Find the moment of inertia for the following objects:
A. A uniform disc of mass M and radius R rotating about its axis. Replace the sum in 3.31 by the appropriate integral and do the integral in polar coordinates.
B. A uniform solid sphere rotating about a diameter. Replace the sum in 3.31 by the appropriate integral and do the integral in spherical coordinates.

D. Elastic because that's what an elastic collision is.

Tension is a force along the length of a medium, especially a force carried by a flexible medium, such as a rope or cable.

The tension in the cord is approximately 10624 N.

To solve this problem, we can use the principles of Newton's laws and apply them to each of the objects involved. We will also use the fact that the tension in the cord is the same on both sides of the pulley (neglecting any friction or mass in the pulley).

First, we can consider the forces acting on the block (m1). The only forces acting on the block are its weight (mg) and the tension in the cord (T), which is directed upward. We can resolve these forces into components parallel and perpendicular to the inclined plane:

The weight of the block has a component parallel to the inclined plane given by [tex]mg*sin(θ)[/tex].

The tension in the cord has a component parallel to the inclined plane given by [tex]T*sin(θ)[/tex].

Using Newton's second law, we can write:

[tex]m1 * a = T * sin(θ) - m1 * g * sin(θ)[/tex]

where a is the acceleration of the block down the inclined plane.

Next, we can consider the forces acting on the sphere ([tex]m2[/tex]). Since the sphere is hanging from the cord, the only force acting on it is its weight ([tex]mg[/tex]), which is directed downward. Using Newton's second law, we can write:

[tex]m2 * a = m2 * g - T[/tex]

where a is the acceleration of the sphere downward.

Since the cord is assumed to be massless and the pulley is assumed to be frictionless, the tension in the cord is the same on both sides of the pulley. Therefore, we can set the two expressions for T equal to each other:

[tex]T * sin(θ) - m1 * g * sin(θ) = m2 * g - T[/tex]

Solving for T, we get:

T = [tex](m2 + m1) * g / (sin(θ) + 1)[/tex]

Substituting the given values, we get:

T = [tex](540 kg + 2.00 kg) * 9.81 m/s^2 / (sin(49.0°) + 1)[/tex]

T = 10624 N (to three significant figures)

for such more question on tension

brainly.com/question/24994188

#SPJ4

A resistor is connected to a 9.0V battery with a 0.50A current flowing through it. Then the resistance is 18 Ω.

When a 9.0-volt battery is connected to a resistor, an electric field is created that pushes electrons through the resistor. The voltage of the battery represents the potential energy that each electron has when it enters the circuit, while the resistor creates a resistance that slows down the flow of electrons. According to Ohm's law, the current (I) through a resistor is directly proportional to the voltage (V) applied across it and inversely proportional to the resistance (R) of the resistor. The relationship can be expressed as:

I = V / R

In this case, the current is given as 0.50 A, and the voltage of the battery is 9.0 V.

= R

= V / I

= 9.0 V / 0.50 A

= 18 Ω

So the resistor in the circuit has a resistance of 18 ohms, and it is causing a current of 0.50 A to flow through it when the 9.0-volt battery is connected.

To know more about resistor please refer: https://brainly.com/question/17390255

#SPJ4

Question - A 9. 0-v battery is connected to a resistor so that there is a 0. 50-a current through the resistor. Then the resistance is?

In A. part, the magnetic field at (0, 50) is in west direction. In B. part, the strength of the field at (0,50) is 2.06 G.

A. The current is flowing up for west as shown by the front view figure at the bottom of the gadget. Your fingers will curve to the west if you wrap your right hand around the wire with your thumb up. Put a compass at (0,50) to check the direction as well. It indicates west.

B. By using the Pythagorean Theorem to determine the strength of the combined field, the strength of the field at (0,50) is 2.06 G.

The earth's magnetic field strength= 0.50 G

The induced current magnetic field strength= 2.0

B is given by=

[tex]\sqrt{0.50^{2} - 2.00^{2} }\\ =\sqrt{0.25-4.00}\\ =2.06[/tex]

Hence, we can also check by putting the probe on (0,50) and the probe reads 2.06 G.

Therefore, the strength of the field at (0,50) is 2.06 G.

Here is more information about Pythagoras theorem: brainly.com/question/343682

#SPJ4

We can start by calculating the volume of the gold in the alloy and then use its density to determine its weight.

First, let's find the weight of the alloy when it's not submerged in water:

Weight of alloy = 49 N

Next, let's find the buoyant force, which is equal to the weight of the water that's displaced by the object:

Buoyant force = weight of water displaced = 39.2 N

So, the weight of the object in water can be calculated as:

Weight in water = Weight of alloy - Buoyant force = 49 N - 39.2 N = 9.8 N

Next, let's calculate the volume of the object using its density:

Volume = Weight in water / (Density of alloy - Density of water)

Since the density of water is 1 g/cm^3, we can simplify the equation as:

Volume = 9.8 N / (Density of alloy - 1)

Since the specific gravity of Aluminium is 2.5, its density can be calculated as:

Density of Aluminium = 2.5 * Density of water = 2.5 * 1 g/cm^3 = 2.5 g/cm^3

So, the volume of the object can be calculated as:

Volume = 9.8 N / (2.5 g/cm^3 - 1 g/cm^3) = 9.8 N / 1.5 g/cm^

Answer:

play used his in but been been by in BBC in in in just not is suspension as SBB is is abbess a

Explanation:

no exception

The new acceleration of the wagon is 20 m/s.

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

                                               a = F/m

Where,

a is the acceleration,

F is the net force, and

m is the mass of the wagon.

                             m = F/a = 10 N / 10 m/s = 1 kg

                                               a' = F'/m

Where,

a' is the new acceleration,

F' is the new net force, and

m is the mass of the wagon.

Substituting the values, we get:

a' = 20 N / 1 kg = 20 m/s/s

Therefore, the new acceleration of the wagon is 20 m/s/s when it is pushed with a force of 20 Newtons on a frictionless surface.

This result shows that the acceleration of the wagon is directly proportional to the net force acting on it, as predicted by Newton's Second Law.

To know more about motion visit:

https://brainly.com/question/30162024

#SPJ1

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Lets examine all three properties stated here ~

I) holes in lattice allow the electricity to flow through ?

- holes aren't a majority charge carrier in a conductor, in conductors electricity is conducted by free elecrons. so this statement is incorrect.

ll) Electricity flows easily through this type of material?

- That's true, conductors (usually metals) have free electrons to conduct electricity, which is responsible for good electricity Conductivity.

lll) A few electrons in every atom are loosely held by the nuclei.

- That's also true, Conductors (mainly metals) have a few electrons (say, 1, 2 or maybe 3) in there valence shell which experience quite less force of attraction from nucleus, hence they are free to move around the whole conductor randomly, making a sea of electrons.

So, the correct choice will be : D) ll and lll

Option D: the link between the total heat flow and the temperature difference between the sample's Centre and the water at a specific time.

[tex]Q\:=\:m_sc_s\left(T_{s,i}-T_s\right)[/tex]

[tex]T_s\right =(T_{s,i}-T_s\right))[/tex]

[tex]Q=m_wc_w\left(T_w-T_{w,i}\right)[/tex]

[tex]Q=m_wc_w\left(T_w-T_{w,i}\right)[/tex]

[tex]T_{diff} =(T_{s}-T_w\right))[/tex]

        = [tex]T_{s,i} -\frac{Q}{m_{s}C_{s}} -(T_{w,i}\right +\frac{Q}{m_{s}C_{s}} )[/tex]

        =[tex](T_{s,i} - T_{w,i} )-Q(\frac{1}{m_{s}C_{s}} +\frac{1}{m_{w}C_{w}})[/tex]

Specific time refers to a precise moment in time, often denoted by a particular time and date. It can be expressed in different ways depending on the context, such as using a 24-hour clock or the AM/PM system. Specific time is essential for scheduling events, meetings, and appointments, and for coordinating activities across different time zones. It is also crucial for time-sensitive activities such as transportation, where schedules must be coordinated down to the minute. The concept of specific time is used in many fields, including science, technology, business, and everyday life. In modern times, technologies such as smartphones and computers have made it easier than ever to track and coordinate specific times across the globe.

Learn more about Specific time here:

https://brainly.com/question/13196427

#SPJ4

The complete question is:

1. we know that the total amount of heat that flows out of the sample and into the water at a specific time is given by LaTeX: [tex]Q\:=\:m_sc_s\left(T_{s,i}-T_s\right)Q=mscs(Ts,i−Ts)[/tex], where LaTeX: [tex]T_sTs[/tex] is the temperature of the sample at a specific time and, again, LaTeX: [tex]T_{s,i}Ts,i[/tex]is the initial temperature of the sample (at time 0). To simplify the math, we may neglect the heat leak term here to say that this is roughly the same amount of heat the flows into the water, so LaTeX: [tex]Q=m_wc_w\left(T_w-T_{w,i}\right)Q=mwcw(Tw−Tw,i)[/tex], where LaTeX:[tex]T_wTw[/tex] is the temperature of the water at this same specific time and LaTeX:  is the initial temperature of the water.

In the lab, we will measure both the sample and water temperatures as a function of time, but the important quantity is the difference between these temperatures since this is what drives the heat flow between the center of the sample and the water. Using the above equations (solving for the temperatures of the sample and the water bath at a particular time), we can find the relationship between the total amount of heat flow and the difference in the temperatures of the center of the sample and water at some moment in time. This yields _________________________________.

sample and water at some moment in time. This yields _________________________________.

Group of answer choices

A. [tex]T_{dif}=T_{s\:}-T_w=\left(T_{s,i}-T_{w,i}\right)-\left(\frac{1}{m_sc_s}-\frac{1}{m_wc_w}\right)Q[/tex]

B [tex]T_{dif}=T_{s\:}-T_w=\left(T_{s,i}-T_{w,i}\right)+\left(\frac{1}{m_sc_s}+\frac{1}{m_wc_w}\right)Q[/tex]

C.[tex]T_{dif}=T_{s\:}-T_w=\left(T_{s,i}-T_{w,i}\right)+\left(\frac{1}{m_sc_s}-\frac{1}{m_wc_w}\right)Q[/tex]

D. [tex]T_{dif}=T_{s\:}-T_w=\left(T_{s,i}-T_{w,i}\right)-\left(\frac{1}{m_sc_s}+\frac{1}{m_wc_w}\right)Q[/tex]

the work done by the ball is 38.72 J.

define work done ?

In physics, work is defined as the product of force and displacement. It is a measure of the energy transferred when a force is applied over a distance, resulting in the displacement of an object. Mathematically, work is represented by the formula:

Work = Force x Distance x Cos(theta)

where Force is the applied force, Distance is the displacement of the object, and theta is the angle between the force and the displacement vectors. The unit of work is the Joule (J), which is equivalent to one Newton-meter (N·m). Work can be positive, negative, or zero, depending on the direction of the force and displacement. If the force is in the same direction as the displacement, work is positive, and if the force is in the opposite direction to the displacement, work is negative. If the force and displacement are perpendicular, the work is zero.

Work = Force x Distance x Cos(theta)

where:

Force = 484 N (given)

Distance = 8 cm = 0.08 m (given)

Cos(theta) = 1 (since the force and displacement are in the same direction)

Plugging in the values, we get:

Work = 484 N x 0.08 m x 1

Work = 38.72 Joules (J)

Therefore, the work done by the ball is 38.72 J.

To learn more about work done follow the given link: https://brainly.com/question/10049331

#SPJ1

Explanation:

a) To determine the position of the snowboarder when t = 4 seconds, we can substitute t = 4 into the equation x = 0.5t^3 + 6t^2 + 3t:

x = 0.5 * 4^3 + 6 * 4^2 + 3 * 4

x = 64 + 96 + 12

x = 172

So when t = 4 seconds, the snowboarder's position is 172 meters.

b) To determine the velocity of the snowboarder when t = 4 seconds, we'll need to find the first derivative of the displacement function x = 0.5t^3 + 6t^2 + 3t with respect to time:

dx/dt = 3 * 0.5 * t^2 + 2 * 6 * t + 3

Next, we can substitute t = 4 into this expression to find the velocity when t = 4 seconds:

dx/dt = 3 * 0.5 * 4^2 + 2 * 6 * 4 + 3

dx/dt = 72 + 48 + 3

dx/dt = 123

So the velocity of the snowboarder when t = 4 seconds is 123 meters per second.

c) To determine the acceleration of the snowboarder when t = 4 seconds, we'll need to find the second derivative of the displacement function x = 0.5t^3 + 6t^2 + 3t with respect to time:

d^2x/dt^2 = 6 * 0.5 * t + 2 * 6

Next, we can substitute t = 4 into this expression to find the acceleration when t = 4 seconds:

d^2x/dt^2 = 6 * 0.5 * 4 + 2 * 6

d^2x/dt^2 = 24 + 12

d^2x/dt^2 = 36

So the acceleration of the snowboarder when t = 4 seconds is 36 meters per second squared.

The law of Newton that is related to momentum is:

B.) Newton's second law

Newton's second law states that the rate of change of momentum of an object is directly proportional to the force applied to the object and occurs in the direction in which the force is applied. This law is often expressed as F = ma, where F is the force, m is the mass of the object, and a is the acceleration of the object. This law provides the mathematical relationship between force, mass, and acceleration, which is crucial in understanding the concept of momentum.

Option C is the accurate answer. The act of preservation of instigation is grounded on Newton’s third act because of the act of conservancy of instigation.

It can subsist deduced from the act of act and response, which states that every workforce has a repaying level and contrary force. However, the hedge pushes ago against you with an equal quantum of workforce, if you drive against a barrier.  

This act signifies individual harmony in complexion workforces always do in dyads, and one core can not ply a workforce on another without passing a workforce itself.  

Newton’s third act of motion states that:    

“When one core exerts a workforce on the different mass, the foremost core gests a workforce which is collected at the moment on the contrary direction of the force which is wielded ”.  

The above statement means that in every commerce, there's a brace of forces acting on the interacting objects. The magnitude of the workforces are level and the command of the workforce on the foremost thing is contrary to the order of the workforce on the alternate thing.

Learn more about Newton's Law here:

brainly.com/question/27573481

If rope of length L is clamped at both ends then, 4L is not a possible wavelength for standing waves on this rope.

A string's shortest wavelength is L = λ/2. There is a node where the rope is clamped; at this point, the rope is fixed at zero and cannot travel up or down. Therefore, this is λ/2 if the rope's midsection is oscillating up and down. There are two visible loops if there is a node in the middle of the rope, which indicates that there are 2λ/2. The options are 3λ/2, 4λ/2, etc. So, aside from b, all other methods work.

You would have 2/3 of a wavelength if b were accurate. One of the nodes would have to be moving up and down as a result.

Every circle in my lovely image is a node; they appear every half-wavelength. Note that the square, which is at a wavelength of 2/3, is not a node. A standing wave cannot contain wavelengths that are divided into thirds.

Only standing waves whose length is an integral multiple of half wavelength can occur in a string that is fixed at both ends.

L = n* (λ/2)

Only in instance (e) is n = 1/2, and that is unacceptable.

(e) is the proper response.

To learn more about wavelength visit;

https://brainly.com/question/13533093

#SPJ4

Answer: the correct answer is A

Explanation: the correct answer is A. The force would be one-fourth the original force.

Scientist 1 would most likely explain this result by saying, The experiment allowed the magnetic domains of the bar to line up, causing the bar to become magnetic.

Scientist 1 would most likely explain this outcome as follows: The experiment caused the magnetic domains of the bar to align, leading the bar to become magnetic.

Because, according to Scientist 1, magnetism originates when magnetic domains in a material align. Because the iron bar initially exhibited no magnetism, we may suppose that its magnetic domains were oriented randomly at first, with no magnetic poles. When the iron bar became magnetic after being heated and chilled, the heating and chilling process most likely reoriented the magnetic domains in the iron, resulting in two magnetic poles.

To know more about magnetic field lines, visit,

https://brainly.com/question/17011493

#SPJ4

The final momentum is 25 Kg m/s

In physics, momentum is a measure of an object's motion, calculated by multiplying the object's mass by its velocity. Mathematically, momentum is represented by the symbol "p" and can be expressed as:

p = mv

where "p" is momentum, "m" is mass, and "v" is velocity. Momentum is a vector quantity, meaning that it has both a magnitude (the amount of momentum) and a direction (the direction of the motion).

Given that;

Ft = mv - mu

It then follows that;

F = force

m = mass

v and u are the initial and the final velocities

Thus;

5 * 5 = 5v

v = 25/5

= 5 m/s

The final momentum is thus;

5 m/s * 5 Kg

= 25 Kg m/s

Learn more about momentum:https://brainly.com/question/30487676
#SPJ1

Answer:

you would have difficulty hearing on a daily basis, as mentioned in the example, but you would also have trouble getting jobs, you would have fewer educational opportunities, and also a lack of awareness of your everyday surroundings.

Explanation:

The minimum radius of the circular path for the cyclist traveling at a speed of 20 m/s and a tilt angle of 30° is approximately 17.32 meters.

The formula for the minimum radius of a circular path for a cyclist traveling at a certain speed can be determined using the relationship between the speed, the angle of tilt, and the gravitational force acting on the cyclist.

The minimum radius of the circular path can be calculated using the formula:

r = (v^2) / gtan(θ)

where:

Plugging in the values, we get:

r = (20^2) / (9.8 x tan(30°))

r ≈ 17.32 m

Learn more about radius here: https://brainly.com/question/390660

#SPJ1

The amount of heat that flows out of the copper sample during this temperature drop is approximately 4,953.75 J.

The amount of heat that flows out of the copper sample can be calculated using the formula:

Q = mcΔT

where;

Plugging in the given values, we get:

Q = (0.35 kg) x (387 J/kg C) x (74.0 °C - 21.0 °C)

Q = 4,953.75 J

Learn more about heat flow here: https://brainly.com/question/14437874

#SPJ1

a) It takes the bicyclist 9.09 seconds to catch up to his friend.

b) The bicyclist has traveled 40.0 meters in 9.09 seconds to catch up to his friend.

c) The bicyclist is moving at a speed of 20.0 m/s when he catches up to his friend.

a) To find out how much time it takes for the bicyclist to catch up to his friend, we need to use the equation for motion with constant acceleration:

d = v_0 t + 0.5 a t^2

where d is the total distance traveled,

v_0 is the initial velocity (0 m/s in this case),

t is the time, and a is the acceleration (2.2 m/s^2).

Since the friend was already moving at a constant speed of 4.0 m/s when the bicyclist started pedaling, we know that the total distance d that the bicyclist has to travel to catch up is equal to 4.0 m/s * t + 0.5 * 2.2 m/s^2 * t^2.

Setting d equal to 4.0 m/s * t, we can solve for t:

4.0 m/s * t = 4.0 m/s * t + 0.5 * 2.2 m/s^2 * t^2

0.5 * 2.2 m/s^2 * t^2 = 0

t = sqrt(0 / (0.5 * 2.2 m/s^2)) = 0 s

Since the square root of zero is zero, the time t is also zero. This means that the bicyclist starts moving at the same time as the friend, so he needs to accelerate for the entire time to catch up.

Using the equation for motion with constant acceleration, we can find the time t it takes for the bicyclist to catch up:

d = v_0 t + 0.5 a t^2

d = 4.0 m/s * t

4.0 m/s * t = 0 m/s * t + 0.5 * 2.2 m/s^2 * t^2

4.0 m/s = 0.5 * 2.2 m/s^2 * t

t = 4.0 m/s / (0.5 * 2.2 m/s^2) = 9.09 s

So it takes the bicyclist 9.09 seconds to catch up to his friend.

b) To find out how far the bicyclist has traveled in this time, we can use the equation for motion with constant acceleration again:

d = v_0 t + 0.5 a t^2

d = 0 m/s * 9.09 s + 0.5 * 2.2 m/s^2 * 9.09 s^2

d = 40.0 m

So the bicyclist has traveled 40.0 meters in 9.09 seconds to catch up to his friend.

c) To find out the bicyclist's speed when he catches up, we can use the equation for velocity:

v = v_0 + a * t

v = 0 m/s + 2.2 m/s^2 * 9.09 s

v = 20.0 m/s

So the bicyclist is moving at a speed of 20.0 m/s when he catches up to his friend.

Learn more on velocity here https://brainly.com/question/80295

#SPJ1

Answer:

The correct option is D. 4.3×10¹⁴ Hz

Explanation:

It is because the frequency and the wavelength are inversely proportional to each other.

So, c=f × lambda

And, frequency = velocity/wavelength

The frequency of the laser beam is D. 4.3×10¹⁴ Hz

One hertz (Hz) equals one cycle per second. A complete AC or voltage wave is called a cycle. The first half of the cycle is alternating. Period is the time it takes a waveform to complete a complete cycle. Frequency is essentially how often something repeats.

The rate at which the current changes direction in one second is called the frequency. Expressed in hertz (Hz), the international unit of measurement. One hertz equals one cycle per second. 

It is because the frequency and the wavelength are inversely proportional to each other.

So, c=f × lambda

And, frequency = velocity/wavelength

To learn more about frequency visits:

https://brainly.com/question/14316711

#SPJ1

Complete Question is:

A laser beam of wavelength 700 nanometers, traveling at a speed of 3.0 x 108 m/s,

is shot from outer space toward earth. What is the frequency of the laser beam?

[tex]A. 3.0 x 10^8 HzB. 700 x 10^-9 HzC. 210 HzD. 4.3 x 10^14 HzE. 233 x 10^-17 Hz[/tex]

According to the question the soccer ball was in the air for a total of 2.26 seconds.

Air is a mixture of gases made up of nitrogen (78%), oxygen (21%), and other trace gases like argon and carbon dioxide (1%). This mixture of gases makes up a unseen fluid we call air. It is all around us, surrounding us and filling the space between us and the Earth.

The time that the soccer ball was in the air can be determined using the kinematic equations of motion. First, we need to calculate the initial vertical and horizontal velocity components of the ball when it is kicked. The vertical velocity component is given by Vy = V*sin(angle) = 15.6 m/s * sin(52.5°) = 11.2 m/s.

The horizontal velocity component is given by Vx = V*cos(angle) = 15.6 m/s * cos(52.5°) = 9.2 m/s.

Now we can solve for time using the equation t = (2*Vy)/g, where Vy is the vertical velocity component and g is the acceleration due to gravity (9.8 m/s2). Thus, t = (2*11.2 m/s)/9.8 m/s2 = 2.26 s.

Therefore, the soccer ball was in the air for a total of 2.26 seconds.

To learn more about air

https://brainly.com/question/179051

#SPJ1

No, because covering uniform distance in uniform units of time ( which the graph one represents) is constant speed, and not uniform speed (as represented in the second graph).

What is a graph?

To know more about graph, click the link given below:

https://brainly.com/question/17267403

#SPJ1

To determine the cation exchange capacity (CEC), calculate the milliequivalents of H, K, Mg, and Ca per 100g of soil (meq/100g soil) by using the following formulas: H, meq/100g soil = 8 (8.00 - buffer pH) K, meq/100g soil = lbs/acre extracted K ÷ 782. Mg, meq/100g soil = lbs/acre extracted Mg ÷ 240.

To begin, multiply the total CEC by the percentage for that ion to determine the cmolc of each cation on the exchange complex. It is 0.05 * 30 cmolc/kg for hydrogen. The cmolc/kg for each ion is then converted to mass of ion per kg by multiplying by the mass of 1 cmolc.
Soil testing laboratories calculate CEC by adding the calcium, magnesium, and potassium levels measured during the soil testing procedure to an estimate of exchangeable hydrogen derived from the buffer pH. In general, CEC values obtained through this summation method will be slightly lower than those obtained through direct measurementsdirect.

The percentage of CEC occupied by bases (Ca2+, Mg2+, K+, and Na+) is represented by base saturation (BS). The%BS increases as soil pH rises (Figure 5). Ca2+, Mg2+, and K+ availability increases as %BS increases. An 80% BS soil, for example, provides cations to plants more easily than a 40% BS soil.
Base saturation is the percentage of base cations (Ca2+, Mg2+, K+, and Na+) held onto soil exchange sites divided by total CEC.

To know more about Cation go through:-

https://brainly.com/question/28971609

#SPJ4

Answer:

Halogen

Explanation:

Answer:

A car light emits visible light, which is a type of electromagnetic energy.

Explanation:

Answer:

Explanation:

A

To sketch the processes in a p-V diagram, we need to first determine the initial and final states of each process, as well as the path each process takes.

Process 1-2 is a constant pressure expansion from state 1 to state 2. So, the path is a straight horizontal line on the p-V diagram, from (0.2, 5) to (1, 5) (in units of m^3 and bar).

Process 2-3 is a constant volume cooling from state 2 to state 3, so the path is a straight vertical line on the p-V diagram, from (1, 5) to (1, 1).

Process 3-1 is a compression process during which the pressure-volume relationship is pV=constant. This implies that the path on the p-V diagram is a hyperbola, passing through state 3 and returning to state 1.

The work done in each process can be calculated using the following equations:

W = P(V2 - V1) for constant pressure process (1-2)

W = 0 for constant volume process (2-3)

W = -nRT ln(V2/V1) for isothermal process (3-1), where n is the number of moles of CO, R is the gas constant, and T is the temperature of the gas.

Assuming standard temperature and pressure conditions (STP), which is 1 atm and 273.15 K, the gas constant R can be taken as 0.0821 Latm/(molK).

Using these equations, we can calculate the work for each process as follows:

W1-2 = 5*(1-0.2) = 4 kJ

W2-3 = 0

W3-1 = -nRT ln(V2/V1) = -10.0821273.15 ln(1/0.2) = 11.1 kJ

Therefore, the total work done on the gas in the three processes is the sum of the work done in each process, which is 4 kJ + 0 kJ + 11.1 kJ = 15.1 kJ.

learn more about work done: https://brainly.com/question/25573309

#SPJ1

Here are some possible percentages and their corresponding estimated z-scores:

These percentages are based on the empirical rule, which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.

The empirical rule, also known as the 68-95-99.7 rule, is a statistical principle that describes the approximate distribution of data in a normal distribution. The rule states that:

This rule is based on the assumption that the data is normally distributed, meaning that it follows a symmetrical bell-shaped curve. The empirical rule is widely used in statistics and is helpful in understanding the range of values that are likely to occur in a normal distribution.

It is important to note that the empirical rule provides only approximations and can vary in accuracy depending on the specific data and distribution being analyzed.

To know more about the empirical rule, visit:

https://brainly.com/question/28873888

#SPJ4

Option: B, The percentage of people with blood pressure between 114 and 166 mm

The empirical rule, also known as the 68-95-99.7 rule, is a statistical principle that describes the approximate distribution of data in a normal distribution. The rule states that:

=> P(114 < x < 166)

=> P((114-140)/20 < z < (166-140)/20)

=> P(-1.3 < z < 1.3)

=> 0.8064

=> 80.6% rounded

option: D The percentage of people with blood pressure between 114 and 166 mm

=> P(140 < x < 166)

=> P((140-140)/20 < z < (166-140)/20)

=> P(0 < z < 1.3)

=> 0.4032

=> 40.3% rounded

option: C The percentage of people with blood pressure over 166 mm

=> P(x > 166)

=> P(z > (166-140)/20)

=> P(z > 1.3)

=> 0.0968

=> 9.7% rounded

This rule is based on the assumption that the data is normally distributed, meaning that it follows a symmetrical bell-shaped curve. The empirical rule is widely used in statistics and is helpful in understanding the range of values that are likely to occur in a normal distribution.

It is important to note that the empirical rule provides only approximations and can vary in accuracy depending on the specific data and distribution being analysed.

To know more about the empirical rule, visit:

brainly.com/question/28873888

#SPJ4

The magnitude of the parallel component of the velocity is 1.4 m/s

The direction is in the direction of rotation of the carousel.

The velocity of the child can be calculated using the equation for centripetal acceleration:

a = v^2 / r

where

Rearranging the equation to solve for velocity:

v = √(ar)

The centripetal acceleration is equal to the square of the angular velocity, w, multiplied by the radius:

a = w^2 x r

where

Since the carousel completes one revolution every 14.1 seconds, the angular velocity can be calculated as:

w = 2π / T

w = 2π / 14.1

Now we can calculate the centripetal acceleration:

a = w^2 x r

a = (2π / 14.1)^2 x 7.0

a = 1.41 m/s²

Finally, we can use this value to calculate the velocity of the child:

v = √(ar)

v = √(1.41 x 7.0)

v = 3.14 m/s

The magnitude of the velocity is the scalar value, or the size of the velocity vector without direction.

The direction of the velocity is perpendicular to the radial line connecting the child to the center of the carousel. It is in the direction that the child is moving.

The parallel component of the velocity is in the direction of the rotation of the carousel and can be calculated using the projection of the velocity onto a line tangent to the circle.

dp/dt = v dθ/dt

where

Substituting the values for velocity and angular velocity:

dp/dt = vw

= 3.14 x (2π / 14.1)

v = 1.4 m/s

Learn more about component of velocity here: https://brainly.com/question/24949996

#SPJ1