The moment of inertia of a solid cylinder about its axis is given by 1/2MR 2 . If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is:A. 1:1
B. 2:2
C. 1:2
D. 1:3

(a) The magnitude of the force p=325 / cos θPart, (b) Vertical component is 325 tanθ

(a) Given: Force F = P And horizontal component Fcos θ = 325N. Here, θ is the angle made by the force with the horizontal, and θ is unknown. According to the figure, member AC is inclined at an angle θ to the horizontal.

Let's resolve the force P into vertical and horizontal components. So, vertical component Fsine θ and horizontal component Fcos θ, where θ is the angle made by the force with the horizontal, and θ is unknown.

Thus, we get: Fcos θ = 325Fcos θ / F = 325 / cos θPart

(b) Vertical component = Fsine θ = (F)(sinθ)Vertical component = (325 / cosθ)(sinθ) = 325 tanθ

Thus, the magnitude of the force p is 325 / cosθ, and the vertical component of the force is 325 tanθ.

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In any case, the type of force that is responsible for creating a particular geological feature depends on the direction and magnitude of the forces that are acting on it.

Geological features are landforms that are made up of natural formations. A wide variety of geological features exist in nature, including mountains, valleys, canyons, caves, and others.

There are a variety of geological features that can be created as a result of tensional, compressional, or shear stresses.

Let's take a closer look at each type of stress:

Tensional: Tensional forces act to pull rocks apart. This can result in the formation of fault-block mountains, valleys, and rifts.

Compressional: Compressional forces act to push rocks together. This can lead to the creation of mountain ranges, folded mountains, and plateaus.

Shear Stresses: Shear stresses act to twist or bend rocks. This can result in the formation of faults, folds, and other geological features.

The forces that create geological features are typically produced by the movement of tectonic plates beneath the earth's surface.

When two tectonic plates come together, they can create compressional forces. When they move apart, they can create tensional forces.

When they slide past each other, they can create shear stresses. Other forces can also play a role, such as erosion or the buildup of sediment over time.

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A particle's velocity is described by the function vx=kt2 , where vx is in m/s , t is in s , and k is a constant. The particle's position at t0=0s is x0 = -5.40 m. At t1 = 2.00 s , the particle is at x1 = 5.80 m. The value of k is 2.80 m/s2.

The given equation describes the velocity of a particle in terms of a constant, k, and time, t. The velocity, vx, is given in m/s. The initial position of the particle at t0=0s is x0=-5.40 m, and at t1=2.00 s the particle is at x1=5.80 m. To find the value of the constant k, we can solve the equation for the change in velocity Δvx.

Δvx = vx1 – vx0 = k(t12 – t02)
Δvx = 5.80 – (-5.40) = 11.20 m/s

k = (11.20 m/s) / (2.002 s2) = 2.80 m/s2

Now that we have found the value of the constant k, we can use it to find the velocity of the particle at any time t. For example, at t2=4.00 s the velocity of the particle is vx2=11.20 m/s. This can be calculated using the equation vx2 = k(t22) = 2.80(4.002) = 11.20 m/s.

From the velocity equation, we can also calculate the position of the particle at any time t. The position of the particle at t2=4.00 s is x2= 11.20(4.00) = 44.80 m. We can also calculate the position of the particle at any other time t, by simply substituting in the corresponding value of t into the equation.

In conclusion, the equation vx = kt2 describes the velocity of a particle in terms of a constant, k, and time, t. Using this equation, we can calculate the velocity and position of the particle at any given time.

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Complete Question:

A particle’s velocity is described by the function vx = [tex]kt^2m/s[/tex], where k is a constant and t is in s. The particle’s position at [tex]t_0[/tex] = 0s is [tex]x_0[/tex] = -5.40 m. At [tex]t_1[/tex] = 2.00 s, the particle is at [tex]x_1[/tex] = 5.80 m. Determine the value of the constant k. Be sure to include the proper units

Explanation:

Refer to pic...........

If a tsunami warning is issued for the island, they will have approximately 11.7 hours before the waves arrive.

What is Magnitude?

Magnitude is a measure of the strength or intensity of a physical quantity or phenomenon, such as an earthquake or a sound wave. It is often expressed using a numerical scale, with higher values indicating greater strength or intensity. In the case of earthquakes, magnitude is typically measured using the Richter scale or the moment magnitude scale, which take into account the amplitude of seismic waves and the energy released by the earthquake.

To calculate the time it takes for a tsunami to travel from Japan to the island, we can use the following formula:

t = (2 * pi * d) / g * ln(1 + sqrt(h/d))

where t is the time it takes for the tsunami to travel, d is the average water depth, h is the wave height, and g is the acceleration due to gravity (9.8 m/s^2).

Magnitude of the earthquake: 8.5

Wavelength of the tsunami: 200 km = 200,000 m

Average water depth: 4,900 m

To calculate the wave height, we can use the following formula:

h = (M / 5) * (D / 10)^1/2

where M is the magnitude of the earthquake and D is the distance between the earthquake epicenter and the observation point (in this case, the island). Note that this formula is an approximation and may not be accurate for all cases.

Using the given values, we get:

D = 8,000 km = 8,000,000 m

h = (8.5 / 5) * ((8,000,000 / 10)^1/2) = 2,738.6 m

Substituting these values into the formula for t, we get:

t = (2 * pi * 4,900) / 9.8 * ln(1 + sqrt(2,738.6/4,900)) = 11.7 hours

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The mass flow rate of air that is entering the tank is 15.3 kg/s.

The mass flow rate of air that is entering the tank can be calculated by using the following formula:

Mass flow rate = density × volume flow rate

The term "density" refers to the amount of mass per unit volume. It is calculated as the mass of an object divided by its volume. Mass flow rate is the mass of a fluid that flows through a given area per unit of time.

The volume of the tank is 3 m³.

The initial density of air is 1.2 kg/m³.

At the end of the charging process, the density of air reaches 6.3 kg/m³.

We will first find the volume flow rate.

The volume flow rate is equal to the change in volume over time.

Volume flow rate = Volume change / Time taken = 3 m³ / 1 sec = 3 m³/s

Now, we can calculate the mass flow rate using the formula:

Mass flow rate = density × volume flow rate

Density = 6.3 kg/m³ − 1.2 kg/m³ = 5.1 kg/m³

Mass flow rate = 5.1 kg/m³ × 3 m³/s = 15.3 kg/s

Therefore, the mass flow rate of air entering the tank is 15.3 kg/s.

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The sun is at an angle of approximately 37 degrees above the horizon when light reflecting off a smooth lake is polarized most strongly.

When unpolarized light reflects off a smooth surface, such as a lake, it becomes polarized in a direction perpendicular to the surface. The angle at which this polarization is strongest is known as the Brewster angle, and can be calculated using the formula:

θB = arctan(n2/n1)

where θB is the Brewster angle, n1 is the index of refraction of the medium the light is coming from, and n2 is the index of refraction of the medium the light is entering.

For water, the index of refraction is approximately 1.33, and for air it is approximately 1.00. Plugging these values into the formula, we get:

θB = arctan(1.33/1.00) = 53.1 degrees

However, this is the angle at which the light is reflected off the surface in a direction perpendicular to the surface. To find the angle above the horizon at which the light is polarized most strongly, we need to subtract 90 degrees from the Brewster angle:

37 degrees = 90 degrees - 53.1 degrees

Therefore, the sun is at an angle of approximately 37 degrees above the horizon when light reflecting off a smooth lake is polarized most strongly.

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a.  the depth of cut  is 0.625 inches.

b. the material removal rate is 0.003125 cubic inches per minute.

c. the time required to complete the cutting pass is 20 minutes.

a) The required depth of cut can be determined by :

DOC = (4 in - 2.75 in)/2 = 0.625 in

Therefore, the depth of cut is  0.625 inches.

b) The material removal rate can be found by applying:

MRR = DOC x Width of cut x Feed rate

assuming we are using a standard carbide insert tool with a width of cut of 0.5 inches.

MRR = 0.625 in x 0.5 in x 0.010 in/rev = 0.003125 cubic inches per minute

c) The time required to complete the cutting pass is determined by:

Time = Length of cut / (Cutting speed x Width of cut x Feed rate)

Time = 48 in / (400 ft/min x (0.5 in) x (0.010 in/rev) x (1/12 ft/in)) = 20 minutes

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Answer:

Yo dude, if you had a beaker of liquid in outer space, it wouldn't push down on the bottom or the sides of the beaker like it would on Earth. In space, there's no gravity to make the liquid settle down, so it forms a round shape because of surface tension. So basically, the liquid would just float around in a ball inside the beaker. If you moved the beaker around, the liquid would just roll around with it like a bouncy ball.

Given equal-sized samples (volumes) of galena and quartz, the Galena sample will feel heavier because of its higher specific gravity. Thus, the correct option is A.

Specific gravity is the ratio of the density of a substance to the density of a standard substance in physics. It's typically applied to liquids and solids, but it may also be applied to gases. The most often utilized standard material for liquids and solids is water at 4°C. A substance's specific gravity is dimensionless and is often represented by the Greek symbol ρ.

Relative Density of the given substances:

Galena's specific gravity is 7.5, Quartz's specific gravity is 2.65, and Liquid mercury's specific gravity is 13.6. An object with a specific gravity greater than 1 sinks in water, while one with a specific gravity less than 1 floats in water. The specific gravity of water is 1.0. An object with a specific gravity greater than 1 sinks in water, while one with a specific gravity less than 1 floats in water.

We can conclude from the values above that liquid mercury is heavier than galena, which is in turn heavier than quartz. Therefore, since both quartz and galena are being measured with equal sizes or volumes, galena will feel heavier than quartz.

Therefore, the correct option is A.

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Acceleration due to gravity is 9.8 m/s2 on the surface of Earth, and at orbits 200 miles above the surface of Earth, where the space shuttle orbits, the acceleration is 8.78 m/s².

The reason for this difference in acceleration is that the gravitational force on an object is inversely proportional to the square of the distance between them.

Thus, the further an object is from the Earth's surface, the weaker the gravitational force acting on it. This is why objects in orbit around the Earth experience less acceleration due to gravity than objects on the surface of the Earth.

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Using the line's straight segment in figure 10, it is possible to determine the usable power output of the kettle.

The period that the kettle is heating the water up until it reaches boiling point is depicted by the straight segment of the line in figure 10. Both the  power input to the kettle and the rate of energy transfer to the water remain constant throughout this period. Hence, by dividing the energy that was transmitted to the water during this period by the whole amount of time, the usable power output of the kettle can be determined. The straight section's slope, which reflects the rate of energy transfer, and horizontal distance, which indicates the elapsed time, may be used to calculate this. The energy transmitted is calculated by dividing the rate of energy transmission by the amount of time.

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The kinetic energy of the trunk increases by ½ mvf² = ½ m(10.65 m/s)²= 71.44 J during the displacement.

Net work = ΔK

W = Fd cosθ

W1 = F1d cosθ = (5.86 N)(3.010 m) cos(67.8°) = 6.99 J

W2 = F2d cosθ = (9.180 N)(3.010 m) cos(67.8°) = 10.97 J

W3 = F3d cosθ = (3.850 N)(3.010 m) cos(67.8°) = 4.58 J

Net work = W1 + W2 + W3 = 6.99 J + 10.97 J + 4.58 J = 22.54 J

Therefore, the net work done on the trunk by the three forces is 22.54 J.

ΔK = ½ mvf² - ½ mvi²

Since the trunk moves a distance of 3.010 m and is initially at rest, we can use the equation:

vf² = 2ad

where a is the acceleration of the trunk, which is given by:

a = ΣF / m

where ΣF is the net force on the trunk, which we can find using:

ΣF = F1 + F2 + F3

ΣF = (5.86 N + 9.180 N + 3.850 N) = 18.89 N

Therefore, the acceleration of the trunk is:

a = ΣF / m = 18.89 N / m

Since the trunk moves leftward, the acceleration is also leftward, so we can use a negative value for a.

Substituting the values for a and d, we get:

vf² = -2(-18.89 N / m)(3.010 m) = 113.51 (m/s)²

Taking the square root, we get:

vf = 10.65 m/s

Therefore, the change in kinetic energy of the trunk is:

ΔK = ½ mvf² - ½ mvi² = ½ m(10.65 m/s)²- 0 = ½ mvf²

Kinetic energy is a type of energy that an object possesses by virtue of its motion. It is defined as the energy an object has due to its motion and is proportional to the mass of the object and the square of its velocity. The formula for kinetic energy is KE = 1/2mv^2, where m is the mass of the object and v is its velocity.

Kinetic energy is a scalar quantity and has units of joules in the International System of Units (SI). It is a fundamental concept in physics and is used to describe many physical phenomena, including the motion of particles, the behavior of gases, and the motion of waves. In many cases, kinetic energy can be transformed into other forms of energy. For example, when a ball is thrown upwards, its kinetic energy is gradually converted into gravitational potential energy as it moves higher and higher.

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The translational speed of the cylinder when it reaches the foot of the incline is approximately 9.43 m/s.

We can use conservation of energy to solve this problem. The initial energy of the cylinder is all potential energy, and the final energy is all kinetic energy. The potential energy at the bottom of the incline is zero.

The potential energy of the cylinder at the top of the incline is given by:

PE = mgh

where m is the mass of the cylinder, g is the acceleration due to gravity, and h is the height of the incline. Substituting the given values, we get:

PE = (mass of cylinder) x (acceleration due to gravity) x (height of incline) = mgh

The kinetic energy of the cylinder at the bottom of the incline is given by:

KE = (1/2)mv^2

where v is the translational speed of the cylinder at the bottom of the incline.

According to the conservation of energy, the initial potential energy is equal to the final kinetic energy, so we can set these two expressions equal to each other:

mgh = (1/2)mv^2

We can cancel the mass of the cylinder from both sides, and solve for v:

v = sqrt(2gh)

Substituting the given values, we get:

v = sqrt(2 x 9.81 m/s^2 x 7.20 m) ≈ 9.43 m/s

Therefore, the translational speed of the cylinder when it reaches the foot of the incline is approximately 9.43 m/s.

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In the case where the car is traveling in the -x direction and decreasing in speed, it has a negative velocity and a positive acceleration. Therefore, option D is the correct answer. In this case, the car is traveling in the - direction and decreasing in speed. Therefore, it has a negative velocity and a positive acceleration.

Let's discuss the given options one by one:

(A) In this case, the car is traveling in the -x direction at a constant speed. Therefore, it has a negative velocity and zero acceleration. This option is incorrect.

(B) In this case, the car is traveling in the - direction and increasing its speed. Therefore, it has a negative velocity and a positive acceleration. However, the given direction is not specified, and thus this option is not accurate.

(C) In this case, the car is traveling in the +x direction and increasing in speed. Therefore, it has a positive velocity and a positive acceleration. This option is incorrect.

(D) In this case, the car is traveling in the - direction and decreasing in speed. Therefore, it has a negative velocity and a positive acceleration. This option is correct.

(E) In this case, the car is traveling in the +x direction and decreasing in speed. Therefore, it has a positive velocity and a negative acceleration. This option is incorrect.

Therefore, Option D ( - direction decreasing in speed) is correct.

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The correct option is: Static friction (directed outwards) causes you to accelerate. (Option C)

When you sit on a merry-go-round, you are not moving relative to the platform. Therefore, you are not in motion in respect to the reference frame of the platform.

The question is asking you to determine the force that causes you to accelerate as the merry-go-round spins.

Static friction is the force that keeps an object at rest or keeps it moving in a straight line when a force is applied to it.

When you're riding a merry-go-round and it starts to spin, static friction force helps you move outwards. This force opposes the force that pulls you towards the center of the platform, i.e., centripetal force.

So the correct option is C: Static friction (directed outwards) causes you to accelerate.

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The researcher's observation that more auxin collects in the sides of stems and roots that are not exposed to light is likely due to the phenomenon of phototropism.

In the process of phototropism, light influences the direction and rate of growth of plant cells. In particular, light induces the cells on one side of a stem or root to create less auxin than the cells on the shaded side. Less auxin is produced on the lighted side and more auxin is produced on the shaded side as a result. The hormone auxin is essential for controlling the growth and development of plants. Auxin generally promotes cell growth and elongation at greater concentrations while inhibiting cell elongation at lower concentrations. Since the cells on the lighted side of the stem or root will contain less auxin when there is light.

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The maximum energy of photoelectrons from aluminium is 2.3 eV for radiation of 2000 Å and 0.90 eV for radiation of 3130 Å.

To calculate Planck's constant and the work function of aluminium, we need to use the equation:

 h = E2 - E1/ λ2 - λ1

Where h is Planck's constant, E1 and E2 are the maximum energy of photoelectrons for each wavelength, and λ1 and λ2 are the wavelengths.

Using the given data, we have:

h = (2.3 - 0.90) / (2000 - 3130)

Therefore, h = -1.4 eV / -930 Å, which simplifies to h = 0.0015 eVÅ.

The work function of aluminium is equal to the maximum energy of the photoelectrons for the longest wavelength, in this case, 0.90 eV. Therefore, the work function of aluminium is 0.90 eV.

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The answer is C.  Sphere A is repelled from sphere B

Step by step explanation:

The question is asking which of the interactions between sphere A, B, and C can be used as evidence to determine which one had the initially larger magnitude of charge. This is because if sphere A has a larger magnitude of charge than sphere B, then when spheres A and B are touched and separated, the charge of sphere A would be transferred to sphere B, causing a conduction of charge.

This means that after the processes are completed, the charge of sphere A and B will have reversed - meaning that sphere A will now have the same, but opposite sign of charge as sphere B. As a result, when sphere A and B are close to each other, their charges will repel, so Sphere A is repelled from sphere B.

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The sailplane which is going from Earth to Mars is accelerating at 0.033 m/s² in the direction of solar radiation force.

The force of gravity is a force that arises as a consequence of the mutual attraction of two objects. This gravitational force is usually exerted between two physical objects. Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is proportional to the product of their masses.

Acceleration is the rate at which an object changes its speed or direction. Acceleration is a vector quantity that can be positive or negative. If the acceleration is negative, the object slows down. If the acceleration is positive, the object speeds up.

The acceleration on the sailplane can be determined using the following formula:

[tex]F_{net} = ma[/tex]

Where Fnet is the net force acting on the sailplane, m is the mass of the sailplane a is the acceleration on the sailplane.[tex]F_{net} = ma[/tex]

The net force acting on the sailplane can be calculated as:

[tex]F_{net} = F_{rad} - F_{gravitySun} - F_{gravityEarth}[/tex]

Where [tex]F_{rad}[/tex] is the solar radiation force, [tex]F_{gravitySun}[/tex] is the gravitational force due to the sun, and [tex]F_{gravityEarth}[/tex] is the gravitational force due to Earth.

Putting the given values in the above formula:

[tex]F_{net} = 7.70 \times 10^2 N - 173 N - 1.00 \times 10^2 N = 497 N[/tex]

The acceleration on the sailplane is given as:

[tex]a = F_{net} / ma = (497\  N) / 14,900 \ kg = 0.033 \ m/s^2[/tex]

The magnitude of the acceleration on the sailplane is 0.033 m/s² (rounded to three significant figures).

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The two planets that are coming together are Saturn and Jupiter. On December 21st, 2020, the two planets will be at their closest point, an event known as the Great Conjunction.

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A change in velocity in short period of time means the acceleration is large, hence the net force must be proportionately large as well.

A force is a physical quantity that induces a body to undergo an alteration in speed, direction of motion, or shape. A force can be classified as a push or a pull. When forces are equal, the forces are balanced and the object is not moving. Otherwise, if the forces are not equal, making it unbalanced will not give the object any movement.

The force that induces the change in the speed or direction of an object is referred to as a net force. The net force is equal to the product of the mass of the object and its acceleration. Newton (N) is the unit of measurement for force.

When a ball bounces against a wall, there will be a large change in velocity in a short period of time. This means the acceleration is large, hence the net force must be proportionately large as well.

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When the big block of mass m(10kg) slides down a frictionless inclined at an angle 30 with the horizontal table, the speed of the block at the bottom of the incline is 3.14 m/s.

Given that

Mass of the block, m = 10 kg.

Angle of inclination, θ = 30°

Initial velocity, u = 0.

Frictional force, f = 0.

Using the formula for gravitational force, F = mg

where, g = 9.8 m/s² (acceleration due to gravity)

F = mg= 10 kg × 9.8 m/s²= 98 N

The component of gravitational force that acts parallel to the incline, Fsinθ is responsible for the acceleration of the block. Fsinθ = ma; Where a is the acceleration of the block.

a= (98 N)sin 30° / 10 kg= 4.9 m/s²

Using the formula for speed, v = u + at where,

u = initial velocity = 0m/s

t = time taken = time taken to slide from top to bottom of the incline.= √(2h/g) where,

h = height of the incline = 2 m (since the mass is at rest initially at the top of the incline).

Therefore, t = √(2 × 2 m / 9.8 m/s²)= 0.64 s

Substituting the values in the above formula, v = u + at= 0 + (4.9 m/s² × 0.64 s)= 3.14 m/s.

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Answer:

4 km/hr^2

Explanation:

We can use the formula for acceleration:

a = (v_f - v_i) / t

where:

a = acceleration

v_f = final velocity

v_i = initial velocity

t = time taken

Substituting the given values, we get:

a = (70 km/hr - 50 km/hr) / 5 hr

a = 20 km/hr / 5 hr

a = 4 km/hr^2

The angular acceleration of the fan is 0.740 rad/s^2,

Angular acceleration which represents the rate at which the angular velocity changes over time. The unit used to measure angular acceleration is radians per square second (rad/s2), according to the International System of Units. The Greek alphabet symbol alpha (α) is used to denote angular acceleration.

To calculate the angular acceleration of the fan, the formula α = Δω/Δt is used. Here, α represents angular acceleration, Δω represents the change in angular speed, and Δt represents the change in time.

In this scenario, Δω is equal to 10.0 - 6.30 = 3.70 rad/s, and Δt is equal to 5.00 s. By substituting these values into the formula, we obtain α = 3.70/5.00 = 0.740 rad/s^2.

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Ceteris paribus, a decrease in capital productivity is the event that would cause both the equilibrium interest rate and the equilibrium quantity of investment to fall. The correct answer is option C.

Ceteris paribus is a Latin expression that means "all other things being equal." Ceteris paribus is a model in which economists use to analyze the effect of one independent variable on a dependent variable while keeping all other independent variables constant. This implies that only one variable is allowed to change while all other variables are held constant at their current level or position.

Therefore, Ceteris paribus, an increase in investor confidence, an increase in cosmetic income and wealth, and a strength of time preference will not cause both the equilibrium interest rate and the equilibrium quantity of investment to fall. However, a decrease in capital productivity is an event that would cause both the equilibrium interest rate and the equilibrium quantity of investment to fall.

When capital productivity is low, firms are unable to produce goods and services efficiently, and as a result, the demand for investment falls. When the demand for investment falls, the equilibrium quantity of investment will also decrease, leading to a decrease in the equilibrium interest rate.

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Unproven theories ultimately cannot be regarded as scientific facts or principles and are not generally recognised by the scientific community.

A well-supported explanation of a natural occurrence in science that has passed rigorous examination and is backed by empirical data is referred to as a theory. A hypothesis, however, cannot be regarded as a scientific fact or principle if it is not backed up by empirical data or if it has not undergone extensive testing and verification. The scientific community frequently rejects unproven notions with scant empirical backing and may even label them as pseudoscientific or non-scientific. This is so that scientific theories and findings may be evaluated and verified frequently. Science does this by using evidence-based reasoning and critical thinking. Unproven theories are therefore eventually not regarded as being a part of the corpus of scientific knowledge.

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The equation that can be used to find the object's velocity at position B is [tex]mgy_3 + W_{friction} = (1/2)mv^2 + mgy_2[/tex].

Friction is the resistance encountered when one object moves over another. Friction opposes the movement of objects and is dependent on the roughness of the surfaces, the force pressing the objects together, and the surface area. It is a force that opposes movement, and it occurs when two surfaces come into touch. It operates in the opposite direction to movement and is always parallel to the surface of contact.

Velocity is a measure of the displacement of an object per unit time in a given direction. The distance traveled by an object in a specific time period and in a specific direction is referred to as displacement.

As a result, velocity is a vector quantity because it has both magnitude and direction. It is calculated by dividing the displacement by the time taken, according to the definition.

Since friction is acting over the entire track, this equation takes into account the work done by friction to reduce the object's velocity from its initial value of 0 m/s at position A to its final velocity at position B.

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The capacitance of the circuit (in f) is  2.31×10⁻⁵F for the rc circuit with a time constant of 5.35 s. if the total resistance in the circuit is 231.2 k.

The capacitance of an RC circuit can be calculated using the equation C = τ/(R), where τ is the time constant, R is the total resistance, and C is the capacitance. For this RC circuit, the time constant is 5.35s and the total resistance is 231.2 k. Therefore, the capacitance is 5.35s/(231.2k) = 2.31×10⁻⁵F.

Time constant of the RC circuit, τ = 5.35s

Total resistance in the circuit, R = 231.2 kΩ = 231200 Ω

Capacitance of the circuit = ?

We know that, Time constant (τ) of a RC circuit = R × C.

where, R is the resistance in ohms, C is the capacitance in farads. Substitute the given values in the above equation:

τ = RC

5.35 s = R × C231200 Ω × C = 5.35 s

C = 5.35 s / 231200 Ω

C = 2.31 × 10⁻⁸ F.

Therefore, the capacitance of the circuit is 2.31 × 10⁻⁸ F.

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Answer to following (a) , (b) and (c) question are: 63.00 J, 40.0 J, 63.00 J

(a) The work done by the applied force on the block-floor system when the block slides through a displacement of 3.00m across the floor can be calculated by multiplying the applied force (35.0 N) and the displacement (3.00 m), with a coefficient of kinetic friction (0.600) for the system. Thus, the work done is 35.0N * 3.00m * 0.600 = 63.00 J.

(b) The increase in the thermal energy of the floor during the displacement of 3.00m is equal to the thermal energy of the block (40.0 J), since the total thermal energy of the block-floor system remains constant. Therefore, the increase in thermal energy of the floor is 40.0 J.

(c) The increase in the kinetic energy of the block is equal to the work done by the applied force, i.e., 63.00 J.

To know more about "coefficient of kinetic friction" refer here:

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