A glass marble whose mass is 0.1 kg falls from a height of 40 m and rebounds to a height of 10 m. Find the impulse and the average force between the marble and the floor if the time during which they are in contact is 0.1 sec.
[Take g= 9.8 ms^-2]​

The statements (A) both toy cars will acquire equal but opposite momenta and (C) the massive toy car will acquire least speed are true.

The statement "both toy cars will acquire equal but opposite momenta" is true. This is because momentum is always conserved in a system, and in this case, the initial momentum of the system is zero. When the spring is released, the two toy cars will move in opposite directions, but because they have different masses, they will have different speeds. Therefore, their momenta will be equal but opposite in direction.

The statement "both toy cars will acquire equal kinetic energies" is false. This is because kinetic energy is not conserved in this system, and the two toy cars will have different kinetic energies due to their different masses and speeds.

The statement "the massive toy car will acquire the least speed" is true. This is because the massive toy car has greater inertia than the smaller toy car, meaning it requires more force to move at the same speed. Therefore, it will accelerate more slowly and reach a lower maximum speed than the smaller toy car.

The statement "the smaller toy car will experience an acceleration of the greatest magnitude" is false. This is because acceleration is dependent on both the force applied and the mass of the object. While the smaller toy car may experience a greater force than the larger toy car, it also has less mass, so the acceleration of the two cars will be the same.

Overall, the true statements are A and C, and the false statements are B and D.

The Question was Incomplete, Find the full content below :

Two toy cars with different masses originally at rest are pushed apart by an ideal spring and released. Which of the following statements (s) are TRUE?

(A) both toy cars will acquire equal but opposite momenta  

(B) both toy cars will acquire equal kinetic energies  

(C) the massive toy car will acquire least speed  

(D) the smaller toy car will experience an acceleration of the greatest magnitude

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The perimeter of the pool is approximately 206.85 feet if we use 3.14 as the approximation of the value of π.

In this case, the angle AOB is 360 degrees, so the arc length is:

arc length = (360/360) x 2π(25) = 50π feet

Finally, we can find the perimeter of the pool by adding up the lengths of the two semicircles and the arc AB:

perimeter = 2πr + 2r + arc length

perimeter = 2π(25) + 2(25) + 50π

perimeter = 50π + 50

Perimeter is a measurement of the distance around the edge of a two-dimensional shape, such as a square, rectangle, or circle. It is the sum of the lengths of all the sides that make up the shape. The perimeter is an important concept in geometry and is used to determine the amount of material needed to enclose or surround a shape, as well as to calculate the distance around a given route or path.

To find the perimeter of a shape, you simply add up the lengths of its sides. For example, if you have a square with sides that are each 5 units long, the perimeter would be 5 + 5 + 5 + 5 = 20 units. Similarly, if you have a circle with a radius of 10 units, the perimeter (also known as the circumference) would be 2πr or approximately 62.8 units.

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Complete Question: -

If AO is 50 feet, find the perimeter of the pool. (O is the center of the sector AOB. OA and OB are the diameters of two semi-circles.)

The correct answer to this question is : the colours of the star's light by the amount that is absorbed by the clouds is blue, green, yellow, orange, red.

An interstellar dust cloud, also known as an interstellar medium (ISM), is a region of space that is filled with gas (mostly hydrogen and helium) and dust particles. These clouds are typically found in the vast, empty spaces between stars in a galaxy, where the density of matter is relatively low.

Interstellar dust clouds can be extremely large, with sizes ranging from a few light years to hundreds of light years across. They are also quite cold, with temperatures ranging from a few degrees above absolute zero to a few hundred Kelvin.

The dust particles in interstellar dust clouds are primarily made up of silicates, carbon, and other heavy elements that are formed in the interiors of stars and are ejected into space during supernova explosions. These particles can absorb and scatter light, and are responsible for the reddish or bluish appearance of many celestial objects.

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The full question is:

The following plots show the spectrum of a star before (left) and after (right) its light has passed through an interstellar dust cloud. Rank each color of the star's light by the amount it is absorbed by the dust cloud as its light passes through it. most-least: yellow, red, orange, green, blue.

The equivalent capacitance of the combination is 2.2405 μF.

To find the equivalent capacitance of the combination, we can use the formula:

1/C = 1/C1 + 1/C2 + 1/C3

where C1, C2, and C3 are the capacitances of the three capacitors.

Plugging in the values, we get:

1/C = 1/5.2μF + 1/7μF + 1/9μF

1/C = 0.1923077 + 0.1428571 + 0.1111111

1/C = 0.4462759

C = 1/0.4462759

C = 2.2405 μF (rounded to 4 significant figures)

Therefore, the equivalent capacitance of the combination is 2.2405 μF.

A system's capacitance is its capacity to store an electric charge. The proportion of the electric charge held on a conductor to the difference in potential between the conductors is what is meant by this term.

The farad (F), which is equal to one coulomb per volt, is the unit of capacitance.

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The pressure exerted by the man on the lilo is 450 pascals (Pa).

The pressure is the force per unit area, so we can calculate it using the formula:

pressure = force / area

In this case, the force is the weight of the man, which is 900 N, and the area is the surface area of the lilo, which is 2 m². Therefore, we can substitute these values into the formula:

pressure = 900 N / 2 m²

Simplifying, we get:

pressure = 450 Pa

Therefore, the pressure exerted by the man on the lilo is 450 pascals (Pa).

What is pressure?

Pressure is the amount of force applied per unit area over a surface. It is defined as the force per unit area perpendicular to the surface on which the force is acting. The unit of pressure is pascal (Pa), which is equivalent to one newton per square meter (N/m²).

What is force?

Force is a physical quantity that describes the interaction between two objects that can change the state of motion or shape of an object. It is defined as an influence that causes an object to undergo acceleration, or a change in velocity, or deformation.

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Answer:

Explanation:

R/^5*r^6 Ok so  then this is simple once u get the answer u need to use the given formula in order to plug in the numbres sorry .

So basically

12 x r^6(u must fill in the number s ) and then u need to do `13x14xr the answer and use the rest of the numbers in order to figure out the quantities of each side for the shape . Then ur answer would be the r^x + x = ???

So yeah hope this helped

I think

Kind of

K Thanks Bye

At point B, the ball is moving at a speed of around 2.05 m/s. At point C, the ball is moving at a speed of roughly 3.67 m/s.

Speed is the rate at which an object travels along a path over time, whereas velocity is the speed and direction of an item's motion.

(a) The ball has plummeted to a height at point B of h = r(1 - cos), where r is the hemisphere's radius and is the angle formed by the vertical and the line connecting A and B.

The ball loses as much potential energy as it gains in kinetic energy:

mgh = (1/2)mv² + (1/2)Iω²

Since the ball is rolling without slipping, we have v = rω. Also, for a solid sphere or ball, I = (2/5)mr^2.

By simplifying and substituting these formulas, we obtain:

mgh = (7/10)mv²

Solving for v, we get:

v = √((10/7)gh)

Substituting the given values, we get:

v = √((10/7) x 9.8 m/s² x 0.5 m x (1 - cos(30°)))

≈ 2.05 m/s

(b) The ball has dropped through a height of h = 2r at point C. Applying the same simplifications and conservation of energy equation as before, we arrive at:

mgh = (7/5)mv²

Solving for v, we get:

v = √((5/7)gh)

By simplifying and substituting these formulas, we obtain:

v = √((5/7) x 9.8 m/s² x 1.0 m)

≈ 3.67 m/s.

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The absolute pressure on the bottom of a swimming pool 28.0 m by 8.5 m whose uniform depth is 1.8 m is 287 kPa

the absolute pressure on the bottom of the pool is 17.6 kPa.

Pressure is defined as the amount of force per unit area applied to an object's surface. Pressure may also be defined as a scalar amount of stress exerted on a surface that is perpendicular to the direction of the force. Pressure is frequently represented by the symbol p, which stands for pressure.

Given,

Length of the pool, l = 28 m

Width of the pool, w = 8.5 m

Depth of the pool, h = 1.8 m

The density of water,

p = 1000 kg/m³

g = 9.81 m/s²

Absolute pressure formula:

p = ρgh

Absolute pressure p is given by,

p = ρgh

p = 1000 kg/m³ × 9.81 m/s² × 1.8 mp

  = 17604 Pa

Then, Converting the answer to kPa,

1 Pa = 1 × 10⁻³ kPa⇒ 17604 Pa = 17.6 kPa

Therefore, the absolute pressure on the bottom of the pool is 17.6 kPa rounded to two significant figures.

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Answer:

both are only physical changes

Explanation:

Physical changes are changes that do not alter the identity of a substance.

The liquid soap is still liquid soap when mixed into water.

The dry ice is still dry ice when it changes state from solid to gas.

You must be at least 0.54 meters (or about 1.8 feet) away from the cable to experience a magnetic field less than the Earth's magnetic field.

A magnetic field is a physical field generated by moving electric charges or the intrinsic magnetic moments of elementary particles associated with their spin. A magnetic field is a vector field, which means that it has both magnitude and direction. It can exert a force on other moving charges or magnetic materials, causing them to experience a magnetic force.

In the classical picture, a magnetic field is created by a magnet or by a moving electric charge, such as an electric current. The strength of the magnetic field at a given point is proportional to the magnitude of the current or the strength of the magnet, and it decreases with distance from the source.

To calculate the distance from the cable at which the magnetic field is less than the Earth's magnetic field, we can use the formula for the magnetic field around a long, straight wire:

B = μ0 * I / (2πr)

where B is the magnetic field, μ0 is the permeability of free space (4π x  10⁻⁷T m/A), I is the current, and r is the distance from the wire.

Rearranging the formula, we get:

r = μ0 * I / (2π * B)

Plugging in the given values, we get:

r = (4π x 10⁻⁷T m/A) * 135 A / (2π * 5.00 x 10⁻⁵ T)

r = 0.54 meters

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Answer:

They are approaching at speed 1.8 + 1.4 = 3.2 m/s

T = 111.8 / 3.2 = 34.94 sec to reach each other

S = V T     where V = 6.5 m/s      Spot's speed

6.5 m/s * 34.9 = 227.1 m

(D) 227.1 m    the distance Spot has to run

When the snow melts, it will form liquid water, and the volume of the water will be equal to the volume of the original snow sample. Therefore, the volume of liquid water produced by the melting of the 24 ml sample of snow is also 24 ml.

If the snow has a density of 0.5 g/ml, then the mass of the snow is:

mass = density x volume = 0.5 g/ml x 24 ml = 12 g

Therefore, the volume of liquid water produced by the melting of the 24 ml sample of snow is also 24 ml.

What is volume?

Volume of liquid refers to the amount of space that a liquid occupies. It is a measure of the three-dimensional space that the liquid occupies and is usually measured in units such as liters, milliliters, gallons, or fluid ounces. The volume of a liquid is determined by the shape of the container in which it is placed, and it can be measured directly using a graduated cylinder or other volumetric measuring device.

What is density?

Density is a physical property of matter that describes how much mass is present in a given volume of a substance. It is defined as the mass of a substance per unit volume, and is typically measured in units such as grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³).

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Volcanic eruptions are a nonanthropogenic source of carbon dioxide emissions into the atmosphere.

What is volcanic eruption?

A volcanic eruption is a natural or nonanthropogenic source of carbon dioxide emissions into the atmosphere. During a volcanic eruption, carbon dioxide and other gases are released from the Earth's mantle and can contribute to the atmospheric concentration of carbon dioxide.

However, the amount of carbon dioxide emitted by volcanoes is relatively small compared to the amount emitted by human activities such as burning fossil fuels. While volcanic eruptions are a natural source of carbon dioxide emissions, the amount emitted by volcanoes is relatively small compared to the amount emitted by human activities such as burning fossil fuels.

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Complete question is: Volcanic eruptions are a nonanthropogenic source of carbon dioxide emissions into the atmosphere.

Answer:

v= ir

Here, I = 0.26

R = 852

So,

v = 0.26 x 852

= 221.52 V

If R = 85.2 and I = 0.26,

V= ir

v = 0.26 x 85.2

v = 22.152.

Hope it helps.

The correct answer is C) 55 m/s. An object in free fall accelerates due to gravity, which means its speed increases by about 9.8 m/s2 every second. So in one second, its speed increased from 50 m/s to 50 + 9.8 = 59.8 m/s. Since it is impossible for the object to have a speed of 59.8 m/s, the closest answer is C) 55 m/s.

Given,An object in free fall is moving downward at 50 meters per second.At one-second later its speed is about.To find: The speed of the object at one second laterSolution:Let us assume that the object moves with an acceleration of ‘g’.Given, Initial velocity, u = 50 m/s

Time taken, t = 1sWe know that the velocity of an object in freefall is given by:v = u + gtFrom the above equation, we can calculate the final velocity of the object after one secondv = u + gtv = 50 + 9.8 × 1v = 50 + 9.8v = 59.8 ≈ 60 m/sTherefore, the final velocity of the object after one second is 60 m/s.Hence, the correct option is (D) 60 m/s.

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Answer:

160 watts

Explanation:

To calculate the power of the pump required to lift 160kg of water through a vertical height of 3m in 30 seconds, we can use the formula:

Power = Work done / Time taken

Work done = force x distance

The force required to lift the water is equal to its weight, which is:

Force = mass x gravity = 160 kg x 10 m/s^2 = 1600 N

The distance the water is lifted is 3m.

Therefore, work done = Force x distance = 1600 N x 3 m = 4800 J

The time taken is 30 seconds.

Now we can substitute these values into the formula for power:

Power = Work done / Time taken = 4800 J / 30 s = 160 W

Therefore, the power required to lift 160kg of water through a vertical height of 3m in 30 seconds is 160 watts.

Job enrichment is a strategy used to motivate workers by adding the responsibility and diversity of their work. variant d

Feedback is essential to effective plant enrichment. Successful job enrichment depends on numerous effects, including acceptable backing and operation support, and clear performance norms.

Job Enrichment is a system of hand engagement in which jobs are designed to have intriguing and grueling tasks that may bear further chops and may increase pay.

The purpose of job enrichment is to compound the tasks performed by each hand, allow them to perform tasks in different ways, and eventually give them more control over the work they perform.

One of the most important motorists of change in professional enrichment programs is feedback. This not only needs to be done at the hand- director position, but also needs to be encouraged within the brigades.

Question

According to J. Richard Hackman and Gerg Oldham, which of the following is necessary for job enrichment to be effective?

a) Hygiene

b) Dissatisfied

c) Valencia

d) feedback

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(1a) The potential energy of the body is 980 J

(1b) The kinetic energy of the body halfway down is 490 J and

(1c) The kinetic energy just before impact is 9807 J.

(2) The work done by the trailer on the car is 15,750,000 J.

(3)The initial speed of the vehicle was 10.6 m/s and the work required to stop the car is 269.9 kJ.

Problem 1:

The potential energy of the body is given by the formula:

potential energy = mass x gravity x height

where mass = 50 kg, gravity = 9.8 m/s², and height = 2 m

So, potential energy = 50 x 9.8 x 2 = 980 J

When the body is halfway down, its height above the ground is 1 m. At this point, the potential energy is:

potential energy = mass x gravity x height

potential energy = 50 x 9.8 x 1 = 490 J

The total energy of the body (at any point) is the sum of its potential energy and kinetic energy.

Therefore, the kinetic energy of the body halfway down is:

kinetic energy = total energy - potential energy

kinetic energy = (50 x 9.8 x 2) - (50 x 9.8 x 1) = 490 J

Just before impact with the floor, the height of the body above the ground is zero, so the potential energy is also zero.

At this point, the total energy of the body is equal to its kinetic energy:

kinetic energy = (1/2) x mass x velocity²

where mass = 50 kg, and velocity = ?

To find the velocity, we can use the conservation of energy principle:

total energy at the top = total energy just before impact

potential energy at the top = kinetic energy just before impact

potential energy at the top = 50 x 9.8 x 2 = 980 J

kinetic energy just before impact = 980 J

So, (1/2) x 50 x velocity^2 = 980 J

Solving for velocity, we get:

velocity = √(2 x 980 / 50) = 19.8 m/s

Therefore, the kinetic energy just before impact is:

kinetic energy = (1/2) x 50 x (19.8)^2 = 9,807 J

Problem 2:

The work done by the trailer on the car is given by the formula:

work = force x distance

where force = 900 N, and distance = (70 km/h) x (15/60) h = 17.5 km

Converting km to meters, we get:

distance = 17.5 km x 1000 m/km = 17,500 m

So, work = 900 x 17,500 = 15,750,000 J

Problem 3:

The work done by the brakes is equal to the change in kinetic energy of the vehicle:

work done by brakes = change in kinetic energy

Let the initial speed of the vehicle be v m/s. Then, the initial kinetic energy of the vehicle is:

kinetic energy = (1/2) x 1600 x v²

After the brakes are applied, the final kinetic energy of the vehicle is zero (since the vehicle comes to a stop).

Therefore, the work done by the brakes is equal to the initial kinetic energy:

work done by brakes = (1/2) x 1600 x v²

Given that the work done by the brakes is 90 kJ, we can solve for the initial speed:

90,000 J = (1/2) x 1600 x v²

v² = 112.5

v = √(112.5) = 10.6 m/s

So, the initial speed of the vehicle was 10.6 m/s.

The work required to stop the car:

W = ¹/₂(1600)(15² + 10.6²)

W = 269,888 J = 269.9 kJ

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The potential energy of an electron moving parallel to an electric field decreases as it moves from higher voltage to lower voltage. The work done by the electric field on the electron is equal to the decrease in potential energy. The potential energy of the electron is proportional to its charge and the voltage difference between the two points.

When an electron moves parallel to an electric field, its potential energy is conserved. The potential energy of an electron is proportional to its charge and the voltage through which it moves. As the electron moves from higher voltage to a lower voltage, its potential energy decreases. The work done by the electric field on the electron is equal to the decrease in potential energy. When the electron is at rest, it has a certain potential energy due to its position in the electric field. If the electron is allowed to move freely, it will accelerate towards the lower voltage region, gaining kinetic energy. As it moves, the electric field continues to do work on the electron, converting its potential energy into kinetic energy. If the electric field is uniform, the potential energy of the electron will be given by the equation U = -qV, where q is the charge of the electron and V is the voltage difference between the two points. The negative sign indicates that the potential energy decreases as the voltage difference decreases.

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Based on what you learned about the roller coaster ride, the following statements about energy transformations that are true are: A. Kinetic energy can be converted into several other types of energyC. A change in an object's speed is evidence that the object's kinetic energy is changing.

The process of energy transformation is the conversion of one form of energy into another. This term describes the scientific process by which energy, in various forms, is transformed to do work. Energy transformation occurs in every physical system in the universe.

Kinetic energy can be converted into several other types of energy.Kinetic energy is the energy of a moving object. The energy is converted into various types of energy, such as electrical and thermal energy, as a result of movement. In a roller coaster, kinetic energy is converted into potential energy as the train goes up the lift hill. The potential energy is converted back into kinetic energy as the train goes down the first drop.

A change in an object's speed is evidence that the object's kinetic energy is changing.Kinetic energy changes when an object's speed changes. If an object slows down, its kinetic energy decreases, while if it speeds up, its kinetic energy increases. On the roller coaster, as the train moves up and down the track, its speed varies, causing changes in its kinetic energy.

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Co-ordinates are (-3, 9), ( -6, -6), ( 9, -3), for this we have to learn scale factor.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given coordinates of triangle (-1, 3), (-2, -2) and (3, -1)

As, the figure dilated by factor 3

Then the coordinates after dilation is

(-1 * 3, 3 * 3 ) = ( -3, 9 )

(-2 * 3, -2 * 3 ) = ( -6, -6 )

(3 * 3, -1 * 3 ) = ( 9, -3 )

Hence co-ordinates are :

(-3, 9), ( -6, -6), ( 9, -3).

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the work done is 24,442 J.

As for the second part of the question, putting on a bigger engine could have other benefits besides increasing the distance traveled. For example, it could increase the speed of the cart or allow it to carry heavier loads. Additionally, the purpose of the cart may have changed, requiring a bigger engine to meet new demands.

The work done is calculated using the formula:

work = force x distance x cos(theta)

where force is the net force acting on the cart, distance is the distance traveled, and theta is the angle between the direction of force and the direction of motion.

Assuming that the cart moves along a horizontal surface, theta is 0 and cos(theta) is 1. Therefore, the work done is:

work = force x distance

To calculate the force, we can use Newton's second law, which states that force is equal to mass times acceleration:

force = mass x acceleration

The acceleration can be calculated using the equation:

acceleration = net force/mass

Since the cart moves forward, the net force must be in the forward direction. Therefore, the force is equal to the maximum force that the engine can provide, which is 1111 N.

The mass of the cart is not given, so we cannot calculate the acceleration and force precisely. However, we can use the distance traveled to estimate the force.

If the cart moves forward 22 m and the engine provides a constant force, then the work done is:

work = force x distance = (1111 N) x (22 m) = 24,442 J

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The expression for the Young Modulus E of the metal is E = mgl / Ae. The Young Modulus E of the metal is calculated using the equation  E = (F l) / (A e2 m), where F is the force applied to the wire.

To find the expression for the Young modulus E of a metal wire with length l, cross-sectional area A, and mass m hung from the other end of the wire, we need to use the following formula:Stress (σ) = Load (F) / Area (A)Strain (ε) = Extension (Δl) / Original length (l)Young Modulus (E) = Stress (σ) / Strain (ε)We know that the metal wire is fixed at one end and the wire extends a distance e when a mass m is hung from the other end of the wire. Therefore, the extension Δl is equal to e.

Let's assume that g is the acceleration due to gravity. Therefore, the load F is equal to m * g.Substituting the values of F, A, and Δl in the above formula, we get:Stress (σ) = F / A = (m * g) / AStrain (ε) = Δl / l = e / lYoung Modulus (E) = Stress (σ) / Strain (ε)= (m * g) / (A * e / l) = mgl / AeTherefore, an expression for the Young Modulus E of the metal is E = mgl / Ae.

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Answer:

F.  The forces exerted by the meteor and the spacecraft on each other will be of equal strength.

Answer:

Explanation:

Distance is the total length of the path taken from point A to B (the total distance of the whole curvy train route).

Displacement is the straight-line distance from the start point to the end point.  Draw a straight line from A to B, then measure it in exact cm.  Multiply your measurement in cm by 5 to get the answer in km.

1. Based on the periodic trends for ionization energy, which element has the highest ionization energy?

2) Nitrogen has a larger atomic radius than oxygen.

3) Which has more metallic character, Lead (Pb) or Tin (Sn)?

4.) Which element has a higher melting point chlorine (Cl) or bromine (Br)?

5) Which element is more electronegative, sulfur (S) or selenium (Se)?

6) Why is the electronegativity value of most noble gases zero?

Ans. Because Noble gases has fully filled valance shell and thus cannot accept or donate any electron. So, electronegativity value of most noble gases is zero.

7) Arrange these atoms in order of decreasing effective nuclear charge by the valence electrons: Si, Al, Mg, S

8) Rewrite the following list in order of decreasing electron affinity fluorine (F), phosphorous (P). sulfur (S), boron (B).

9) An atom with an atomic radius smaller than that of sulfur (S) is

10) A nonmetal has a smaller ionic radius compared with a metal of the same period.

The disruption of His 146 - Lys 40 interaction directly contributes towards removing 2,3-BPG from HB. This interaction has a low binding affinity (Kd) when pO2 is at 100 Torr compared to when pO2 is at 20 Torr, where it has a higher affinity (Kd).

This means that at a higher pO2, 2,3-BPG is more likely to be removed, allowing HB to bind oxygen with higher affinity.
When answering questions on Brainly, you should always be factually accurate, professional, and friendly, be concise and not provide extraneous amounts of detail, and provide a step-by-step explanation in your answer. The disruption of His 146 - Lys 40 interactions directly contributes towards removing 2,3-BPG from HB.

This is because the 2,3-bisphosphoglycerate (2,3-BPG) molecule interacts with hemoglobin by creating salt bridges with specific amino acid residues, resulting in oxygen unloading in tissues at high altitudes.

The residue lysine 40, which forms a salt bridge with the carboxylate groups of 2,3-BPG, is one of the most important 2,3-BPG-binding residues in hemoglobin.To remove 2,3-BPG from hemoglobin, it is necessary to disrupt the salt bridge between lysine 40 and 2,3-BPG. This can be accomplished by modifying the lysine residue or by increasing the oxygen tension of the blood. Increasing oxygen tension can displace 2,3-BPG from hemoglobin, making it available for oxygen transport.

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Answer:

Explanation:

The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. Therefore, we can use this theorem to calculate the final kinetic energy of the ball in each case.

We know that the work done by a constant force is given by the equation W = Fd cos(theta), where F is the magnitude of the force, d is the displacement of the ball, and theta is the angle between the force and displacement vectors.

Using the work-energy theorem, we can write:

W = ΔK = Kf - Ki

where ΔK is the change in kinetic energy, Kf is the final kinetic energy, and Ki is the initial kinetic energy.

We can rearrange this equation to solve for Kf:

Kf = Ki + W = Ki + Fd cos(theta)

a) Kf = 150 J + (10 N)(15 m)cos(90°) = 150 J

b) Kf = 300 J + (200 N)(1.5 m)cos(180°) = 0 J

c) Kf = 200 J + (25 N)(4 m)cos(0°) = 300 J

d) Kf = 450 J + (15 N)(30 m)cos(150°) = 112.5 J

Ranking from greatest to least final kinetic energy:

c) Ki=200J F=25N d=4m theta=0 degrees

a) Ki=150J F=10N d=15m theta=90 degrees

d) Ki=450J F=15N d=30m theta=150 degrees​

b) Ki=300J F=200N d=1.5m theta=180 degrees