If a series circuit has two loads of 8 ohms and 4 ohms what do you know about their voltage drops.

Answers

Answer 1

The voltage drops will have the ratio of 2 : 1

Assuming the loads have the same power factor, the voltage drop will be proportional to the load impedance. The loads have a ratio of 8 : 4, 2 : 1, so the voltage drops will have a ratio of 2 : 1

What is voltage drop ?

Voltage drop is the reduction in electrical potential along an electrical current's path in a circuit. Because some of the energy supplied is lost, voltage drops in the source's internal resistance, across conductors, across contacts, and across connectors are undesirable.

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Related Questions

a 1 kg ball is hung at the end of a rod 1 m long. if the system balances at a point on the rod 0.25 m from the end holding the mass, what is the mass of the ro

Answers

The mass of the rod is 1 kg.

Solution:

So 1*25=x*25

1 kg

The product of the total mass of the system and the position vector of the center of mass equals the sum of the products of the masses of the two particles and their respective position vectors. If the mass is unevenly distributed, the centroid is in the area of ​​higher mass.

If the density increases decrease continuously from left to right or right to left the centroid is not at the center of a particular rod. Mass is the amount of matter in the physical body. It is also a measure of body inertia, resistance to acceleration when a net force is applied. An object's mass also determines the strength of gravity on other objects.

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A piece of what nasa space shuttle was recently discovered by a film crew in the atlantic ocean?.

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Divers Unintentionally Discover a Challenger Space Shuttle Piece. A television documentary team dove into the waters near Florida in quest of a sunken World War II aircraft.

which two space shuttles exploded?

All seven astronauts upon board died when the Space Shuttle Columbia exploded during the STS-107 mission over Texas as it reentered in atmosphere. Following Challenger's loss and the deaths of all seven crew members during ascent, this mission was the second in the Space Shuttle program to end in catastrophe.

What are the uses of a space shuttle?

The U.S. National Aeronautics and Space Administration (NASA) developed the space shuttle, also known as the Space Transportation System, a partially reusable rocket-launched spacecraft that can travel to and from orbiting spacecraft while carrying people and cargo, and land on a runway when it returns to Earth's surface.

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Here is a write up of an experiment on heat transfer. The independent variable in this experiment is the _________ of the container. What one word completes the sentence?.

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The independent variable in this experiment is the temperature of the container, while the dependent variable is the heat transfer rate.

What is the dependent experimental variable?

The dependent experimental variable is any variable in an experiment that changes according to the modification of the independent variable that remains unaltered, which is then considered the cause of this change.

Therefore, with this data, we can see that the dependent experimental variable is associated with changes in the independent variable which is unaltered during all experimental procedures and is recognized as the cause of change.

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What is the collision formula?.

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The collision formula is m₁u₁+m₂u₂=m₁v₁+m₂v₂ and  [tex]V=\frac{m_1v_1+m_2v_2}{m_1+m_2}[/tex].

A collision is an event in which two or more objects exert forces on one another quickly. Elastic collision and inelastic collision are two types of collision.

The term "elastic collision" refers to a collision between two bodies where the total kinetic energy of both bodies after the collision is equal to their total kinetic energy before the collision.  The formula to calculate this is m₁u₁+m₂u₂=m₁v₁+m₂v₂.

Here, m₁ and m₂ are the mass of object 1 and object 2. u₁ and u₂ initial velocities of object 1 and object 2. v₁ and v₂ are the final velocities of object 1 and object 2.

An inelastic collision is one in which some energy is lost when two objects collide. The formula to calculate this is [tex]V=\frac{m_1v_1+m_2v_2}{m_1+m_2}[/tex].

Here, V is the final velocity, m₁ and m₂ are the mass of object 1 and object 2. v₁ and v₂ are the initial velocities of object 1 and object 2.

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two particles of masses m1 and m2 ( m1

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More than five meters, but less than ten meters, separate two particles with mass m1 and m2 from the atom of mass m1.

Describe mass.

In physics, mass is a quantification of inertia, a basic characteristic of all matter. It essentially refers to a body of matter's resistance to changing its speed or location in response to the use of a force. The change caused by a force applied is smaller the more mass a body has.

Describe the mass formula.

The mass with one mole of a chemical substance or the ratio of a mass of a chemical to its number of chemicals substance is known as the molar mass (M), which is a physical attribute.

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Claire sits on a bar stool, with her feet off of the floor. The seat of the bar stool is free to rotate. Claire is holding a wheel (moment of inertia = 1.75 kg m^2) that is spinning counterclockwise at an angular speed of 16.20 rad/s, as shown below. Claire and the bar stool are stationary. (Claire + the bar stool have a moment of inertia of 44.20 kg m^2.) Claire, being adventurous, flips the axle of the wheel by 180 degree (applying an internal torque) and holds the wheel in place. What happens to Claire and the wheel? (a) What is ''the system" for this problem? O Just wheel. O Just Claire.
O The wheel and Claire. O The wheel. Claire, and the bar stool. (b) What is the total angular momentum of the system? Magnitude kg m^2/s Direction (One Submission) O up (counterclockwise) O down (clockwise) (c) What is the angular momentum of the wheel after Claire flips it over? Magnitude kg m^2/s Direction (One Submission) O down (clockwise) O up (counterclockwise) (d) What is (the bar stool + Claire)'s angular momentum after Claire flips the wheel over? Magnitude? kg m^2/s Direction? (One Submission)
O down (clockwise) O up (counterclockwise) (e) What is Claire s angular velocity after she flips the wheel over? Magnitude? rad/s Direction? (One Submission) O down (clockwise) O up (counterclockwise)

Answers

That the combination of an object's mass, speed, and distance from the center of rotation determines its angular momentum.

What is the system's overall angular momentum?L = I, where L is angular momentum, I is rotational inertia, and (the Greek letter omega) is angular velocity, is the formula for angular momentum.To put it simply, you can say that the angular momentum of an object is equal to the sum of its mass, speed, and separation from the point of rotation.Symbol = The angular momentum is represented by the letter L because it is a vector quantity. Units = The unit of measurement is the kilogram-meter-second.Dimensional equation: M L2 T 1 Angular momentum (L) is calculated using the formula mvr, where m stands for mass, v for speed, and r for radius.The system's total angular momentum is equal to I=1.87 x 17.80=33.286 in the up (counterclockwise) direction.The vector sum of the individual angular momenta near the origin represents the system of particles' total angular momentum.Radius times linear momentum is what determines an object's angular momentum. [L = I x, I = inertia, and = angular velocity or L = r x p, where p is linear momentum]

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which of the following statements best justifies the inclusion of test tube v as a control in the experiment? responses it will provide a measurement of amylase activity at an acidic ph.

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The following statement which best justifies the inclusion of test tube v as a control in the experiment is that it will show the color change that occurs in the absence of enzyme activity and is denoted as option C.

What is an Enzyme?

This is referred to as a biological catalyst which is involved in the speeding up of the rate of a reaction by lowering the activation energy used to initiate the reaction.

Enzymes are known as proteinous in nature and are denatured by heat and other substances is included in the test tube v as a control in the experiment is that it will show the color change that occurs in the absence of enzyme activity.

This therefore helps to differentiate the enzymatic processes which takes place in a substance or body therefore making option C the correct choice.

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The options are:

It will provide a measurement of amylase activity at an acidic pH.it will provide a measurement of amylase activity at a basic pH. It will show the color change that occurs in the absence of enzyme activity.it will show the color change that occurs in the absence of the amylase protein.

It will show the color change that occurs in the absence of enzyme activity.

What evidence have you discovered to explain how kinetic energy and mass are related

Answers

Explanation:

Kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m v2. If the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared.

behavior therapists look to current environmental events that maintain problem behaviors and help clients produce behavior change by changing environmental contingencies (T/F).
(T)rue

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Through the process of functional assessment, behavior therapists look to the current environmental events that maintain problem behaviors and help clients produce behavior change by changing environmental events.

Functional assessment is used to determine an individual's level of functioning and his or her ability to perform specified tasks on a safe and predefined environment over a defined period. An FBA is the process of determining the reasons (or “functions”) of behavior before producing an intervention, which is based upon hypothesized causes (functions) of behavior and understanding why a behavior occurs facilitates a more targeted and effective intervention.There are components of functional assessment, which includes- Vision and hearing, mobility, continence, nutrition, mental status, affect, home environment, social support, activities of day to day life such as transferring, ambulating, bathing, etc.

Hence, through the process of functional assessment, behavior therapists look to the current environmental events that maintain problem behaviors and help clients produce behavior change by changing environmental events.

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17) what is the net power needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s in 4.00 seconds?

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The net power needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s in 4.00 seconds is 275,000Watts.

Define power?

The ratio of work completed to the amount of time required is known as power. It can be expressed as-     P = W/t

The following informations are provided in the question,

Mass of the sport vehicle, m = 1600 kg

Initial velocity, u = 15 m/s

Final velocity, v = 40 m/s

Time required, t = 4 seconds

Using the formula  F = m(v-u)/t, we can find the force required to change the velocity of the vehicle.

Putting the values in the above equation we get,

F = 1600(40-15)/4

F = 1600(25)/4

F = 400 * 25

F = 10,000N

Therefore the required net power is calculated using the expression-

P = 1/2*F(u+v)

Putting the values of F, u and v we get net power P as,

P = 1/2(10000)*(15+40)

P = 5000(55)

P = 275,000Watts

Hence, the required power is 275,000Watts

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if the 36.0- n force continues, the box accelerates at 0.38 m/s2 . what is the coefficient of kinetic friction?

Answers

The coefficient of kinetic friction is 0.54

Kinetic friction is characterized as a force that acts between moving surfaces. A body moving on the surface encounters a force in the opposite direction of its movement. The magnitude of the force will depend on the coefficient of kinetic friction between the two materials. Here we are given the information of a force of   36.0 N required to a 6.0-kg box moving across a horizontal concrete floor and the acceleration is at 0.60 m/s2.The formula we can refer to in order to the calculate the  kinetic friction is : F- u[tex]_{k}[/tex](mg)=ma

=>36-u[tex]_{k}[/tex](mg)= 6* 0.60

=> u[tex]_{k}[/tex](mg) =  36 -(3.6)

=> u[tex]_{k}[/tex]=  32.4/mg

=>u[tex]_{k}[/tex]= 32.4/6*10 = 0.54

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A force of 36.0 n is required to start a 6.0-kg box moving across a horizontal concrete floor.  if the 36.0-n force continues, the box accelerates at 0.60 m/s2 . What is the coefficient of kinetic friction?

when this guitar string vibrates in the second harmonic, it creates a sound wave in air, traveling at 343 m/s. what is the frequency of this sound wave?

Answers

The waves produced in string and the waves produced in the air are different from each other. The only similarity they have is that their frequencies are equal—otherwise, there's no similarity between them. One of the waves is a transverse wave which is on the wire and the other wave is a longitudinal wave which is in the air. But their velocities too are different from each other.

velocity = wavelength x frequency

if the frequency is constant

wavelength ∝ velocity

Here, in this question, the velocity is given to be 343 m/s

From the above formula, we can solve for frequency,

Frequency = velocity/wavelength

Frequency = 343*λ⁻¹

Thus, the frequency of the sound is directly commensurable (proportional) to the haste(velocity) of the sound and here it's 343 * λ ⁻¹.

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which of the following happens when the frequency of electromagnetic radiation decreases? explain your reasoning.

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As the electrical field corresponds to amplitude; so when the frequency decreases, waves broaden and the extent of the change decreases.

What happens when frequency of electromagnetic radiation decreases?

When the frequency decreases, then the wavelength gets longer. There are two types of waves: mechanical and electromagnetic. Mechanical waves like sound, ocean, seismic, or earthquake travel through a solid, liquid, or gas medium whereas electromagnetic waves travel through a medium or a vacuum.

The energy equation is given as, E = hν, where E represents energy, h is Planck's constant whose value is 6.626 x 10 -34 J.s and v represents frequency. The energy equation is direct relationship between frequency and energy. As frequency increases,  energy. also increases.

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a block of mass 0.4 kg on a horizontal surface is attached to a horizontal spring of negligible mass. the other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. the center of mass of the block is stretched a horizontal distance x

Answers

Soli energy from the potential energy distance is x = 0.25m. Then plenty of horizontal position graph, we get to that when hor.

Time - period of oscillation, T=21m k Mass = 0.4 +10 = 114 kq = 14 kg 114 320 T = 0.415 second T = 0.42 second us hoolzent.

If you hang a shape from one point you'll find that the center of mass is always directly below that point. So if you hang a shape from two different points and draw a line down from each point the center of mass is where those lines intersect.

The product of the total mass of the system and the position vector of the center of mass equals the sum of the products of the masses of the two particles and their respective position vectors. The center of mass is a position defined relative to an object or system of objects.

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a 62.6 kg runner has a speed of 5.10 m/s at one instant during a long-distance event.hint(a)what is the runner's kinetic energy at this instant (in j)?814.11correct: your answer is correct.j(b)how much net work (in j) is required to triple his speed?

Answers

a)The runner's kinetic energy at the given  instant is  814.11Joules b)net work required to triple his speed is 6653.361Jolues

Mechanical energy is divided into two parts- one kinetic energy and second one is potential energy.

a) The kinetic energy is given by the following expression =(1/2)mv² where m is the mass of the body and v is the velocity of the body.

Now, we have runner mass as 62.5kg and speed as 5.10m/sec

So, after putting in the formula we get,

K.E=(1/2)×62.6×(5.10)²

=>K.E.=31.3×(26.01)

=>K.E=814.11Joules.

b)According to the definition of work energy theorem, work done on the body is equal to change in kinetic energy of the body

W=ΔK.E

When velocity is tripled, final kinetic energy(KE₂)=(1/2)×62.6×(3×5.10)²

=>KE₂=31.3×9×26.01

=>KE₂=7467.471Jolues.

Initial kinetic energy(KE₁)=814.11Joules.

So, net work required=KE₂-(KE₁)

                           =>W=7467.471-814.11

                           =>W=6653.361Jolues

Hence, a)kinetic energy is 814.11Joules and b)net work required is 6653.361Jolues.

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What is her speed vi at the bottom of the arc if she swings out to a 45. 0 ∘ angle before reversing direction?.

Answers

The bottom of the arc would be equal to v0 * 0.707, or 70.7% of her initial velocity.

What is initial velocity?
A physical system's behaviour in terms of the its motion is described using equations of motion. The equations are relationships between different terms and quantities. There are primarily three equations of motion, also known as the laws of constant acceleration, that apply when there is uniform acceleration. Any object subject to forces will accelerate. The object's velocity changes as a result of this acceleration. As a result, the initial velocity is indeed the object's speed before the change brought on by acceleration. The velocity will become the final velocity after the object has been accelerating for a while.

Her speed at the bottom of the arc would depend on the magnitude of the initial velocity and the angle she is swinging out to.

Assuming that the initial velocity is constant, the speed at the bottom of the arc can be calculated using the equation:

v = v0 * cos(θ)

where v0 is the initial velocity and θ is the swing angle.

In this case, v0 is the initial velocity and θ is 45°, so the speed at the bottom of the arc would be:

v = v0 * cos(45°)

Therefore, her speed at the bottom of the arc would be equal to v0 * 0.707, or 70.7% of her initial velocity.

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How will you explain the behavior of the food dye when the water is agitated?.

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The water will eventually become colored as a result of the molecules' random movement. The diffusion process will be accelerated by agitation.

What brings about agitated behavior?

Extreme motor activity or interior restlessness, sometimes known as agitation, can be a sign of an illness or be a normal physiological response to a circumstance. The most common reasons for agitation are being in a new environment, using or withdrawing from drugs, having alcohol in your system, and general medical issues.

What sets off an individual's agitation?

It can start as a result of events, words, deeds, or in some situations, for unknown reasons. Although feeling irritated occasionally is common (for example, in reaction to stress from work or school), it can occasionally be an indication of an underlying medical condition.

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sea breezes group of answer choices involve onshore (toward the land) air flows that often develop in the afternoon. occur because warmer air is denser and settles to the surface of the land.

Answers

Sea breezes involes onshore air flows that often developes in afternon.

Hence, option A is the correct answer.

Sea Breeze is inflow of wind ocean towards land. This landward movement of wind caused due to lower heat capacity of land. Land portion gets hotted snappily as compared to ocean so due to hotting wind gets lower thick and low pressure zone devlopes on land while ocean water get hotted veritably slow so there's high pressure zone over ocean. High pressure wind over ocean face is thick and its thresholds to flow towards low pressure land.This process takes place in the evning but at night land breaths takes places which is rear of ocean breath i.e wind inflow from land towards ocean.

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in the first step of k-means with the standard euclidean distance metric, which points will be assigned to the cluster centered at p?

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In the first step of the k-means with the standard euclidean distance metric,  the mean of the observation values are assigned to the cluster.

K-means clustering is one of the commonly used clustering algorithms for partitioning observations into a set of k groups. This method tries to classify observations into mutually exclusive groups, so that observations within the same cluster are as similar as possible.

In k-clustering, each cluster is represented by its centre which corresponds to the mean of the observation values assigned to the cluster.

This implies that k-algorithm recognizes the k number of centroids.

The following required of k-means clustering are defined distance metric, number of clusters, initial guess of centroids.

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solar photovoltaic energy is highly versatile and can be used in a variety of dispersed settings. which of the following would not be a good location to harness large amounts of this form of energy?

Answers

The location that is not good for photovoltaic cells is the farm.

What is a photovoltaic  cell?

In the recent years, there have been a lot of clamor for the return to clean energy and the first port of call have been the consideration of the use of renewable energy sources as a power source for the future. This has engendered the return to the solar energy.

In the harvesting of the solar energy, solar cells are displayed in such a place that they can be able to absorb the energy from the sun and this is converted to electrical energy.

Unfortunately, if we are to harness the use of the photovoltaic cells, we need a large expanse of land that can be used to mount the cells and these lands would  cease to be available for use in agriculture.

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Missing parts;

Solar photovoltaic energy is highly versatile and can be used in a variety of dispersed settings. Which of the following would NOT be a good location to harness large amounts of this form of energy?Roof tops of commercial buildings Base-load Power Facilities Airports Agricultural Fields Residential Neighborhoods

The free-fall acceleration at the surface of planet 1 is 26m/s^2 . The radius and the mass of planet 2 are twice those of planet 1. What is on planet 2?

Answers

The acceleration on planet 2 is 13 m/s².

Acceleration is the rate of change of the velocity of an item with appreciation to time. Accelerations are vector portions. The orientation of an item's acceleration is given by the orientation of the net pressure appearing on that object.

Calculation:-

The acceleration of gravity near the surface of a planet is:

g = MG / R²

For planet 1, g = 26 m/s^2.

The gravity on planet 2 in terms of the mass and radius of planet 1 is:

g = (2M)G / (2R^2)

g = 1/2 MG / R²

Since MG/R² = 26 m/s², then:

g = 13 m/s²

Acceleration is the charge at which velocity modifications with time, in terms of each speed and route. A factor or an object moving in a straight line is accelerated if it quickens or slows down. movement on a circle is extended despite the fact that the rate is consistent because the course is continually changing.

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What is the wavelength of a 200 Hz wave?.

Answers

The answer is 150 cm!!!

a car drives around a 75 m radius curve at a constant speed of 18 m/s. a car freshener hangs by a string from the rearview mirror. determine the angle between the string and the vertical as the car rounds the curve.

Answers

The angle between the string and the car is 23.79° When the car drives around a 75 m radius curve with a constant speed of 18m.s.

Radius of the curve = r = 75m

Speed of the car = v = 18 m/s

To calculate centripetal acceleration,

Centripetal acceleration is the acceleration experienced by the car when in constant motion around the curve.

Centripetal Acceleration = Cₐ =

= v² / r

= 18² / 75

= 4.35 m/s²

Gravitational acceleration = g = 9.8 m/s²

To find the angle between the string and the car= θ =

= θ = tan (Cₐ /g)

= θ = tan (4.35 / 9.8)

= θ =23.79°

Thus, the string attached to the car moving at the constant force is at an angle of 23.79 degrees.

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What is a substance

Answers

Ursula’s answer as a chemical is any substance consisting of matter; this includes solids, liquids, and gas. Chemicals can either be of a pure substance or a mixture of substances.

how much heat is needed to raise the temperature of 12 kg/s of argon from 20 deg c to 120 deg c? the specific heat of argon is 0.3122 kj/(kg-k).

Answers

To elevate 12 kg/s of argon from 20 degrees Celsius to 120 degrees Celsius, 520.3 heat must be used.

What does "heat" actually mean?

Heat is the outcome of kinetic energy moving within a material or an object, or from a power source to a medium or an object. Such energy can be transported through three different mechanisms: radiation, conduction, and convection.

What does heat actually mean?

Heat energy is created by the motion of tiny atoms, molecules, or ions in solids, liquids, and gases. Heat energy is transferable from one thing to another. Heat is the flow or transfer that happens as a result of temperature difference between two objects.

[tex]C_{p} = 0.3122 = \frac{8.314}{39.95 X 10^{3} } = 0.2081 X 10^3\\ C_{p} = 0.2081 X 10^3 + 0.3122\\ C_{p} = 0.5203 X 10^3\\ C_{p} = 520.3[/tex]

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if their original solder sample weighed 3.1564g, what is the percent silver in the solder? calculate the concentration in ug/ ml of the four standards you will prepare in week 2 of the instrumental procedure

Answers

The process of joining two or more parts using silver solder, also referred to as "hard" soldering or silver brazing, involves melting and flowing filler metal into the joint.

What is silver soldering?The filler metal flows into the joint via capillary action and has a melting point above 420°C. A silver soldered joint is much stronger than a soft soldered joint because it consists of multiple layers that are all metallurgically connected to the surface of the parts being joined. Due to the fact that the filler material frequently contains silver, it is known as "silver" soldering.In contrast, welding involves melting the base metal during the joining process, letting the two halves of the molten joint flow together, and then allowing the joint to cool. The discussion below solely pertains to silver/hard soldering.In hard soldering, the surface's metallurgy is altered, the joints are metallurgically connected, and they become a permanent part of the underlying metal surface. Because of this, a joint that has been silver soldered is often times stronger than the base materials being joined and much stronger than one that has been soft soldered.

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A 120 kg hoop rolls along a horizontal floor so that the hoop's center of mass has a speed of 0.180 m/s. How much work must be done on the hoop to stop it?
___ J

Answers

The work that must be done on the hoop to stop it is calculated to be -3.888 J.

As the mass of the hoop is 120 kg and the hoop's center of mass has a speed of 0.180 m/s, the rotational inertia can be given as follows;

I= mr^2

I=120r^2

The kinetic energy of hoop = Linear kinetic energy + Rotational kinetic energy

K= (1/2mv^2) + (1/2Iw^2)

But; w= (v/r)^2

K= (1/2mv^2) + (1/2×120r^2(v/r)^2)

K = (1/2×120×0.180^2) + (1/2×120×0.180^2)

K = 3.888 J

To stop the hoop, its final kinetic energy must be 0, therefore;

Work done = Kfinal-Kinitial = 0 - 3.888

W= -3.888 J

Hence, -3.888 J of work must be done to stop the hoop.

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a piano hangs from a steel cable. as it s lowered from a third- floor apartment to the groundt,he work done on the piano by the cable is (a) positive; (b)negative; (c) zero; or (d) it cannot be determined without more information

Answers

The correct option is option B.

For this exercise we must use the work definition

   W = F. s

Where the bold characters indicate vectors and the point is the scalar producer

   W = F s cos θ

Where θ is the angles between force and displacement.

Here, in this case, the cable creates an upward tension and with the piano going down the angle between them is 180º so the work of the cable on the piano is negative.

The evade has a downward force, its weight so the force goes down and the displacement goes down, as both are in the same direction the work is positive.

Therefore, the cable does negative work on the piano and piano does positive work on the cable and we can say work done on the piano by the cable is negative.

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A cubical block of mass m and side 'a' is moving horizontally on a smooth horizontal surface with a velocity v 0

. The block collides with a ridge P and starts rotating about P. Find the minimum value of v 0

needed to overcome the ridge.

Answers

A cubical block of mass m and side a is moving horizontally on a smooth horizontal surface with a velocity v₀. The minimum value of v₀ is 4aω/3.

Consider the initial angular momentum of the block,

Li = Mv × x

Angular momentum of the block after it hits a certain point O is

Lf = Ic *ω

where, Ic is the moment of inertia

ω is angular velocity

From the parallel axis theorem, we have

Io = Ic + M * OC² = 1/6 M a² + M ( AC² + AO² ) = 1/6 M a² + 1/2 M a² = 2/3 M a²

Using the law of conservation of angular momentum, we have

1/2 M v = 2/3 M a² ω

v = (4a ω)/3

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A race car starts from rest on a circular track. The car increases its speed at a constant rate at as it goes once around the track in the counterclockwise direction. Find the angle that the total acceleration of the car makes with the radius of the circle, at the moment when the car completes first half of the circle. A) 9.04o B) 4.55o C) 3.14o D) ) 0.08o E) none of the above

Answers

Option A is correct.

9.04 degree is the angle that the total acceleration of the car makes with the radius of the circle.

What is speed?

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement. Put another way, speed is a scalar value, while velocity is a vector.

What is acceleration?

Acceleration, rate at which velocity changes with time, in terms of both speed and direction. A point or an object moving in a straight line is accelerated if it speeds up or slows down. Motion on a circle is accelerated even if the speed is constant, because the direction is continually changing.

How to calculate angle when the car completes first half of the circle?

When car completes half of the circle it means distance covered would be half the perimeter of the circle.

s = ut + 1/2at²

2πr/2 = 0 + 1/2at²

a(tangential) = 2πr/t²............(1)

where s = distance

           u = initial velocity

           a = acceleration

            t = time

We know that centripetal force is :

a(centripetal) = v²/r ............ (2)

Now we using first equation of kinematics,

v = u +at

Put the values from equation(1):

We get,

v = 0 + 2πr/t² × t

where v = final velocity

           u = initial velocity

            a = acceleration

           t = time

Now the put the obtained value in equation(2)

a = 4π²r/t²

To get the angle we can use this expression :

θ = tan⁻¹ [ a(T)/a(C) ]

= tan⁻¹ [1/2π]

= 9.04 degree.

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