how to calculate the efficiency of a transformers

Answers

Answer 1

Answer:

The efficiency of a transformer is the ratio of its output power to its input power, expressed as a percentage. You can calculate it by dividing the output power by the input power and multiplying by 100%. The formula for efficiency is:

Efficiency = (output power / input power) x 100%

Transformers have losses due to factors such as resistance, core losses, and leakage inductance, which reduce their efficiency. Therefore, the actual efficiency of a transformer is always less than 100%.


Related Questions

A car is traveling at 60 mph. If the rate of speed increases 4 mph each hour,
how long will it be before the car is traveling at a rate of 80 mph?
A) 4 hours
B) 5 hours
C) 6 hours
D 7 hours​

Answers

Answer:

5 hours ................

Answer:

B=5 hrs

explanation:

becoz if you add 4 mph/hr

it will graually be 80 in 5 hrs

A hypothetical planet has a radius 1.8 times that of Earth but has the same mass. What is the acceleration due to gravity near its surface?

Answers

The acceleration due to gravity near the surface of the hypothetical planet is 3.02 m/s².

The formula for acceleration due to gravity is:

g = GM/r² Where, g = acceleration due to gravity G = universal gravitational constant M = mass of the planet r = radius of the planet

In this case, since the mass of the hypothetical planet is the same as that of Earth, we can use the mass of Earth instead of M.

Therefore, g is proportional to 1/r².

So, using the ratio of radii given (1.8), we can write:

r = 1.8 x r Earth, where r Earth is the radius of Earth.

Substituting this value of r in the formula for acceleration due to gravity, we get:

g = GM/(1.8 x r Earth)² = GM/(3.24 x rEarth²) = (1/3.24)GM/rEarth²

We know that the acceleration due to gravity on Earth (g Earth) is 9.8 m/s².

Therefore, we can calculate the acceleration due to gravity on the hypothetical planet (gh) as follows:

gh = (1/3.24) x g Earth = 3.02 m/s²

Thus, the acceleration due to gravity near the surface of the hypothetical planet is 3.02 m/s².

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Definition of Xenophobia​

Answers

Answer:

dislike of or prejudice against people from other countries.

Explanation:

Answer: dislike of or prejudice against people from other countries.

Explanation:

3. The Impact was the first commercial electric car to be developed in over 60
years. During performance tests in 1994, the car reached a top speed of nearly
296 km/h. Suppose the car started at rest and then underwent a constant
acceleration of 1.6 m/s² until it reached its top speed. How long did it take the
Impact to reach its top speed?

Answers

According to the question, the impact of an electric car to reach its top speed is found to be 51 sec.

What is Acceleration?

Acceleration may be defined as the process of the rate of change of the velocity of an object with respect to time. It is a vector quantity as it has both magnitude and direction.

According to the question,

The acceleration of an electric car = 1.6 m/s²

The speed of an electric car = is 296 km/hour = 1000 m/hour. = 82.2 m/sec.

The acceleration of any moving object is calculated with the help of the following formula:

Acceleration, a = change in velocity/time taken.

         1.6 m/s²            =  82.20 - 0/t

           t = 51.45 sec ≅ 51 seconds.

Therefore, the impact of an electric car to reach its top speed is found to be 51 sec.

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You have two identical looking spools (same mass, same shape, same size). However, one is hollow, made from iron, the other is solid, made from aluminum. A string is wound around each spool. If you pull on both strings with equal forces, which spool is going to have the larger angular acceleration

Answers

Answer:

The one made from AL will have a smaller moment of inertia and thus a  greater acceleration:  

α = I ω

I = M R^2     for the iron (all the mass at a distance R)

Replacing any of the Fe with Al (and putting at a smaller radius) is going to reduce the total moment of inertia,

I need help please someone !!!!! Would appreciate it

I need help please someone !!!!! Would appreciate it

Answers

Answer:

Yes, it would make it back up.

Explanation:

If it has 100,000 Joules of gravitational potential energy at the top of the hill, by the time the cart gets to the bottom, it will become PE = 0, KE = 90,000 since 10% of 100,000 is 10,000. The cart only requires 80,000J to climb back up so it should easily do so.

I didn't quite understand if the 10% energy loss is total, or every time it goes up or down, but it isn't a problem because 10% of 90,000 is 9,000, which means it would have 81,000J of energy on the way back up IF it loses energy due to friction on the way back up also.

The only physical law you need to prove this is the Law of Conservation of Energy: no energy is lost, only transformed; 10% of the energy becomes heat, the rest remains mechanical energy, which is the reason why the reasoning above works.

The density of water is about 1 gram per milliliter. A milliliter is a cubic centimeter (i.e., cm3 ). A red blood cell has a density similar to water and is shaped like a one micrometer thick disk with a diameter of about 10 micrometers. About what is the mass in grams of a red blood

Answers

Answer:

The mass in grams of a red blood cell is about 7.85 ×  10⁻¹¹ grams

Explanation:

To find the mass in grams of a red blood cell,

From,

\(Density = \frac{Mass}{Volume}\)

Then,

\(Mass = Density \times Volume\)

From the question,

Density of a red blood cell is similar to that of water

Density of water = 1 g/mL = 1 g/ cm³

Then, Density of a red blood cell = 1 g/cm³

Now, we will find the volume a red blood cell.

From the question,  

A red blood cell is shaped like a one micrometer thick disk with a diameter of about 10 micrometers

Since the shape is like that of a thick disc, we can determine the volume by using the formula for volume of a cylinder.

Hence,

Volume of a red blood cell = \(\pi r^{2}h\)

Where \(\pi\) Is a constant (Take \(\pi\) = 3.14)

\(r\) is the radius

and \(h\) is the thickness

Diameter of a red blood cell = 10 micrometers

Then, radius of a red blood cell = 10/2 micrometers = 5 micrometers

\(r\) = 5 micrometers = 5 × 10⁻⁶ meters

and \(h\) = 1 micrometer = 1 × 10⁻⁶ meters

Hence,

Volume of a red blood cell = 3.14 × (5 × 10⁻⁶)² × 1 × 10⁻⁶

∴ Volume of a red blood cell = 7.85 × 10⁻¹⁷ cubic meter (m³)

Convert this to cubic centimeter

(NOTE: 1 cubic meter = 1000000 cubic centimeter)

Hence,

Volume of a red blood cell = 7.85 ×  10⁻¹¹ cubic centimeter (cm³)

Now, for the mass

\(Mass = Density \times Volume\)

Density of a red blood cell = 1 g/cm³

Volume of a red blood cell = 7.85 ×  10⁻¹¹ cubic centimeter (cm³)

Then,

Mass = 1 g/cm³ ×  7.85 ×  10⁻¹¹ cm³

Mass = 7.85 ×  10⁻¹¹ g

Hence, the mass in grams of a red blood cell is about 7.85 ×  10⁻¹¹ grams

Calculate the absolute pressure at an ocean depth of 1.0 x 10³ m. Assume that the density of the water is 1.025 x 10³ kg/m³ and that Po = 1.01 x 10^5 Pa.

Answers

The absolute pressure at an ocean depth of 1.0 x 10^3 m is 1.002 x 10^8 Pa.

What is hydrostatic pressure?

Hydrostatic pressure is the pressure that a fluid exerts on a surface due to the weight of the fluid above it. It is the result of the force of gravity acting on a column of fluid, and it is directly proportional to the height of the column of fluid and the density of the fluid.

The absolute pressure at an ocean depth of 1.0 x 10^3 m can be calculated using the hydrostatic pressure equation:

P = ρgh + Po

where:

P is the absolute pressure at the given depth

ρ is the density of the water

g is the acceleration due to gravity (assumed to be 9.81 m/s²)

h is the depth of the ocean

Po is the atmospheric pressure at the surface (assumed to be 1.01 x 10^5 Pa)

Substituting the given values, we get:

P = (1.025 x 10^3 kg/m³) x (9.81 m/s²) x (1.0 x 10^3 m) + 1.01 x 10^5 Pa

P = 1.025 x 9.81 x 10^6 Pa + 1.01 x 10^5 Pa

P = 1.002 x 10^8 Pa.

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A skateboarder is inside of a half pipe, shown here. Explain her energy transformations as she jumps off at point A, slides to point B, and finally reaches point C.

Answers

Point A would be the build up and leverage to slide down the half pipe to point b she would be bending her knees to increase speed to go up the other side and meet point c

14. Neglecting air resistance, what maximum height will be reached by a stone thrown straight up with an initial speed of 35 m/s?
(a) 98 m
(b) 18 m
(c) 160 m
(d) 63 m​

Answers

Answer:

D

Explanation:

The maximum height reached by a stone thrown straight up with an initial speed of 35 m/s can be found using the kinematic equation:

v^2f = v^2i - 2gh

where vf is the final velocity (0 m/s at the maximum height), vi is the initial velocity (35 m/s, the magnitude of the velocity with which the stone is thrown upwards), g is the acceleration due to gravity (-9.8 m/s^2), and h is the maximum height reached by the stone.

Rearranging the equation, we get:

h = (vi^2)/(2g)

Substituting the given values, we have:

h = (35 m/s)^2 / (2 * 9.8 m/s^2)

= 62.6 m

Therefore, the maximum height reached by the stone is approximately 63 m.

The answer is (d).

When a car is stopped, facing upwards on a hill, which way does friction act?

Answers

When a car is stopped, facing upwards on a hill, the friction acts in the opposite direction to the motion that the car would naturally take if it were not stopped.

In this case, the car would roll backwards down the hill due to the force of gravity. The friction between the tires and the road surface acts in the opposite direction to this motion, providing a force that opposes the car's tendency to roll backwards. Therefore, the friction acts in the forward direction, up the hill, to prevent the car from rolling backwards.

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Mona said, "I think that, when there is no lid, convection is the main way that
energy escapes from the water."
Has she drawn a good conclusion from her results? Explain your ideas

Answers

Mona's conclusion that convection is the main way that energy escapes from the water when there is no lid may or may not be a good conclusion, depending on the context and information provided.

Convection is a process of heat transfer that involves the movement of fluids (in this case, the water) due to differences in temperature. It occurs when warmer portions of the fluid rise and cooler portions sink, creating a circulating flow.

To determine if Mona's conclusion is valid, additional information is needed. Factors such as the presence of other heat transfer mechanisms (such as radiation or evaporation), the specific setup of the experiment, and the conditions under which the observations were made are essential.

If Mona's experiment only considered convection as the primary mechanism for energy escape and excluded other factors, her conclusion might be incomplete or inaccurate. To draw a more comprehensive conclusion, it is necessary to consider other potential heat transfer mechanisms and perform further investigations or provide additional supporting data.

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Which phrase is an example of kinetic energy?

Answers

A roller coaster going up and down, I’m literally studying this in my science class 8th grade

Have an AWESOME day! :)

An insect lands 0.1m from the centre of a turn table while the record is turning at 55 rev/min at what linear speed will the insect be carried
collision with the near stationary photograph

Answers

The linear speed will be the insect be 0.5759 meter/second carried collision with the near stationary photograph.

What is speed?

Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity With SI unit meter/second.

Given that an insect lands 0.1m from the center of the turn table.

Rotational speed of the turn table = 55 rev/min

= (55×2π/60) rad/second

= 5.759 rad/second.

Hence, the speed of the insect be = Rotational speed × length

= 5.759 rad/second × 0.1 M.

= 0.5759 meter/second.

Therefore, the speed of the insect be 0.5759 meter/second.

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A coin is dropped into a deep well and the time taken to hit the bottom is measured to be 2.48s. Calculate the following: a) The depth of the well b) The final velocity of the coin c) The mass of the coin, if the water slows it to a stop in 0.72s exerting an average force of 0.41N on the coin On the basis of which of Newton’s laws is this calculated? What does this law say?

Answers

Answer: I’m not sure but my guess would be A.

Explanation:

To solve this we must be knowing each and every concept related to velocity and its calculation. Therefore, the final velocity of the coin is 24.3 m/s.

What is velocity?

Velocity is a vector-based evaluation of an object's rate of motion and direction of motion. As a result, in order to calculate velocity using this definition, we must be familiar with both magnitude and direction.

For example, if an item travels west with 5 meters a second (m/s), its velocity to the west will be 5 m/s. The most frequent and simplest approach to determine velocity is using the formula shown below.

Mathematically,

elapsed time = 2.48 s

depth of well = 30.17 m

final velocity = ?

V = g × t

g=acceleration due to gravity=9.81 m/s²

t=time

substituting all the given values in the above equation, we get

V = 9.81 ×2.48

   =24.3 m/s

Therefore, the final velocity of the coin is 24.3 m/s.

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An aluminum wing on a passenger jet is
25 m
long when its temperature is
19°C.
At what temperature would the wing be 3 cm (0.03 m) shorter?

Answers

The wing is made of aluminum, therefore: α = 25 x 10-6 /oC Length: l = 29 m, Temperature: T1 = 29  C and Change in length: Δl = -7 cm (-0.07 m)

What is Aluminium wire?

α = 25 x 10-6 /oC,Δl = αlΔT = αl(T2 - T1)

The equation for what you don't know: Δl = αl(T2 - T1); divide both sides by αl Δl/ αl = (αl/ αl )(T2 - T1) = T2 - T1; add T1 to both sides. Δl/αl + T1 = T2 - T1 + T1 = T2 and Δl/ αl + T1 = T2

Δl/ αl + T1 = T2

= (-0.07 m)/( 25 x 10-6 /oC x 29 m) + 29 C = -96.551 oC + 29 C

= -67.551 oC = -67.6 C.

Therefore, The wing is made of aluminum, therefore: α = 25 x 10-6 /oC Length: l = 29 m, Temperature: T1 = 29 C and Change in length: Δl = -7 cm (-0.07 m).

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A motorcycle stoop is at a traffic light, when the light turns green, the motorcycle accelerates to a speed of 78 km/h over a distance of 50 m. What is the average acceleration of the motorcycle over this distance?

Answers

The average acceleration of the motorcycle over the given distance is approximately 9.39 m/s².

To calculate the average acceleration of the motorcycle, we can use the formula:

Average acceleration = (final velocity - initial velocity) / time

First, let's convert the final velocity from km/h to m/s since the distance is given in meters. We know that 1 km/h is equal to 0.2778 m/s.

Converting the final velocity:

Final velocity = 78 km/h * 0.2778 m/s = 21.67 m/s

Since the motorcycle starts from rest (initial velocity is zero), the formula becomes:

Average acceleration = (21.67 m/s - 0 m/s) / time

To find the time taken to reach this velocity, we need to use the formula for average speed:

Average speed = total distance/time

Rearranging the formula:

time = total distance / average speed

Plugging in the values:

time = 50 m / 21.67 m/s ≈ 2.31 seconds

Now we can calculate the average acceleration:

Average acceleration = (21.67 m/s - 0 m/s) / 2.31 s ≈ 9.39 m/s²

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If you are given values for Δx, v, and Δt, which kinematic equation could be used to find v0?​
V = v0 + aΔt
Δx= (v + v0/ 2) Δt
v^2 = v0^2 2aΔx
Δx = v0Δt + 1/2 a (Δt)^2

Answers

The  kinematic equation which could be used to find v₀ is Δx= (v + v₀/ 2) Δt; option B.

What are kinematic equations?

Kinematic equations are equations which relates the motion of a body.

Kinematic equations shows the relationship between the various parameters of motion of a body:

change in position, Δxchange in time, Δtacceleration. ainitial velocity, v₀final velocity, v

The kinematic equations are given below:

V = v + a*ΔtΔx= (v + v₀/ 2) Δtv^2 = v₀² + 2aΔxΔx = v₀Δt + 1/2 a * (Δt)²

Given the values for Δx, v, and Δt, the kinematic equation which could be used to find v₀ is Δx= (v + v₀/ 2) Δt

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1
A car travels 4 km due north and then 2 km due west going from town
A to town B. The distance traveled by the car is km

Answers

Answer:

pretty sure it is 6km

Explanation:

the car traveled 4km north then 2km west 4+2=6 so yah

Which graph represents the relationship between the magnitude of the gravitational force exerted by earth on a spacecraft the distance between the center of the spacecraft the center of earth

Answers

Answer:

B as distance increase force decrease, but it is not a linear relationship.

1)Answer the following question in sort
a)Define pressure ?
b)What is the value of standard atmospheric pressure?
c)Mention any one application of liquid pressure in our daily life?
d)Mention in the name of the instruments used to measure the pressure of compressed air?
e)Which instrument is used to measure atmospheric pressure ?
f)What is the unit of compressed air?
g)Define standard atmospheric pressure?
h)Which property of liquid is applicable in water supply system in cities?
i)Which property of liquid supports to use in it in hydraulic machine?

2)Answer the following questions in detail a)Define atmospheric pressure? Prove the presence of atmospheric pressure with the help of an activity?
b)Derive that P=dgh?
c)Describe the structure and working method of mercury barometer briefly?
d)Enlist any three points to show the importance of atmospheric pressure?
e)Enlist any four application of liquid pressure?f)Mention any three events occurred in our daily life which are directly related with pressure?​

Answers

1)a) Pressure is the force exerted per unit area, measured in units such as pascals (Pa) or pounds per square inch (psi).

b) The value of standard atmospheric pressure is approximately 101.3 kilopascals (kPa) or 1 atmosphere (atm).

c) One application of liquid pressure in our daily life is in hydraulic systems, like car brakes, where liquid pressure is used to transmit force and amplify it.

d) The instruments used to measure the pressure of compressed air include pressure gauges or manometers.

e) An instrument called a barometer is used to measure atmospheric pressure.

f) The unit of compressed air is typically measured in pounds per square inch (psi) or pascals (Pa).

g) Standard atmospheric pressure is the pressure exerted by the Earth's atmosphere at sea level. It is approximately equal to 1 atm or 101.3 kPa.

h) The property of liquid that is applicable in water supply systems in cities is its ability to flow and exert pressure, allowing water to be distributed through pipes and reach different levels in buildings.

i) The property of liquid that supports its use in hydraulic machines is its incompressibility, allowing it to transmit force and energy effectively.

2) a)Atmospheric pressure is the force exerted by the weight of the Earth's atmosphere on a surface.

b) The equation P = dgh. This equation can be derived by considering the weight of the fluid column and the force it exerts on a unit area at the base.

c) A mercury barometer consists of a glass tube filled with mercury, inverted into a dish of mercury. The mercury in the tube adjusts its height based on the atmospheric pressure.

d) The importance of atmospheric pressure can be seen in its role in weather patterns, maintaining the balance of gases in the atmosphere, and facilitating breathing for humans and animals.

e) Applications of liquid pressure include hydraulic systems in machinery, such as lifts and cranes, hydraulic brakes in vehicles, and water towers for maintaining water pressure in buildings.

f) Events in daily life directly related to pressure include inflating a balloon, using a bicycle pump to inflate tires, and squeezing toothpaste out of a tube.

1)a) Pressure is defined as the force per unit area. Its unit in the S.I system is newtons per square meter (N/m²) or Pascal (Pa).

b) The value of standard atmospheric pressure at sea level is 101.3 kPa (kilopascals) or 1 atm (atmosphere). c) Liquid pressure has numerous applications in our daily life, but one of the most common ones is the hydraulic braking system used in cars.

d) An instrument used to measure the pressure of compressed air is called a pressure gauge. e) An instrument used to measure atmospheric pressure is called a barometer.

f) The unit of compressed air is generally psi (pounds per square inch).

g) Standard atmospheric pressure is the pressure exerted by the atmosphere at sea level and is equal to 101.3 kPa or 1 atm.

h) The property of liquids that is applicable in water supply systems in cities is their incompressibility. i) The property of liquids that supports their use in hydraulic machines is their incompressibility.

2)a) Atmospheric pressure is defined as the force per unit area exerted by the weight of the atmosphere on the surface. It is proven with the help of the following activity: Take a glass full of water and place a cardboard over it. Hold the cardboard tight and invert the glass. The water will not spill out of the glass, which is because the atmospheric pressure is greater on the cardboard than the pressure inside the glass.

b) The pressure exerted by a fluid can be derived using P = dgh, where P is the pressure, d is the density, g is the acceleration due to gravity, and h is the height of the fluid column.

c) A mercury barometer is made up of a glass tube that is closed at one end and filled with mercury. The tube is inverted and placed in a container of mercury. The pressure of the atmosphere on the open surface of the container forces the mercury in the tube to rise to a height that is proportional to the atmospheric pressure.

d) The importance of atmospheric pressure can be explained by the following points: it enables breathing, regulates the weather, and causes the ocean tides.

e) Some applications of liquid pressure include hydraulic brakes in cars, hydraulic lifts, and hydraulic jacks.

f) Some events that are directly related to pressure include gas escaping from a pressurized container, balloons being inflated, and soda cans being opened.

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What does the first law of thermodynamics state about energy?

Answers

The first law states that the internal energy change of that system is given by Q − W . Since added heat increases the internal energy of a system, Q is positive when added to the system and negative when removed from the system.

What is the independent variable if a scientist is turning bulb on and off to check behaviour of the earthworm?





Answers

The independent variable in this experiment is the act of turning the bulb on and off, while the dependent variable is the behavior of the earthworm in response to changes in light. The scientist can analyze the data collected to determine the impact of light on the earthworm's behavior.

In the experiment where a scientist is turning a bulb on and off to check the behavior of an earthworm, the independent variable is the manipulation performed by the scientist, which is the act of turning the bulb on and off.

The independent variable is the variable that the scientist deliberately changes or controls in order to observe its effect on the dependent variable. In this case, the scientist is interested in investigating how the earthworm responds to changes in light. By turning the bulb on and off, the scientist is manipulating the presence or absence of light in the environment of the earthworm.

The behavior of the earthworm, which is the dependent variable, will be observed and measured in response to the changes in light. The scientist may record various behaviors such as movement, burrowing, or changes in activity level exhibited by the earthworm when the light is turned on and off.

By systematically controlling the independent variable (turning the bulb on and off) and observing the dependent variable (behavior of the earthworm), the scientist can analyze the relationship between light exposure and the earthworm's behavior. This allows for drawing conclusions about how the earthworm responds to light stimuli.

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A 3.0 kg pendulum swings from point A of height ya = 0.04 m to point B of height yb = 0.12 m, as seen in the diagram below.

A 3.0 kg pendulum swings from point A of height ya = 0.04 m to point B of height yb = 0.12 m, as seen

Answers

Answer:

3.0−0.12=2.88 or 2.88÷0.04=72

0.04×3.0=0.12 and 0.04+3.0=3.04

Answer: 2.4 J

Explanation: Khan Academy

What force is required to stop a 1800-kg car in a distance of 0.20 m if it is initially moving at 2.2 m/s? What if the car is moving at 4.5 m/s

Answers

The formula for the force required to stop the automobile is F = m x a, where m = 1200 kg and F = 1200 x (-12.5) N = - 15000 N.

What force does an automobile need to stop?

As a car brakes, the rotating wheels create friction inside the wheel assemblies, bringing the vehicle to a stop. The kinetic energy of the automobile is lost as heat in the braking components due to this friction force, which slows the spinning of the wheels.

The automobile can come to a stop with any force higher than zero. The only difference is that it will take longer and cover a bigger distance before stopping.

Unless a force acts on a body, it stays at rest or moves in a straight path at a constant speed.

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please help

question in the picture ​

please help question in the picture

Answers

B because it accelerates by 40m/s same as from 0 to 40

Describe at least two gravitational forces that exist in the diagram above.

Describe at least two gravitational forces that exist in the diagram above.

Answers

There are just two factors that matter when discussing the gravitational pull of one item on another: the mass of each object and the distance between them.

This is further explained below.

What are gravitational forces?

Generally, According to Newton's global law of gravitation, the amount of force exerted by the attraction between any two bodies is directly related to the sum of their masses and inversely related to the square of the distance that separates them from one another.

In conclusion, The magnitude of the gravitational pull between two objects is proportional to the product of their respective masses and the square of the distance that separates them.

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6. When you pick up an ice cube, your hand gets cold. Using the laws of thermodynamics, explain
why your hand feels cold.

Answers

Answer:

The transfer of thermal energy from your hand to the ice cube, as dictated by the second law of thermodynamics, causes the sensation of coldness. The third law of thermodynamics also plays a role in reducing the thermal energy and increasing the order of the molecules in the ice cube, contributing to the overall sensation of coldness.

Explanation:

When you pick up an ice cube, your hand feels cold due to the transfer of thermal energy from your hand to the ice cube. This transfer of energy occurs as a result of the second law of thermodynamics, which states that thermal energy always flows spontaneously from a hotter object to a colder object.

In this case, the ice cube is colder than your hand, and therefore has a lower thermal energy. When you touch the ice cube, heat flows from your hand to the ice cube in an attempt to equalize the temperature of the two objects. This transfer of heat causes the thermal energy of your hand to decrease, resulting in the sensation of coldness.

Another factor that contributes to this sensation is the third law of thermodynamics, which states that as the temperature of an object approaches absolute zero (the theoretical limit of zero Kelvin or -273.15 degrees Celsius), its entropy approaches a minimum value. This means that when the thermal energy of an object, such as an ice cube, is much lower than that of your hand, the disorder of its particles is greatly reduced. As a result, the molecules in the ice cube vibrate more slowly and produce less heat, leading to the sensation of coldness when touched.

A computer model displays the motion of a particle on a coordinate system in real time. At time t = 0, the particle is at the origin of the coordinate system and has velocity components-= 0 and yy= 6,4 m/s. The partide has acceleration components of a, = -4.0 m/s? and ay= O

A computer model displays the motion of a particle on a coordinate system in real time. At time t = 0,

Answers

Since the acceleration on the y-axis is 0, then the movement in the vertical direction can be modeled as a constant speed motion:

\(\begin{gathered} v_y(t)=v_{0y} \\ y(t)=y_0+v_{0y}t \end{gathered}\)

On the other hand, since the acceleration on the x-axis is different from 0 and it is a constant acceleration, then, the horizontal movement of the particle can be modeled as a uniformly accelerated motion:

\(\begin{gathered} v_x(t)=v_{0x}+a_xt \\ x(t)=x_0+v_{0x}+\frac{1}{2}a_xt^2 \end{gathered}\)Part a)

Since the particle is at the origin at t=0, then x₀=0 and y₀=0.

Replace v_0x=0, v_0y=6.4m/s and a_x=-4m/s^2 into the equations to find the expressions for x(t), y(t), v_x(t) and v_y(t):

\(\begin{gathered} x(t)=\frac{1}{2}(-4.0\frac{m}{s^2})t^2 \\ \\ \therefore x(t)=(-2.0\frac{m}{s^2})t^2 \end{gathered}\)\(y(t)=(6.4\frac{m}{s})t\)\(\begin{gathered} v_x(t)=(-4.0\frac{m}{s^2})t \\ \\ v_y(t)=6.4\frac{m}{s} \end{gathered}\)

Evaluate the expressions for x(t) and y(t) at t=4.5s to find the x and y positions of the particle at t=4.5s:

\(\begin{gathered} x(4.5s)=(-2.0\frac{m}{s^2})(4.5s)^2=-40.5m \\ \\ y(4.5s)=(6.4\frac{m}{s})(4.5s)=28.8m \end{gathered}\)Part b)

Replace t=4.5s into the expressions for the velocities of the particle to find v_x and v_y at t=4.5s:

\(\begin{gathered} v_x(4.5s)=(-4.0\frac{m}{s^2})(4.5s)=-18\frac{m}{s^2} \\ \\ v_y(4.5s)=6.4\frac{m}{s} \end{gathered}\)Part c)

Initially, the horizontal component of the velocity was 0 while the vertical component of the velocity was 6.4m/s. After 4.5 seconds, the vertical component of the velocity stays the same but the horizontal component changes to -18m/s. The magnitude of the velocity increases because the magnitude of one of the components increases while the other remains the same.

Therefore, the answers are:

Part a)

x = -40.5 m

y = 28.8 m

Part b)

v_x = -18 m/s

v_y = 6.4 m/s

Part c)

The particle's speed increases with time.

Gold forms a solid solution with silver. Since the densities of pure gold and silver are 19.32 g/cm³ and 10.49 g/cm³, respectively, calculate the number of gold atoms per cubic centimeter for a silver-gold alloy containing 10% Au and 90% Ag by weight.

Answers

There are 3.37 × \(10^{22}\) gold atoms per cubic centimeter in the silver-gold alloy.

The density of a binary alloy can be calculated using the following equation:

ρ = w1ρ1 + w2ρ2

where,

ρ = density of the alloy

w1 and w2 = weight fractions of the two components (in this case, gold and silver)

ρ1 and ρ2 = densities of the pure components.

We are given that the alloy contains 10% gold and 90% silver by weight, so we can calculate the weight fractions as:

\(w_{Au}\) = 0.10

\(w_{Ag}\) = 0.90

We are also given the densities of pure gold and silver as:

ρ_Au = 19.32 g/\(cm^{3}\)

ρ_Ag = 10.49 g/\(cm^{3}\)

Now we can substitute these values into the density equation to find the density of the alloy:

ρ = \(w_{Au}\)ρ_Au +\(w_{Ag}\)ρ_Ag

ρ = (0.10)(19.32 g/\(cm^{3}\)) + (0.90)(10.49 g/\(cm^{3}\))

ρ = 11.08 g/\(cm^{3}\)

Next, we need to calculate the number of gold atoms per cubic centimeter in the alloy.

To do this, we can use Avogadro's number and the atomic weights of gold and silver:

\(N_A\) = 6.022 × \(10^{23}\) atoms/mol

Aum = 196.97 g/mol

Agm = 107.87 g/mol

The number of gold atoms:

\(n_{Au}\) = (\(w_{Au}\)ρ/ Aum) × \(N_{A}\)

Substituting the values, we get:

\(n_{Au}\) = (0.10 × 11.08 g/\(cm^{3}\)/ 196.97 g/mol) × 6.022 × \(10^{23}\) atoms/mol

\(n_{Au}\) ≈ 3.37 × \(10^{22}\) atoms/\(cm^{3}\)

Therefore, there are approximately 3.37 × \(10^{22}\) gold atoms per cubic centimeter in the silver-gold alloy.

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