A ball swings in a vertical circle at the end of a rope 1.50 m long. When the ball is 36.9° past the lowest point on its way up, its total acceleration is (-22.5i + 20.2j) m/s2 . For that instant, (a) sketch a vector diagram showing the components of its acceleration, (b) determine the magnitude of its radial acceleration, and (c) determine the speed and velocity of the ball.​

X, Y, and Z components of the vector are 398, 384 and 279 resp.

Vector is a physical quantity which has both magnitude and direction. Vector A can be written as A = a₁i + a₂j + a₃k where a₁, a₂, a₃ are components along X, Y, Z axis resp. and i,j,k, are the unit vectors along X,Y,Z axis resp.

In this figure

vector F is at angle 36° from y axis, hence

x = Fcos33 = 475cos33 = 398 N

y = Fcos36 = 475cos36 = 384 N

z = Fsin36 =  475sin36 = 279 N

The vector can be written as

F = 398i + 384j + 279k

Hence x, y and z components of this force is 398, 384 and 279 resp.

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The two factors that affect the amount of thermal energy an object has are;

Thermal energy  can be regarded as the energy which is been contained within a system it can be considered as the one that is responsible for its temperature.

It should be noted that the Heat is the flow of thermal energy and it can be seen as opne that deals with how heat is transferred between different systems .

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The magnitude of the magnetic field at P₂ is 6.06 x 10⁻⁵ T.

Using the Biot-Savart Law, we can determine the magnetic field at point P2 due to the current-carrying wire. The magnitude of the magnetic field B at P2 is given by:

B = μ₀i/4π (sinθ₁ - sinθ₂)

where μ₀ is the magnetic constant, i is the current, θ₁ is the angle between the wire and the line joining the wire and point P₂, and θ₂ is the angle between the wire and the line perpendicular to the wire and passing through point P₂.

From the given diagram, we can see that sinθ₁ = L/2R and sinθ₂ = (R - L/2)/R. Substituting these values and the given values of i, L, and R into the equation, we get:

B = (4π x 10⁻⁷ Tm/A) x 0.780 A / 4π (L/2R - (R - L/2)/R)

= 6.06 x 10⁻⁵ T

As a result, the magnetic field magnitude at P₂ is 6.06 x 10⁻⁵ T.

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Answer:

Explanation:

Something that cannot be broken down into simpler substances through chemical reactions

Answer: Our day-to-day life highly relates to physics.

Explanation: We know that in physics there are many laws such as gravitational laws, laws of friction, and inertia.For example

All substance listed in the chart is made up of the atoms.

Atom is smallest entity of a substance. Body is made up of atoms. it is basic building block of a body. An atom consist of electrons, protons and neutrons as sub atomic particle. whole mass of the atom is concentrated at the center of the atom which we call it as nucleus, nucleus consist of proton and neutron. Electron revolve around the nucleus at determined(fixed) orbit. Total number of protons in the atom decides the atomic number and the elements in the periodic table. The electrons which are completely filled orbitals are called as core shell electrons and which are not filled completely are called as valence electron. valence electrons are responsible for physical and chemical properties of the element. Elements which are on same column in periodic table have same number of valence electrons . Hence they have same properties.

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The half-life period of the radioactive source is approximately 693.15 days.

The activity of a radioactive source is known to follow an exponential decay law given by:

A(t) = A(0) × (1/2)[tex]^{t/T}[/tex]

where,

A(t) = activity at time t

A(0) = initial activity

T = half-life period and (1/2)[tex]^{t/T}[/tex] is the fraction of the original activity remaining after time t.

We are given that the activity of the source has decayed to 1/10 of 1% of its initial activity, which is equivalent to 0.001 times the initial activity. This means that:

A(t) = 0.001 ) × A(0)

We are also given that this has occurred in 100 days, so:

t = 100

Substituting these values in the equation, we get:

0.001 × A(0) = A(0) × (1/2)¹⁰⁰/[tex]^T[/tex]

Simplifying and solving for T, we get:

T = -100 / In(1/2) × log(0.001))

T ≈ 693.15 days

Therefore, the half-life period of the radioactive source is approximately 693.15 days.

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The half-life of a radioactive source that decayed to 1/10 of 1% of its initial activity in 100 days is approximately 14.61 days.

The given problem can be solved using the formula for radioactive decay, which is N = N0 * (1/2)^(t/h), where N is the final quantity, N0 is the initial quantity, t is time passed, and h is the half-life time. Here, the radioactive source has decayed to 1/10 of 1% of its initial activity, meaning N = 0.001 * N0. The time passed is 100 days. Plugging these values into the formula we have: 0.001 = (1/2)^(100/h). Solving for h, the half-life time, gives us a half-life of approximately 14.61 days.

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The pollution from the first plant would be half that of the second plant for the same amount of energy produced.

The energy efficiency of a coal plant refers to the amount of energy produced per unit of fuel consumed. If the first plant is twice as energy efficient as the second plant, it means that it can produce the same amount of energy using half the amount of fuel.

Since pollution from coal plants is directly proportional to the amount of fuel consumed, the first plant would produce half the pollution of the second plant for the same amount of energy produced. This assumes that the two plants have the same level of emissions per unit of fuel consumed, which may not necessarily be the case.

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The potential energy of an 11kg object that is 11m off the ground is 1199.8J.

The potential energy of the body is defined as the energy which is possessed by the body when the position of the body is at rest. When the object is at rest the potential energy is possessed by the body and then when the body starts moving the potential energy is converted into kinetic energy.

The potential energy of a body is given by the expression:

P.E=mgh;

where 'm' is the mass of the body which is given as 11kg given in the question, and 'g' is the acceleration due to gravity which is equal to (9.8 m/s^2).

So the potential energy here is:

P.E = (11kg)*(9.8 m/s^2)*(11m)

P.E = 1199.8 Joules.

Therefore, the potential energy of an 11kg object that is 11m off the ground is 1199.8J.

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The speed of the car is 6 m/s. The acceleration vector at point B has a direction of (-1, -1) and a magnitude of approximately 16.97 m/s².

We can start by finding the speed of the toy car. Since it is moving with constant speed around the circle, its speed is the same at points A and B. To find the speed, we can use the fact that the velocity vector has a magnitude equal to the speed:

|v| = √((6 m/s)²) = 6 m/s

So the speed of the car is 6 m/s.

Next, we can find the direction of the velocity vector at point B. We know that the car is moving around a circle centered at the origin, and that point B is on the circle. Therefore, the velocity vector at point B is tangent to the circle and perpendicular to the line connecting the origin to point B.

The line connecting the origin to point B is given by:

y = (0 - 3)/(0 - (-3)) * (x - (-3)) + 0

y = -x + 3

The velocity vector at point B is therefore perpendicular to this line, which means it has a direction given by the vector (1, -1).

Finally, we can find the acceleration vector at point B. Since the car is moving with constant speed around a circle, it is undergoing uniform circular motion, which means it is accelerating towards the center of the circle. The magnitude of the acceleration is given by:

a = v² / r

where v is the speed and r is the radius of the circle. We don't know the radius of the circle, but we can find it using the fact that point B lies on the circle. The distance from the origin to point B is:

d = √((-3 - 0)² + (0 - 3)²) = 3√(2) m

Therefore, the radius of the circle is:

r = d / 2 = (3√(2)) / 2 m

Substituting in the values for v and r, we get:

a = (6 m/s)² / ((3√(2)) / 2 m) ≈ 16.97 m/s²

To find the direction of the acceleration vector, we can use the fact that it is pointing towards the center of the circle. The center of the circle is at the origin, so the acceleration vector at point B is given by the vector (-3, 0) minus the vector (0, 3), which is:

(-3, 0) - (0, 3) = (-3, -3)

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(A)The water will shoot out of the hole at a speed of 4.77 m/s, and the pressure of the water at the hole will be 9.91 × 10^4 Pa, and (B) The water will shoot out of the larger hole at a speed of 0.529 m/s, and the pressure of the water at the hole will be 1.012 × 10^5 Pa.

We can use Bernoulli's equation to solve this problem, which relates the pressure, velocity, and height of a fluid. The equation states that:

P + (1/2)ρv^2 + ρgh = constant

where P is the pressure, ρ is the density of the fluid, v is the velocity of the fluid, g is the acceleration due to gravity, and h is the height of the fluid.

(A) The diameter of the hole is 4.51 cm, which corresponds to a radius of 2.255 cm = 0.02255 m. The area of the hole is A = πr^2 = 1.587 × 10^-4 m^2. The volume flow rate of water is Q = 0.757 m^3/s.

We can calculate the velocity of the water as it exits the hole using the equation:

Q = Av

where A is the area of the hole and v is the velocity of the water. Solving for v, we get:

v = Q/A = 4.77 m/s

Now, we can use Bernoulli's equation to find the pressure of the water at the hole. Assuming that the height of the fountain is negligible compared to the height of the atmosphere, we can set the height term to zero. Also, we can assume that the pressure at the surface of the fountain is atmospheric pressure, which we can take as P = 1.013 × 10^5 Pa. Then, the equation becomes:

P + (1/2)ρv^2 = constant

Solving for P, we get:

P = constant - (1/2)ρv^2

At the hole, the velocity of the water is v = 4.77 m/s, and the density of water is ρ = 1000 kg/m^3. Substituting these values, we get:

P = 1.013 × 10^5 Pa - (1/2) × 1000 kg/m^3 × (4.77 m/s)^2 = 9.91 × 10^4 Pa

So, the water will shoot out of the hole at a speed of 4.77 m/s, and the pressure of the water at the hole will be 9.91 × 10^4 Pa.

(B) If the diameter of the hole is three times as large, then the area of the hole will be nine times as large. Therefore, the volume flow rate of water will be distributed over a larger area, resulting in a lower velocity. The new area of the hole is A = 9 × 1.587 × 10^-4 m^2 = 1.43 × 10^-3 m^2. The volume flow rate of water is still Q = 0.757 m^3/s.

Using the equation Q = Av, we can find the new velocity of the water:

v = Q/A = 0.529 m/s

Using Bernoulli's equation, we can find the pressure of the water at the larger hole:

P = 1.013 × 10^5 Pa - (1/2) × 1000 kg/m^3 × (0.529 m/s)^2 = 1.012 × 10^5 Pa

So, the water will shoot out of the larger hole at a speed of 0.529 m/s, and the pressure of the water at the hole will be 1.012 × 10^5 Pa.

Hence, Water will flow out of the smaller hole at a speed of 0.529 m/s and a pressure of 1.012 × 10^5 Pa, and the water will shoot out of the hole at a speed of 4.77 m/s and a pressure of 9.91 × 10^4 Pa.

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The value of Q for which the net electric field produced by the particles at the center of the triangle vanishes is, Q = −5.63 × 10⁻³ C, with a negative sign indicating that the charge is negative.

Let's choose a coordinate system where the center of the equilateral triangle is at the origin, and the particles are located at the vertices of an equilateral triangle of edge length a. Then, the electric field produced by each particle at the center is:

E₁ = k * q₁ / r₁², where q₁ = +8.45 mC, r₁ = a / √3

E₂ = k * q₂ / r₂², where q₂ = +8.45 mC, r₂ = a / √3

E₃ = k * Q / r₃², where r₃ = a

Here, k is Coulomb's constant, which is approximately equal to 9 × 10⁹ N⋅m²/C².

Since the three particles are equally distant from the center of the triangle, the magnitude of the net electric field at the center is:

|E_net| = |E₁ + E₂ + E₃|

Using the above equations for E₁, E₂, and E₃, we can substitute the values and simplify the expression:

|E_net| = k * (q₁ / r₁² + q₂ / r₂² + Q / r₃²)

= k * [8.45 × 10⁻³ C / (a² / 3) + 8.45 × 10⁻³ C / (a² / 3) + Q / a²]

= k * [(16.9 × 10⁻³ C) / (a² / 3) + Q / a²]

For the net electric field to be zero, we need:

|E_net| = k * [(16.9 × 10⁻³ C) / (a² / 3) + Q / a²] = 0

This implies:

(16.9 × 10⁻³ C) / (a² / 3) + Q / a² = 0

Solving for Q, we get:

Q / a² = −(16.9 × 10⁻³ C) / (a² / 3)

Q = −16.9 × 10⁻³ C / 3

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The following would expect to be a strong electrolyte in solution (b) KCI is correct option.

When dissolved in water, a strong electrolyte produces a large concentration of ions in solution by totally dissociating into ions.  The following compounds are typically strong electrolytes in solution according to this definition:

These substances readily dissociate into ions in water and exhibit high electrical conductivity, making them strong electrolytes in solution.

Therefore, the correct option is (b).

The complete question is,

Which of the following would be a strong electrolyte in solution?

a) Al(OH)₃ b) KCI c) Pbl₂

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The number of pool noodles that  would be needed to support the weight is 20.

The volume of a single pool noodle is calculated as follows;

V = πr²h

V = π (0.025)² x 1.65

V = 0.00324 m³

The weight of the water displaced is calculated as follows;

W = ρVg

where;

W = 1000 x 0.00324 x 9.8

W = 31.75 N

The number of pool noodles needed to support a person is calculated as follows;

= (65 x 9.8 ) / (31.75)

= 20

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Answer: D. They can determine the elements that make up the surface of astronomical bodies.

Explanation: Spectroscopy and infrared technology are useful in space because they allow scientists to determine the elements that make up the surface of astronomical bodies, such as planets, moons, and asteroids.

Spectroscopy involves the analysis of light or radiation emitted or absorbed by these bodies.  When light interacts with matter, it gets absorbed or emitted in specific wavelengths that correspond to the energy levels of atoms and molecules.  By studying the pattern of these wavelengths, scientists can identify the unique "fingerprint" or spectral lines of elements and compounds.

Infrared technology, on the other hand, detects and measures the infrared radiation emitted by objects.  This radiation is produced due to the thermal energy or heat emitted by celestial bodies.  By analyzing the specific wavelengths of infrared radiation, scientists can gain insights into the composition and temperature of these bodies.

By combining spectroscopy and infrared technology, scientists can gather valuable data about the chemical composition of astronomical bodies.  This information helps in understanding the geological processes, formation, and evolution of these bodies.  It also provides insights into the presence of specific elements or compounds that may be important for studying habitability, potential resources, or even the origins of life in the universe.

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When describing motion, speed indicates the pace at which an object is travelling. It has one scalar component identifying its magnitude, irrespective of direction.

The unit for measuring speed can be either meters per second (m/s) or miles per hour (mph). For velocity, it's a different story. Its definition encompasses both speed and direction since it's a vector quantity. Measureable just like speed using m/s or mph.

In plain physic terms, acceleration reveals how much speed changes over time; hence it is also a vector quantity with not only size but also direction. Depending on whether a physical item is increasing in momentum, slowing down or static, the value could be positive, negative, or zero. Acceleration is calculated using units metres per second squared (m/s2).

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Answer: It is Reflection

Explanation: Reflection occurs when incoming solar radiation bounces back from an object or surface that it strikes in the atmosphere, on land, or water, and is not transformed into heat.

A neutron has a neutral charge because it is composed of an equal number of protons and electrons. Hence option C is correct.

The neutron is a subatomic particle with a neutral (neither positive nor negative) charge and a slightly larger mass than a proton. Atomic nuclei are made up of protons and neutrons. Protons and neutrons are both referred to as nucleons because they function similarly within the nucleus and each have a mass of around one atomic mass unit. Nuclear physics describes their characteristics and interactions. Protons and neutrons are not elementary particles; they are made up of three quarks apiece.

Hence option C is correct.

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The example of energy transformation that could never occur, as explained by the second law of thermodynamics, is the 400 J of heat added to the operating gas of a heat engine is transformed into 400 J of work. Option A is correct.

The second law of thermodynamics states that in any energy transformation, the total entropy (measure of disorder) of a closed system will always increase or remain constant. It means that some energy will always be wasted as heat and cannot be completely converted into useful work. The second law of thermodynamics is a fundamental law of nature that governs energy transformations.

It states that in any energy transformation process, the total entropy (measure of disorder) of a closed system will always increase or remain constant. Entropy can be thought of as a measure of the amount of energy that is unavailable to do useful work. It is impossible to transform all 400 J of heat into work without generating any waste heat. This is because the heat engine must expel some heat to the cold reservoir to comply with the second law. Option A is correct.

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The voltage across the compressor is 12 V.

Power of the power source, P = 54 W

Current utilized, I = 4.5 A

The equation for power of a circuit is given by,

P = VI

Therefore, voltage across the compressor,

V = P/I

V = 54/4.5

V = 12 V

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A capacitor with two lines of charge on its parallel plates. The bottom plate has an equal line of negative charges that are the opposite in charge to the positive charges on the top plate, while the top plate has a line of positive charges.

As a result, an electric field (E-field) is produced between the plates that can be measured with a sensor.

In a parallel-plate capacitor, the E-field between the plates is uniform and pointed perpendicularly to the plates. It is represented by the equation E = σ/ε, where ε is the permittivity of the medium between the plates and σ is the charge density (charge per unit area) on the plates.

In this instance, the charge density on the top and bottom plates is the same but with opposing signs since the lines of charges on the plates are equal in size and opposite in charge. Assume that the top plate has positive charges and the bottom plate has negative charges, and that the charge density on both plates equals.

A sensor placed between the capacitor's plates will now allow us to measure the E-field, which will reveal that it is constant and perpendicular to the plates. E = σ/ε, where σ, is the charge density and is the permittivity of the medium between the plates, will be the magnitude of the E-field.

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The energy of the skater at each position is:

At position A, the skater is at the lowest point, so the PE is zero. The KE can be calculated using the formula KE = (1/2)mv², where m is the mass of the skater and v is the velocity:

KE = (1/2)(60 kg)(8 m/s)²

KE = 1920 J

Therefore, at position A, the skater has 1920 J of kinetic energy and 0 J of potential energy.

At position B, the skater has gained some height, so there is some potential energy. The KE can be calculated as before, and the PE can be calculated using the formula PE = mgh, where m is the mass of the skater, g is the acceleration due to gravity (9.81 m/s²), and h is the height:

KE = (1/2)(60 kg)(8 m/s)²

KE = 1920 J

PE = (60 kg)(9.81 m/s²)(3 m)

PE = 1764 J

Therefore, at position B, the skater has 1920 J of kinetic energy and 1764 J of potential energy.

At position C, the skater has reached the highest point, so the KE is zero. The PE can be calculated as before:

PE = (60 kg)(9.81 m/s²)(6 m)

PE = 3528 J

Therefore, at position C, the skater has 0 J of kinetic energy and 3528 J of potential energy.

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The magnitude of a uniform electric field between two plates of capacitor is about 1.7 ✕ 106 N/C. If the distance between these plates is 3.7 cm then the potential difference between the plates is 62.5 kV.

A capacitor is a device that stores electrical energy in an electric field by collecting electric charges on two isolated surfaces. It is a two-terminal passive electrical component.

Electric field of the parallel plate capacitor is given as,

E = V/d

Given,

E =  1.7 ✕ 10⁶ N/C.

d = 3.7 cm,

V= Ed

V = 1.7 ✕ 10⁶ N/C × 3.7 × 10⁻² m

V = 62.5 kV.

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The nucleons have less mass, because matter is converted into binding energy. Option D is correct.

During the process of combining a neutron and a proton to form a nucleus, a small amount of mass is converted into binding energy. This is due to the strong nuclear force that holds the nucleus together. The mass of the nucleus is slightly less than the sum of the masses of the individual nucleons, and the difference in mass is referred to as the mass defect.

This mass defect is related to the binding energy of the nucleus through Einstein's famous equation E=mc², where E is energy, m is mass, and c is the speed of light. The mass defect represents the amount of mass that is converted into binding energy to hold the nucleus together. Option D is correct.

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