his mass is 67kg.
calculate his momentum when his velocity is 31 m/s

projectile's vertical speed v yv y v, start , y,  drops prior to reaching its maximum height since its acceleration is in the opposite direction. Since the object's height is rising, the initial direction of the velocity is upward

.

At the projectile's highest point, vertical velocity zeroes out. After reaching the highest point, the vertical speed increases due of the same-direction acceleration. As the object's height lowers, the vertical velocity has a downward direction.

In projectile The beginning vertical velocity determines the maximum height. Increasing the launch angle raises the maximum height because steeper launch angles have a larger vertical velocity component.

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A low latitude, the energy transferred from the sun is high while at a high altitude the energy transferred from the sun is low.

Latitude is an angle which ranges from 0 degree at the Equator to 90 degrees at the poles of the Earth.

At higher latitudes, the sun's rays are less direct and a lower latitude the ray's of the sun are more direct. The farther an area is from the equator, the lower its temperature.

Thus, a low latitude, the energy transferred from the sun is high while at a high altitude the energy transferred from the sun is low.

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The magnitude of the frictional force Fr acting on the object is 10 N.

option B.

The magnitude of the frictional force Fr acting on the object is calculated by applying the following formula.

F - Fr = ma

where;

50 N - Fr = 4 kg  x  10 m/s²

50 N - Fr = 40 N

Fr = 50 N - 40 N

Fr = 10 N

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Answer:

See answers below

Explanation:

a.

F = mg,

15.5 N = m(9.8 m/s²)

m = 1.58 kg

b.

Fnet = Applied force - resistance,

Fnet = 18 N - 4.30 N,

Fnet = 13.70 N

Fnet = ma

13.70 N = (1.58 kg)a

a = 8.67 m/s²

For the free body diagram, draw a box with an upward arrow labeled 15.5 N, a downward label labeled 15.5 N, a right label labeled 18 N, and a left label labeled 4.30 N.

Answer:

a) 103.176 m / min

b) 1751.28 meters

Explanation:

Given:-

- Emma's and Lily's velocities ( E(t) and L(t) ) are given as functions respectively:

                         \(E(t) = \frac{7510}{t^2-7t + 80.22} \\\\L ( t ) = 12t^3*e^-^0^.^5^t\)

- Where, E ( t ) and L ( t ) are given in m / min

- Both run for a total time of 15 minutes in the same direction along the straight track defined by the absolute interval:

                         ( 0 ≤ t ≤ 15 ) mins                  

- It is known that Emma is 10 meters ahead of Lily at time t = 0.

Find:-

a) Find the value of \(\frac{1}{6}*\int\limits^8_2 {E(t)} \, dt\) using correct units, interpret the meaning of

b) What is the maximum distance between Emma and Lily over the time interval 0 ≤ t ≤ 15?  

Solution:-

- The average value of a function f ( x ) over an interval [ a , b ] is determined using calculus via the following relation:

                          \(f_a_v_g = \frac{1}{b-a}\int\limits^a_b {f(x)} \, dx\)

- The first part of the question is asking us to determine the average velocity of Emma over the time interval of ( 2 , 8 ). Therefore, ( E_avg ) can be determined using the above relation:

                         \(E_a_v_g = \frac{1}{8 - 2}*\int\limits^8_2 {E(t)} \, dt\\\\E_a_v_g = \frac{1}{6}*\int\limits^8_2 {E(t)} \, dt\\\)

- We will evaluate the integral formulation above to determine Emma's average velocity over the 2 ≤ t ≤ 8 minute range:

                         \(E_a_v_g = \frac{1}{6}*\int\limits^8_2 {\frac{7510}{t^2 - 7t + 80.22} } \, dt\\\\E_a_v_g = \frac{1}{6}*37550\int\limits^8_2 {\frac{1}{50t^2 - 350t + 4011} } \, dt\\\\\)

- Complete the square in the denominator:

                          \(E_a_v_g = \frac{1}{6}*37550\int\limits^8_2 {\frac{1}{(5\sqrt{2}*t - \frac{35}{\sqrt{2} })^2 + \frac{6797}{2} } } \, dt\\\\\)

- Use the following substitution:

                          \(u = \frac{5*(2t - 7 )}{\sqrt{6797} } \\\\\frac{du}{dt} = \frac{10}{\sqrt{6797} } \\\\dt = \frac{\sqrt{6797}}{10}.du\)

- Substitute the relations for (u) and (dt) in the above E_avg expression.

                          \(E_a_v_g = \frac{1}{6}*37550\int {\frac{\sqrt{6797} }{5*(6797u^2 + 67997) } } \, du\\\\E_a_v_g = \frac{1}{6}*37550*\frac{1}{5\sqrt{6797}} \int {\frac{1 }{(u^2 + 1) } } \, du\)

- Use the following standard integral:

                          \(arctan(u) = \int {\frac{1}{u^2 + 1} } \, du\)

- Evaluate:

                         \(E_a_v_g = \frac{1}{6}*37550*\frac{1}{5\sqrt{6797}}* arctan ( u ) |\)

- Apply back substitution for ( u ):

                        \(E_a_v_g = \frac{1}{6}*[\frac{75100* arctan ( \frac{5*(16 - 7 )}{\sqrt{6797} } )}{\sqrt{6797} } - \frac{75100* arctan ( \frac{5*(4 - 7 )}{\sqrt{6797} } )}{\sqrt{6797} } ]\\\\\)

- Plug in the limits and find Emma's average velocity:

                        \(E_a_v_g = 151.82037*[arctan (0.54582 ) - arctan ( -0.18194 ) ]\\\\E_a_v_g = 103.176 \frac{m}{min}\)

Answer: Emma's average speed over the interval ( 2 ≤ t ≤ 8 ) is 103.179 meters per minute.

- The displacement S ( E ) of Emma from time t = 0 till time ( t ) over the absolute interval of  0≤t≤15 is given by the relation:

                    \(S (E) = S_o + \int\limits^t_0 {E(t)} \, dt\\\\S ( E ) = 10 + \frac{75100*arctan( \frac{5*(2t - 7 )}{\sqrt{6797} }) }{\sqrt{6797} } |_0^t\\\\S ( E ) = 10 + [ \frac{75100*arctan( \frac{5*(2t - 7 )}{\sqrt{6797} }) }{\sqrt{6797} } - \frac{75100*arctan( \frac{5*(0 - 7 )}{\sqrt{6797} }) }{\sqrt{6797} } ]\\\\S ( E ) = \frac{75100*arctan( \frac{5*(2t - 7 )}{\sqrt{6797} }) }{\sqrt{6797} } + 375.71098\\\)

- The displacement S ( L ) of Lily from time t = 0 till time ( t ) over the absolute interval of  0 ≤ t ≤ 15 is given by the relation:

                    \(S (L) = \int\limits^t_0 {L(t)} \, dt\\\\S (L) = \int\limits^t_0 ({12t^3 *e^-^0^.^5^t } )\, .dt\\\)

 Apply integration by parts:

  \(S ( L ) = 24t^3*e^-^0^.^5^t - 64*\int\limits^t_0 ({e^-^0^.^5^t*t^2} \,) dt\\\)

 Re-apply integration by parts 2 more times:

 \(S ( L ) = -24t^3*e^-^0^.^5^t + 64*[ -2t^2*e^-^0^.^5^t - 2\int\limits^t_0 ({e^-^0^.^5^t*t} \,) dt ]\\\)             \(S ( L ) = -24t^3*e^-^0^.^5^t + 64*[ -2t^2*e^-^0^.^5^t - 2*( -2t*e^-^0^.^5^t - (4e^-^0^.^5^t - 4 ) ]\\\\\)    

\(S ( L ) = e^-^0^.^5^t* ( -24t^3 -128t^2+ 256t + 512) - 512 \\\)

- The distance between Emma and Lily over the time interval 0 < t < 15 mins can be determined by subtracting S ( L )  from S ( E ):

                    \(S = S ( E ) - S ( L )\\\\S = \frac{75100*arctan( \frac{5*(2t - 7 )}{\sqrt{6797} }) }{\sqrt{6797} } - e^-^0^.^5^t* ( -24t^3 -128t^2+ 256t + 512) + 887.71098\\\)

- The maximum distance ( S ) between Emma and Lily is governed by the critical value of S ( t ) for which function takes either a minima or maxima.

- To determine the critical values of the function S ( t ) we will take the first derivative of the function S with respect to t and set it to zero:

              \(\frac{dS}{dt} = \frac{d [ S(E) - S(L)]}{dt} \\\\\frac{dS}{dt} = E(t) - L(t) \\\\\frac{dS}{dt} = \frac{7510}{t^2 - 7t+80.22} - 12t^3*e^-^0^.^5^t = 0\\\\( 12t^5 - 84t^4 + 962.64t^3) *e^-^0^.^5^t - 7510 = 0\\\\t = 4.233 , 11.671\)

- We will plug in each value of t and evaluate the displacement function S(t) for each critical value:

Answer:

1) c. Helium

2) Iron

3) False.

Explanation:

1. Red dwarf is the smallest and the coolest star on the sequence. These are common stars in the milky way. Red dwarfs contains metals and the elements with higher atomic number. It is found that Helium is produced in red dwarf stars.

2. Iron is the highest atomic number element that is produced in cores of largest stars. The highest mass stars can make all elements up to iron, which is the heaviest element they can produce.

3. The end of stars life is dependent on the mass they are born with. It is not necessary that all red dwarf stars will become white dwarf stars faster than sun like star.

In a DC generator, the generated electromotive force (emf) is directly proportional to the rotational speed of the generator's armature and the strength of the magnetic field within the generator.

This relationship is described by the equation for the generated emf in a DC generator:

Emf = Φ * N * A * Z / 60

Where:

Emf is the generated electromotive force (in volts),

Φ is the magnetic flux density (in Weber/meter^2\(meter^2\) or Tesla),

N is the number of turns in the armature winding,

A is the effective area of the armature coil (in square meters),

Z is the total number of armature conductors, and

60 is a constant representing the conversion from seconds to minutes.

From this equation, we can see that the generated emf is directly proportional to the magnetic flux density (Φ) and the product of the number of turns (N), effective area (A), and the total number of armature conductors (Z). This means that increasing any of these factors will result in a higher generated emf.

The magnetic flux density (Φ) can be increased by using stronger permanent magnets or increasing the strength of the field windings in the generator.

The number of turns (N) and the effective area (A) are design parameters and can be optimized for a specific generator. Increasing the number of turns or the effective area will result in a higher generated emf.

Similarly, the total number of armature conductors (Z) can be increased to enhance the generated emf.

By controlling and optimizing these factors, the generated emf in a DC generator can be increased, resulting in higher electrical output. However, it is important to note that there are practical limits to these factors based on the design and construction of the generator.

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Answer:

180 LUV:)

Explanation:

The change in the tension if the radii r changes from 4.0 cm to 4.1 cm, and R changed from 0.8 cm to 0.9 cm is negative, therefore, tension reduces.

Mass of the yoyo = 0.001 kg

Initial value of the spindle radius, R = 4 cm

Initial length of the radius of the yo–yo, r = 0.8 cm

The final values are;

R2 = 4.1 cm, r2 = 0.9 cm

Which gives;

\(T_{r \:R} = \frac{0.001 \cdot g \cdot R }{2 \cdot r^{2} + R^2} \)

Which gives;

\(T_{{r _1 \:R _1 }} = \frac{0.001 \times 9.8 \times 0.04 }{2 \times 0.008^{2} + 0.04²} = \frac{49}{216} \)

\(T_{{r _2 \:R _2 }} = \frac{0.001 \times 9.8 \times 0.041 }{2 \times 0.009^{2} + 0.041^2} = frac{2009}{9215} \)

Therefore;

\( \Delta T_{{r \:R }} = frac{2009}{9215} - \frac{49}{216} = - \frac{17591}{1990440} \)

Given that difference between the final and the initial states is negative, the the value of the tension decreases

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The distance from the positive plate at which the two pass each other is  2.39 μm.

With a voltmeter, the difference in electric potential energy is measured in volts. By aligning two substantial flat conducting plates parallel to one another, a continuous electric field can be created. V = E d is the formula for the electrical potential difference in a uniform electric field.

we have the:-

F = q E

F =1.6e-(19 * 640)= 1.024e-16 N

ap = F/mp

ap = 1.024e-16/1.673e-27) = 6.1207e10 m/s2

now for distance of plate

ae = F/me

ae = 1.024e-16/(9.109e-31) = 1.12416e14 m/s2

xp = 0.5 ap t2 = 0.5 * (6.1207e10) * t2 = 3.0604e10 t2

xe = 0.5 ae t2 = 0.5 * (1.12416e14) * t2 = 0.56208e14 t2

(xp + xe) = 4.4 cm = 4.4e-2 m

(3.0604e10) t2 + (0.56208e14) t2 = 4.4e-2

(5.6239e14) t2 = 4.4e-2

t = 8.8452e-9 s

xp = 0.5 ap t2 = 0.5 * (6.1207e10) * (8.8452e-9*8.8452e-9)

xp = 2.39 μm

The distance from the positive plate at which the two pass each other is xp = 2.39 μm

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The missing species of the nuclear reaction obtained is ³⁰₁₅P

The missing species of the equation can be obtain as follow:

Now, we can obtain the value of x, y and Z as follow:

²⁷₁₃Al + ⁴₂He -> ʸₓZ + ¹₀n

For x

13 + 2 = x + 0

15 = x

x = 15

For y

27 + 4 = y + 1

31 = y + 1

Collect like terms

y = 31 - 1

y = 30

For Z

ʸₓZ => ³⁰₁₅Z

From the period table, the element with atomic number of 15 is phosphorus, P. Thus, we have

ʸₓZ => ³⁰₁₅Z => ³⁰₁₅P

Therefore, we can write the complete equation as:

²⁷₁₃Al + ⁴₂He -> ³⁰₁₅P + ¹₀n

Thus, the missing species is ³⁰₁₅P

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Answer:

It is a colorless crystalline compound which is the main nitrogenous breakdown product of protein metabolism in mammals and is excreted in urine.

Answer:

Urea is a compound of nitrogen that is the chief solid substance dissolved in the urine of a mammal and is formed by the breaking down of protein.

(Hope this helps! Btw, I answered first. Brainliest please! :D)

The energy transferred by the heater that has a power of 2500W and is turned on for 180s is 450,000J.

Electrical energy is the energy made available for consumption or consumed in the form of electricity or electric power.

Electrical energy can be calculated as follows:

Electrical energy = Power x Time.

The total amount of electrical energy used depends on the total power used by all electrical devices and the total time they are used in the home.

According to this question, a heater has a power of 2500W and is turned on for 180 seconds. The energy can be calculated as follows;

E = 2500W × 180s

E = 450,000J

Therefore, 450,000J is the energy transferred to the heater.

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Answer:

0.882 m/s average velocity and 1.71 m/s average speed

Explanation:

The dog travels a total of 35 m west and 110 m east.

110-35 = 75 m east of the starting position. Since velocity is a vector you must consider its first and final position and not the total distance traveled.

75 m / 85 s = 0.882 m/s average velocity

Speed is not concerned with direction so we instead add the total distance traveled which is 35+110 = 145 m. We then perform the same operation as before and divide by the time it took to run this distance.

145 m / 85 s = 1.71 m/s average speed

a) The main advantages of an epicyclic gearbox are:

b) i) Using the formula for the gear ratio of an epicyclic gear train:

T4/T3 = (t2/t1) x (t5/t2) x (t4/t5)

T4/30 = (1/2) x (60/20) x (40/60)

T4 = 40 Nm

ii) From the law of gearing for an epicyclic gear train:

w21 = (t3/t2) x (t5/t4) x w31 - (t3/t2) x w2

Substituting the given values:

w21 = (30/20) x (60/40) x 200 - (30/20) x 100

w21 = 150 rad/s

iii) The fixing couple that must be applied to wheel 5 can be found from the power transmitted by the gear train:

P = w3 x T3 = w2 x T2 = w1 x T1

Substituting the given values:

9 kW = 200 rad/s x 30 Nm = w2 x T2 = w2 x 20 Nm

w2 = 450 rad/s

T2 = (9 kW) / (450 rad/s) = 20 Nm

The fixing couple that must be applied to wheel 5 is equal in magnitude and opposite in direction to T2, so it is -20 Nm.

iv) The tangential force at the pitch point between wheels 3 and 4 can be found from the formula:

Ft = (2 x Pd) / (m x z3)

where Pd is the diametral pitch, m is the module, and z3 is the number of teeth on wheel 3.

Substituting the given values:

Pd = 25.4 / 5 = 5.08 teeth/inch

z3 = t3 / m = 30 / 5 = 6 teeth

Ft = (2 x 5.08) / (5 x 6) = 0.846 N

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Answer:

21.73 kg

Explanation:

Applying,

T = 2π√(m/k)............... Equation 1

Where T = period, m = mass on the spring, k = spring constant, π = pie.

make m the subject of the equation

m = T²k/4π²................. Equation 2

From the question,

Given: T = 3.45 s, k = 72.0 N/m, π = 3.14

Substitute these values into equation 2

m = (3.45²×72)/(4×3.14²)

m = 21.73 kg.

Hence the mass should be 21.73 kg

Answer:

In a material, the magnetic behavior depends on the alignment of magnetic moments of the atoms. Magnetic moments are generated by the motion of the electrons in the atoms. When the magnetic moments of atoms in a material are aligned in a specific pattern, it creates a magnetic field which results in the material being magnetic.

In many materials, the magnetic behavior arises due to the alignment of magnetic domains, which are regions of atoms with magnetic moments aligned in the same direction. When many domains with aligned magnetic moments are present in a material, the material becomes magnetic.

The magnetic behavior of a material depends on the number of electrons and the arrangement of those electrons in the atoms. In particular, for an atom to have a magnetic moment, it must have unpaired electrons, meaning electrons that are not paired with another electron with the opposite spin. When these unpaired electrons in the atoms are aligned, they generate a magnetic moment. If all electrons are paired, there will not be a net magnetic moment, so the material will not be magnetic.

So, in summary, the magnetic behavior of a material is determined by the alignment of magnetic moments of atoms. When the magnetic moments of many atoms in a material align in the same direction, it creates a magnetic field, leading to a material being magnetic. This alignment is usually present in magnetic domains consisting of atoms with unpaired electrons.

Energy is a fundamental concept in physics that represents the ability or capacity of a system to do work.

It is a scalar quantity, meaning it has magnitude but no specific direction. Energy exists in various forms and can be converted from one form to another. The characteristics of energy include:

1. Forms of Energy: Energy can exist in different forms such as kinetic energy (energy of motion), potential energy (stored energy), thermal energy (heat), chemical energy, electrical energy, and many more.

2. Conservation of Energy: The law of conservation of energy states that energy cannot be created or destroyed; it can only be transformed from one form to another. The total amount of energy in a closed system remains constant.

3. Transfer and Conversion: Energy can be transferred from one object to another or converted from one form to another. For example, electrical energy can be converted into light energy in a light bulb.

4. Units of Measurement: Energy is typically measured in joules (J) in the International System of Units (SI). Other common units include kilowatt-hours (kWh) for larger quantities of energy and calories (cal) for thermal energy.

5. Energy and Work: Energy is closely related to the concept of work. When work is done on an object, energy is transferred to it or from it, resulting in a change in its energy state.

Understanding the nature and characteristics of energy is crucial in various fields, including physics, engineering, and environmental science, as it plays a central role in explaining and analyzing various phenomena and processes.

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Work done on an object depends on the distance and force but independent of time.

Work is the product of force and the distance move in the direction of the force. It is measured in Joule.

If you use more force to move an object, there will be more amount of work because Work done = force x distance.

More force will give more about of work.

If you lift a 20 N object faster, you will experience the same amount of work because work is independent of time.

If you raise an object a shorter height, there will be less work done since work depends on the distance move in the direction of the force.

If you move a lighter object, you will experience a less work done because the weight of the object will reduce the work done

If you move an object farther, there will be more work to be done because of the increase in distance.

Therefore, Work done on an object depends on the distance and force but independent of time.

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The scientific symbol are matched with their respective unit of measurement as follows:

The amount of work that is required for each situation is given by:

A force (F) can be defined as a push or pull of an object, which typically causes a change of motion (acceleration), especially due to the interaction of the object with another. Also, force (F) is measured in Newton (N).

The work done (W) by an object is calculated by multiplying the force acting on it by the perpendicular distance covered by the object. Thus, work done (W) and energy (E) have the same unit i.e Joules (J).

In this exercise, you're required to match the scientific symbol with their respective unit of measurement and this is represented as follows:

The amount of work that is required for each situation is given by:

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The absolute pressure at an ocean depth of 1.0 x 10^3 m is 1.002 x 10^8 Pa.

Hydrostatic pressure is the pressure that a fluid exerts on a surface due to the weight of the fluid above it. It is the result of the force of gravity acting on a column of fluid, and it is directly proportional to the height of the column of fluid and the density of the fluid.

The absolute pressure at an ocean depth of 1.0 x 10^3 m can be calculated using the hydrostatic pressure equation:

P = ρgh + Po

where:

P is the absolute pressure at the given depth

ρ is the density of the water

g is the acceleration due to gravity (assumed to be 9.81 m/s²)

h is the depth of the ocean

Po is the atmospheric pressure at the surface (assumed to be 1.01 x 10^5 Pa)

Substituting the given values, we get:

P = (1.025 x 10^3 kg/m³) x (9.81 m/s²) x (1.0 x 10^3 m) + 1.01 x 10^5 Pa

P = 1.025 x 9.81 x 10^6 Pa + 1.01 x 10^5 Pa

P = 1.002 x 10^8 Pa.

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The number of generations that have passed since the beginning of recorded history is approximately equal to 150.

Half-life can be defined as an interval of time that is required for one-half of the atomic nuclei of a radioactive element to spontaneously decay into other species of elements, especially through the emission of particles and energy.

Based on scientific experiment and research conducted, we can infer and logically conclude that half of a radioactive nuclei can become nonradioactive after each half-life cycle because it's independent of the initial amount and unaffected by laboratory conditions.

First of all, we would determine the amount of time per generation by using the following mathematical expression:

Time per generation = 1/3 × time per lifetime

Time per generation = 1/3 × 2 × 10⁹ s

Time per generation = 2/3 × 10⁹ s

Mathematically, the number of generations can be calculated by using this formula:

Number of generations = Total time/Time per generation

Number of generations = (10¹¹ s)/(2/3 × 10⁹ s)

Number of generations = 300/2

Number of generations = 150.

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The cone emits a single-frequency sound of 100 Hz and moves in a straightforward harmonic manner. The cone moves a maximum of 2.0 millimetres when it is making a loud sound.

Simple harmonic motion is a particular type of periodic motion of a body that arises from a dynamic equilibrium between an inertial force that is proportional to the acceleration of the body away from the static equilibrium position and a restoring force on the moving object that is directly proportional to the magnitude of the object's displacement and acts towards the object's equilibrium position.

In mechanics and physics, SHM is sometimes used to refer to this motion. If friction or any other energy dissipation is not present, it leads to an oscillation that is represented by a sinusoid and that lasts indefinitely.

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Answer:

The correct difference between chronic and acute stress is:

Acute stress is short-term, while chronic stress endures over time.

Explanation:

Acute stress refers to the immediate and temporary response of the body to a specific stressful event or situation. It is often characterized by a rapid increase in heart rate, heightened alertness, and the release of stress hormones like adrenaline. Acute stress is a normal and natural response to perceived threats or challenges, and once the stressor is removed or resolved, the body returns to its normal state.

On the other hand, chronic stress is long-term and persists over an extended period. It is typically caused by ongoing or recurring stressors, such as work pressures, financial difficulties, relationship problems, or chronic health conditions. Chronic stress can have a cumulative and prolonged impact on physical and mental well-being. It may lead to a range of health issues, including cardiovascular problems, weakened immune system, digestive disorders, anxiety, depression, and burnout.

Chronic stress is considered detrimental to overall health, while acute stress, when experienced in moderation, can actually be beneficial as it can enhance performance and help individuals deal with immediate challenges. It is important to manage chronic stress effectively through stress-reducing techniques, self-care practices, and seeking support when needed to prevent its negative consequences on health and well-being.

Answer:depends on the masses of the objects and the distance between them

Explanation:

According to Newton's law of universal gravitation,the force of attraction between two objects depends on the masses of the objects and the distance between them

Following are the answers:

1. To calculate the pressure exerted by the water column on the surface of the mercury, we can use the formula:

Pressure = force/area

The force is the weight of the water column and the area is the cross-sectional area of the container.

The weight of the water column is given by the mass of the water times the acceleration due to gravity:

mass = density x volume

volume = area x height

So, mass = density x area x height = 1000 kg/m^3 x pi x (0.025 m)^2 x 0.25 m = 0.196 kg

Weight = mass x acceleration due to gravity =\(0.196 kg * 9.8 m/s^2\) = 1.92 N

The cross-sectional area of the container is pi x (0.025 m)^2 =\(0.196 m^2.\)

So, Pressure = force/area = \(1.92 N/0.196 m^2 = 9.79 N/m^2\) or 9.79 Pa

2. To calculate the density of the oil, we can use the formula:

density = mass/volume

Since the height of the oil column is 0.92 m and the cross-sectional area of the container is 0.196 m^2, the volume of the oil column is 0.196 m^2 x 0.92 m = 0.18012 m^3.

We do not know the mass of the oil, but we can calculate it using the pressure exerted by the oil column on the surface of the mercury:

Pressure = force/area = density x acceleration due to gravity x height

So, density = Pressure/ (acceleration due to gravity x height) = 9.79 N/m^2 / (9.8 m/s^2 x 0.92 m) = 1060 kg/m^3.

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Using a scale of 1 centimeter = 1 newton, the following displacement vector is

(a) 5 newtons west 5 centimeter.

(b) 3 newtons, 270° 3 centimeter.

(c) 4 newtons, 0°, 4 centimeter.

The International System of Units (SI) uses the centimetre (cm) as a measure of length. It is a handy unit for measuring short distances because its definition is one tenth of a metre. 0.01 metres or 0.3937 inches make up one centimetre.

In the SI system, a newton (N) is a unit of force. It is described as the amount of pressure necessary to accelerate a mass of one kilogramme at a speed of one metre per second squared (m/s2). The force required to accelerate a mass of one kilogramme by one metre per second squared is comparable to one newton, in other words.

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Emptying trenches, filling tanks, supplying water for boilers, and all of the above tank refuelling

An exclusive variety of floor drain with a predominately trough- or channel-shaped body is known as a trench drain (also known as a channel drain, line drain, slot discharge, linear drain, or strip drain). It is utilised to contain utility lines or industrial pollution as well as for the quick evacuation of surface water.

Aside from what we've mentioned here, the distinction between a French dump and a trench drain is that the former French drain is used for water that is underground, whilst a trench drain redirects extra water from a surfac.e

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Explanation:

Yes, there are differences in the shapes of position-time graphs for uniform acceleration and uniform deceleration in different directions. Let's consider each case separately:\(\hrulefill\)

(1) - Uniform acceleration towards the positive direction:

In this case, the object is moving in the positive direction with a constant acceleration. The displacement-time graph will typically be a curve that starts from an initial position and shows a steady increase in displacement over time. The shape of the graph will depend on the specific acceleration value.

(2) - Uniform acceleration towards the negative direction:

In this case, the object is moving in the negative direction with a constant acceleration. The displacement-time graph will also be a curve, but it will show a steady decrease in displacement over time.

(3) - Uniform deceleration towards the positive direction:

In this case, the object is initially moving in the positive direction but is slowing down with a constant deceleration. The displacement-time graph will be a curve that starts with a positive slope and gradually levels off.

(4) - Uniform deceleration towards the negative direction:

In this case, the object is initially moving in the negative direction but is slowing down with a constant deceleration. The displacement-time graph will be a curve that starts with a negative slope and gradually levels off.