will be required for the constant-pressure process than for the constant-volume process.
Also, it should be noted that the change in the thermal energy of the gas will be the same for the constant-pressure process and the constant-volume process.
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1. Which of these is not a natural fibre?
a. leather
b. jute
C.Wool
d. cotton
Answer:
leather
Explanation:
plz mark as brainliest......hope it helps
Answer:
a. leather
Explanation:
Hello friend!!!!
a. leather is the correct option because jute, wool and cotton are all natural fibres whereas leather is a synthetic fibre.
Hope this helps
plz mark as brainliest!!!!!!
a car is moving at 12 m/s and has a mass of 600 kg what is the. kinetic energy of the car?
Answer:
43200 J
Explanation:
(1/2(mass)) (speed)^2
A baseball is thrown through the air. It's initial velocity, described as a vector, is → v ( t = 0 ) = 17.1 ˆ i + 14.7 ˆ j m / s The ball accelerates only due to gravity. You can take the magnitude of this acceleration to be 9.8 m / s 2 . What is the acceleration of the ball, described as a vector?
Answer:
a = - 9.8 j ^ m/s²
Explanation:
This is a projectile launch problem, they give us the initial velocity in the two components
v₀ₓ = 17.1 m / s
[tex]v_{oy}[/tex] = 14.7 m / s
They indicate that the only acceleration that exists is the acceleration of gravity, which acts in the direction towards the center of the Earth, in general in a coordinate system it coincides with the direction of the y axis.
a = - g j ^
a = - 9.8 j ^ m /s²
A soccer player kicking a ball; the ball soaring through the air and landing on the ground
What is the probability that a junior non-Physics major and then a freshman non-Physics major are chosen at random?
Answer:
Probability = 0.0244
Explanation:
Probability that Junior Non Physics Major & then a Freshman Non Physics Major are chosen:
Prob (Jr No-Ph Mjr) = Jr No-Ph Mjr / Total
= 18 / 82 = 0.2195
Prob (Fr No-Ph Mjr) = Fr No-Ph Mjr / Total (remaining)
= 9 / 81 = 0.1111
Prob [ Jr No-Ph Mjr & Fr No-Ph Mjr ] = 0.2195 x 0.1111 = 0.02439
≈ 0.0244
Scientific method has been invented in 21st century *
A. Yes
B. No
Answer:
No
Explanation:
It was made in the 17th century
A 12 kg bowling ball would require what force to accelerate it down an alley at a rate of 2.5 m/s ^ 2
Answer:
hi
Explanation:
hiijjjjjjjjjjjjjjj
A 6 gram coin is which is initially at rest is dropped from the observation deck of a skyscraper 300 meters above the street below.
Required:
a. What is the work done by gravity on the coin as it falls?
b. Because there is air resistance the coin was slowed and hit the ground with a final velocity of 60 m/s. What is the kinetic energy of the coin at this speed? Joules
c. How much work was lost to air resistance as the coin fell? Joules
d. What is the average force exerted on the coin due to the air resistance as it fell?
Answer:
a) The work done by gravity on the coin as it falls is 17.653 joules.
b) The kinetic energy of the coin at a speed of 60 meters per second is 10.8 joules.
c) The work lost due to air resistance is 6.853 joules.
d) The average force exerted on the coin due to air resistance as it fell is 0.023 newtons.
Explanation:
a) We must remind that situation with Earth-coin system must be represented by Principle of Energy Conservation and Work Energy Theorem. According to this latter, work done by gravity equals to the change in gravitational potential energy:
[tex]\Delta U_{g} = m\cdot g \cdot \Delta z[/tex] (Eq. 1)
Where:
[tex]\Delta U_{g}[/tex] - Change in gravitational potential energy, measured in joules.
[tex]m[/tex] - Mass, measured in kilograms.
[tex]g[/tex] - Gravitational accelerations, measured in meters per square second.
[tex]\Delta z[/tex] - Height of the skyscraper, measured in meters.
If we know that [tex]m = 0.006\,kg[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]\Delta z = 300\,m[/tex], the work done gravity on the coin is:
[tex]\Delta U_{g} = (0.006\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (300\,m)[/tex]
[tex]\Delta U_{g} = 17.653\,J[/tex]
The work done by gravity on the coin as it falls is 17.653 joules.
b) By definition of translation kinetic energy, we get the following model:
[tex]K = \frac{1}{2}\cdot m\cdot v^{2}[/tex]
Where:
[tex]K[/tex] - Kinetic energy of the coin right before hitting the street, measured in joules.
[tex]v[/tex] - Speed of the coin, measured in meters per second.
If we get that [tex]m = 0.006\,kg[/tex] and [tex]v = 60\,\frac{m}{s}[/tex], the kinetic energy at this speed is:
[tex]K = \frac{1}{2}\cdot (0.006\,kg)\cdot \left(60\,\frac{m}{s} \right)^{2}[/tex]
[tex]K = 10.8\,J[/tex]
The kinetic energy of the coin at a speed of 60 meters per second is 10.8 joules.
c) The work lost due to air resistance is obtained derived from Principle of Energy Conservation and Work-Energy Theorem:
[tex]W_{lost} = \Delta U_{g}-K[/tex] (Eq. 2)
Where [tex]W_{lost}[/tex] is the work lost due to air resistance, measured in joules.
If we know that [tex]\Delta U_{g} = 17.653\,J[/tex] and [tex]K = 10.8\,J[/tex], the work lost due to air resistance is:
[tex]W_{lost} = 17.653\,J-10.8\,J[/tex]
[tex]W_{lost} = 6.853\,J[/tex]
The work lost due to air resistance is 6.853 joules.
d) The average force exerted on the coin due to air resistance can be determined by applying definition of work, as air resistance force was antiparallel to the displacement of the coin. That is:
[tex]W_{lost} = F\cdot \Delta z[/tex]
[tex]F = \frac{W_{lost}}{\Delta z}[/tex] (Eq. 3)
Where [tex]F[/tex] is the average force exerted on the coin due to air resistance, measured in newtons.
If we know that [tex]W_{lost} = 6.853\,J[/tex] and [tex]\Delta z = 300\,m[/tex], then the average force exerted on the coin is:
[tex]F = \frac{6.853\,J}{300\,m}[/tex]
[tex]F = 0.023\,N[/tex]
The average force exerted on the coin due to air resistance as it fell is 0.023 newtons.
A student studies the effect of an object's speed on its amount of kinetic energy. This graph summarizes the data from the study Kinetic energy Speed Which statement best describes what the graph shows?
A. As speed increases, kinetic energy increases exponentially
B. As speed increases, kinetic energy stays the same
C. As speed decreases, kinetic energy doubles each time.
D. As kinetic energy increases, speed decreases exponentially
The answer is A I Hope this answer helps you (i got the question right)
Answer:
A. As speed increases, kinetic energy increases exponentially.
Explanation:
The amount of kinetic energy an object has depends on the speed. Kinetic energy is also known as "motion energy." This being said, if speed is increasing, decreasing, or staying constant, the kinetic energy of the object will too.
HELP ASAP. will mark brainiest
Answer:
4.8min
Explanation:
The police car is traveling at 100/km and is 1.6km away from red car that is traveling at 80/km
When the air resistance can be ignored the velocity of an object dropped initially from rest is given by the following equation where g is free-fall acceleration
A. g*t^2/2
B. g*t
C. g*t/2
D. g
Answer:
I am confused of your question. Do you want final velocity? To get final velocity, use (initial V)+(Gravity*Time)
Explanation:
Answer:
B. g*t
Explanation:
in a controlled experiment do none of the variables change?
Answer:
Yes
Explanation:
The variables change in and experiment.
Answer:
If you are carefully enough to control everything, then everything that could change the result of your experiment won't happen.
Explanation:
A region around the nucleus of an atom where electrons are likely to be found
Answer:
The region where an electron is most likely to be is called an orbital. Each orbital can have at most two electrons. Some orbitals, called S orbitals, are shaped like spheres, with the nucleus in the center.
Explanation:Hope this helps :)
By definition, a region around the nucleus of an atom where electrons are likely to be found is called an orbital.
First of all, an atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element.
All atoms are made up of subatomic particles: protons and neutrons, which are part of their nucleus, and electrons, which revolve around them. Protons are positively charged, neutrons are neutrally charged, and electrons are negatively charged.
In other words, every atom consists of a nucleus in which neutrons and protons meet and energy levels where electrons are located.
This is, the atomic nucleus is the central part of the atom that is made up of protons and neutrons, while the orbitals or peripheral region is an area where electrons are found.
In summary, a region around the nucleus of an atom where electrons are likely to be found is called an orbital.
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https://brainly.com/question/10866484?referrer=searchResultshttps://brainly.com/question/1275002?referrer=searchResultsbrainly.com/question/1814899?referrer=searchResults brainly.com/question/2449569?referrer=searchResultsWhat is it called when scientists in the same or similar field of study judge the quality of a fellow scientist’s scientific claim?
academic claim
academic review
peer claim
peer review
Answer:
When scientists in the same or similar field of study judges the quality of a fellow scientist’s scientific claim, it is known as peer review.
When scientists in the same or similar field of study judge the quality of a fellow scientist’s scientific claim it is called Peer review.
what is the scientific claim?Scientific claims are statements made in science based on an experiment.
These Scientific claims are backed by the experimental data and their true results obtained from scientific investigation and experimentation.
Peer review is done when scientists in the same or similar field of study judge the quality of a fellow scientist’s scientific claims.
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Observe the vertical and horizontal motion of lunar lander in the absence of thrust explain the reason for motion
Answer:
In the absence of thrust, the lunar lander moves downward toward the surface of the moon. At this point, the only force acting on the lunar lander is gravity, which is directed toward the center of the moon. Because the net force is in the downward direction, the lunar lander moves downward.
Explanation: plato
Answer: In the absence of thrust, the lunar lander moves downward toward the surface of the moon. At this point, the only force acting on the lunar lander is gravity, which is directed toward the center of the moon. Because the net force is in the downward direction, the lunar lander moves downward.
Explanation: edmentum sample answer
It took 500 newtons of force to push a car 4 meters. How much work was done?
Answer:
The answer is 2000 JExplanation:
The work done by an object can be found by using the formula
workdone = force × distanceFrom the question
force = 500 N
distance = 4 m
We have
workdone = 500 × 4
We have the final answer as
2000 JHope this helps you
The consequence that an element of society produces for the maintenance of its social system.
Answer:
Function
Explanation:
This question defines a function. It is any consequence that is made up of positive structures which has a way of affecting the society in a positive way. And it also has a way of impacting structural continuity in the society. The functionalism idea has the postulation that all cultural or social phenomena is of positive function and cannot be ignored
Answer:
function
Explanation:
answer EDGE2020
A student rides a bicycle 2400 meters in four minutes to get to school. What is the student's speed?
Answer:
10 mls2
Explanation:
speed =distance /time
During a testing process, a worker in a factory mounts a bicycle wheel on a stationary stand and applies a tangential resistive force of 115 N to the tire's rim. The mass of the wheel is 1.80 kg and, for the purpose of this problem, assume that all of this mass is concentrated on the outside radius of the wheel. The diameter of the wheel is 50.0 cm. A chain passes over a sprocket that has a diameter of 8.50 cm. In order for the wheel to have an angular acceleration of 4.30 rad/s2, what force, in Newtons, must be applied to the chain
Answer:
The force is [tex] F_c = 789.03 \ N [/tex]
Explanation:
From the question we are told that
The tangential resistive force is [tex]F_t = 115 \ N[/tex]
The mass of the wheel is m = 1.80 kg
The diameter of the wheel is [tex]d = 50.0 cm = 0.5 \ m[/tex]
The diameter of the sprocket is [tex]d_c = 8.50 \ cm =0.085 \ m[/tex]
The angular acceleration considered is [tex]\alpha = 4.30\ rad/s^2[/tex]
Generally the radius of the wheel is
[tex]r = \frac{d}{2}[/tex]
=> [tex]r = \frac{0.5}{2}[/tex]
=> [tex]r = 0.25 \ m [/tex]
Generally the radius of the sprocket is
[tex]r_c = \frac{d_c}{2}[/tex]
=> [tex]r_c = \frac{0.085}{2}[/tex]
=> [tex]r_c = 0.0425 \ m [/tex]
Generally the moment of inertia of the wheel is mathematically represented as
[tex]I = m * r^2[/tex]
=> [tex]I = 1.80 * 0.25^2[/tex]
=> [tex]I = 1.1125 \ kg \cdot m^2[/tex]
Generally the torque experienced by the wheel due to the forces acting on it is mathematically represented as
[tex]\tau = F_c * r_c - F_t * r [/tex]
Here [tex]F_c[/tex] is the force acting on the sprocket
So
[tex]\tau = F_c * 0.0425 - 115 * 0.25 [/tex]
[tex]\tau = 0.0425F_c - 28.75 [/tex]
Generally the torques that will cause the wheel to move with [tex]\alpha = 4.30\ rad/s^2[/tex] is mathematically represented as
[tex]\tau = I * \alpha[/tex]
So
[tex] 0.0425F_c - 28.75 = I * \alpha [/tex]
[tex] 0.0425F_c - 28.75 = 1.1125 *4.30 [/tex]
[tex] 0.0425F_c - 28.75 = 1.1125 *4.30 [/tex]
[tex] F_c = 789.03 \ N [/tex]
Which type of force enables all the matter made up of atoms to exist?
A. Electromagnetic
B. Normal
C. Strong nuclear
D. Gravitational
Answer:
D
Explanation:
Answer:
The answer is C. Strong Nuclear
Explanation:
I took this test and it was correct!
Tutorial Exercise An unstable atomic nucleus of mass 1.83 10-26 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.03 10-27 kg, moves in the y direction with a speed of 6.00 106 m/s. Another particle, of mass 8.47 10-27 kg, moves in the x direction with a speed of 4.00 106 m/s. (a) Find the velocity of the third particle. (b) Find the total kinetic energy increase in the process
Answer:
A) v3 = -[6.29 × 10^(6)]j^ - [7.06 × 10^(6)]i^
B) K_total = 373.08 × 10^(-15) J
Explanation:
We are given;
Mass of unstable atomic nucleus; M = 1.83 × 10^(-26) kg
Mass of first particle; m1 = 5.03 × 10^(-27) kg
Speed of first particle in y-direction; v1 = (6 × 10^(6) m/s) j^
Mass of second particle; m2 = 8.47 × 10^(-27) kg
Speed of second particle in x - direction; v2 = (4 × 10^(6) m/s) i^
Now, we don't have the mass of the third particle but since we are told the unstable atomic nucleus disintegrates into 3 particles, thus;
M = m1 + m2 + m3
1.83 × 10^(-26) = (5.03 × 10^(-27)) + (8.47 × 10^(-27)) + m3
m3 = (1.83 × 10^(-26)) - (13.5 × 10^(-27))
m3 = 4.8 × 10^(-27) kg
A) Applying law of conservation of momentum, we have;
MV = (m1 × v1) + (m2 × v2) + (m3 × v3)
Now, the unstable atomic nucleus was at rest before disintegration, thus V = 0 m/s.
Thus, we now have;
0 = (m1 × v1) + (m2 × v2) + (m3 × v3)
We want to find the velocity of the third particle v3. Let's make it the subject of the formula;
v3 = [(m1 × v1) + (m2 × v2)]/(-m3)
Plugging in the relevant values, we have;
v3 = [(5.03 × 10^(-27) × 6 × 10^(6))j^ + (8.47 × 10^(-27) × 4 × 10^(6))i^]/(-4.8 × 10^(-27))
v3 = [(30.18 × 10^(-21))j^ + (33.88 × 10^(-21))i^]/(-4.8 × 10^(-27))
v3 = -[6.29 × 10^(6)]j^ - [7.06 × 10^(6)]i^
B) Formula for kinetic energy is;
K = ½mv²
Now,total kinetic energy is;
K_total = K1 + K2 + K3
K1 = ½ × 5.03 × 10^(-27) × (6 × 10^(6))²
K1 = 90.54 × 10^(-15) J
K2 = ½ × 8.47 × 10^(-27) × (4 × 10^(6))²
K2 = 67.76 × 10^(-15)
To find K3, let's first find the magnitude of v3 because it's still in vector form.
Thus;
v3 = √[(-6.29 × 10^(6))² + (-7.06 × 10^(6))²]
v3 = 9.46 × 10^(6) m/s
K3 = ½ × 4.8 × 10^(-27) × (9.46 × 10^(6))²
K3 = 214.78 × 10^(-15) J
K_total = (90.54 × 10^(-15)) + (67.76 × 10^(-15)) + (214.78 × 10^(-15))
K_total = 373.08 × 10^(-15) J
PLEASE SOLVE FAST!!! If the average American watches hours of TV every day , how many minutes will be spent in front of the TV by a person's 65th birthday? Solve using Dimensional Analysis.
Answer:
5694000 min
Explanation:
Let's suppose the average American watches 4 hours of TV every day. First, we will calculate how many minutes they watch per day. We will use the conversion factor 1 h = 60 min.
(4 h/day) × (60 min/1 h) = 240 min/day
They watch 240 minutes of TV per day. Now, let's calculate how many minutes they watch per year. We will use the conversion factor 1 year = 365 day.
240 min/day × (365 day/year) = 87600 min/year
They watch 87600 min/year. Finally, let's calculate how many minutes they spend watching TV in 65 years.
87600 min/year × 65 year = 5694000 min
A single living thing.
Answer:
What do you mean ma´am/sir?
Explanation:
To pull a nail out of a wood board a carpenter does 1000 J of work. The hammer he uses does 835 J of work. What is the efficiency of the hammer?
Answer:
83.5%
Explanation:
The speed of a wave on a rope is 50cm/s an its wave length is 10cm. What is its frequency
Taking into account the definition of wavelength, frecuency and propagation speed, the frequency is 5 Hz.
Wavelength (λ) is the distance between two consecutive points that are in the same state of vibration (the state of vibration is called phase). It is expressed in units of length (m).
Frequency (f) is the number of waves per unit of time and is normally expressed in Hertz (Hz) which is the number of waves per second.
The velocity of propagation is the speed with which the wave propagates in the medium. Relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation:
v = f * λ
In this case, you know:
v= 50 cm/sf= ?λ= 10 cmReplacing in the previous expression:
50 m/s= f× 10 cm
Solving;
f= 50 m/s÷ 10 cm
f= 5 Hz
Finally, the frequency is 5 Hz.
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brainly.com/question/2232652?referrer=searchResults brainly.com/question/7321084?referrer=searchResults brainly.com/question/14946166?referrer=searchResultsHelp pleaseee is this correct?
Answer:
Maybe.
Explanation:
***ECONOMICS***
A government that wants to increase its GDP would most likely take which
action?
A. Increase the money supply to make it easier to borrow money
Ο Ο
B. Decrease the money supply to slow the growth of inflation
C. Increase taxes on businesses that operate outside the country
O O
D. Decrease taxes on citizens who are poor or unemployed
Answer:
The correct answer is A. A government that wants to increase its GDP would most likely increase the money supply to make it easier to borrow money.
Explanation:
If the government wanted to increase its GDP, the most appropriate way to do so would be to increase the money supply both through issuance and through a reduction in bank reserve requirements, thereby increasing the circulating money in the hands of society.
This, in turn, would make citizens reinvest that money, increasing economic production and, therefore, the national GDP.
Answer: A. Increase the money supply to make it easier to borrow money
Explanation: I just took the test on Ap ex
Rhea kicks a soccer ball at 13km/h to Sean after kicking the ball the speed of the soccer ball from Rhea reference frame is 13km/h the speed of the soccer ball from Sean rrefrence frame is 13km the speed of the soccer ball from Sean's reference frame 22km/h.
Answer:
Sean is standing still, and Rhea is running toward Sean while kicking the ball.
Note: The question is in complete. The complete question is given below:
Rhea kicks a soccer ball at 13 km/h to Sean. After kicking the ball, the speed of the soccer ball from Rhea's reference frame is 13 km/h. The speed of the soccer ball from Sean's reference frame is 22 km/h. Which conclusion is best supported by the information?
Sean is standing still, and Rhea is running toward Sean while kicking the ball.
Rhea is standing still after kicking the ball, and Sean is running away from Rhea.
Both soccer players are standing still after the ball is kicked.
Both soccer players are running while the ball is in motion.
Explanation:
A reference frame is a position from which something is observed.
Since from the reference frame of Rhea, the ball is moving at a speed of 13 km/h after he kicks the ball at a speed of 13km/h whereas from the frame of reference of Sean, the ball is moving at a speed of 22km/h, there is a difference in the speed of the ball as seen from Rhea's and Sean's frame of reference of about 9 km/h. This difference can only be due to relative motion between the ball and Rhea.
Therefore, the best conclusion supported by the given information is that Sean is standing still, and Rhea is running toward Sean while kicking the ball.
Answer:
Sean is standing still, and Rhea is running toward Sean while kicking the ball.
Note: The question is in complete. The complete question is given below:
Rhea kicks a soccer ball at 13 km/h to Sean. After kicking the ball, the speed of the soccer ball from Rhea's reference frame is 13 km/h. The speed of the soccer ball from Sean's reference frame is 22 km/h. Which conclusion is best supported by the information?
Sean is standing still, and Rhea is running toward Sean while kicking the ball.
Rhea is standing still after kicking the ball, and Sean is running away from Rhea.
Both soccer players are standing still after the ball is kicked.
Both soccer players are running while the ball is in motion.
Explanation:
A reference frame is a position from which something is observed.
Since from the reference frame of Rhea, the ball is moving at a speed of 13 km/h after he kicks the ball at a speed of 13km/h whereas from the frame of reference of Sean, the ball is moving at a speed of 22km/h, there is a difference in the speed of the ball as seen from Rhea's and Sean's frame of reference of about 9 km/h. This difference can only be due to relative motion between the ball and Rhea.
Therefore, the best conclusion supported by the given information is that Sean is standing still, and Rhea is running toward Sean while kicking the ball.
Under the assumption that the beam is a rectangular cantilever beam that is free to vibrate, the theoretical first natural frequency of the beam in terms of the length, L, width, b, thickness, h, density, p, and Young's Modulus, E, in Hertz is given by:
fn= h/2πL^2 √E/rho
The density of steel used in the beam is 7800 kg/m^3, and its Young's Modulus is 210 GPa. You measure the dimensions of the clamped steel beam with a set of calipers and gather the following data:
L = 233.5 mm, b = 24.9 mm, h = 3.3 mm
The calipers used to measure the dimensions of beam have a resolution of 0.01 mm and therefore have an uncertainty of +0.005 mm.
Required:
a. What is the uncertainty of the natural frequency (in Hz) due to the uncertainty of the length measurement?
b. What is the uncertainty of the natural frequency (in Hz) due to the uncertainty of the width measurement?
c. What is the uncertainty of the natural frequency (in Hz) due to the uncertainty of the thickness measurement?
d. What is the total uncertainty of the natural frequency due to the beam measurements (in Hz)?
e. What is the theoretical first natural frequency of the beam including the measurement uncertainty?
Answer:
a) Δf = 0.7 n , e) f = (15.1 ± 0.7) 10³ Hz
Explanation:
This is an error about the uncertainty or error in the calculated quantities.
Let's work all the magnitudes is the SI system
The frequency of oscillation is
f = n / 2π L² √( E /ρ)
where n is an integer
Let's calculate the magnitude of the oscillation
f = n / 2π (0.2335)² √ (210 10⁹/7800)
f = n /0.34257 √ (26.923 10⁶)
f = n /0.34257 5.1887 10³
f = 15.1464 10³ n
a) We are asked for the uncertainty of the frequency (Df)
Δf = | df / dL | ΔL + df /dE ΔE + df /dρ Δρ
in this case no error is indicated in Young's modulus and density, so we will consider them exact
ΔE = Δρ = 0
Δf = df /dL ΔL
df = n / 2π √E /ρ | -2 / L³ | ΔL
df = n / 2π 5.1887 10³ | 2 / 0.2335³) 0.005 10⁻³
df = n 0.649
Absolute deviations must be given with a single significant figure
Δf = 0.7 n
b, c) The uncertainty with the width and thickness of the canteliver is associated with the density
In your expression there is no specific dependency so the uncertainty should be zero
The exact equation for the natural nodes is
f = n / 2π L² √ (E e /ρA)
where A is the area of the cantilever and its thickness,
In this case, they must perform the derivatives, calculate and approximate a significant figure
Δf = | df / dL | ΔL + df /de Δe + df /dA ΔA
Δf = 0.7 n + n 2π L² √(E/ρ A) | ½ 1/√e | Δe
+ n / 2π L² √(Ee /ρ) | 3/2 1√A23 |
the area is
A = b h
A = 24.9 3.3 10⁻⁶
A = 82.17 10⁻⁶ m²
DA = dA /db ΔB + dA /dh Δh
dA = h Δb + b Δh
dA = 3.3 10⁻³ 0.005 10⁻³ + 24.9 10⁻³ 0.005 10⁻³
dA = (3.3 + 24.9) 0.005 10⁻⁶
dA = 1.4 10⁻⁷ m²
let's calculate each term
A ’= n / 2π L² √a (E/ρ A) | ½ 1 /√ e | Δe
A ’= n/ 2π L² √ (E /ρ) | ½ 1 / (√e/√ A) |Δe
A ’= 15.1464 10³ n ½ 1 / [√ (24.9 10⁻³)/ √ (81.17 10⁻⁶)] 0.005 10⁻³
A '= 0.0266 n
A ’= 2.66 10⁻² n
A ’’ = n / 2π L² √ (E e /ρ) | 3/2 1 /√A³ |
A ’’ = n / 2π L² √(E /ρ) √ e | 3/2 1 /√ A³ | ΔA
A ’’ = n 15.1464 10³ 3/2 √ (24.9 10⁻³) /√ (82.17 10⁻⁶) 3 1.4 10⁻⁷
A ’’ = n 15.1464 1.5 1.5779 / 744.85 1.4 10⁴
A ’’ = 6,738 10²
we write the equation of uncertainty
Δf = n (0.649 + 2.66 10⁻² + 6.738 10²)
The uncertainty due to thickness is
Δf = 3 10⁻² n
The uncertainty regarding the area, note that this magnitude should be measured with much greater precision, specifically the height since the errors of the width are very small
Δf = 7 10² n
d) Δf = 7 10² n
e) the natural frequency n = 1
f = (15.1 ± 0.7) 10³ Hz
