Paulina kicks a football. It accelerates towards the goal at 10 m/s². The ball has a mass of 430 g. With what force did Paulina kick the ball?

Answers

Answer 1

Force did Paulina kick the ball 4.3 N

What is force?

A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.

Paulina kicks a football. It accelerates towards the goal at 10 m/s². The ball has a mass of 430 g. Force = mass * acceleration

Force = .430*10 = 4.3 N

Force did Paulina kick the ball 4.3 N

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Answer 2

Answer:Remember to convert the mass from grams to kilograms first by dividing by 1000. Force = mass × acceleration = 0.43 kg × 10 m/s2 = 4.3 N


Related Questions

A book is sitting on a table. Which of the following is true about the table? O A. It is pushing up on the book. O B. It exerts no force on the book at all. O C. It is pulling down on the book. D. It can affect the mass of the book.​

Answers

Answer:

yes it does exert a force, it pushes it up

Explanation:

this is called normal force

if it didn't exert a force the book would keep going down

according to newton every force has an equal amd opposite reaction

so the book exerts a force on the table and vice versa

hope this helped

can someone help with the blank questions please?​

can someone help with the blank questions please?

Answers

It would effect his aim be cause in salt water it’s more dense

Match each physical property of matter to the appropriate definition
conductivity
density
buoyant force
solubility
boiling point

Match each physical property of matter to the appropriate definitionconductivitydensitybuoyant forcesolubilityboiling

Answers

probably a little late on this but the dude got everything wrong heres a screenshot of the answers.

Match each physical property of matter to the appropriate definitionconductivitydensitybuoyant forcesolubilityboiling

Solubility: the ability of a substance to dissolve in another.

Density: the amount of mass in a given volume.

Buoyant force: the upward force on an object in a fluid.

Conductivity: the ability of a substance to transfer heat or electricity.

Boiling point: the temperature at which a liquid becomes a gas.

Solubility can be defined as a measure of how readily a substance dissolves in a solvent to form a solution.

Hence, a substance is typically considered to be soluble if it is able it dissolve completely in a solvent.

Density can be defined as mass all over the volume of an object.

Simply stated, density is mass per unit volume of an object.

Buoyancy can be defined as an upward force created by the fluid (liquid) displaced by an object.

Conductivity can be defined as the ability of an object, substance or body to transfer heat or electricity to another.

Boiling point is the temperature at which a physical matter changes phase from liquid to gas.

For example, the boiling point of water is 100 degree Celsius (100°C).

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Florida is a peninsula bound by the Atlantic Ocean on the east and the Gulf of Mexico on the west. The sea affects temperatures along Florida’s coast. How do coastal temperatures compare to those inland?

Answers

They are usually warmer

Safety belts protect people in cars in the event of an accident because, according to Newton’s laws of motion, when an impact causes the car to suddenly change its motion -

A.the speed of the people always increases, since now they have not one but two forces acting on them.
B.the speed of the car always increases, giving it greater force since the mass will remain the same.
C.the car now has a greater overall mass - its own mass plus the mass of the object by which it has been struck.
D.the people in the car will continue to move in the same direction and at the same speed as before the impact.

Answers

Answer:

D :)

Explanation:

When an impact causes the car to suddenly change its motion, (D) the people in the car will continue to move in the same direction and at the same speed as before the impact.

What is Newton's first law of motion?

Newton's first law of motion states that Unless influenced by an imbalanced force, a body at rest stays at rest, and a body in motion keeps moving in a straight path at a constant pace. This law is commonly known as law of inertia and the resistance of a body to maintain its state of rest is called inertia of rest, same as, the resistance of a body to maintain its state of motion is called inertia of motion.

When a car is moving with certain speed, the car along with the people inside the car is in inertia of motion. In an event of accident, the car comes in rest in no time but the man in the car is still in inertia of motion. So, his body moves forward in the car which may cause injuries. To prevent such injuries, the people inside a car are advised to use safety belts.

So, correct answer  is option (D).

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How can you obtain the vertical and horizontal components of a projectile’s velocity?

Answers

A projectile is an object that is launched into the air and moves under the influence of gravity alone. The velocity of a projectile can be broken down into two components: the vertical component and the horizontal component. The vertical component of the velocity is the speed at which the object moves up or down, while the horizontal component is the speed at which it moves side to side.

The following are the methods to obtain the vertical and horizontal components of a projectile's velocity:

   If the initial velocity and the launch angle of the projectile are known, we can use trigonometry to calculate the vertical and horizontal components of velocity.

The horizontal component of the velocity is given by:

Vx = V * cosθ

where Vx is the horizontal velocity, V is the initial velocity of the projectile, and θ is the angle of launch.

The vertical component of the velocity is given by:

Vy = V * sinθ

where Vy is the vertical velocity.

   If the time of flight and the maximum height of the projectile are known, we can use kinematic equations to calculate the vertical and horizontal components of velocity.

The time of flight of a projectile is the time it takes to reach its maximum height and then fall back down to its original height. The maximum height reached by the projectile is the highest point in its trajectory.

The vertical component of the velocity can be calculated using the formula:

Vy = (2gh)^0.5

where Vy is the vertical velocity, g is the acceleration due to gravity, and h is the maximum height of the projectile.

The horizontal component of the velocity can be calculated using the formula:

Vx = d / t

where Vx is the horizontal velocity, d is the horizontal distance traveled by the projectile, and t is the time of flight.

In summary, the vertical and horizontal components of a projectile's velocity can be obtained using trigonometry if the initial velocity and launch angle are known or by using kinematic equations if the time of flight and maximum height are known.

The table shows the specific heat capacities of various substances. How much energy is required to raise the temperature of 5g of air by 10°C? Use the table below to help you.

The table shows the specific heat capacities of various substances. How much energy is required to raise

Answers

Answer:

50.25 j

Explanation:

Alex HEYYYYYYYYY

Answer:

The table shows the specific heat capacities of various substances. How much energy is required to raise the temperature of 5g of air by 10°C? Use the table below to help you.

"10 J" is WRONG

The right answer is "50.25 J"

Explanation:

hope this helps

A toy car has a 1. 5 A current, and its resistance is 2 Ω. How much voltage does the car require? V.

Answers

Answer: Voltage = (current) x (resistance)

Voltage = (1.5 A) x (2 ohms)

In order to MAKE 1.5 A of current flow through the toy car, you have to PROVIDE 3 volts from the battery.

HELP PLEASE QUICK QUICK QUICK I’ll give BRAINLIEST

HELP PLEASE QUICK QUICK QUICK Ill give BRAINLIEST

Answers

Answer:

Dude this is based on some egg you have

Explanation:

What is the force on a 1 000 kilogram-elevator that is falling freely under the acceleration of
gravity only (9.8m/s²)?

Answers

Answer:

9800N

Explanation:

Since it is falling freely, the only force on it is its weight, w. w = m ⋅ g = 1000kg ⋅ 9.8ms2 = 9800N

An action/reaction pair of forces ....
Select all that are True.
act on the same object.
point in the opposite direction.
act on two different objects.
point in the same direction.

Answers

Action-reaction pairs are forces that operate on separate objects in opposing directions and at identical magnitudes. Never do they affect the same thing. We learn that forces are interactions from Newton's third law.

An action-reaction pair is what?

When two bodies contact, they exert an equal and opposite force on one another in accordance with Newton's third rule of motion. Action-reaction forces are made up of these forces.

What do action and reaction forces look like in practice?

Think about how a baseball bat and a ball interact, for instance. The bat forces the ball to the right while the baseball forces the bat to the left. The action-reaction force pair is made up of these two forces acting on two separate objects together.

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The equation y = 2x + 3 represents the cost y (in dollars) of mailing a package that weighs x pounds.

Answers

Answer:

what is your question though

Explanation:

??? ??? ??? ??? ???


A weather balloon has a volume of 35 L at sea level (1.0 atm). After the balloon is released it rises to where the air pressure is 0.75 atm. What will the new volume of the weather balloon be

Answers

Answer:

P₁ = 1.0 atm

V₁ = 35 L

P₂ = 0.75 atm

Formula:

P₁V₁ = P₂V₂

Solution:

P₁V₁ = P₂V₂

V₂ = P₁V₁ / P₂

V₂ = (1.0 atm)(35 L) / 0.75 atm

V₂ = 47 L

Final Answer:

V₂ = 47 L

A ball is thrown straight down from the top of a 220-foot building with an initial velocity of −22 feet per second. What is its velocity after 3 seconds? What is its velocity after falling 108 feet?

Answers

A ball is thrown straight down from the top of a 220-foot building with an initial velocity of −22 feet per second. What is its velocity after 3 seconds is 7.4 feet per second.  Its velocity after falling 108 feet ix  50.99 feet per second.

Given data: the height of the building = 220 feet, initial velocity of the ball = -22 feet per second, time taken to fall = 3 seconds.

After 3 seconds, the velocity of the ball can be calculated using the following formula: Vf = Vi + gt

Where, Vf = final velocity of the ball, Vi = initial velocity of the ball, g = acceleration due to gravity (9.8 m/s^2) for downward motion, t = time taken to fall

Vf = -22 + (9.8 x 3)

Vf = -22 + 29.4

Vf = 7.4 feet per second

Therefore, the velocity of the ball after 3 seconds is 7.4 feet per second.

After falling 108 feet, the velocity of the ball can be calculated using the following formula:Vf² = Vi² + 2gh,

Where,Vf = final velocity of the ball, Vi = initial velocity of the ball, g = acceleration due to gravity (9.8 m/s^2) for downward motion, h = distance fallen

Vf² = (22²) + 2(9.8 x 108)Vf² = 484 + 2116.8

Vf² = 2600.8Vf = √2600.8Vf = 50.99 feet per second

Therefore, the velocity of the ball after falling 108 feet is 50.99 feet per second.

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A sound wave traveling through dry air has a frequency of 15 Hz, a
wavelength of 23 m, and a speed of 345 m/s. When the sound wave passes
through a cloud of ammonia gas, its wavelength changes to 28 m, while its
frequency remains the same. What is its new speed? (The equation for the
speed of a wave is v= f xx.)
A. 22 m/s
B. 420 m/s
C. 350 m/s
D. 9,700 m/s

Answers

Answer: b. 420 m/s

Explanation: ap3x

The frequency of the wave with the speed of 345 m/s and wavelength of 23 m is 15 Hz. With the same frequency the speed of wave t 28 m wavelength will be 420 m/s.

What is frequency ?

Frequency of a wave is the number of wave cycles per unit volume. It is the inverse of time period thus have the unit of s⁻¹ which is equivalent to one Hz. Frequency is inversely proportional to the wavelength.

The relation between frequency, wavelength and speed of a wave is written as follows:

c = νλ

Given that, speed of the wave = 345 m/s

wavelength =23 m

frequency = speed/wavelength

v = 345 m/s /23 m = 15 Hz.

New wavelength = 28 m

frequency = 15 Hz

then speed = 15 Hz × 28 m = 420 m/s.

Hence, the speed of the wave become 420 m/s. Option B is correct.

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How much time does it take if an object is traveling at 55 m/s and going for a distance of 6.5 meters?

Answers

Answer:

0.12 seconds

Explanation:

If it is 2:00 AM at 90 East longitude, what time is it at 75 East longitude? 11. If it is 8:00 PM at 15 East, what time is it at 135 East longitude? 12. How many hours difference is there between 105 West longitude and the Prime Meridian? 13. If it is 9:30 AM in New York which is located 41 North Latitude, and 75 West Longitude, what t is it in Lima Peru which is located at 15 South latitude, and 75 West Longitude?
Previous question

Answers

11.The time at 75° East longitude would be 1 hour and 20 minutes behind. 12.The time at 135° degrees East longitude would be 4 hours ahead. and 13. the time in Lima, Peru (15° South latitude, 75° West longitude) would also be 9:30 AM.

At 2:00 AM at 90° East longitude, the time at 75° East longitude would be 1 hour and 20 minutes behind. This is because for every 15 degrees of longitude, there is a time difference of approximately 1 hour. Since the two longitudes in question have a difference of 15 degrees, we can divide this by 15 to calculate the time difference.

If it is 8:00 PM at 15° East longitude, the time at 135° East longitude would be 4 hours ahead. Similarly, for every 15 degrees of longitude, there is an approximate time difference of 1 hour. Since the two longitudes in question have a difference of 120 degrees, we can divide this by 15 to calculate the time difference.

There is a 7-hour difference** between 105° West longitude and the Prime Meridian (0° longitude). The Prime Meridian, passing through Greenwich, England, serves as the reference point for determining time zones. As one moves westward from the Prime Meridian, each 15 degrees of longitude corresponds to a time difference of approximately 1 hour. Therefore, the time at 105° West longitude would be 7 hours behind the time at the Prime Meridian.

If it is 9:30 AM in New York (41° North latitude, 75° West longitude), the time in Lima, Peru (15° South latitude, 75° West longitude) would also be 9:30 AM. The latitude does not affect the time difference between the two locations. However, since both locations have the same longitude (75° West), they would experience the same local time. The time difference between different latitudes is primarily significant for determining time zones rather than the actual time within a specific time zone.

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If the photon scatters at an angle of 60.0 ∘ from its original direction, what is the magnitude of the linear momentum of the electron just after it collides with the photon?

Answers

the magnitude of the linear momentum of the electron just after it collides with the photon is (7.558 × 10⁻²⁶) kgm/s.

Let the photon's wavelength before it collides. =  λ

After a collision, the photon's wavelength equal = λ'

before a collision, the photon's frequency = f

After-collision photon frequency = f'

Pp = (h/) is the momentum of the photon prior to collision.

Prior to collision, the photon's momentum is given by Pp' = (h/'), where h is Planck's constant.

Let P represent the electron's post-collision momentum.

According to Compton's theory, the elastic collision between a photon and an electron abides by the principles of momentum and energy conservation.

The conservation of momentum

Momentum before collision = momentum after collision

Before momentum collision = Pp.

After-collision momentum = (Pp' + P)

Pₚ = (Pₚ' + P)

P =  (Pp - Pp') = (h/) - (h/') = h[(1/) - (1/')]

With the exception of the photon's after-collision wavelength, all of the variables needed to determine the electron's momentum are known.

We utilize the Compton's wavelength formula to determine this.

Compton established from the principle of conservation of mass and momentum that the wavelength of the electron following a collision i λ's given by

λ' - λ = (h/m₀c) (1 - cos θ)

where; h = Planck's constant = 6.63 × 10⁻³⁴ J.s

m₀ = mass of the electron = 9.11 × 10⁻³¹ kg

c = speed of light = 3.0 × 10⁸ m/s

θ = angle of scattering of the photons after collision = 60°; cos 60° = 0.5

λ = 0.102 nm = 1.02 × 10⁻¹⁰ m

λ' - λ = [(6.63 × 10⁻³⁴/(9.11 × 10⁻³¹ × 3.0 × 10⁸)] × 0.5

λ' - λ = 1.213 × 10⁻¹² m

λ' = λ + (1.213 × 10⁻¹²) = (1.02 × 10⁻¹⁰) + (1.213 × 10⁻¹²) = (1.032 × 10⁻¹²) m

P = (Pₚ - Pₚ') = (h/λ) - (h/λ') = h[(1/λ) - (1/λ')]

P = h[(1/λ) - (1/λ')] = (6.63 × 10⁻³⁴) [(1/(1.02 × 10⁻¹⁰)) - (1/(1.032 × 10⁻¹²))] = (6.63 × 10⁻³⁴) (113999088) = (7.558 × 10⁻²⁶) kgm/s

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helppppppppppppppppppppppppp

helppppppppppppppppppppppppp

Answers

Answer:

value of x=35°

y=72.5°

hope it helps you

make me brainliest plz

PHYSICS HELP!! NEED IT BY/ON MARCH 3!!
(a) A typical steam jet shoots 3. 62 kg of 157°C water vapor onto an intruder. How much energy is released by the cooling of the water vapor from 157°C down to the point where it can condense, 100°C? Specific heat of water vapor is 2020J/kg°C


(b) Once cooled how much heat is released by the condensation of the water vapor? The Latent Heat of Vaporization is 2,260,000 J/kg


(c) Now that the water is in liquid form, find how much more heat is released by the water as it cool to skin temperature of 26°C, then add the other energy to find the total heat released during the entire ordeal

Answers

From the calculations, the total heat involved in the entire process is 9.72 × 10^6 J.

What is specific heat capacity?

The term specific heat capacity is the heat that is gained when 1 Kg of a body undergoes a temperature rise of 1 K.

a) H = mcdT

m = mass

c = specific heat

dT = temperature change

H = 3.62 kg ×  2020J/kg°C × (157 - 100)

H = 416806.8 J

b) H = mL

H = 3.62 kg × 2,260,000 J/kg

H = 8181200 J

c) H = 3.62 kg × 4200 J/kg°C × ( 100 -26)

H = 1125096 J

Total heat: 416806.8 J + 8181200 J + 1125096 J = 9.72 × 10^6 J

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The liquid pressure exerted in one direction only​

Answers

the pressure exerted by a liquid on an object increases as we go more deep into the liquid and this pressure is called as hydro static pressure . if we consider a part of the static fluid then all the horizontal forces will cancel out while the vertical forces will add vectorilly and due to which a pressure difference is created . so as we go more deep the pressure increase .

Now pressure is a scalar so it does not depend on direction but when two objects are on the same level with respect to a reference level then the pressure exerted on them by fluid is always the same . hope this helps

Hydrogen bonding is a weak attractive force.
O A. True
O B. False

Answers

Answer:

The Answer is gonna be True

Explanation : A hydrogen bond is a weak type of force that forms a special type of dipole-dipole intermolecular attraction when a hydrogen atom is bonded directly to one of the most electronegative elements like nitrogen (N), oxygen (O) or fluorine (F). This causes the hydrogen to acquire a significant amount of positive charge.

Or

Hydrogen bond is an attractive force between a partially positive charged hydrogen and a partially negative charged atom (oxygen and nitrogen). This is a very weak bond and strength of hydrogen bond (5-10 Kcal per bond) is much less than the strength of covalent bond. Hydrogen bonds are usually showed as dotted lines between two atoms.

This is the Answer for your question :3

I hope you are having a great day ❤️❤️❤️❤️❤️

Answer: The attraction of opposite charges between hydrogen and oxygen does not form a weak bond because oxygen-hydrogen makes hydrogen bonding. Hydrogen bonding is a very attraction force

Base your answers to questions 11 through 13 on the information and diagram below and on your
knowledge of physics.
A ray of light with a frequency of 5.09 x 104 hertz traveling in medium X is refracted at point P.
The angle of refraction is 90°, as represented in the diagram.
Normal
Air
Refracted ray
Medium X
f = 5.09 x 1014 Hz
11. Calculate the wavelength of the light ray in air. [Show all work, including the equation and
substitution with units.]
12. Measure the angle of incidence for the light ray incident at point P.
13. Calculate the absolute index of refraction for medium X. [Show all work, including the equation and
substitution with units.]
Incident ray

Answers

11. The wavelength of the light ray in air is 0.589 x 10⁻⁶ m.

12. Angle of incidence for the light ray at point P is 43.23°.

13. The absolute index of refraction for medium X is 1.46

What is Snell's law?

It states that the ratio of sine of angle of incidence and angle of refraction is equal to the refractive index of first medium to the second medium.

sini/sinr = n₁/n₂

11. The wavelength is related to the frequency as

λ = c/f

where c = 3 x 10⁸ m/s and frequency f = 5.09x 10¹⁴ Hz

Put the values, we get

λ = 3 x 10⁸/ 5.09x 10¹⁴

λ =0.589 x 10⁻⁶ m

Thus, the wavelength of the light ray in air is 0.589 x 10⁻⁶ m.

12. Given the angle of incidence is i, angle of refraction r =90° ,  n₂ = Refractive index of medium X = 1.46 and n₁ = Refractive index of air = 1

Substituting the values into Snell's law expression we get,

sin i= sin 90 x 1/1.46

i = 43.23 degrees

Thus, the angle of incidence is  43.23 degrees.

13. The refractive index is the ratio of speed of light  in vacuum to the speed of light in the medium X.

n = c/v

If v₂ is the velocity of light in medium X, then

sin i / sin r  = v₂/v₁

sin 43.23 / sin 90 =  v₂/ 3 x 10⁸

v₂ = 2.055 x 10⁸ m/s

So, the refractive index be

n = 3 x 10⁸/2.055 x 10⁸

n = 1.46

Thus, absolute index of refraction for medium X is 1.46

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A runner is jogging in a straight line at a
steady vr= 8.2 km/hr. When the runner is
L= 2.5 km from the finish line, a bird begins
flying straight from the runner to the finish
line at vb= 41 km/hr (5 times as fast as the
runner). When the bird reaches the finish
line, it turns around and flies directly back to
the runner.
What cumulative distance does the bird
travel? Even though the bird is a dodo, assume that it occupies only one point in space
(a “zero” length bird), travels in a straight
line, and that it can turn without loss of
speed.
Answer in units of km.

Answers

The cumulative distance traveled by the bird is 3.12 km.

Cumulative distance of the bird

The cumulative distance of the bird is calculated as follows;

Apply the principle of relative velocity.

Vbt - Vrt = L

(Vb - Vr)t = L

where;

Vb is the velocity of the birdVr is the velocity of the runnert is time of motion

Substitute the given parameters and solve for time of motion,

(41 - 8.2)t = 2.5

32.8t = 2.5

t = 2.5/32.8

t = 0.076 hr

Distance traveled by the bird = 0.076hr x 41 km/hr = 3.12 km

Thus, the cumulative distance traveled by the bird is 3.12 km.

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What is a satellite?
A) any object affected by Earth's gravitational pull

B) a manmade object that allows us to communicate or observe our environment

C) any object that revolves around a planet in a circular or elliptical path

D) a network of 24 objects in space that help people determine their location

Answers

Answer:

c

Explanation:

answer is c I hope it is correct

A bullet of mass m = 6.90 g is fired into and embeds itself in a large 1.10-kg block of wood, initially at rest. What was the original speed of the bullet if that block with the embedded bullet were moving at a speed of 1.80 m/s immediately after the collision?

Answers

The bullet's initial speed was roughly 0.108 metres per second.

We can use the conservation of momentum to solve this problem. Before the collision, the bullet has momentum p1 = m1 * v1, where m1 is the mass of the bullet and v1 is its velocity. After the collision, the bullet and the block have a combined momentum p2 = (m1 + m2) * v2, where m2 is the mass of the block with the embedded bullet and v2 is their common velocity.

Because momentum is conserved, we can equate the two momenta:

p1 = p2

m1 * v1 = (m1 + m2) * v2

We are given the masses m1 = 6.90 g and m2 = 1.10 kg. We are also given the final velocity v2 = 1.80 m/s. Solving for the initial velocity v1, we get:

v1 = (m1/m2) * (v2 - v1)

v1 = (6.90 g / 1.10 kg) * (1.80 m/s - 0)

v1 = 0.108 m/s

Therefore, the original speed of the bullet was approximately 0.108 meters per second.

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Studying neutrinos helped to explain how our Sun works but led to changes in theories of particle physics, how is this process consistent with the scientific process? How can details about a theory be adjusted without undermining other discoveries made through the theory's predictions?

Answers

Explanation:

Yes,  evidently, the process is consistent with the scientific process because in scientific process falsification and modification are two very important traits. So this new concept have modified the existing theories.

Through the modification a theory is adjusted without undermining other discovering made through the theory's prediction.

There are many other evidences that prove this fact for example Einstien's Theory of relativity also changes the existing concepts.

2. The dust usually sticks ton TV iscreen because dust
A. Falls on the TV screen
B.Particles are metallic conductors
C.Is attracted by magnets in the TV screen
D. Is attracted
by static charges on the TV scien.​

Answers

Answer:c

Explanation:

What value of resistor R gives the circuit in the figure a time constant of 22 μs ?

Answers

The value of resistor R that gives the circuit in the figure a time constant of 22 μs is 220 Ω.

The circuit that is in the figure is shown below:Given that time constant (RC) = 22 μs. To find the value of resistor R, we need to use the formula for the time constant:

RC = τ, where R is the resistance and C is the capacitance of the circuit.

Rearranging the above formula, we get:R = τ / C

Where τ is the time constant and C is the capacitance of the circuit.

From the figure, the capacitance is given as 0.1 μF

.Substituting the values of τ and C in the above formula, we get:

R = (22 × 10⁻⁶ s) / (0.1 × 10⁻⁶ F)

R = 220 Ω

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Q.7. For a system with a transfer function of G(s)=- co² s² +2a+w² if the natural frequency is 0.5 and the damping ratio is 1.3, which of the following statements is correct regarding the unit step response of the system?
O A) Damped
O B) Undamped
O C) Underdamped
O D) Crittically Damped
O E) Overdamped

Answers

The system described by the transfer function G(s) = -co² s² + 2a + w², with a damping ratio of 1.3 and a natural frequency of 0.5, has an overdamped unit step response. So, the correct option is (E)

The transfer function of the system is given as G(s) = -co² s² + 2a + w², where co represents the damping ratio, a represents an arbitrary constant, and w represents the natural frequency of the system. We are given that the natural frequency is 0.5 and the damping ratio is 1.3.

To determine the type of unit step response, we need to analyze the damping ratio (co) in relation to the critical damping value (co_critical).

The critical damping ratio (co_critical) is defined as the value where the system is on the threshold between being overdamped and underdamped. It is given by the formula co_critical = 2 * sqrt(a * w²).

In our case, the natural frequency (w) is 0.5, so we can calculate co_critical as follows: co_critical = 2 * sqrt(a * 0.5²).

Since the damping ratio (co) is given as 1.3, we can compare it with co_critical to determine the type of unit step response.

If co > co_critical, the system is considered overdamped (Option E).

If co = co_critical, the system is considered critically damped (Option D).

If co < co_critical, the system is considered underdamped (Option C).

Based on the given values, we can determine that the system is overdamped (Option E) because the damping ratio (1.3) is greater than the critical damping ratio.

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