What is the condition for maximum torque in induction motor Mcq?.

Answers

Answer 1

Torque is maximum in an induction motor when rotor resistance is equal to the rotor reactance.

Let us mathematically represent the equation of Torque of a three-phase induction motor:

T = [180/(2piNs)] [sV^2R2/(R2^2 + s^2X2^2)]

where Ns: Synchronous speed

V: Voltage of supply

R2: Rotor resistance

X2: Rotor reactance

From above formula, it can be concluded that induction motor torque varies with Slip and rotor resistance.

To get maximum torque, we apply the condition:

sm = Rm/Xm = 1

Therefore, Rm = Xm

where Rm: Motor Resistance/Phase

Xm: Motor Reactance/Phase

At the beginning of a three-phase slip ring induction motor where Nr = 0

Slip = 1

sm = Rm/Xm = 1

Xm = Rm

Therefore, maximum torque is when resistance and reactance of rotor are equal.

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Related Questions

The motion of atomic or subatomic objects deal with?

Answers

Quantum mechanics is the study of the motion of atomic or subatomic sized bodies, demonstrating the duality of waves and particles.

Quantum mechanics is the basic theory of physics that explains the physical properties of nature at the atomic and subatomic particle level. It is the basis of all quantum physics, including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Applications of quantum mechanics include explaining phenomena that occur in nature and developing technologies based on quantum effects, such as integrated circuits and lasers. Quantum mechanics is also important for understanding how individual atoms are covalently attached to molecules.

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a change in the magnetic field surrounding the conductor induces a voltage in the conductor. this induced voltage is known as ___.

Answers

A change in the magnetic field surrounding the conductor induces a voltage in the conductor, this induced voltage is known as Self-Inductance.

What is the term for the induction of voltage caused by a change in the magnetic field surrounding a conductor?

In order to cause a current to flow as a result of a shifting magnetic field, a process known as electromagnetic induction must be used.

A current will be induced in a coil of wire if the coil is placed in a magnetic field that is changing. Since there is an electric field causing the charges to be forced around the wire, current is flowing as a result. Since the charges are initially stationary, it cannot be the magnetic force.

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What causes latency lag?.

Answers

Latency lag is due to distance, processing time, quality of server ,etc

1. Distance: The physical distance that data has to travel is one of the main causes of latency. The further the data has to travel, the longer the latency will be.

2. Network Congestion: When there is too much data trying to travel through a network at the same time, it can cause delays and increase latency.

3. Number of hops: Data packets often have to pass through multiple routers and other devices before reaching their destination. Each hop adds a small amount of latency.

4. Processing time: Data packets have to be processed by various devices and networks along the way. The time taken for processing can add to the latency.

5. Quality of the network: The quality of the network also plays a role in latency, older networks and equipment may not be able to handle data as efficiently as newer technologies.

6. Interference: Interference from other devices, such as cordless phones, can disrupt the signal and increase latency.

7. Malware: Malware can slow down your computer and increase the latency.

8. Quality of the Server: the location of the server, the server's processing power, and the workload of the server can affect the latency.

These are some of the factors that can cause latency lag. In some cases, multiple factors can contribute to latency lag and it may be difficult to pinpoint the exact cause.

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Student 1 claims that the work done by the gravitational force on an object as it falls depends only on the vertical distance of the fall. Student 2 claims that the gravitational force does less work on an object that falls gradually along a shallow incline than one that falls along a steeper incline.

Answers

The gravitational force on object falling always depends on vertical distance.

Gravitational force : The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them.Gravity is a force that attracts a body towards the centre of the earth or any other physical body having mass.Gravity has the same effect on all objects. If you drop an iron road and a feather, they will fall at the exact same speed. Due to the effect of air resistance on gravity, it might look like the iron rod falls at a greater speed. However, if they were dropped in the vacuum, they would fall at the exact same time. The gravity of an object depends on its size. To be more specific, the Gravity of an object depends on the mass of that object. It is undoubtedly the weakest known force in nature and thus plays no role in determining the internal properties of everyday matter.

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What is magnitude explain?.

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Physicists use the term "magnitude" to refer to the "distance or quantity" of anything. In the context of motion, it represents the direction and/or scale of such motion.

It's a great way to emphasize how large or extensive something is. Magnitude is a physics term for either distance or quantity. We can establish a relationship between the size and velocity of a moving object and its overall magnitude. Magnitude refers to how big something is or how much money there is. Magnitude can serve a variety of purposes. Some examples are the size of an earthquake or the charge on an electron. force, displacement, and acceleration can all be measured in terms of their respective magnitudes.

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What do the 1 and 2 in m1 m2 in the universal gravitation equation mean?.

Answers

r represents the distance between mass centers, and m1 and m2 are the first and second masses, respectively.

What do the 1 and 2 in m1m2 mean?

The Relationship between M1 and M2 Money. M1 and M2 money have several definitions, ranging from narrow to broad. M1 = coins and currency in circulation + checkable (demand) deposit + traveler's checks. M2 = M1 + savings deposits + money market funds + certificates of deposit + other time deposits.

What does G stand for in gm1m2 r2?

Force is proportional to mass and distance, related by a proportionality symbol known as the gravitational constant (G). The force of gravity occurs even at the smallest of particles, yet at this scale, force and motion is dominated by the electric force.

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Can mass exist without gravity?.

Answers

No, mass cannot exist without gravity. Gravity is a fundamental force of nature that acts on all matter, including mass. Without gravity, the mass could not exist because it is the force that holds matter together.

Gravity is a relativistic force that is described by the curvature of space-time. It is the force that binds the universe together and causes objects to move and interact with each other. Without gravity, the universe would be an empty void, devoid of all matter and energy.  

Gravity is the force that keeps objects orbiting each other and it is the force that keeps planets in their orbits around stars. Without gravity, the universe would be chaotic and unstable. The planets, stars, and galaxies that we currently observe would not exist.  

Gravity is also responsible for the formation and evolution of galaxies, stars, and planets. Without gravity, stars and planets would never form and exist.

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A highway curves to the left with a radius of curvature of 46 m and is banked at 27o, so that cars can take this curve at higher speeds. Consider a car of mass 1664 kg whose tires have a static friction coefficient 0.61 against the pavement. How fast can the car take this curve without skidding to the outside of the curve? The acceleration of gravity is 9.8 m/s2. Answer in units of m/s.

Answers

The car can take the curve at a speed of 32.11 m/s without skidding to the outside of the curve.

To calculate the maximum speed at which the car can take the curve, we need to first determine the maximum force of static friction that can act on the car. This can be calculated using the formula:

F_friction = friction coefficient * normal force

The normal force is equal to the weight of the car and can be calculated using the formula:

N = m * g (where m is the mass of the car and g is the acceleration of gravity)

So:

N = 1664 kg * 9.8 m/s^2 = 16,297.2 N

F_friction = 0.61 * 16,297.2 N = 9,941.33 N

Next, we need to determine the centripetal force required to keep the car moving in a circle of radius 46 m. This can be calculated using the formula:

F_centripetal = m * a

Where a is the centripetal acceleration and can be calculated using the formula:

a = v^2 / r

So we have to find v:

v = sqrt(F_friction*r /m)

v = sqrt(9,941.33 N * 46 m / 1664 kg) = 32.11 m/s

So, the car can take the curve at a speed of 32.11 m/s without skidding to the outside of the curve.

It's important to mention that this is a theoretical speed, it's always recommended to drive at lower speeds for safety reasons.

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What is angular controller MCQ?.

Answers

An application is defined by an AngularJS module. The module is a container for the various components of an application. The module serves as a home for the application controllers. Controllers are always associated with a module.

What is angular controller?

An application is defined by an AngularJS module. A module is a container for the various components of an application. The module houses the application controllers. Controllers are always associated with a module. In AngularJS, a Controller is specified via a JavaScript constructor function, which is used to expand the AngularJS Scope. Controllers can be linked to the DOM in several ways. Controllers are often used in AngularJS applications to govern the flow of data. In essence, it handles data in AngularJS apps, and the controller is a Javascript object constructed with a typical JavaScript object constructor.

Here,

An AngularJS module defines an application. A module is a container for an application's various components. The application controllers are housed in the module. Controllers are always linked to a module.

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What is the formula of weight in gravitation?.

Answers

Mass and weight are related by the equation Weight = mass x gravity. You might know this equation as Newton's II Law of Motion Force = mass x acceleration (F = ma) where Force (or weight) is measure in Newtons, N, and the mass is measured in kilograms, kg.

A 175g piece of iron and a 175g piece of aluminum are both warmed to 99.7°C. The metal samples are allowed to cool to 21.5°C. Which sample underwent the greatest heat change?​

Answers

The aluminum sample will undergo the greatest heat change.

What is heat transfer formula?

The amount of heat that a substance absorbs or loses is equal to the change in its internal energy. The heat change, also known as the heat transfer, is given by the formula Q = mcΔT, where ΔT is the change in temperature.

Q is the heat transfer; c is the specific heat and m is the mass. Since both samples have the same mass, the sample that has the greater heat change is the one that has the greater specific heat. The specific heat of aluminum is about 0.90 J/g°C and the specific heat of iron is about 0.45 J/g°C. So, the aluminum sample underwent the greatest heat change.

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Laura is riding her bike at a speed of 15 m/s when she spots a dog in his path. If she needs to come to a full stop in 3 seconds what must her deceleration be?

Answers

The deceleration of Laura is obtained as - 5m/s^2.

What is the deceleration?

We know that the deceleration would have to be the rate of the decrease in the speed of the object with time. We would use the formula for the acceleration to be able to obtain the deceleration of the object as follows;

a = v - u/t

a = deceleration

v = final velocity

u = initial velocity

t = time taken

Then;

a = 0 - 15/3

a = - 5m/s^2

Thus she would have a deceleration of - 5m/s^2 from the calculation that we have done above.

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A lever is used to lift an object with a weight of 60 newtons. The effort force is 15 meters from the fulcrum, while the load force is 5 meters from the fulcrum. What is the mechanical advantage?(1 point).

Answers

The mechanical advantage in this case is 3.

How can a lever's load force be calculated?

When applied to a class one lever, the force of the effort (Fe) multiplied by the distance from the fulcrum (de) of the effort equals the force of the resistance (Fr) multiplied by the distance from the fulcrum of the resistance (dr).

The ratio of the lengths of the effort arm and resistance arm determines a lever's ideal mechanical advantage. The effort force, Fe, is typically calculated as the resistance force, Fr, divided by the effort force, Fe.

We know that

MA = effort arm / load arm

MA = 15 m/5 m

MA = 3

Thus, the mechanical advantage in this case is 3.

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Complete question:

A lever is used to lift an object with a weight of 60 newtons. The effort force is 15 meters from the fulcrum, while the load force is 5 meters from the fulcrum. What is the mechanical advantage?(1 point).

What are the 3 types of levers *?.

Answers

Levers come in three varieties.First-rate lever with the fulcrum situated between the exertion and the load.The load lies midway between both the pivot and the effort of a second-class lever.

Third-class lever: the effort is distributed evenly between the load and the fulcrum.

The first degree lever is what?

First-order levers are devices with the fulcrum situated halfway between the input and output forces. Imagine a see-saw. In this instance, the distances of the input and output forces from the fulcrum are equal .

A speed lever is what?

The most prevalent form of lever in the body is the velocity lever (third class). The bicep curl is an illustration of a 3rd leverage system in the body. The biceps brachi has a short force arm because its insertion is near to the axis of the joint.

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What is torque write its unit and dimensional formula?.

Answers

In 3 dimensions, a torque is in fact a that are derived for particle by mixing a centroid (length vector) or a stress virus linear. If Q is its derived item, so Q = MᵃLᵇTᶜ is known as 3d ratio, or the notation a, b, but c are known as the dimensions.

What exactly does torque mean?

Torque is a twisted or twisting force that frequently results in rotation around in an axis, which may be a fixed point or the center of mass. The capacity of something spinning, such as a cog or a shafts, to resist turning resistance is another way to think of torque.

What does the word "torque" mean and what does it mean graphically?

Although a capital "T" is typically used to represent torque, the true sign is indeed the Greek letter omega, or "ω" The letter "M" is used to denote torque when it is alluded to as a second of force.

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Consider a beaker with two holes X and Y near the base, such that hole X is ABOVE hole Y. The holes are closed with water-resistant tape and the beaker is filled with water.

Both the holes are then uncovered at the same time. If water from hole X comes out in a stream that touches the ground at a distance of 5 cm away from the beaker, how far from the beaker will the stream from hole Y touch the ground?

1. exactly 5 cm
2. less than 5 cm
3. more than 5 cm
4. (It will be more or less than 5 cm depending on the distance between the two holes.)

Answers

As the height of the hole increases, the velocity of the stream increases, results in a higher distance from the beaker. Therefore, the distance of the stream from the hole Y will be less than that from X thus, less than 5 cm is correct.

What is stream speed ?

The speed of stream can be determined using the height and acceleration due to gravity g. We can use the equation for velocity using the parameters g and h.

v = √2gh

Therefore, as the height h increases, v increases.

Similarly the distance s = vt

therefore, the distance increases with v.

Here, the hole x is above the hole Y. Then the stream from X will have the greater speed and it covers greater distance (5 cm )from the beaker. Stream from Y slow compared to that in X hence covers a distance less than 5 cm. Hence, option 2 is correct.

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Enter an equation for the net horizontal force acting on the charge located at the lower left corner of the rectangle in terms of the magnitude of the forces from the three other charges, f1, f2, f3, and the angle θ.

Answers

The net force required to maintain a particle in a circle route is F = m (v2/R), where v2/R is the velocity of an item moving uniformly in a circle.

How can you get a vector's magnitude from its horizontal and vertical components?

To do this, multiply the vector's magnitude by its angle's cosine or sine to find the linear acceleration and its magnitude by its angle's sine or cosine to obtain the vertical component.

How do you calculate horizontal and vertical angles?

A verticals line is defined as a line that really is perpendicular towards the x-axis of cartesian coordinate system and has the equation y = b, where b is a constant. a line that is perpendicular to a y-axis and with the equation x = a, where 'b' is a constant.

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A student pushed a large rubber ball on a flat,
frictionless surface. The ball rolled at a speed of
1 meter per second.

Which statement best describes the motion of the ball when the student stopped pushing the ball?

A. The ball accelerated.
B. The ball did not move.
C. The ball changed direction.
D. The ball continued to move in the same
direction.

Answers

a the ball accelerated because it's not in motion

How do you calculate torque examples?.

Answers

Torque is calculated using the formula, τ = r × F, where, r is the perpendicular distance, F is the force.

It is also described as the cross product of distance vector and force vector. Mathematically, τ = r × F = r F sinθ, where, θ is the angle between r and F.

For example, a force is applied to a particle free to rotate about a fixed axis. Force is shown divided into perpendicular and parallel components. Torque is pointed outward from the page and has the magnitude

τ = r F sinθ.

Newton-meters, sometimes known as N.m, are the SI units for torque. Although these units are the same as joules, torque isn't considered to be work or energy, therefore N.m should be used instead.

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HELP PLEASE SHOW ALL WORK!

Answers

a. At the bottom of the circle, the ball is moving in a circle, so it is experiencing a centripetal acceleration towards the center of the circle. The free body diagram for the ball would show the tension force (T) acting towards the center, and the gravitational force (m*g) acting downwards. The direction of acceleration is towards the center of the circle.

b. Using the free body diagram, we can set up the equation needed to determine the tension in the string:

T = m * a

Where T is the tension in the string, m is the mass of the ball (0.65 kg) and a is the centripetal acceleration of the ball (v^2/r).

c. To calculate the tension in the string, we need to first find the centripetal acceleration. We can use the equation:

a = v^2/r

where v is the velocity of the ball at the bottom of the circle (2.8 m/s) and r is the radius of the circle (0.50 m).

a = (2.8 m/s)^2 / 0.50 m = 11.2 m/s^2

Now, we can use the equation T=m*a to find the tension in the string:

T = 0.65 kg * 11.2 m/s^2 = 7.28 N

So the tension in the string is 7.28 N

how much work is done when a 100 lb rock is lifted to a height of 3 ft?

Answers

Work done when a 100 lb rock is lifted to height of 3 ft is 9652.215 ft-lb.

What is meant by work done?

The work done on an object is equal to the force applied to it multiplied by the distance over which the force is applied. In this case, the force applied is the weight of the rock, which is equal to the force of gravity acting on it.

The weight of an object is given by the formula:

W = mg

Where m is the mass of the object (in this case, 100 lb) and g is the acceleration due to gravity (approximately 9.8 m/s^2 or 32.17405 ft/s^2).

So the weight of the rock is:

W = (100 lb)(32.17405 ft/s^2) = 3,217.405 ft-lb

The work done on the rock is equal to the force applied (its weight) multiplied by the distance it is lifted (3 ft), so the work done is:

Work = (3,217.405 ft-lb) x (3 ft) = 9652.215 ft-lb

Therefore, the work done when a 100 lb rock is lifted to a height of 3 ft is 9652.215 ft-lb.

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what creates the protective magnetic field around the earth?

Answers

The protective magnetic field around the earth is created by the movement of molten iron in the Earth's core.

The Earth's protective magnetic field is generated by the movement of molten iron and nickel in the Earth's core. The movement of this molten metal creates electrical currents, which in turn generates a magnetic field. This process is known as a dynamo.

The Earth's core, which is about 2,900 km in radius, is divided into two layers: the outer core, which is liquid and the inner core, which is solid.

The movement of the liquid outer core, driven by heat from the solid inner core, generates the Earth's magnetic field. The Earth's magnetic field is not a perfect dipole, but it is relatively symmetric around the Earth's rotational axis and it's mostly aligned with the axis, but it is tilted at an angle of about 11 degrees. The magnetic field extends from the Earth's surface out into space, and it shields the Earth from harmful solar radiation and charged particles from the solar wind. The magnetic field is important for life on earth, as it helps to prevent the harmful effects of solar radiation, and it helps to protect the planet's atmosphere.

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which law states that volume increases with temperature

Answers

Charle's law states that volume increases with temperature.

According to Charles' Law, while pressure is maintained constant, the volume of a given amount of gas varies in direct proportion to the absolute temperature of the gas. The Kelvin scale is used to measure temperature to determine the absolute temperature. Since 0 on the Kelvin scale equates to a total cessation of molecular motion, it must be employed.

The aroma and flavour of freshly baked bread are enjoyed by many. As a result of yeast reacting with sugar, it is light and fluffy. When the temperature is high, the yeast turns the sugar into carbon dioxide, which causes the dough to expand. The final product is a tasty treat, especially when melted butter is added.

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How many Newton laws are there?.

Answers

There are three laws of motion described by Sir Isaac Newton. These laws describe the behavior of objects in motion and form the foundation of classical mechanics. The laws are as follows:

1. The first law states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity unless acted upon by an external force. This is often referred to as the law of inertia.

2. The second law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. The acceleration of an object is given by the equation F = ma, where F is the net force, m is the mass of the object, and a is the acceleration.

3. The third law states that for every action, there is an equal and opposite reaction. This means that if an object exerts a force on another object, the second object will exert an equal and opposite force on the first object.

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A boy is pulling a box with a force of 50N which makes an angle of 60
with theground. Its perpendicular components are:
A. 4.33N, 25N B. 25N, 43.3N
C. 28.3N, 40N D. 15.5N, 35.5N

Answers

To find the perpendicular components of the force, we need to use the trigonometric functions sine and cosine.

The horizontal component of the force is given by Fx = F * cos(theta), where F is the force applied, and theta is the angle between the force and the horizontal axis.

The vertical component of the force is given by Fy = F * sin(theta)

In this case, the force applied is F = 50 N and the angle is theta = 60 degrees.

So, the horizontal component of the force is:

Fx = F * cos(theta) = 50 N * cos(60) = 25 N

The vertical component of the force is:

Fy = F * sin(theta) = 50 N * sin(60) = 43.3 N

Therefore, the correct answer is B. 25N, 43.3N

The boy is pulling a box with a force of 50N which makes an angle of 60 with the ground And Its perpendicular components are 25N, 43.3N

The force of 50N can be broken down into two components: the horizontal component and the vertical component.

To find the horizontal component, we use the formula:

Fx = F * cos(theta)

where F is the force (50N), theta is the angle (60 degrees), and Fx is the horizontal component.

To find the vertical component, we use the formula:

Fy = F * sin(theta)

where F is the force (50N), theta is the angle (60 degrees), and Fy is the vertical component.

Therefore, the horizontal component is:

Fx = 50N * cos(60) = 25N

And the vertical component is:

Fy = 50N * sin(60) = 43.3N

So, the answer is option B: 25N, 43.3N

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What happens when two forces are parallel?.

Answers

Two parallel forces that are equal in strength, sense-opposite, and do not share an action path make comprise a couple force. Only rotation is produced; there is no translation. A couple's resulting force is zero.

What outcome may two parallel pressures produce?

Two parallel forces may be moving in the same direction or in opposition to one another. Two forces combine when they move in the same direction. Balanced forces are two equal forces acting in opposition to one another. Couple: A couple is a pair of opposing, parallel, equal forces that have lines of action that are parallel to one another and act in different directions. When two forces engage in opposition to one another, the lesser force is subtracted from the larger force to form the combined force. The direction of the larger original force is the direction of the generated force (resultant).

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Help w/ physics
1. A car travels from point A to point B which is 25 miles. Determine the average velocity, in meters/second, the car was travelling to reach its destination, point B, in 25 minutes.

2. Determine the average velocity and average speed for the following situation. A dog runs west for 35 meters then turns east for 45 meters stops then continues east for 65 meters. The time for the total trip is 85 seconds.

3. A car travels north on the highway for 75 kilometers then turns west for 25 kilometers then turns south for 75 kilometers determine the distance the car travelled and determine the displacement of the car.

Answers

To determine the average velocity in meters/second, we need to convert the distance from miles to meters and the time from minutes to seconds.

To convert miles to meters, we multiply by 1609.34.

To convert minutes to seconds, we multiply by 60.

So, distance = 25 miles * 1609.34 meters/mile = 40233.5 meters

time = 25 minutes * 60 seconds/minute = 1500 seconds

Average velocity = distance / time = 40233.5 meters / 1500 seconds = 26.856 meters/second

To determine the average velocity, we need to calculate the total distance traveled and divide it by the total time taken.

Distance = 35 meters + 45 meters + 65 meters = 145 meters

Time = 85 seconds

Average velocity = distance / time = 145 meters / 85 seconds = 1.71 meters/second

To determine the average speed, we just need to calculate the total distance traveled / total time taken.

Average speed = distance / time = 145 meters / 85 seconds = 1.71 meters/second

To determine the distance traveled, we need to add the distance traveled in each direction: 75 kilometers + 25 kilometers + 75 kilometers = 175 kilometers.

To determine the displacement, we need to calculate the final position of the car relative to its initial position. Displacement is a vector quantity, so it takes into account the direction of the motion. The car traveled north 75 kilometers, then west 25 kilometers, then south 75 kilometers. So, the final position of the car is 25 kilometers west of its initial position. Therefore, the displacement of the car is 25 kilometers west.

Answer:

Physics problem solutions

1 To determine the average velocity of the car, you will need to divide the distance traveled (in meters) by the time it took to travel that distance (in seconds).

First, you will need to convert the distance from miles to meters.

1 mile = 1609.344 meters

So 25 miles = 40,233.6 meters

Then, you will need to convert the time from minutes to seconds.

1 minute = 60 seconds

So 25 minutes = 1500 seconds

Average velocity = distance traveled / time = 40,233.6 meters / 1500 seconds = 26.822 m/s

2 To determine the average velocity and average speed, you will need to divide the distance traveled (in meters) by the time it took to travel that distance (in seconds).

Distance traveled: 35 meters + 45 meters + 65 meters = 145 meters

Average velocity = distance traveled / time = 145 meters / 85 seconds = 1.71 m/s

Average speed = total distance / total time = (35 + 45 + 65) / 85 = 2.71 m/s

3 To determine the distance the car travelled, you will need to add up the distance traveled in each direction.

Distance traveled = 75 km + 25 km + 75 km = 175 km

To determine the displacement of the car, you will need to find the straight-line distance and direction from the starting point to the ending point.

Displacement = sqrt(75km^2 + 75km^2) = sqrt(5625 + 5625) = sqrt(11250) = 105.8 km, this is the north-south distance,

It's important to notice that the displacement is a vector quantity that has a magnitude and direction, and displacement is not the same as distance.

Is gravity dependent on mass or size?.

Answers

Gravity depends on mass and distance between the objects. Gravity is the force with which bodies attract other objects towards its Centre.

Gravity depends on two factors, Mass of the object and the distance between them. Gravity is calculated using the formula,

 F=   [tex]\frac{Gm_{1}m_{2} }{R^{2} }[/tex]

    F  is Gravitational force

    G is Gravitational constant

    m₁ , m₂ are masses, R is the distance.

Gravitational force is directly proportional to mass of the two bodies. That means gravity increases with the mass. If we take earth's gravity as example a heavier object will fall faster than a lighter object.

So gravity is directly proportional to mass.

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A highway curves to the left with a radius of curvature of 46 m and is banked at 27o, so that cars can take this curve at higher speeds. Consider a car of mass 1664 kg whose tires have a static friction coefficient 0.61 against the pavement. How fast can the car take this curve without skidding to the outside of the curve? The acceleration of gravity is 9.8 m/s2. Answer in units of m/s.

Answers

The car can take the curve at a speed of 32.11 m/s without skidding to the outside of the curve.

To calculate the maximum speed at which the car can take the curve, we need to first determine the maximum force of static friction that can act on the car. This can be calculated using the formula:

F_friction = friction coefficient * normal force

The normal force is equal to the weight of the car and can be calculated using the formula:

N = m * g (where m is the mass of the car and g is the acceleration of gravity)

So:

N = 1664 kg * 9.8 m/s^2 = 16,297.2 N

F_friction = 0.61 * 16,297.2 N = 9,941.33 N

Next, we need to determine the centripetal force required to keep the car moving in a circle of radius 46 m. This can be calculated using the formula:

F_centripetal = m * a

Where a is the centripetal acceleration and can be calculated using the formula:

a = v^2 / r

So we have to find v:

v = sqrt(F_friction*r /m)

v = sqrt(9,941.33 N * 46 m / 1664 kg) = 32.11 m/s

So, the car can take the curve at a speed of 32.11 m/s without skidding to the outside of the curve.

It's important to mention that this is a theoretical speed, it's always recommended to drive at lower speeds for safety reasons.

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A National Guard helicopter is helping to fight a wildfire by dumping water from a large external container. The container holds 2,500 liters (L) of water (density of water is 1 kg/L). If the water is released from a height of 75 m above the ground, what is the change in potential energy as it falls to the ground?

Answers

This part applies to each person who offers a hazardous material for transportation.

What is potential energy?Potential energy, stored energy that depends upon the relative position of various parts of a system. A spring has more potential energy when it is compressed or stretched. A steel ball has more potential energy raised above the ground than it has after falling to Earth. In the raised position it is capable of doing more work. Potential energy is a property of a system and not of an individual body or particle; the system composed of Earth and the raised ball, for example, has more potential energy as the two are farther separated.

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