The rock weighs 2.25N when suspended in air. In water, it appears to weigh only
1.8N.Why?

Answers

Answer 1

Answer:

due to upthrust

Explanation:

when immersed in a liquid the liquid exerts an upward force on the body immersed causing it to appear lighter than it's original weight


Related Questions

why do these two magnets attract each other

Answers

The force that magnets use to either attract or repel one another is known as magnetism. Electric charges in motion are what generate magnetism.

What is Magnetism?

The smallest building blocks of matter are called atoms. There are electrons in every atom, which are charged particles. The electrons that make up an atom's nucleus, or core, spin like tops.

The magnetism of most things is cancelled out by the equal amounts of electrons that spin in opposing directions. Because of this, substances like fabric and paper are referred to as weakly magnetic.

Most electrons in materials like iron, cobalt, and nickel spin in the same direction. The atoms in these become this way.

Therefore, The force that magnets use to either attract or repel one another is known as magnetism. Electric charges in motion are what generate magnetism.

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motorcycle has a constant speed of 25.0 m/s as it passes over the top of a hill whose radius of curvature is 126 m. The mass of the motorcycle and driver is 342 kg. Calculate: 1.3.1 the centripetal force, the normal force that acts on the cycle.

Answers

Motorcycle has a constant speed of 25.0 m/s as it passes over the top of a hill whose radius of curvature is 126 m. The mass of the motorcycle and driver is 342 kg.  The normal force acting on the motorcycle at the top of the hill is approximately 11,370 N.

The centripetal force and the normal force acting on the motorcycle as it passes over the top of the hill, we need to consider the forces acting on the motorcycle at that point.

1. Centripetal Force:

The centripetal force (Fc) is the force directed towards the center of the circular path and keeps the motorcycle moving in a curved trajectory. It can be calculated using the following formula:

Fc = (m * v^2) / r

Where:

m is the mass of the motorcycle and driver (342 kg),

v is the constant speed of the motorcycle (25.0 m/s),

r is the radius of curvature of the hill (126 m).

Substituting the given values into the formula:

Fc = (342 kg * (25.0 m/s)^2) / 126 m

Calculating the value:

Fc ≈ 17,180 N

Therefore, the centripetal force acting on the motorcycle is approximately 17,180 N.

2. Normal Force:

The normal force (N) is the force exerted by the surface of the hill perpendicular to the surface. At the top of the hill, the normal force will be different from the weight of the motorcycle and driver due to the centripetal force.

To calculate the normal force, we can use the following equation:

N = mg + Fc

Where:

m is the mass of the motorcycle and driver (342 kg),

g is the acceleration due to gravity (9.8 m/s^2),

Fc is the centripetal force (17,180 N).

Substituting the given values into the equation:

N = (342 kg * 9.8 m/s^2) + 17,180 N

Calculating the value:

N ≈ 11,370 N

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Which arrow is the action and which arrow is the reaction?

Which arrow is the action and which arrow is the reaction?

Answers

Up is the reaction and down is the action

For each item below, write whether it is opaque, translucent, or transparent.
a. plastic wrap
b. wax paper
c. wedding vell
d. thick rug
e. text book
f. window​

Answers

The answer response are:

a. plastic wrap - transparent

b. wax paper - translucent

c. wedding veil - sheer/transparent

d. thick rug - opaque

e. textbook - opaque

f. window - transparent

What is the terms about?

a. Plastic wrap is a thin, clear material that allows light to pass through it, making it possible to see objects behind it. Therefore it's transparent.

b. Wax paper is a thin, translucent material that allows some light to pass through it, making it possible to see through it, but not clearly as in the case of transparent materials. The objects behind it can be seen but appear somewhat cloudy or blurry.

Hence c. A wedding veil is a thin, sheer material that is often made of tulle or other lightweight fabrics. This makes it transparent, allowing light to pass through it easily and making it possible to see objects behind it.

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A solar-powered car has a kinetic energy of 110250 J. Its mass is 180 kg. Work out how fast the car is travelling Enter a number m/s​

Answers

Answer: Velocity = v = 35 m/s

Explanation:

Kinetic energy of an object is defined as the energy possess by an object due to its motion. Kinetic energy K.E of an object is equal to the half of the mass of that object multiplied by square of the object's velocity.

Mathematically,

v = 35 m/s

A solar-powered car has a kinetic energy of 110250 J. Its mass is 180 kg. Work out how fast the car is

what are ways that iron man's repulsor rays don't break newton's third law of motion.

Answers

Tony's Arc Reactor serves as the power source for the Repulsors, which are located in the palms of the armor.Originally intended to stabilize the flight of the armor and add more agility.

How is push produced by the Iron Man suit?

Hydrogen is the gas utilized, and a sophisticated suit like Iron Man can easily extract it from the air by electrolysis. The water was condensed even as suit overpressurized ram air into form water, as well as the hydrogen gas is formed and sent right to the rocket boots.

What fuels Tony Stark's armor?

The nuclear core which Tony Stark creates and implants in his heart to save his life also fuels all of his armor.In essence, it is a very energy-dense battery.

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A 1 kg apple and a 2 kg baseball are 2 m apart. What is the force of gravity between each fruit?

Answers

Answer:

\(\boxed {\boxed {\sf 3.335 \times 10^{-11} \ N}}\)

Explanation:

We are asked to find the force of gravity between 2 objects. The following formula is used to calculate the attractive force of gravity:

\(F_g= \frac{Gm_1m_2}{r^2}\)

G is the universal gravitational constant or 6.67 × 10⁻¹¹ N*m²/kg². 1 mass is 1 kilogram and the other mass is 2 kilograms. R is the distance between the 2 objects, or 2 meters.

G= 6.67 × 10⁻¹¹ N*m²/kg²m₁ = 1 kg m₂ = 2 kg r= 2 m

Substitute the values into the formula.

\(F_g= \frac {(6.67 \times 10^{-11} \ N*m^2/kg^2)(1 \ kg)(2\ kg)}{( 2 \ m)^2}\)

Multiply the numerator. The units of kilograms squared cancel.

\(F_g= \frac {(6.67 \times 10^{-11} \ N*m^2/kg^2)(2 kg^2)}{(2 \ m)^2}\)

\(F_g= \frac {(6.67 \times 10^{-11} \ N*m^2)(2 )}{( 2 \ m)^2}\)

\(F_g= \frac {(1.334 \times 10^{-10} \ N*m^2)}{ (2 \ m)^2}\)

Solve the exponent in the denominator.

(2 m)²= 2 m*2m = 4 m²

\(F_g =\frac {(1.334 \times 10^{-10} \ N*m^2)}{ 4 \ m^2}\)

The units of meters squared cancel.

\(F_g =\frac {(1.334 \times 10^{-10} \ N)}{ 4}\)

\(F_g=3.335 \times 10^{-11} \ N\)

The force of gravity between the fruit is 3.335 × 10⁺¹¹ Newtons.

how to determine which compound has the highest boiling point

Answers

When deciding which compound has the highest boiling point, it is essential to consider intermolecular forces, molecular weight, and geometry.

Here are some points to keep in mind is Intermolecular forces. The strength of intermolecular forces influences the boiling point. The greater the intermolecular forces, the higher the boiling point of a compound. Molecular weight When two molecules have identical intermolecular forces, the one with the higher molecular weight will have a higher boiling point.

Geometry The shape of a molecule affects its boiling point. When two molecules have similar intermolecular forces and molecular weights, the molecule with the greater surface area will have a higher boiling point. For example, hydrogen chloride (HCl) has a higher boiling point than hydrogen sulfide (H2S). Despite being similar in molecular weight, HCl has a higher boiling point because it has stronger intermolecular forces.

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A 6.0 kg metal ball moving at 4.0 m/s hits a 6.0 kg ball of putty at rest and sticks to it. The two go on at 2.0 m/s.

(a) What is the kinetic energy of the metal ball before it hits?

(b) What is the kinetic energy of the metal ball after it hits?

(c) What is the kinetic energy of the putty ball after being hit?

(d) How much energy does the metal ball lose in the collision?

(e) How much kinetic energy does the putty ball gain in the collision?

(f) What happened to the rest of the energy?

Answers

The metal ball lost energy while the putty ball gained energy.

What is momentum?

Momentum is the product of mass and velocity of the body. We must note that momentum before collision is equal to momentum after collision.

1) Kinetic energy before collision = 1/2mv^2 = 0.5 * 6 * 4 = 12 J

2) kinetic energy after collision = 0.5 * 6 *  2= 6 J

3) Kinetic energy of putty ball = 0.5 * 6 *  2= 6 J

4) Energy lost by the metal ball = 12 J -  6 J = 6 J

5) Energy gained by the putty ball = 6 J - 0J = 6 J

6) The rest of the energy was converted to heat after the collision.

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An elevator has mass 700 kg , not including passengers. The elevator is designed to ascend, at constant speed, a vertical distance of 20.5 m (five floors) in 15.8 s , and it is driven by a motor that can provide up to 36 hp to the elevator.
What is the maximum number of passengers that can ride in the elevator? Assume that an average passenger has mass 65.0 kg.

Answers

The maximum number of passengers that can ride in the elevator is 31, considering the elevator's mass of 700 kg (not including passengers) and the motor's maximum power of 36 hp.

Determine how to find the maximum number of passengers?

To find the maximum number of passengers, we need to consider the maximum force the motor can provide and compare it with the total force required to lift the elevator and passengers.

First, let's convert the power of the motor from horsepower (hp) to watts (W):

1 hp = 745.7 W

So, the motor can provide a maximum power of 36 hp × 745.7 W/hp = 26,845.2 W.

The total force required to lift the elevator and passengers can be calculated using Newton's second law:

Force = mass × acceleration

The acceleration can be found using the equation of motion:

distance = (initial velocity × time) + (0.5 × acceleration × time²)

Since the elevator ascends at a constant speed, the initial velocity is 0. Therefore, the equation simplifies to:

distance = 0.5 × acceleration × time²

Rearranging the equation, we can find the acceleration:

acceleration = (2 × distance) / (time²)

          = (2 × 20.5 m) / (15.8 s)²

          = 0.1704 m/s²

Now, let's calculate the total force required to lift the elevator and passengers:

Force = (elevator mass + passenger mass) × acceleration

Substituting the given values:

Force = (700 kg + 65.0 kg) × 0.1704 m/s²

     = 765 kg × 0.1704 m/s²

     = 130.584 N

To find the maximum number of passengers, we divide the maximum force the motor can provide by the force required to lift the elevator and passengers:

Maximum number of passengers = Maximum motor force / Force required per passenger

The force required per passenger is the weight of an average passenger:

Force required per passenger = passenger mass × acceleration due to gravity

                            = 65.0 kg × 9.8 m/s²

                            = 637 N

Maximum number of passengers = 26,845.2 W / 637 N

                         ≈ 42.1

Since the maximum number of passengers cannot be in decimal form, the maximum number of passengers that can ride in the elevator is 42. However, considering the elevator's mass of 700 kg (not including passengers), we subtract this from the total number to obtain the maximum number of passengers:

Maximum number of passengers = 42 - (700 kg / 65.0 kg)

                         ≈ 42 - 10.8

                         ≈ 31.2

Since the number of passengers must be a whole number, the maximum number of passengers that can ride in the elevator is 31.

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two trains, each having a speed of 23 km/h, are headed at each other on the same straight track. a bird that can fly 46 km/h flies off the front of one train when they are 46 km apart and heads directly for the other train. on reaching the other train it flies directly back to the first train, and so forth. (we have no idea why a bird would behave in this way.) what is the total distance the bird travels?

Answers

The bird travels a total distance of 92 km. When the two trains are 46 km apart, the bird starts flying from one train toward the other train.

Let's assume that the distance between the bird and the first train is x km. Since the bird is flying towards the other train at a speed of 46 km/h and the trains are moving towards each other at a combined speed of 46 km/h, the relative speed of the bird with respect to the first train is

69 km/h (46 km/h + 23 km/h).

Therefore, it takes the bird x/(69 km/h) hours to reach the second train.

During this time, the two trains move towards each other and reduce the distance between them by

23 km/h)x/(69 km/h) = x/3 km.

Therefore, the distance between the bird and the second train is also x km. Now, the bird starts flying towards the first train at the same speed of 46 km/h. Again, it takes the bird

x/(69 km/h)

hours to reach the first train.

During this time, the two trains move towards each other and reduce the distance between them by another x/3 km. Therefore, the total distance traveled by the bird in one round trip is 2x km.

Since x + x/3 + x/3 = 92 km (the initial distance between the trains)

the total distance traveled by the bird in all the round trips is

2(92 km) = 184 km.

However, since the bird only flies halfway towards each train before turning back, the actual distance traveled by the bird is half of 184 km, which is 92 km.

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Determine the forces in members cd, cj, and dj. The forces are positive if in tension, negative if in compression. Assume a = 7 ft, b = 5 ft, d = 3 ft

Answers

The forces are positive if in tension, negative if in compression. the forces in members cd, cj, and dj are

Fcd = 23.09 ft (tension)

Fcj = 11.54 ft (compression)

Fdj = -10 ft (compression)

To determine the forces in members cd, cj, and dj, we need to analyze the truss and solve for the reactions at the supports.

First, we can find the reaction at support A by taking the sum of the vertical forces to be zero

RA + RB - 20 = 0

RA + RB = 20

Next, we can take moments about point B to find the reaction at support A

RA * 5 + 10 * 7 - 15 * 3 = 0

RA = 3

RB = 17

Now that we have found the reactions at the supports, we can use the method of joints to solve for the forces in the members. Starting at joint C, we can write the equations of equilibrium for the horizontal and vertical forces

Horizontal Fcd * cos(60) - Fcj = 0

Vertical  Fcd * sin(60) + Fdj = 3

Solving for Fcj and Fdj in terms of Fcd, we get

Fcj = Fcd * cos(60)

Fdj = 3 - Fcd * sin(60)

Next, we can move to joint D and write the equations of equilibrium for the horizontal and vertical forces

Horizontal Fdj = 0

Vertical Fcd * sin(60) - Fdj - 20 = 0

Solving for Fcd and plugging in the values for Fdj, we get

Fcd = 20 / sin(60) = 23.09 ft

Finally, we can use the equations we found earlier to solve for Fcj and Fdj

Fcj = Fcd * cos(60) = 11.54 ft

Fdj = 3 - Fcd * sin(60) = -10 ft

Therefore, the forces in members cd, cj, and dj are

Fcd = 23.09 ft (tension)

Fcj = 11.54 ft (compression)

Fdj = -10 ft (compression)

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A car starts from rest with an acceleration of 5.0 m / s² and travels a distance of 1.0 km. What is the speed value of this car?

Answers

Answer:

100 m/s

Explanation:

We'll begin by converting 1 km to m. This can be obtained as follow:

1 km = 1000 m

Finally, we shall determine the final velocity of the car. This can be obtained as follow:

Initial velocity (u) = 0 m/s

Acceleration (a) = 5.0 m/s²

Distance (s) = 1000 m

Final velocity (v) =?

v² = u² + 2as

v² = 0² + (2 × 5 × 1000)

v² = 0 + 10000

v² = 10000

Take the square root of both side

v = √10000

v = 100 m/s

Therefore, the speed value of the car is 100 m/s.

Help please!!
How many atoms of C would you have if there were 1.23 moles of C? Show your work for this.

Answers

The number of atoms of carbon (C) in 1.23 moles of carbon is 7.41 x 10²³ atoms.

What is the number of atoms?

The number of atoms of carbon (C) in 1.23 moles of carbon is calculated by using Avogadro's number as shown below;

n_A = An

where;

n_A is the number of atomsA is Avogadro's numbern is the number of moles

n_ A  = A x n

n_ A = 1.23 moles x 6.022 x 10²³ atoms/mole

n_A = 7.41 x 10²³ atoms

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A periodic wave has a fixed pattern that is repeated. what is one completion of the wave pattern called? a. equilibrium b. frequency c. amplitude d. cycle e. phase

Answers

Answer:

D.

Explanation:

cycle.

I think it’s a cycle because a wave pattern is kind of like a type of cycle because it happens over and over again.

why does the moon have more impact craters than the earth?

Answers

Answer:

Why does the Moon have so many craters compared to the Earth? Unlike the Earth, the Moon has no atmosphere to protect itself from impacting bodies. It also has very little geologic activity (like volcanoes) or weathering (from wind or rain) so craters remain intact from billions of years.

1. The distance between two identical parts of a transverse wave is the

Answers

yup i agree with the other person

p45. an 820 n marine in basic training climbs a 12.0 m vertical rope at a constant speed in 8.00 s. what is his power output?

Answers

The power output of a marine in basic training that climbs a rope at constant speed is 1230 W

How is the power output calculated?

Given-

Force(Fg) = 820N

Height(h) = 12 m

Time consumed(t) = 8 sec

Hence,

Work done =force × displacement

W = Fg × h

W = 820×12

W =9840 J

We know,

Power = W/t

           = 9820/ 8

Therefore, power output is 1230W

What is Force?

A force is an external factor that can change the body's state of rest or motion. It has size and direction. The direction in which the force is applied is called the force direction, and the point at which the force is applied is called the force application point. A spring balance can be used to measure force. His SI unit of force is the Newton (N). Objects can accelerate, decelerate, or change direction in response to forces.

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High energy waves have what

Answers

High energy waves have Gamma rays

Answer:

It means that the frequency will be a lot higher with a shorter wave.

1.Under normal atmospheric pressure what temperature does:

i.Ice turn to water?
ii.water turn to steam?

2.In which order do the following take place during water purification?

a)chlorination b)screening c)filtration d)sedimentation

b.Which of these processes ensures that the water contains no harmful microorganisms

Answers

Answer:

1.i)heat

ii.)heat

2.a.)b,c,d,a

b.)a.chlorination

Answer:

B

Explanation:

B

Which of the following describes a mixture? (2 points)

a Matter that is composed of a single element and has all the same physical properties
b Matter that is made of molecules of all the same type
c Two atoms chemically bonded together
d A substance made of two or more types of atoms that are not chemically bonded

Answers

I think it’s d I’m not sure tho

Answer:

d  - A substance made of two or more types of atoms that are not chemically bonded

Explanation:

i got a 100% on the quiz

Please help with this problem

Please help with this problem

Answers

Mineralogically, barite is a sulfate, bornite is a sulfide, cuprite is an oxide, magnesite is a carbonate.

Which minerals fall under the main categories?Based on their chemical compositions, scientists divide minerals into groups. Nine major mineral classes were originally specified in the Dana Classification System: Native Elements, Sulfides, Sulfates, Halides, Oxides, Carbonates, Phosphates, Silicates, and Organic Minerals.There are four basic types of mineral formation: (1) igneous, or magmatic, when minerals form crystals from a melt, (2) Sedimentary, where minerals are produced by a process called sedimentation that uses fragments of other rocks that have suffered weathering or erosion as their raw material, and (3) Metamorphic.Mineralogically, barite is a sulfate, bornite is a sulfide, cuprite is an oxide, magnesite is a carbonate.          

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Among the mineral groups, barite is a sulfide mineral, bornite is a sulfide mineral, cuprite is an oxide mineral, and magnesite is a carbonate mineral.

What are the different mineral groups?Scientists mainly classifies the minerals based on their chemical compositions. The Dana Classification System originally defined nine major mineral classes: Native Elements, Sulfides, Sulfates, Halides, Oxides, Carbonates, Phosphates, Silicates, and Organic Minerals.There have been mainly four basic types of mineral formation: (1) igneous, or magmatic, in which minerals form crystals from a melt, (2) sedimentary, in which minerals are produced by a process called sedimentation, which uses fragments of other rocks that have weathered or been eroded as their raw material, and (3) metamorphic.Barite is a sulfate, bornite is a sulfide, cuprite is an oxide, and magnesite is a carbonate mineral.

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calculate the magnitude of the centripetal force acting on earth as it orbits the sun

Answers

The magnitude of the centripetal force acting on Earth as it orbits the Sun can be calculated using Newton's law of universal gravitation and the principles of circular motion.

According to Newton's law of universal gravitation, the force of gravity between two objects is given by the equation F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.

In the case of Earth orbiting the Sun, Earth's mass (m1) is much smaller than the Sun's mass (m2), so we can consider Earth as the smaller mass. The centripetal force acting on Earth is provided by the gravitational force between Earth and the Sun.

The centripetal force can be expressed as Fc = m1 * (v^2) / r, where m1 is the mass of Earth, v is the velocity of Earth in its orbit, and r is the distance between the centers of Earth and the Sun.

Since the centripetal force is provided by the gravitational force, we can equate the two equations: Fc = F. Therefore, m1 * (v^2) / r = G * (m1 * m2) / r^2.

Simplifying the equation, we find that (v^2) / r = G * m2 / r^2.

The magnitude of the centripetal force can be obtained by rearranging the equation as Fc = m1 * (v^2) / r = (m1 * G * m2) / r^2.

Therefore, the magnitude of the centripetal force acting on Earth as it orbits the Sun is given by (m1 * G * m2) / r^2, where m1 is the mass of Earth, m2 is the mass of the Sun, G is the gravitational constant, and r is the distance between their centers.

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The bus covered a distance of 120 km in 2 hours and covered 80 km in the first half of the time and 40 km in the second half. What is the average speed of the bus?​

Answers

The average speed of the bus is 60 km/hr.

What is the average speed of the bus?​

To find the average speed of the bus, we can use the formula:

Average speed = total distance traveled / total time taken

The total distance traveled by the bus is 80 km + 40 km = 120 km, which is given in the problem statement.

The total time taken by the bus is also given as 2 hours.

Therefore, the average speed of the bus can be calculated as:

Average speed = total distance traveled / total time taken

= 120 km / 2 hours

= 60 km/hr

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suppose your 50.0 mm focal length camera lens is 52.5 mm away from the film in the camera. (a) how far away is an object that is in focus?

Answers

the distance of the object from the camera lens is dependent on the type of camera and lens used, as well as the are distance of the lens from the film 1/f = 1/d₀ + 1/dᵢ  where f is the focal length, d₀ is the distance between the lens and the object, and is the distance.

the object that is in focus is 500 mm away from the camera lens.  the distance between the camera lens and the film is important in determining the distance of the object in focus because it affects the position of the image formed on the film. The lens equation is a helpful tool in calculating this distance, as it takes into account both the focal length of the lens and the distances of the lens and object from each other 1/f = 1/d_o + 1/d_i

Where f is the focal length, d_o is the object distance, and d_i is the image distance  Rearrange the equation to solve for d_o d_o = 1 / ((1/f) - (1/d_i)  Plug in the values for f and d_i d_o = 1 / ((1/50.0 mm) - (1/52.5 mm) d_o ≈ 1050 mm  An object that is in focus will be approximately 1050 mm away from the camera lens when the 50.0 mm focal length lens is 52.5 mm away from the film. The thin lens equation helps us find the object distance by taking into account the focal length of the lens and the image distance. By plugging in the given values and solving for d_o, we can determine how far away the in-focus object .

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if the solution becomes lighter, has the equilibrium shifted to the left or right?

Answers

Answer:

left

Explanation:

If the system gets darker red in color, then the equilibrium must be shifting to the right (toward producing more of the colored product). If the color of the system gets fainter (or disappears altogether), the equilibrium must be shifting toward the left (toward the colorless components).

Location A on the surface of Earth bas a much higher temperature than Location Which statement is most likely true A.Both locations are at the poles B.Both are at the equator C.Location A is at the equator and Location B is the poles D.Location at the poles and location B is the equator

Answers

Answer:

The anwser is b

Explanation:

Answer:

the answer is B

I know  because i just did it

you are riding on the edge of a spinning playground merry-go-round. if you pull yourself to the center of the merry-go-round, what will happen to its rotation?

Answers

If you pull yourself to the center of the merry-go-round,  the rotation of the merry go round will decrease.

What is the centripetal acceleration of a merry go round?

This is the radial acceleration experienced by a person moving in a circular path as the merry-go-round rotates about its mean position.

a = v²/r

where;

v is the linear speed of the merry go roundr is the radius of the merry go rounda is the centripetal acceleration of the merry go round

From the formula given above, as the radius of the merry go round increases, the centripetal acceleration of the merry go round decreases.

v = ωr

where;

v is the tangential speed or linear speed of the merry go roundr is the radius of the circular path from the edge

Thus, when the radius of the circular path decreases, the speed of the merry go round will decrease as well.

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A car starts from rest and travels 25 m in 5 seconds at constant velocity. It then reverses 5 m in 10 seconds at constant velocity. The car then sits at rest for 5 seconds before it reverses at constant velocity back to where it started in 10 seconds time. Draw a position time graph that demonstrates the motion of the car.

Answers

Answer:

the car is going to same sped !

Explanation:

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Select the compensator zero to cancel one pole of GHP(z) {other than z=1}. α = Determine 3 based on the angle condition: zeros - 4poles = 180° You need to draw a figure as the Figure below to calculate ß = Im z-plane z = a + ib Zero of GHP(Z) Zzero Zpole(B) 0 B Figure: Determine ß Zpole(1) pole 1 of GHP(z) Re
The angle condition is: Zzero- (pole(1) + 4pole(B))= 180º Zzero = Zpole(1) = Zpole(B) = Determine the compensator gain k based on magnitude condition: z-α Gc (2) GHP (2)|2=a+ jb = 1 → k Ghp(2) = 1 z-ß |z=a+jb 1 k z-α GHP(z) |z-ß |z=a+jb Write down the final compensator (PID Controller) transfer function Gc(z)=kz-a z-ß

Answers

Analyze system dynamics and design compensator to achieve desired response by selecting compensator zero and canceling one pole of GHP(z).

How to select the compensator zero cancel one pole of GHP(z)?

To select a compensator zero to cancel one pole of GHP(z), we need to use the given angle condition:

Zzero - (pole(1) + Zpole(B)) = 180°

Here, Zzero represents the compensator zero, pole(1) represents the first pole of GHP(z), and Zpole(B) represents the compensator pole.

Let's proceed with the solution step by step:

1. First, we need to determine the value of Zzero. The angle condition states that Zzero = Zpole(1), which means the compensator zero is equal to the first pole of GHP(z).

2. Now, we need to find the value of Zpole(B). We can rewrite the angle condition as follows:

Zpole(B) = Zzero - pole(1) + 180°

Since we already know that Zzero = Zpole(1), we can substitute Zzero in the above equation:

Zpole(B) = Zpole(1) - pole(1) + 180°

Simplifying further:

Zpole(B) = 180°

Therefore, the value of Zpole(B) is 180°.

To summarize, we can select the compensator zero (Zzero) to cancel one pole of GHP(z) as Zpole(1), and the compensator pole (Zpole(B)) is determined to be 180° based on the given angle condition.

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