What is the function of the metal case cover in a thermos flask?​

The net work done (in J) required to accelerate a 1500 kg car from 55 m/s to 65 m/s is 3127500 J

First, we shall obtain the initial kinetic energy. Details below:

KE₁ = ½mu²

= ½ × 1500 × 55²

= 41250 J

Next, we shall final kinetic energy. Details below:

KE₂ = ½mv²

= ½ × 1500 × 65²

= 3168750 J

Finally, we shall determine the net work done. Details below:

W = KE₂ - KE₁

= 3168750 - 41250

= 3127500 J

Thus, the net work done is 3127500 J

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The momentum of the zombie is 535.3 kg m/s.

Momentum is a fundamental concept in physics that describes the amount of motion that an object has. It is defined as the product of an object's mass and its velocity.

Here,

The momentum (p) of an object is defined as the product of its mass (m) and velocity (v)

p = m * v

In this case, the mass of the zombie is 101 kg and its velocity is 5.3 m/s. So, the momentum of the zombie can be calculated as:

p = 101 kg * 5.3 m/s

p = 535.3 kg m/s

Therefore, the momentum of the zombie is 535.3 kg m/s.

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Answer:

The EMF of the battery can be calculated using the following formula:

EMF = V + Ir

where:

EMF = electromotive force (unknown)

V = terminal voltage = 12 V

I = current flowing through the circuit (unknown)

r = internal resistance = 0.5 Ω

To find I, we can use Ohm's law:

V = IR

where R is the total resistance of the circuit (including the internal resistance), so:

R = 20 Ω + 0.5 Ω = 20.5 Ω

Rearranging Ohm's law to solve for I, we get:

I = V / R

I = 12 V / 20.5 Ω

I ≈ 0.585 A

Now we can substitute the values of V, I, and r into the first formula:

EMF = V + Ir

EMF = 12 V + 0.585 A × 0.5 Ω

EMF ≈ 12.2925 V

Therefore, the EMF of the battery is approximately 12.2925 volts.

Answer:

P = 1 (14,045 ± 0.03 )  k gm/s

Explanation:

In this exercise we are asked about the uncertainty of the momentum of the two carriages

            Δ (Pₓ / Py) =?

 Let's start by finding the momentum of each vehicle

car X

        Pₓ = m vₓ

        Pₓ = 2.34 2.5

        Pₓ = 5.85 kg m

car Y

        Py = 2,561 3.2

        Py = 8,195 kgm

How do we calculate the absolute uncertainty at the two moments?

          ΔPₓ = m Δv + v Δm

          ΔPₓ = 2.34 0.01 + 2.561 0.01

          ΔPₓ = 0.05 kg m

         Δ\(P_{y}\) = m Δv + v Δm

         ΔP_{y} = 2,561 0.01+ 3.2 0.001

         ΔP_{y} = 0.03 kg m

now we have the uncertainty of each moment

          P = Pₓ / \(P_{y}\)

          ΔP = ΔPₓ/P_{y} + Pₓ ΔP_{y} / P_{y}²

          ΔP = 8,195 0.05 + 5.85 0.03 / 8,195²

          ΔP = 0.006 + 0.0026

          ΔP = 0.009 kg m

The result is

           P = 14,045 ± 0.039 = (14,045 ± 0.03 )  k gm/s

This is a case of institutional discrimination. ​

The term institutional discrimination has to do with a situation in which  some group of people are knowing denied the opportunity for inclusion by the polies of a particular institution. In this case, we are told that some universities have had campus facility security deposit requirements that disproportionately affected Black American students In Greek organizations because more of the white Greek organizations owned bet own social facilities. This has proven to be a big problem in many of the developed countries of the world even as it continues until date.

This implies that there is already a policy that is in place that tends to prevent  Black American students from accessing the said facilities. In this case whereby some group of persons in this case the Black American students are being discriminated against, we have a case of institutional discrimination. ​

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The tangential acceleration of the short player's ball is twice the tangential acceleration of the tall player's ball.

The ball of the shorter player experiences twofold of the ball of the taller player's tangential acceleration. The reason behind this is that the magnitude of the tangential acceleration correlates directly with the radius of the circle.

The ball belonging to the smaller player is positioned nearer to the elbow, resulting in a decreased radius. It can be deduced from this statement that the ball of the short player experiences twice the magnitude of tangential acceleration compared to the ball of the tall player.

The answer is: ashort = 2atall

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The Complete Question

A short tennis player hits a ball that is r meters from their elbow with an angular acceleration a. A tall tennis player hits a ball with the same angular acceleration where the ball is 2r from their elbow. How does the tangential acceleration of the short player's ball Ashort compare with the tall player's ball a tall? Choose 1 answer: ashort 2atall ashort Otall ashort 1 atall 2

The owl started out at a height of about 3.2 metres.

Gravity is the force that draws objects toward the center of a planet or other object.

Gravitational potential energy (GPE) is calculated as follows:

GPE = mass x gravity x height. Since we are aware of the owl's mass (4 kg) and the change in GPE (-800 J) in this case, we can rewrite the formula to account for the height: tallness = GPE / (mass x gravity).

On Earth, the acceleration caused by gravity is roughly 9.8 m/s2.

By entering the known numbers, we obtain the height change as follows: -800 J / (4 kg x 9.8 m/s2) = -0.408 metres.

By combining the ultimate height (which is believed to be 0 metres) with the height change, we may get the initial height as follows: 0 m + (-0.408 m) = -0.408 m = 0.408 m = 3.2m.

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The statement that describes the transformation of the graph of function f onto the graph of function g is: The graph shifts 2 units right and 7 units down.

To determine the transformation of the graph of function f onto the graph of function g, we compare the two functions f(x) and g(x) and observe the changes in the equations.

The function f(x) = (1/x - 3) + 1 represents a reciprocal function that is shifted vertically 1 unit up and horizontally 3 units to the right. The reciprocal function is reflected about the line y = x.

The function g(x) = (1/(1 + 4)) + 3 simplifies to g(x) = 4 + 3 = 7, which is a constant function representing a horizontal line at y = 7.

By comparing the equations, we can see that the transformation from f(x) to g(x) involves the following changes:

The term 1/x in f(x) is replaced by the constant 1/(1 + 4) in g(x), resulting in a vertical shift of 7 units up.

The term -3 in f(x) is replaced by 3 in g(x), resulting in a vertical shift of 3 units up.

The +1 in f(x) is replaced by +3 in g(x), resulting in an additional vertical shift of 2 units up.

Therefore, the overall transformation is a shift of 2 units to the right and 7 units down.

Hence, the correct statement is: The graph shifts 2 units right and 7 units down.

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The work done on the crate to move it vertically is 7000 J.

The work done to move a 1400-N crate at constant speed 5.0 m vertically is 7000 J. Here's the explanation:When an object is lifted up at a constant speed, the force applied to it is equal and opposite to the force of gravity acting on it. As a result, no net force is applied to the object, and no work is performed against it.The formula to determine the work done isW = FdwhereW is work doneF is forceand d is distance coveredTo calculate the work done on the crate to move it vertically upwards, we need to determine the force that needs to be applied to overcome gravity acting downwards. We know that force is equal to mass multiplied by acceleration, which means that the force required to overcome gravity acting on the crate is given by:F = mgwhereF is the force in Newtonsm is the mass in kilogram is the due to acceleration, 9.8 m/s²Substitute the given values into the formula:F = 1400 NNext, we need to determine the distance over which the crate is lifted vertically, which is given as d = 5.0 m.Substitute the given values into the formula: d = 5.0 mFinally, substitute the values into the formula to get the work done.W = FdW = 1400 N × 5.0 mW = 7000 J.

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The amount of work required to move the crate is determined as 7,000 J.

The amount of work required to move the crate is calculated from the product of applied force and the displacement of the crate.

Mathematically, the formula for work done is given as;

W = Fd

where;

The amount of work required to move the crate is calculated as;

F = 1400 N x 5.0 m

F = 7,000 J

Thus, the amount of work required to move the crate is calculated from the product of applied force and the displacement of the crate.

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Answer:

A. The brakes used a coil system to convert the kinetic energy into potential energy stored in the brakes

Explanation:

Based on the law of conservation of energy, the brakes used a coil system to convert the kinetic energy into potential energy stored in the brakes.

The law of conservation of energy states that energy is neither created nor destroyed in a system but it is transformed from one form to another.

As the airplane slows down, the kinetic energy which is presented in the motion of the plane is gradually converted to potential energy.

The potential energy is the energy due to the position of a body.

Based on the diagram, the correct statement is: Government and consumers make economic decisions in a mixed economy, while consumers make economic decisions in a market economy.

In a mixed economy, economic decisions are made by both the government and consumers.

The government plays a significant role in regulating and influencing economic activities through policies, regulations, and interventions.

In market economy, economic decisions are primarily made by consumers. The market forces of supply and demand dictate the allocation of resources, production levels, and pricing.

The freedom to buy and sell whatever they choose is what ultimately determines how commodities and services are produced and distributed.

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a) The final pressure and temperature for the isothermal compression are \(4.5*10^5 Pa\) and 293 K, respectively, while  b) the final pressure and temperature for the adiabatic compression are\(5.58*10^5 Pa\) and 515 K, respectively.

a. Isothermal compression:

For an isothermal process, the temperature remains constant. Therefore, we can use the ideal gas law:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.

Since the process is isothermal, we can write:

\(P_1V_1 = P_2V_2\)

where P1 and V1 are the initial pressure and volume, and\(P_2\)and\(V_2\)are the final pressure and volume.

We are given that the volume is compressed to 1/3 of its original volume, so\(V_2 = (1/3)V_1\). Substituting this into the equation above gives:

\(P_2 = (V_1/V_2)P_1 = 3P_1\) = \(4.5*10^5 Pa\)

To find the final temperature, we can use the ideal gas law again:

PV = nRT

Rearranging, we get:

T = PV/(nR)

Substituting the values we know, we get:

T = (\(1.5*10^5\)Pa)(V1)/(nR)

Since the process is isothermal, the temperature remains constant, so the final temperature is the same as the initial temperature:

T2 = T1 = 293 K

b. Adiabatic compression:

For an adiabatic process, there is no heat transfer between the gas and its surroundings. Therefore, we can use the adiabatic equation:

PV^γ = constant

where γ = Cp/Cv is the ratio of specific heats.

Since the process is adiabatic and reversible, we can write:

\(P_1V_1\)^γ = \(P_2V_2\)^γ

We are given that the volume is compressed to 1/3 of its original volume, so V2 = (1/3)V1. Substituting this into the equation above gives:

\(P_2 = P_1(V_1/V_2)\)^γ = \(P_1\)\((3)^{(1.4)\) = \(5.58*10^5 Pa\)

To find the final temperature, we can use the adiabatic equation again:

\(T_2 = T_1(P_2/P_1)\)^((γ-1)/γ) = T1(5.58/1.5)^(0.4) = 515 K

Therefore, the final pressure and temperature for the isothermal compression are \(4.5*10^5 Pa\)and 293 K, respectively, while the final pressure and temperature for the adiabatic compression are \(5.58*10^5\) Pa and 515 K, respectively.

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According to the given statement The time required is 2 seconds.

An unseen factor is an agent that has the power to alter the resting or moving condition of a body. It has a direction or a magnitude. The stress applied is the location at which force is applied, and the direction where the force applied is known also as direction of the force.

The vector composition of mass (m), acceleration, and the amount of force is used to express force (a). Mathematically, the equation or equation for force may be written as follows:

                             Force = mass x acceleration.

We know the force and the mass, so we can write:

6,000 N

= (1,200 kg) x (acceleration).    

      i.e. Acceleration = 6000N/1200kg = 5 m/s² .

That's the acceleration.  The speed changes by 5 m/s each second

that the force acts on it.  If the force pushes from behind, then it goes

5 m/s per second faster. It moves 5 m/s slower each second if the force is pushing from the front.

We wish to slow it down from its current speed of 10 m/s to 0 m/s. Therefore, the force must push from the front, and the task will be finished in (10/5) = 2 seconds.

So, time required is 2 seconds.

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The standard form equation for the circle with center (3, 10) and radius 2 is: \(\rm 2.x^{2} + y^{2} - 6x - 20y + 105 = 0.\)

The radius, diameter, circumference, arc, chord, secant, tangent, sector, and segment are all parts of a circle.

A circle is a round figure with no corners or edges. A circle is a closed shape, a two-dimensional shape, and a curved shape in geometry.

A circle with center (h, k) and radius r has the following standard form equation:

\(\rm (x-h)^{2} + (y-k)^{2} = r^{2}\)

Substituting the values of center and radius:

\(\rm (x-3)^{2} + (y-10)^{2} = 2^{2}\)

Simplifying the equation:

\(\rm x^{2} - 6x + 9 + y^{2} - 20y + 100 = 4\)

\(\rm x^{2} + y^{2} - 6x - 20y + 105 = 0\)

\(\rm x^{2} + y^{2} - 6x - 20y + 105 = 0\)

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Answer: 800

Explanation:

1/2 x m x v^2 = m x g x h

KE = 10 x 10 x 8

KE= 800

The energy of the body by the virtue of its motion is known as the kinetic energy of the body. The kinetic energy of the rock just before it hits the ground will be 784.8 J.

The energy of the body by the virtue of its motion is known as the kinetic energy of the body. It is defined as the product of half of mass and square of the velocity.

According to the law of conservation of energy, energy can not be created nor be destroyed can be transferred from one form to another form.

Kinetic energy= potential energy

Kinetic energy= mgh

Kinetic energy= 10×9.81×8

Kinetic energy=784.8 J

Hence the kinetic energy of the rock just before it hits the ground will be 784.8 J.

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Examples of how the parts of the brain would be involved in the experience of tasting the food and seeing it was awful include:

The hindbrain, which includes the cerebellum and brainstem, is responsible for basic bodily functions such as breathing, heart rate, and digestion. In the scenario of trying a new food and finding it unpleasant, the hindbrain would play a role in initiating the digestive response to the food.

The midbrain is involved in the processing of sensory information, including auditory and visual stimuli. In the scenario of trying a new food and finding it unpleasant, the midbrain would be responsible for processing the sensory information related to taste and smell.

The forebrain is responsible for more complex cognitive processes, including decision-making and problem-solving. In the scenario of trying a new food and finding it unpleasant, the forebrain would be involved in deciding how to respond to the situation.

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The resultant force that water exerts on the overhang sea wall along abc is 179 kN.

Force is a physical quantity that describes the interaction between two objects, such as a push or a pull. It is defined as any influence that causes an object to undergo a change in motion or deformation. Force is a vector quantity, meaning that it has both magnitude (size or strength) and direction.

Component that is horizontal. Because AB is horizontal, there is no horizontal component. The horizontal component of BC's force is.

(Fbc)h =γwhˉA=(1000kg/m3)(9.81m/s2)(1.5m+21(2m))(2m(2m))=98.1(103)N.

Component that is vertical. The weight of the water contained in blocks Abefa and Bcdeb (shown shaded in Fig. a) is equal to the force on AB and the vertical component of the force on BC. Here,

Aabefa=1.5m(2.5m)=3.75m2and

2Abcdeb=(3.5m)(2m)–4π(2m)2=(7–p)m2. Then,

Fab=γwVabefa=(1000kg/m3)(9.81m/s2)[(3.75m2)(2m)] =73.575(103)N=73.6N (FBC)v=γwVbcdeb=(1000kg/m3)(9.81m/s2)[(7–π)m2(2m)] =75.702(103)N

Therefore,

Fbc=(Fbc)²h2+(Fbc)²v2=√[98.1(10³)N]²+[75.702(10³)N]²=123.91(10³)N=124KN

FR²   =(Fbc)²H2+[Fab+(Fbc)v]²

==[98.1(10³)N]² + [(73.6(10³)N)²+75.702(10³)N²]

=178.6(10³)N = 179 kN.

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The frictional force involved when a penny sinks to the bottom of a wishing well is primarily due to viscous drag or fluid friction. As the penny moves through the water, it experiences resistance from the surrounding fluid. This resistance is caused by the frictional forces between the water molecules and the penny's surface.

Answer:

Charging by contact is when the charged object is brought near but never contacted to the object being charged

Explanation:

Answer:

a collision occuring between two objects in an isolated system, the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2.

thank you.

Answer:

Explanation:

From the given information:

Let's assume that the missing function is:

s(t) = t³ - 6t², t ≥ 0

From part (b), we are to find the given  required terms when time t = 2

So; from the function s(t) =  t³ - 6t², t ≥ 0

\(velocity \ v(t) \ = \dfrac{d}{dt}s(t)\)

\(velocity \ v(t) \ = \dfrac{d}{dt}(t^3 - 6t^2)\)

\(velocity \ v(t) \ = 3t^2 - 12t\)

\(acceleration a(t) = \dfrac{d}{dt}*v(t)\)

\(acceleration a(t) = \dfrac{d}{dt}(3t^2 - 12 t)\)

\(acceleration\ a(t) = 6t - 12\)

At time t = 2

The position; S(2) = (2)² - 6(2)²

S(2) = 8 - 6(4)

S(2) = 8 - 24

S(2) = - 16 ft

v(2) = 3(2)² - 12 (2)

v(2) = 3(4) - 24

v(2) = 12 - 24

v(2) = - 12 ft/s

speed = |v(2)|

|v(2)|  = |(-12)|

|v(2)| = 12 ft/s

acceleration = 6t - 12

acceleration = 6(2) - 12

acceleration =  12 - 12

acceleration =  0 ft/s²

The cost of operation for an A.C for 10 hours per day for a month will be 71,100 francs.

Power is the amount of energy transferred or converted per unit time. The unit of power is the watt, equal to one joule per second. Power is a scalar quantity.

Cost of operation for 10 hours a day;

Daily consumption = 3kW x 10 hours

Daily Consumption = 30kW

Since 1kWH = 79 francs;

Daily consumption amount = 30 x 79 francs

Daily consumption amount = 2,370 francs

Therefore, the monthly consumption (using 30days) will be;

2,370 francs x 30 = 71,100 francs

In conclusion, 71,100 francs will be spent in a month (30 days) to run the 3kW rated A.C for 10 hours a day at 1kWH.

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The change in entropy of the gas is -8.14 J/K.

In thermodynamics, entropy is a measure of the system's thermal disorder or randomness, and it is related to the number of ways that a system can be arranged in a given state.

The change in entropy, ΔS, can be calculated using the equation

ΔS=qrev/T, where qrev is the amount of heat transferred reversibly and T is the temperature.

For an ideal gas, the change in entropy during a reversible isothermal process can be calculated using the following equation:

ΔS=nRln(Vf/Vi), where n is the number of moles of the gas, R is the gas constant, Vi is the initial volume of the gas, and Vf is the final volume of the gas.

To solve this problem, we can use the following steps:

Step 1: Calculate the final volume of the gas using the ideal gas law. The ideal gas law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles of the gas, R is the gas constant, and T is the temperature. Since the process is isothermal, the temperature remains constant at 20.00C, or 293.15 K.

Therefore, we can write PV = nRT as P1V1 = P2V2, where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume. Since the gas is compressed, the final pressure is greater than the initial pressure. We can assume that the pressure is constant throughout the compression, so we can write P = F/A, where F is the force and A is the area. Since the work done on the gas is 1850 J, we can write W = Fd, where d is the distance that the force acts over. Since the force is constant, we can write F = W/d.

Therefore, we can write P = W/(Ad). Since the area and distance are not given, we cannot calculate the pressure directly. However, we can write P1V1 = P2V2 as V2/V1 = P1/P2. Therefore, we can write V2 = V1(P1/P2). Since we cannot calculate P2 directly, we need to find a way to relate it to the work done on the gas.

Step 2: Relate the work done on the gas to the change in internal energy of the gas. The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In this case, since the process is reversible and isothermal, the heat added to the system is equal to the work done on the system.

Therefore, we can write ΔU = q + W = W + 1850 J, where ΔU is the change in internal energy, q is the heat added to the system, and W is the work done by the system. Since the process is isothermal, the change in internal energy is zero, so we can write 0 = W + 1850 J, or W = -1850 J.

Therefore, the work done on the gas is negative, which means that the gas is doing work on its surroundings, and the change in internal energy is zero.

Step 3: Calculate the final volume of the gas. Since the change in internal energy is zero, we can write PV = nRT as P1V1 = P2V2, where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume. Since the temperature remains constant, we can write P2 = P1(W/P1V1), or P2 = P1 - (W/V1), where W is the work done on the gas, which is negative, and V1 is the initial volume of the gas.

Therefore, we can write V2 = V1(P1/P2), or V2 = V1/(1 - W/(P1V1)). Substituting the values we know, we get V2 = 4.797 L.

Step 4: Calculate the change in entropy of the gas. We can use the equation ΔS = nRln(Vf/Vi), where n is the number of moles of the gas, R is the gas constant, Vi is the initial volume of the gas, and Vf is the final volume of the gas. Substituting the values we know, we get ΔS = (3 mol)(8.314 J/mol K) ln(4.797 L/5.940 L) = -8.14 J/K.

Therefore, the change in entropy of the gas is -8.14 J/K.

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Answer:

Different ions are deflected by the magnetic field by different amounts. The amount of deflection depends on: the mass of the ion. Lighter ions are deflected more than heavier ones.

The potential energy of the object before it fell is determined as 147 (kg). J.

The potential energy of an object is the energy possessed by an object due to its position above the ground level.

The potential energy of an object depends on the mass and height of the object above the ground.

P.E = mgh

where;

Substitute the given parameters and solve for the potential energy of the object as shown below.

P.E = (m , kg)(15 m)(9.8 m/s²)

P.E = 147 (kg). J

Thus, the potential energy of the object before it fell is determined as 147 (kg). J.

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Answer:

m = 300668.9 kg

L₀ = 12.47 m

Explanation:

The relativistic mass of the space vehicle is given by the following formula:

\(m = \frac{m_{0}}{\sqrt{1-\frac{v^{2} }{c^{2}} } }\)

where,

m = relativistic mass = ?

m₀ = rest mass = 150000 kg

v = relative speed = 2.6 x 10⁸ m/s

c = speed of light = 3 x 10⁸ m/s

Therefore

\(m = \frac{150000kg}{\sqrt{1-\frac{(2.6 x 10^{8}m/s)^{2} }{(3 x 10^{8}m/s)^{2}} } }\)

m = 300668.9 kg

Now, for rest length of vehicle:

L = L₀√(1 - v²/c²)

where,

L = Relative Length of Vehicle = 25 m

L₀ = Rest Length of Vehicle = ?

Therefore,

25 m = L₀√[1 - (2.6 x 10⁸ m/s)²/(3 x 10⁸ m/s)²]

L₀ = (25 m)(0.499)

L₀ = 12.47 m

Answer:

   F = 303,615 10⁻¹¹ N

Explanation:

Let's analyze this problem a little, problem we are asked to find the attractive force of the large sphere and a small sphere, we can find separately the attractive force between the full large sphere and the small sphere, Let's call this force F1 and on the other hand the force is between a sphere representing the gap and the small sphere, let's call this outside F2, the net bone force of the large sphere with gap is the subtraction of these two forces.

             F = F₁ -F₂

Let's start by finding the force of the sphere of complete

           F₁ = G M₁ m / r²

the masses of the sphere is M = 388 kg and the distance is r = d = 14m

           F₁ = 6.67 10⁻¹¹ 380 27/14²

           F₁ = 356.50 10⁻¹¹ N

Now let's calculate the mass of the gap if large sphere

let's use the concept of density

          ρ = m / V

the volume of the gap is

        V = 4/3 π r³

For the radius of the hole they tell us that it touches one side and the center of the sphere, therefore its diameter is the radius of the large sphere

        d = 2.3 m

        r_hole = 1.15 m

        V_hole = 4/3 π r³

        V_hole = 4/3 π 1.15³

        V_hole = 6.37 m³

let's look at the density of the large sphere

         ρ = m / V

          V = 4/3 π r³

           V = 4/3 π 2.3³

           V = 50,965 m³

           ρ = 388 / 50,965

           ρ = 7.613 kg / m³

this is the density of the sphere without the gap

the mass of the gap is

         m_hole = ρ V

         m_hole = 7,613  6.37

         m_hole = 48.49 kg

the distance from the hole to the small building

        r₂ = d - r_hueco

        r₂ = 14 - 1.15

        r₂ = 12.85 m

the strength of this is

        F₂ = 6.67 10⁻¹¹ 48.49 27 / 12.85²

        F₂ = 52,885 10⁻¹¹ N

The strength of the sphere with the gap is

          F = F₁ -F₂

          F = (356.50 - 52,885) 10⁻¹¹

          F = 303,615 10⁻¹¹ N

The surface of the hollow passes through the center of the sphere and “touches” the right side of the sphere, the hollowed-out lead sphere attracts the small sphere with a gravitational force of approximately 2.84 × \(10^{-9\) N.

We may use Newton's law of universal gravitation, which states that the force of gravity between two objects is given by: to calculate the gravitational force the hollowed-out lead spherical exerts on the smaller sphere.

\(F = (G * m_1 * m_2) / r^2\)

V = (4/3) * π * \(R^3\)

The volume of the hollowed-out portion ( \(V_{hollow\)) is then:

\(V_{hollow\) = (1/2) * (4/3) * π * R^3 = (2/3) * π * \(R^3\)

Mass of the remaining lead sphere = M - (2/3) * M = (1/3) * M

F = \((G * m_1 * m_2) / r^2\)

F = (G * [(1/3) * M] * m) / \(d^2\)

Substituting the given values:

F = (6.674 × \(d^2 N m^2/kg^2\) * [(1/3) * 388 kg] * 27 kg) / \((14 m)^2\)

F ≈ 2.84 × \(10^{-9\)N

Thus, the hollowed-out lead sphere attracts the small sphere with a gravitational force of approximately  2.84 × \(10^{-9\)N.

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The car is moving at approximately 12.5 meters per second.

The kinetic energy (KE) of an object can be calculated using the formula:

KE = 1/2 * m * \(v^2\)

where

KE = kinetic energy,

m =Mass of the object, and

v = velocity.

In this case, we are given the mass (m) of the car as 1600 kg and the kinetic energy (KE) as 125,000 J. To find the velocity .

Substituting the  values , we have:

125,000 J = 1/2 * 1600 kg *\(v^2\)

Now, we can solve for v by rearranging the equation:

\(v^2\) = (2 * 125,000 J) / 1600 kg

\(v^2\) = 156.25 \(m^2/s^2\)

Taking the square root, we find:

v = √156.25\(m^2/s^2\)

v ≈ 12.5 m/s

Therefore, the car is moving at approximately 12.5 meters per second.

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The kinetic energy of the flywheel after 1 minute of rotation, given that it has a mass of 50 and radius of 40 cm is 32.4 KJ (Option D)

We'll begin by obtaining the velocity of the flywheel. This is shown below:

v = at

v = 0.6 × 60

v = 36 m/s

Finally, we shall determine the kinetic energy of the flywheel. Details below:

KE = ½mv²

KE = ½ × 50 × 36²

KE = 25 × 1296

KE = 32400 J

Divide by 1000 to express in KJ

KE = 32400 / 1000

KE = 32.4 KJ

Thus, the kinetic energy is 32.4 KJ (Option D)

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