given the expression yc = 140 mv(1 - e - t>2 ms) a. determine yc at t = 1 ms. b. determine yc at t = 20 ms. c. find the time t for yc to reach 100 mv. d. find the time t for yc to reach 138 mv

Answers

Answer 1

In the expression :  a.  yc at t = 1 ms is approximately 65.9 mV.

b. yc at t = 20 ms is approximately 138.1 mV.

c. it takes approximately 3.03 ms for yc to reach 100 mV.

d. it takes approximately 44.7 ms for yc to reach 138 mV.

Given: yc = 140 mV(1 - e^(-t/2 ms))

a. To find yc at t = 1 ms, we substitute t = 1 ms into the equation:

yc = 140 mV(1 - e^(-1/2)) ≈ 65.9 mV

b. To find yc at t = 20 ms, we substitute t = 20 ms into the equation:

yc = 140 mV(1 - e^(-20/2)) ≈ 138.1 mV

c. To find the time t for yc to reach 100 mV, we can set yc = 100 mV and solve for t:

100 mV = 140 mV(1 - e^(-t/2))

Simplifying the equation, we get:

1 - e^(-t/2) = 5/7

e^(-t/2) = 2/7

Taking the natural logarithm of both sides, we get:

-t/2 = ln(2/7)

Solving for t, we get:

t ≈ 3.03 ms

d. To find the time t for yc to reach 138 mV, we can set yc = 138 mV and solve for t:

138 mV = 140 mV(1 - e^(-t/2))

Simplifying the equation, we get:

1 - e^(-t/2) = 69/700

e^(-t/2) = 631/700

Taking the natural logarithm of both sides, we get:

-t/2 = ln(631/700)

Solving for t, we get:

t ≈ 44.7 ms

For more question on expression click on

https://brainly.com/question/13449902

#SPJ11

Answer 2

Yc at t = 1 ms is 55.02 mV.yc at t = 20 ms is 136.97 mV. the time t for yc to reach 100 mV is approximately 2.04 ms.the time t for yc to reach 138 mV is approximately 0.217 ms.

a. To determine yc at t = 1 ms, substitute t = 1 ms into the given expression:

[tex]yc = 140 mV(1 - e^{(-t/2 ms)})[/tex]

[tex]yc = 140 mV(1 - e^{(-1/2)})[/tex]

yc = 140 mV(0.393)

yc = 55.02 mV

Therefore, yc at t = 1 ms is 55.02 mV.

b. To determine yc at t = 20 ms, substitute t = 20 ms into the given expression:

[tex]yc = 140 mV(1 - e^{(-t/2 ms)})[/tex]

[tex]yc = 140 mV(1 - e^{(-20/2)})[/tex]

[tex]yc = 140 mV(1 - e^{(-10)})[/tex]

yc = 136.97 mV

Therefore, yc at t = 20 ms is 136.97 mV.

c. To find the time t for yc to reach 100 mV, we need to solve the given equation for t. Rearranging the equation, we get:

[tex](yc/140 mV) = 1 - e^{(-t/2 ms)[/tex]

[tex]e^{(-t/2 ms)} = 1 - (yc/140 mV)[/tex]

-t/2 ms = ln[1 - (yc/140 mV)]

t = -2 ms * ln[1 - (yc/140 mV)]

Substituting yc = 100 mV into this expression, we get:

t = -2 ms * ln[1 - (100 mV/140 mV)]

t = 2.04 ms

Therefore, the time t for yc to reach 100 mV is approximately 2.04 ms.

d. To find the time t for yc to reach 138 mV, we again need to solve the given equation for t. Rearranging the equation, we get:

[tex](yc/140 mV) = 1 - e^{(-t/2 ms)[/tex]

[tex]e^{(-t/2 ms) = 1 - (yc/140 mV)[/tex]

-t/2 ms = ln[1 - (yc/140 mV)]

t = -2 ms * ln[1 - (yc/140 mV)]

Substituting yc = 138 mV into this expression, we get:

t = -2 ms * ln[1 - (138 mV/140 mV)]

t = 0.217 ms

Therefore, the time t for yc to reach 138 mV is approximately 0.217 ms.

Learn more about time here:

https://brainly.com/question/31732120

#SPJ11


Related Questions

why is the speed of conduction through a reflex arc slower than the speed of conduction of an action potential along an axon?

Answers

The speed of conduction through a reflex arc is slower than the speed of conduction of an action potential along an axon because the reflex arc involves additional synaptic connections, which introduce delays in signal transmission.

The speed of conduction through a reflex arc is slower than the speed of conduction of an action potential along an axon due to additional synaptic connections involved in the reflex arc. In a reflex arc, the sensory neuron carries the signal from the sensory receptor to the spinal cord, where it synapses with an interneuron before reaching the motor neuron. This synaptic transmission introduces a delay as the chemical neurotransmitters need to cross the synaptic cleft. In contrast, in the conduction of an action potential along an axon, there are no synaptic connections involved, allowing for a faster propagation of the electrical signal along the length of the axon.

Learn more about reflex arc here:

https://brainly.com/question/894334

#SPJ11

A spring with a spring constant of 30.0 N/m is compressed 5.00 m. What is the force that the spring would apply? a) 6.00N. b) 150.N. c) 35.0N. d) 25.0N.

Answers

The force applied to spring of spring constant 30 N/m is 150 N.

What is force?

Force is the product of mass and acceleration. Force is a vector quantity and the S.I unit of force is Newton (N).

To caculate the force that is applied on the spring, we use the formula below

Formula:

F = ke...................... Equation 1

Where:

F = Force applied to the springk = Spring constant of the springe = Extension

From the question,

Given:

k = 30 N/me = 5 m

Substitute these values into equation 1

F = 30×5F = 150 N

Hence, the right option is b) 150 N.

Learn more about force here: https://brainly.com/question/25573309

#SPJ1

A string with both ends held fixed is vibrating in its third harmonic. The waves have a speed of 192 m/s and a frequency of 210 Hz . The amplitude of the standing wave at an antinode is 0.400 cm .
Part A
Calculate the amplitude at point on the string a distance of 25.0 cm from the left-hand end of the string.
Part B
How much time does it take the string to go from its largest upward displacement to its largest downward displacement at this point?
Part C
Calculate the maximum transverse velocity of the string at this point.
Part D
Calculate the maximum transverse acceleration of the string at this point

Answers

Part A:
The amplitude at a specific point on a vibrating string depends on its position within the standing wave pattern. In the third harmonic, there are three antinodes and two nodes between the fixed ends. As the distance from the left-hand end is 25.0 cm, this point is exactly at the first node, where the string doesn't oscillate. Therefore, the amplitude at this point is 0 cm.

Part B:
The time it takes for the string to go from its largest upward displacement to its largest downward displacement at a specific point is half of its period (T/2). The period can be calculated using the formula T = 1/frequency. With a frequency of 210 Hz, the period is:

T = 1/210 ≈ 0.00476 s

Half the period is 0.00476/2 ≈ 0.00238 s.

Part C:
At the given point, the amplitude is 0, so the maximum transverse velocity will also be 0 m/s.

Part D:
Similarly, the maximum transverse acceleration at this point will also be 0 m/s², as the amplitude is 0 and there is no oscillation.

Learn more about wave here:

https://brainly.com/question/30783512

#SPJ11

The car has an initial speed v0 = 20 m/s. It increases its speed along the circular track at s = 0, at=(0. 6s)m/s2 , where s is in meters

Answers

The car's initial speed is 20 m/s, and its speed increases at a rate of 0.6s m/s² along the circular track.

The car's initial speed, v0, is given as 20 m/s. Along the circular track, its speed increases with time, denoted as s. The rate of this increase is given as at = 0.6s m/s², where s represents the distance traveled on the track in meters. As time passes, the speed of the car progressively accelerates according to the equation. For example, if s = 5 meters, the rate of speed increase would be 0.6 * 5 = 3 m/s². This equation describes the relationship between the distance traveled and the corresponding acceleration, determining how the car's speed evolves along the circular track.

learn more about speed here:

https://brainly.com/question/13262927

#SPJ11

A 95-kg person climbs some stairs at a constant rate, gaining 2.5 meters in height.Randomized Variables: m = 95 kg, h = 2.5 hFind the work done by the person, in joules, to accomplish this task.

Answers

The person has done 2327.5 joules of work to accomplish the task of climbing the stairs.

To find the work done by the person, we need to use the formula W = Fd, where W is the work done, F is the force applied, and d is the distance moved in the direction of the force. In this case, the force applied is the weight of the person, which can be calculated using the formula F = mg, where m is the mass of the person and g is the acceleration due to gravity (9.8 m/s^2).
So, the force applied is F = 95 kg x 9.8 m/s^2 = 931 N. The distance moved in the direction of the force is the height gained, which is 2.5 meters. Therefore, the work done by the person is W = Fd = 931 N x 2.5 m = 2327.5 joules.
The work done by the person to climb the stairs is 2327.5 joules. Work is defined as the energy transferred when a force is applied to an object and it moves in the direction of the force. In this case, the force applied is the weight of the person, which is a result of the gravitational attraction between the person and the Earth. As the person climbs the stairs, they do work against the force of gravity to lift their body to a higher elevation. This work is calculated by multiplying the force applied (weight) by the distance moved in the direction of the force (height gained). The unit of work is the joule, which is defined as the amount of work done when a force of one newton is applied over a distance of one meter. In this scenario, the person has done 2327.5 joules of work to accomplish the task of climbing the stairs.

To know more about Work Done visit:
https://brainly.com/question/31655489
#SPJ11

If 2200 J of heat are added to a 190 - g object, its temperature increases by 12 ∘C .
A) What is the heat capacity of this object?
B) What is the object's specific heat?

Answers

A) The object's heat capacity is 0.18 kJ/°C.

B) The specific heat of the item is 0.96 kJ/kgK.

A) The following formula may be used to calculate heat capacity:

  Heat Energy / Temperature Change = Heat Capacity

  Given: 2200 J of heat energy

         Change in temperature = 12 °C

  2200 J / 12 °C = 183.33 J/°C Heat Capacity

  Converting from degrees Celsius to kilojoules:

  Heat Capacity = 183.33 J/°C multiplied by (1 kJ/1000 J) = 0.18333 kJ/°C

  As a result, the object's heat capacity is roughly 0.18 kJ/°C.

B) The formula for specific heat is as follows: Specific Heat = Heat Capacity / Mass

  Weight = 190 g = 0.19 kilogramme

  Specific Heat = 0.947 kJ/kgK = 0.18 kJ/°C / 0.19 kg

  As a result, the specific heat of the item is roughly 0.96 kJ/kgK.

For more such questions on heat capacity , click on:

https://brainly.com/question/31963763

#SPJ11

a small rocket burns a mass 0.0550 kg of fuel per second, ejecting it as a gas with a velocity relative to the rocket of magnitude 1650 m/s.
A.) What is the thrust of the rocket? (Answer: 889 N)
B.) What is the rockets change in velocity after it has burned 355kg , of fuel if its total initial mass is 1830kg ?
C.) What is the rockets velocity after 171 s, if it had an initial velocity of 1028 m/s ?

Answers

A) The thrust of the rocket is 889 N.
B) The rocket's change in velocity after burning 355 kg of fuel is 192.5 m/s.
C) The rocket's velocity after 171 s is 1239.7 m/s.


A) Thrust = mass flow rate * exhaust velocity = 0.0550 kg/s * 1650 m/s = 889 N


B) Use Tsiolkovsky rocket equation: Δv = ve * ln(m0 / m1), where Δv is change in velocity, ve is exhaust velocity, m0 is initial mass, and m1 is final mass. Δv = 1650 m/s * ln((1830 kg) / (1830 kg - 355 kg)) = 192.5 m/s


C) Calculate mass after 171 s: m = 1830 kg - (0.0550 kg/s * 171 s) = 1625.45 kg. Apply Tsiolkovsky rocket equation: Δv = 1650 m/s * ln((1830 kg) / (1625.45 kg)) = 211.7 m/s. Final velocity = initial velocity + change in velocity = 1028 m/s + 211.7 m/s = 1239.7 m/s.

To know more about exhaust velocity click on below link:

https://brainly.com/question/31322519#

#SPJ11

Suppose a static charge of 0.22 μC moves from your finger to a metal doorknob in 0.95 ms. What is the current, in amperes?p

Answers

We can use the formula for electric charge and current to calculate the current:

I = Q / t

where I is the current, Q is the charge, and t is the time.

In this problem, the charge Q is given as 0.22 μC, and the time t is given as 0.95 ms. However, we need to convert the charge to units of coulombs (C) before we can use the formula:

0.22 μC = 0.22 × 10^-6 C

Substituting the known values into the formula:

I = (0.22 × 10^-6 C) / (0.95 × 10^-3 s) = 0.23 A

Therefore, the current is 0.23 amperes (A).

To know more about refer electric charge here

brainly.com/question/9194793#

#SPJ11

the number of lines that connect opposite corners of a cube through its center is:

Answers

There are 4 lines that connect opposite corners of a cube through its center.

To find the number of lines that connect opposite corners of a cube through its center, we need to visualize the cube and draw a line connecting two opposite corners that pass through the center of the cube.

We can see that there are two diagonals passing through the center of the cube. Each diagonal connects two opposite corners of the cube. Therefore, the total number of lines that connect opposite corners of the cube through its center is equal to the number of diagonals, which is 4.

In summary, the number of lines that connect opposite corners of a cube through its center is 4.

To know more about center, visit;

https://brainly.com/question/28021242

#SPJ11

The coefficient of expansion of a certain type of steel is 0.000012 per C°. The coefficient of volume expansion is:

Answers

The coefficient of expansion of a steel is 0.000012 per C°. The coefficient of volume expansion (β) can be calculated by multiplying the linear expansion coefficient by three.

β is a measure of how much the volume of a material changes with temperature. It is related to the coefficient of linear expansion (α) by the equation β = 3α.

For the given type of steel, α = 0.000012 per C°. Therefore, β = 3α = 0.000036 per C°. This means that for every 1°C increase in temperature, the volume of this steel will increase by 0.000036 times its original volume.

It's worth noting that the coefficient of volume expansion may not be constant over a wide temperature range. In fact, for some materials, the coefficient may change significantly with temperature. Therefore, it's important to consider the temperature range of interest when selecting a material for a particular application, and to take into account any changes in volume that may occur due to temperature fluctuations.

To know more about the coefficient of expansion refer here :

https://brainly.com/question/14780533#

#SPJ11

The deer stops at a lake for a drink of water and then starts hopping again to the south. Each second the deer velocity increases 2. 5m/s what is the deer velocity after 5s

Answers

The deer's velocity after 5 seconds of hopping to the south will be 12.5 m/s. The initial velocity of the deer is not provided in the question, so we assume it to be zero.

Since the deer's velocity increases by 2.5 m/s each second, after 1 second, the velocity will be 2.5 m/s, after 2 seconds it will be 5 m/s, and so on. We can calculate the deer's velocity after 5 seconds by multiplying the rate of increase (2.5 m/s) by the time (5 seconds). Hence, the deer's velocity after 5 seconds will be [tex]\(2.5 \times 5 = 12.5\)[/tex] m/s.

In this case, we use the formula for uniformly accelerated motion: [tex]\(v = u + at\)[/tex], where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. As the deer's initial velocity is assumed to be zero, the equation simplifies to v = at. Plugging in the given values of acceleration [tex](2.5 m/s\(^2\))[/tex] and time (5 seconds), we get [tex]\(v = 2.5 \times 5 = 12.5\) m/s[/tex]. Therefore, the deer's velocity after 5 seconds is 12.5 m/s.

To learn more about velocity refer:

https://brainly.com/question/29110645

#SPJ11

a 10-kg object is hanging by a very light wire in an elevator that is traveling upward. the tension in the rope is measured to be 88 n. what are the magnitude and direction of the acceleration of the elevator?

Answers

The direction of the acceleration of the elevator is upward.

To determine the magnitude and direction of the acceleration of the elevator, we need to use Newton's second law of motion, which states that force equals mass times acceleration (F=ma).

The tension in the rope, measured to be 88 N, is the force acting on the object. Since the object has a mass of 10 kg, we can use F=ma to calculate the acceleration of the elevator.

88 N = 10 kg x a

a = 8.8 m/s^2

So the magnitude of the acceleration of the elevator is 8.8 m/s^2.

To determine the direction of the acceleration, we need to consider the direction of the forces acting on the object. In this case, the force of gravity is acting downward on the object, while the tension in the rope is acting upward. Since the tension in the rope is greater than the force of gravity, the net force on the object is upward.

Learn more about acceleration here:-

https://brainly.com/question/12550364

#SPJ11

Mass of box is 1.5kg starts with an initial velocity of 3m/s in the direction opposite ot that of the force. It is again acted on by a force of 4N to the right and again ends at a point 3 meters to the right of where is started. What is the work done on the box ? I got this to be 12 Joules . 2) What is the final kinetic energy of the box ?

Answers

The final kinetic energy of the box is 12 Joules.

To calculate the work done on the box, we can use the formula:

Work = force x distance x cos(theta)

where theta is the angle between the force and the direction of motion. In this case, the force is 4N to the right and the displacement is also to the right, so theta is 0 degrees and cos(theta) is 1. Therefore:

Work = 4N x 3m x 1
Work = 12 Joules

So, the work done on the box is 12 Joules.

To find the final kinetic energy of the box, we can use the formula:

Kinetic energy = 0.5 x mass x velocity^2

We know that the mass of the box is 1.5kg and the initial velocity is 3m/s in the opposite direction. When the force is applied to the right, the box starts moving to the right and gains speed. We don't know the final velocity, but we can use the fact that the box ends up 3 meters to the right of where it started. If we assume that the force was applied over this entire distance, we can use the work-energy principle:

Work done by force = change in kinetic energy

We already calculated that the work done by the force is 12 Joules. We can assume that this work is used to increase the kinetic energy of the box. So:

12 Joules = final kinetic energy - initial kinetic energy

The initial kinetic energy is 0, since the box starts from rest. Solving for the final kinetic energy:

final kinetic energy = 12 Joules

So, the final kinetic energy of the box is 12 Joules.

Learn more about kinetic energy

brainly.com/question/26472013

#SPJ11

Electrons are accelerated through a potential difference of 750 kV, so that their kinetic energy is 7.50 x 105 eV.
A) What is the ratio of the speed v of an electron having this energy to the speed of light, c?
b) What would the speed be if it were computed from the principles of classical mechanics?

Answers

1.31 x 10^20 m/s^2  is the ratio of the speed v of an electron having this energy to the speed of light, c and 1.13 x 10^8 m/s would the speed be if it were computed from the principles of classical mechanics.

To determine the ratio of the speed v of an electron with kinetic energy of 7.50 x 105 eV to the speed of light, c, we can use the equation E = 1/2mv^2, where E is the kinetic energy of the electron, m is the mass of the electron, and v is its velocity.

Rearranging this equation, we get v = sqrt(2E/m).

Substituting the values, we get v = sqrt((2 * 7.50 x 10^5 eV) / (9.11 x 10^-31 kg)), which is approximately 1.63 x 10^8 m/s.

The speed of light is 2.99 x 10^8 m/s.

Therefore, the ratio of the electron's speed to the speed of light is 1.63 x 10^8 m/s ÷ 2.99 x 10^8 m/s = 0.544.

To compute the speed of the electron using classical mechanics,

we can use the equation F = ma, where F is the force acting on the electron,

m is its mass, and

a is its acceleration.

The force on the electron is given by F = eE, where e is the charge on the electron and E is the electric field.

Thus, the acceleration of the electron is a = eE/m.

Substituting the values, we get

a = (1.6 x 10^-19 C) (750 x 10^3 V/m) / (9.11 x 10^-31 kg)

= 1.31 x 10^20 m/s^2.

Using the equation v = at, where t is the time taken for the electron to traverse the potential difference,

we get

v = a(sqrt(2qV/m))/a

= sqrt(2qV/m)

= sqrt((2 x 1.6 x 10^-19 C x 750 x 10^3 V)/(9.11 x 10^-31 kg)),

which is approximately 1.13 x 10^8 m/s.

To know more about Kinetic energy visit:

https://brainly.com/question/26472013

#SPJ11

extends by when a force of 50N was used to stretch it from it's end.

Answers

To calculate the stress and strain on the wire, we can use the following formulas:

a) Stress (σ) = Force (F) / Area (A)

b) Strain (ε) = Change in length (ΔL) / Original length (L)

Given information:

Length of the wire (L) = 5 m

Diameter of the wire (d) = 2 mm = 0.002 m

Change in length (ΔL) = 0.25 mm = 0.00025 m

Force (F) = 50 N

First, let's calculate the cross-sectional area of the wire using the diameter:

Area (A) = π * (d/2)^2

A = π * (0.002/2)^2

A ≈ 3.142 * (0.001)^2

A ≈ 3.142 * 0.000001

A ≈ 0.000003142 m^2

Now, we can calculate the stress and strain:

a) Stress (σ) = F / A

σ = 50 / 0.000003142

σ ≈ 15,930,285.25 Pa

b) Strain (ε) = ΔL / L

ε = 0.00025 / 5

ε = 0.00005

So, the answers are:

a) Stress on the wire ≈ 15,930,285.25 Pa

b) Strain on the wire = 0.00005

Please note that the stress is in pascals (Pa) and the strain is a unitless quantity.

Kindly Heart and 5 Star this answer and especially don't forgot to BRAINLIEST, thanks!

measurements of a certain isotope tell you that the decay rate decreases from 8253 decays/minute to 3008 decays/minute over a period of 5.00 days. What is the half-life (T1/2) of this isotope?

Answers

The half-life of the isotope is 2.37 days.

The half-life (T1/2) of the isotope can be calculated using the formula T1/2 = (ln 2) / λ, where λ is the decay constant. First, we need to find the decay constant using the given information.

The change in the decay rate over 5.00 days can be represented as (8253 - 3008) = 5245 decays.

Using the formula N = [tex]N0e^{(- \Lambda t)[/tex], where N is the number of remaining atoms, N0 is the initial number of atoms, and t is the time, we can find λ as ln(8253/3008) / 5.00 days = 0.2701 per day.

Substituting this value into the half-life formula gives T1/2 = (ln 2) / 0.2701 per day = 2.37 days.

Therefore, the half-life of the isotope is 2.37 days.

For more such questions on isotope, click on:

https://brainly.com/question/30548132

#SPJ11

the current in a series circuit is 13.6 a. when an additional 8.66-ω resistor is inserted in series, the current drops to 10.3 a. what is the resistance in the original circuit?

Answers

The resistance in the original circuit is 21.66 Ω.

To find the resistance in the original circuit, we can use Ohm's Law (V = I * R) and the concept of series circuits.

Step 1: Calculate the voltage (V) in the circuit before adding the new resistor.
V_original = I_original * R_original

Step 2: Calculate the voltage (V) after adding the new resistor.
V_new = I_new * (R_original + R_added)

Since the voltage across the circuit remains constant, we can set V_original equal to V_new:

I_original * R_original = I_new * (R_original + R_added)

Now, we can plug in the given values and solve for R_original:

(13.6 A) * R_original = (10.3 A) * (R_original + 8.66 Ω)

After solving for R_original, we get:

R_original = 21.66 Ω

So, the resistance in the original circuit is 21.66 Ω.

To learn more about circuit, refer below:

https://brainly.com/question/27206933

#SPJ11

a plane electromagnetic wave is generated due to the initiation of current along the x direction in a current sheet in the zx plane at y=0. a steady flow current is switched on at t=0

Answers

An electromagnetic wave is generated by the initiation of current in a current sheet along the x direction in the zx plane at y=0. At t=0, a steady flow current is switched on.

How is an electromagnetic wave generated in a current sheet with a steady flow current switched on at t=0?

When a current is initiated in a current sheet along the x direction in the zx plane at y=0, it generates an electromagnetic wave. This wave propagates in space and is characterized by an electric field and a magnetic field that are perpendicular to each other and also perpendicular to the direction of propagation.

At t=0, a steady flow current is switched on, which adds to the existing current in the current sheet. This causes a perturbation in the current, which in turn leads to the emission of radiation in the form of electromagnetic waves.

The electromagnetic wave generated by the current sheet can be described mathematically using Maxwell's equations. These equations relate the electric and magnetic fields to the sources that generate them, such as charges and currents. In the case of the current sheet, the current is the source of the electromagnetic waves.

The propagation of electromagnetic waves has many practical applications, such as in wireless communication, radar, and satellite communication. Understanding the physics of electromagnetic waves is crucial in the design and optimization of these systems.

Learn more about Electromagnetic wave

brainly.com/question/29774932

#SPJ11

A tiny spring, with a spring constant of 1.20 N/m, will be stretched to what displacement by a 0.0050-N force?
a)7.2 mm
b)9.4 mm
c)4.2 mm
d)6.0 mm

Answers

The displacement by 0.0050-N force is 4.2 mm.

Hooke's law states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position. The proportionality constant is called the spring constant and is denoted by k. Mathematically, Hooke's law can be expressed as F = -kx, where F is the force applied to the spring, x is the displacement of the spring from its equilibrium position, and the negative sign indicates that the force exerted by the spring is in the opposite direction to the displacement.

Rearrange the formula to solve for x:

x = F / k

Substitute the values:

x = 0.0050 N / 1.20 N/m

x = 0.0041667 m

Convert meters to millimeters:

x = 0.0041667 m * 1000 = 4.1667 mm

Rounded to one decimal place,

The correct answer is c) 4.2 mm.

To know more about the displacement, click here;

https://brainly.com/question/30087445

#SPJ11

how to find the depth of an object floating given the dnsity of the liquid and the density of the fluid

Answers

Identify the object's density. Continue to the next step if you know the object's density. If not, you might need to compute it using the object's mass and volume.

Find out the fluid's density. It is important to understand the fluid's density in which the object is floating. Verify the densities. An object will float if its density is lower than that of the fluid. In the case of equal densities, the object will float in a neutral manner.

According to Archimedes' principle, an object's buoyant force is equal to the weight of the fluid it is dislodging. Apply this idea to determine the buoyant force.

To know more about object's density, here

brainly.com/question/6838128

#SPJ4

a 3.00 m organ pipe is open at both ends and contains air. the speed of sound in air is 331 m/s. what is the frequency of the lowest frequency mode?

Answers

The frequency of the lowest frequency mode in a 3.00 m organ pipe that is open at both ends is 55.2 Hz.


The lowest frequency mode of a 3.00 m organ pipe open at both ends can be determined using the formula for fundamental frequency (f) of a tube open at both ends:

f = v / (2 * L)

where:
f = fundamental frequency (Hz)
v = speed of sound in air (331 m/s)
L = length of the pipe (3.00 m)

Using the given values, we can calculate the frequency:

f = 331 m/s / (2 * 3.00 m)
f = 331 m/s / 6.00 m
f = 55.17 Hz

Therefore, the frequency of the lowest frequency mode for a 3.00 m organ pipe open at both ends is approximately 55.17 Hz.

Learn more about frequency here:-

https://brainly.com/question/30783512

#SPJ11

A 3-phase, 230 V, 60 Hz, 1176 rpm, Y-connected induction motor draws 3105 W and 42.2 A in a no-load test. The
stator resistance per phase is 15 mΩ. The total power drawn at full load is 82 kW and the current is 248 A.
Determine:
(a) The rotational losses
(b) The full load power factor
(c) The power transmitted to the rotor at full load
(d) The rotor I2R losses at full load
(e) The output power and the efficiency at full load

Answers

The rotational losses of the motor are 27,896.39 W, the full load power factor is 0.891, and the power transmitted to the rotor at full load is 91.57 kW. The rotor I2R losses at full load are 275.18 W. The output power at full load is 78.44 kW, and the efficiency at full load is 95.3%.

(a) The rotational losses can be calculated as follows:

No-load current = 42.2 A

No-load power = 3 x 230 V x 42.2 A x 0.9 (assumed power factor of 0.9 for no-load test) = 27,904.4 W

Stator copper losses at no-load = [tex]$3 \times (0.0422)^2 \times 15 \text{ m}\Omega$[/tex] = 8.01 W

Rotational losses = No-load power - Stator copper losses = 27,904.4 W - 8.01 W = 27,896.39 W

Therefore, the rotational losses are 27,896.39 W.

(b) The full load power factor can be calculated as follows:

Total power is drawn at full load = 82 kW

Full load current = 248 A

Output power = 3 x 230 V x 248 A x Power factor

Power factor = Output power / (3 x 230 V x 248 A) = 0.891

Therefore, the full load power factor is 0.891.

(c) The power transmitted to the rotor at full load can be calculated as follows:

Slip at full load = (1176 - 1176 x 0.891) / 1176 = 0.109

Output power at full load = 82 kW

Power transmitted to the rotor = Output power / (1 - Slip) = 91.57 kW

Therefore, the power transmitted to the rotor at full load is 91.57 kW.

(d) The rotor I2R losses at full load can be calculated as follows:

Rotor resistance per phase = Stator resistance per phase = 15 mΩ

Rotor I2R losses = [tex]$3 \times (248)^2 \times 15 \text{ m}\Omega$[/tex] = 275.18 W

Therefore, the rotor I2R losses at full load are 275.18 W.

(e) The output power and the efficiency at full load can be calculated as follows:

Output power can be calculated using the torque equation and the slip equation:

Torque at full load = (3 x 230 V x 248 A x 0.891 x (1 - 0.109)) / (2 x π x 60 Hz) = 355.5 Nm

Motor speed at full load = 1176 x (1 - 0.109) = 1050.8 rpm

Output power at full load = Torque x 2 x π x Motor speed / 60 = 78.44 kW

Efficiency at full load = Output power / Input power

Input power at full load = 3 x 230 V x 248 A x 0.891 = 82.3 kW

Therefore, the efficiency at full load is:

Efficiency = 78.44 kW / 82.3 kW = 0.953 or 95.3%

Therefore, the output power at full load is 78.44 kW and the efficiency at full load is 95.3%.

To learn more about power factor

https://brainly.com/question/31325309

#SPJ4

The potential energy of a hydrogen atom in a particular Bohr orbit is U = -1.20 * 10^-19 J. Calculate the potential energy of the atom if it moves up to the next higher Bohr orbit.

Answers

In the Bohr model of the hydrogen atom, the potential energy of an electron in a particular orbit is given by the formula:

U = - (2.18 * 10^-18 J) / n^2

Where U is the potential energy, n is the principal quantum number representing the orbit.

To calculate the potential energy of the atom when it moves up to the next higher Bohr orbit, we need to consider the change in the principal quantum number.

Let's assume the initial orbit has a principal quantum number of n1, and the next higher orbit has a principal quantum number of n2 = n1 + 1.

The potential energy in the initial orbit is given as U1 = -1.20 * 10^-19 J.

Substituting these values into the formula, we have:

U1 = - (2.18 * 10^-18 J) / n1^2

U2 = - (2.18 * 10^-18 J) / (n1 + 1)^2

To find the potential energy in the next higher orbit, we can calculate U2 as:

U2 = - (2.18 * 10^-18 J) / (n1 + 1)^2

Now, we can substitute the given values and calculate U2:

U2 = - (2.18 * 10^-18 J) / (n1 + 1)^2

U2 = - (2.18 * 10^-18 J) / (n1^2 + 2n1 + 1)

Please provide the value of n1 so that we can calculate the potential energy in the next higher Bohr orbit.

Learn more about **Bohr model** and **potential energy** of hydrogen atoms here:

https://brainly.com/question/30401859?referrer=searchResults

#SPJ11

An aircraft engine takes in an amount 8900 J of heat and discards an amount 6400 J each cycle. What is the mechanical work output of the engine during one cycle? What is the thermal efficiency of the engine?

Answers

Therefore, the thermal efficiency of the engine is 28.1%. This means that only 28.1% of the energy input to the engine is converted into useful work, while the remaining 71.9% is lost as waste heat.

The mechanical work output of the engine during one cycle can be found using the First Law of Thermodynamics, which states that the energy input to a system must equal the energy output plus any increase in internal energy. In this case, the energy input is 8900 J, and the energy output is 6400 J, so the mechanical work output can be found by

Mechanical work output = Energy input - Energy output
Mechanical work output = 8900 J - 6400 J
Mechanical work output = 2500 J
Therefore, the mechanical work output of the engine during one cycle is 2500 J.
The thermal efficiency of the engine can be found using the equation:
Thermal efficiency = (Mechanical work output / Energy input) x 100%
Plugging in the values we just calculated, we get:
Thermal efficiency = (2500 J / 8900 J) x 100%
Thermal efficiency = 28.1%
Therefore, the thermal efficiency of the engine is 28.1%. This means that only 28.1% of the energy input to the engine is converted into useful work, while the remaining 71.9% is lost as waste heat.

To know more about thermal efficiency visit:-

https://brainly.com/question/13677263

#SPJ11

A current-carrying loop of wire is placed in a uniform b-field as shown. If the direction of the current of the loop is as indicated, what will the loop do?.

Answers

A current-carrying loop of wire is placed in a uniform b-field as shown. If the direction of the current of the loop is as indicated, the loop it will experience a torque that causes it to rotate.

When a current-carrying loop is placed in a uniform magnetic field, it will experience a torque that causes it to rotate. The direction of the rotation can be determined using the right-hand rule: if you point your right thumb in the direction of the current and your fingers in the direction of the magnetic field, the direction of rotation will be perpendicular to both the thumb and fingers.

To explain further, the torque on a current-carrying loop in a magnetic field is given by τ = NIABsinθ, where N is the number of turns in the loop, I is the current, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the plane of the loop and the direction of the magnetic field. The amount of rotation will depend on the strength of the magnetic field and the current in the loop, as well as the shape and size of the loop itself. However, the direction of rotation will always be the same, given by the right-hand rule. So therefore if the loop is placed as shown and the current flows in the direction indicated, the torque will cause the loop to rotate clockwise.

To know more about magnetic field here

https://brainly.com/question/31323435

#SPJ11

a student holds a meter stick straight out with one or more masses dangling from it. in which case, is it the most difficult for the student to keep the meter stick from rotating?

Answers

In the scenario you described, it would be most difficult for the student to keep the meter stick from rotating when the masses are attached at the farthest point from the student's hand. This is because the torque (rotational force) acting on the meter stick increases with the distance of the mass from the axis of rotation (the student's hand).

The difficulty for the student to keep the meter stick from rotating depends on the distribution of the masses. If the masses are distributed evenly on both sides of the meter stick, it will be easier to balance and keep from rotating. However, if the masses are all on one side of the stick, it will be much more difficult to keep it from rotating. This is because the center of mass will be shifted to one side, causing an imbalance and rotational force. Therefore, the most difficult case for the student to keep the meter stick from rotating is when all the masses are on one side of the stick.

Learn more about meter here:-

https://brainly.com/question/4307551

#SPJ11

determine the maximum ram force p that can be applied to the clamp at d if the allowable normal stress for the material is σallow = 180 mpa .

Answers

The maximum ram force (p) that can be applied to the clamp at d is equal to the allowable normal stress (σallow) multiplied by the area (A) of the clamp at that location.

The maximum ram force (p) that can be applied to the clamp at d is determined by the allowable normal stress (σallow) for the material and the area (A) of the clamp at that point. The allowable normal stress represents the maximum stress that the material can withstand without permanent deformation or failure. By multiplying the allowable normal stress (σallow) by the area (A) of the clamp, we can find the maximum force (p) that can be applied. This ensures that the force exerted on the clamp does not exceed the material's strength and avoids any potential damage or failure.

Learn more about allowable normal stress here:

https://brainly.com/question/31984258

#SPJ11

Two spherical waves with the same amplitude, A, and wavelength, lamda, are spreading out from two point sources S1 and S2 along one side of a barrier. The two waves have the same phase at positions S1 and S2. The two waves are superimposed at a position P. If the two waves interfere constructively at P what is the relationship between the path length difference dx = d2 - d1 and the wavelength. If the two waves interfere destructively at P, what is the relationship between the path length difference and the wavelength.
3. What does it mean to say that two sources of waves are coherent, for instance, the waves in questions 2 above? If the sources in question 2 were two flashlights, would you observe interference at P? Explain.

Answers

The relationship between the path length difference dx and the wavelength lambda when the two waves interfere constructively at position P is given by dx = n * lambda, where n is an integer.

This means that the path length difference between the two waves must be an integer multiple of the wavelength for constructive interference to occur. When the two waves interfere destructively at position P, the relationship between the path length difference dx and the wavelength lambda is given by dx = (n + 1/2) * lambda, where n is an integer. This means that the path length difference between the two waves must be a half-integer multiple of the wavelength for destructive interference to occur.

When two sources of waves are coherent, it means that they have a constant phase relationship with each other, which means that they have the same frequency and wavelength. In the case of the waves in question 2, since they have the same amplitude, wavelength, and phase at positions S1 and S2, they are coherent.
If the sources in question 2 were two flashlights, interference would not be observed at position P because the light waves from the two flashlights would not be coherent. The light waves from the two flashlights would have different frequencies, wavelengths, and phases, which would result in a random pattern of light at position P rather than interference.

To know more about wavelength visit:

https://brainly.com/question/31143857

#SPJ11

Soda from a mS = 12 oz can at temperature TS = 13.5°C is poured in its entirety into a glass containing a mass mI = 0.18 kg amount of ice at temperature TI = -15°C. Assume that ice and water have the following specific heats: cI = 2090 J/(kg⋅°C) and cS = 4186 J/(kg⋅°C), and the latent heat of fusion of ice is Lf = 334 kJ/kg. In this problem you can assume that 1 kg of either soda or water corresponds to 35.273 oz.

Answers

The final temperature of the soda-water mixture is approximately 34.9°C.

The task is to determine the final temperature of the soda-water mixture after all of the ice has melted. The solution is calculating the amount of heat received by the ice, the amount of heat lost by the soda, and the amount of heat required to melt the ice.

First, we must convert the soda and ice masses to kilogrammes:

mI = 0.18 kg mS = 12 oz / 35.273 oz/kg = 0.34 kilogramme

The amount of heat lost by the soda as it cools from its initial temperature of 13.5°C to the final temperature can then be calculated:

Qlost = 0.34 kg * 4186 J/(kg°C) * (13.5°C)

Qlost = 0.34 kg * 4186 J/(kg°C) * (13.5°C )

Similarly, we can calculate how much heat the ice gains when it warms from -15°C to 0°C and finally melts at 0°C:

Qgain = mI*cI*T + mI*Lf

T = (0°C - (-15°C)) = 15°C

Because the heat lost by the soda is equal to the heat gained by the ice, we can set Qlost = Qgain and solve for:

0.34 kg * 4186 J/kg°C * (13.5°C - F

= 0.18 kg * 2090 J/kg°C 15°C + 0.18 kg

= 334000 J/kg

When we simplify this equation, we get:

= 34.9°C = 15432 - 1423.88

= 10530 + 60012 49709

= 1423.88

For such more question on temperature:

https://brainly.com/question/26866637

#SPJ11

Which one of the following statements concerning theproper length of a meter stick is true?a. The proper length is the lengthmeasured by an observer who is moving with respect to the meterstick.b. The proper length depends upon thereference frame in which it is measured.c. The proper length depends upon theacceleration of the observer.d. The proper length depends upon thespeed of the observer.e. The proper length is always one meter.

Answers

The correct statement is e. The proper length of a meter stick is always one meter, regardless of the reference frame or the observer's motion.

Proper length refers to the length of an object as measured in its own rest frame, i.e., the frame in which the object is not moving. In the rest frame of the meter stick, its proper length is always one meter. In other frames, such as those of observers who are moving relative to the meter stick, the length of the meter stick may appear shorter or longer due to the effects of length contraction. However, the proper length of the meter stick itself does not change.

In the theory of special relativity, , the concept of proper length is fundamental, as it allows for consistent measurements of distances between objects, even when those objects are moving relative to each other. The proper length of an object is the distance between two points on the object that are at rest relative to each other, as measured in the object's own rest frame. This length is invariant, meaning that it does not change as a result of the object's motion or the observer's motion.

In the case of a meter stick, the proper length is defined as the distance between two points on the stick that are at rest relative to each other. This length is always one meter, regardless of the observer's motion or the reference frame in which the measurement is made. However, the observed length of the meter stick will depend on the observer's motion and the relative velocity between the observer and the meter stick, due to the phenomenon of length contraction.

Length contraction is the effect by which a moving object appears shorter in length than it does when at rest. This effect arises from the time dilation and Lorentz contraction predicted by special relativity. These effects become significant when the relative velocity between the observer and the object approaches the speed of light.

In summary, the proper length of a meter stick is always one meter, as measured in the stick's own rest frame. However, the observed length of the meter stick will depend on the observer's motion and the relative velocity between the observer and the stick, due to the effects of length contraction.

learn more about special relativity here:

https://brainly.com/question/28289663

#SPJ11

Other Questions
precede-proceed is best described as _____,and behavior change theories as specific ______. Find the maximum value of f(x, y, z) = 5xy + 5xz + 5yz xyz subject to the constraint g(x, y, z) = x + y + z = 1, for x>0, y > 0, and z > 0. (Give an exact answer. Use symbolic notation and fractions where needed. Enter DNE if there is no maximum.) maximum: 250 Suppose a monopolist producing self-cleaning jackets can sell 20 jackets at $100, and 21 jackets at $98. The monopolist is unable to price discriminate, so in order to sell a total of 21 jackets, the price per jacket must be $98.1-When charging $100 per jacket, total revenue is?:2-When charging $98 per jacket, total revenue is?:3-So the marginal revenue of selling the 21st jacket is?:4-In the case of any firm facing a downward sloping demand curve, marginal revenue is always?: consider the relation | on s = {1,2,3,4,6}. find al l linear ex- tensions of | on s. how many molecules are present in 4.25 mol of ccl4? Please help, Spanish 1 6.3 Preterite tense of regular verbs (First 2 are not right I think so please give correct answer for those 2 as well) a project manager can compress the project schedule by: a) working overtime b) adding more equipment resources c) increasing crew size d) any of the above What is the mass of 9. 6x10 formula units of ammonium sulfide, (NH)S? A random sample of size $n$ is required to produce a margin of error of $\pm E$. By what percent does the sample size need to increase to reduce the margin of error to $\pm\frac{9}{10}E$ ? Round your answer to the nearest percent. About $\%$ Why were stewart and ellen quoted in the newspaper which of the following statements is true? the value of a global named constant cannot be changed during program execution. unlike using global variables, using global named constants can introduce detrimental side effects to your program. a global named constant must be defined in the main function. the value of a global named constant cannot be accessed from anywhere in the program. what specific computer-based communication could be used to achieve argyle's goal as described in situation 1? since this reaction takes place in the absence of the enzyme, what is the physiological advantage in having such enzyme in the blood? [hint: find what the turnover number is for this enzyme.] Dinitrogen pentoxide (N2O5) decomposes via a first-order reaction into N2O4 and O2 . 225()224()+2() The rate constant (k) for this reaction at 45 C is 6.22 x 10^-4s-1.a. What is the half-life for this reaction?b. If the initial concentration of N2O5is 0.100 M, how long will it take for the concentration of N2O5 to drop to 0.0010M?c. If the initial concentration of N2O5is 0.500 M, what will the concentration of N2O5be after 2.00 hours?d. If the initial concentration of N2O5is 0.445 M, what will the concentration of O2be after exactly 15 minutes? Which of the following represents the impact of a taxable cash sale of $400 on the accounting equation if the sales tax rate is 5%?Multiple Choicea. None of these answer choices is correct.b. An increase to cash for $420, an increase to sales tax expense for $20, and an increase to sales revenue for $400.c. An increase to cash for $400, an increase to sales tax payable for $20, and an increase to sales revenue for $380.d. An increase to cash for $420, an increase to sales tax payable for $20, and an increase to sales revenue for $400. Use a triple integral to find the volume of the given solid.The solid enclosed by the paraboloidsy = x2 + z2andy = 72 x2 z2. fill in the blank. the quantity of labor demanded is ________ related to the wage rate, while the quantity of labor supplied is ________ related to the wage rate, ceteris paribus. A 6.10 kg block is pushed 9.00 m up a smooth 38.0 inclined plane by a horizontal force of 78.0 N . If the initial speed of the block is 3.20 m/s up the plane. a. Calculate the initial kinetic energy of the block. (found to be 31.2 J) b. Calculate the work done by the 78.0 N force. (found to be 553 J) c. Calculate the work done by gravity. (found to be -331 J) d. Calculate the work done by the normal force. (found to be 0 J) e. Calculate the final kinetic energy of the block. ( HELP) how many isomeric (structural, diastereomeric and enantiomeric) tripeptides could be formed from a mixture of racemic phenylalanine? A force vector has components given by Fx = 7.50 N and Fy = 4.15 N. Find the following. (a) the magnitude of the force 8.572 Correct: Your answer is correct. N (b) the direction of the force, measured counterclockwise from the positive x-axis