A 2 µC charge q1 and a 2 µC charge q2 are 0.3 m from the x-axis. A 4 µC charge q3 is 0.4 m from the y-axis. The distances d13 and d23 are 0.5 m.

The name of my community service is “Feed the Homeless”. The aim of this program is to provide nutritious food and basic necessities to the homeless community in my city. The homeless community faces various challenges and difficulties in their everyday life.

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8 μC written in scientific notation is 8 × 10⁻⁶ C.

Scientific notation is a way to express numbers that are either very large or very small in a concise and standardized format. It consists of two parts: a coefficient and a power of 10.

In the case of 8 μC (8 microcoulombs), the prefix "micro" represents a factor of 10⁻⁶ (1 micro = 10⁻⁶)).

So, we can rewrite 8 μC as 8 × 10⁻⁶ C.

The coefficient, in this case, is 8, which is a single-digit number. The power of 10 is -6, indicating that the decimal point needs to be moved 6 places to the left to obtain the actual value.

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What is 8 μC written in scientific notation?

● 8 x 103 C

• 8 × 10-3 C

8 × 106 C

O 8 × 10-6 C

Answer:

The Correct answer is A

to the right

Answer:

V = 108 km/hr = 108 * 1000  m / 3600 s = 30 m/s

V = speed of train = 30 m/s

(L + 120) m / 7 sec = 30 m/s

When front of train reaches station, back of train must travel L + 120 m to clear the station

S = V / t

(L + 120) / 7 = 30

L = 210 - 120 = 90 m    length of train

The charge 0.00068 C can be written using the prefix µ as 680 μC.

The prefix "µ" (pronounced "micro") represents a scaling factor of 10⁻⁶ . This means that when you write a value with the prefix µ, it is equal to the value multiplied by 10⁻⁶. I

In this case, 680 μC means 680 times 10⁻⁶ coulombs, which is equal to 0.00068 C.

So, the correct way to express the charge 0.00068 C using the prefix µ is 680 μC.

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The resultant displacement of the free end of rod B from its present location when the temperature rises from 15°C to 25°C is -0.0012 m.

When a metal is heated, it tends to expand, and when cooled, it tends to contract.

The coefficient of linear expansion for a metal determines how much the metal changes in length per unit of temperature change.

The amount of change in length (L) per unit length (Lo) per unit of temperature change (∆T) is given by

∆L=αL ∆T, where α is the coefficient of linear expansion.

We'll use the following formula to calculate the resulting displacement of the free end of rod B from its present location when the temperature rises from 15°C to 25°C:

ΔL = LαΔT

where L is the length of the metal rod

α is the coefficient of linear expansion

ΔT is the temperature difference.

Let us first calculate the coefficient of linear expansion for aluminum and steel.

ALUMINUM:α (aluminum) = 24 × 10-6 /°C

STEEL:α (steel) = 12 × 10-6 /°C

Now, let's calculate the change in length of the rods as a result of the temperature change.

ΔLA = αA

LΔT= 24 × 10-6/°C × 1.0 m × (25°C − 15°C)

LΔT= 0.0024 m

ΔLB = αB

LΔT= 12 × 10-6/°C × 1.0 m × (25°C − 15°C)

LΔT= 0.0012 m

Now we may calculate the resultant displacement of the free end of rod B from its present location.

ΔLresultant = ΔLB - ΔLA

ΔLresultant = (0.0012 m) - (0.0024 m)

ΔLresultant = -0.0012 m

Therefore, the resultant displacement of the free end of rod B from its present location when the temperature rises from 15°C to 25°C is -0.0012 m.

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Temperature of iron (Ti) = 415 °C Temperature of water (Tw) = 15.0 °CTemperature at equilibrium (Te) = 100 °CMass of water (m) = 0.625 kgMass of steam evaporated (ms) = 0.144 kgHeat lost by iron (Q1) = Heat gained by water (Q2) + Heat required to evaporate steam .

Heat lost by iron  = (mass of iron (m) x specific heat capacity of iron (c) x change in temperature of iron (ΔT1))Heat gained by water = (mass of water (m) x specific heat capacity of water (c) x change in temperature of water (ΔT2))Heat required to evaporate steam  = (mass of steam (ms) x specific latent heat of vaporization of water (L))Now, using the above formula we can calculate the mass of the iron block as:

Q3m x c x ΔT1 = m x c x ΔT2 + ms x L

Let's calculate the value of Q1 first.

Q1 = m x c x ΔT1m = Q1 / (c x ΔT1)

We know that

c = 450 J/kg °C and ΔT1 = Ti - Te = 415 - 100 = 315°CQ1 = m x c x ΔT1= m x 450 J/kg

°C x 315°C= 141750 m Jm = Q1 / (c x ΔT1)= 141750 / (450 x 315)= 1.002 kg

Now, let's calculate the value of Q3.Q3 = ms x L= 0.144 kg x 2.26 x 10^6 J/kg= 325440 J

Now, let's calculate the value of Q2

.Q2 = m x c x ΔT2m = (Q2 + Q3) / (c x ΔT2)

We know that ΔT2 = Te - Tw = 100 - 15 = 85°CQ2 = m x c x ΔT2= 0.625 kg x 4186 J/kg °C x 85°C= 276981.25 JNow, let's calculate the mass of the iron block.m =

(Q2 + Q3) / (c x ΔT2)= (276981.25 + 325440) / (450 x 85)= 1.003 kg

Hence, the mass of the iron block is 1.003 kg rounded off to 3 significant figures.

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Answer:

3,600 years old

Explanation:

To determine the age of the object based on the remaining radioactive atoms, we can use the concept of half-life.

The half-life is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life of the radioactive element is 1,200 years. This means that after 1,200 years, half of the radioactive atoms will have decayed, and the remaining half will still be radioactive.

Half-life formula

[tex]\boxed{N(t)=N_0\left(\dfrac{1}{2}\right)^{\frac{t}{t_{1/2}}}}[/tex]

where:

The initial quantity is 100% and the quantity remaining is 12.5%. The half-life is 1,200 years. Therefore, the values to substitute into the half-life formula are:

Substitute the values into the half-life formula:

[tex]0.125=1\left(\dfrac{1}{2}\right)^{\dfrac{t}{1200}}[/tex]

Solve for t:

[tex]\begin{aligned}0.125&=\left(\dfrac{1}{2}\right)^{\dfrac{t}{1200}}\\\\\dfrac{1}{8}&=\left(\dfrac{1}{2}\right)^{\dfrac{t}{1200}}\\\\\ln \left(\dfrac{1}{8}\right)&=\ln \left(\dfrac{1}{2}\right)^{\dfrac{t}{1200}}\\\\\ln \left(\dfrac{1}{8}\right)&=\dfrac{t}{1200}\ln \left(\dfrac{1}{2}\right)\\\\1200\ln \left(\dfrac{1}{8}\right)&=t\ln \left(\dfrac{1}{2}\right)\\\\1200(\ln1-\ln8)&=t(\ln1-\ln 2)\\\\1200(-\ln8)&=t(-\ln 2)\\\\1200(-\ln2^3)&=t(-\ln 2)\\\\1200(-3\ln2)&=t(-\ln 2)\\\\-3600\ln2&=-t\ln 2\\\\\end{aligned}[/tex]

                  [tex]\begin{aligned}t\ln 2&=3600\ln2\\\\t&=3600\end{aligned}[/tex]

Therefore, if only 12.5% of the radioactive atoms remain, the object is approximately 3,600 years old.

The distance traveled by the girl to complete half way around the circular track is equal to half of the circumference of the circle, which is:

d = (1/2) * 2πr = πr = π(10.0 m) = 31.4 m

The time taken by the girl to travel this distance is given as 15.0 s. Therefore, her average speed is:

average speed = distance / time = 31.4 m / 15.0 s ≈ 2.09 m/s

To calculate the magnitude of the girl's average velocity, we need to determine her displacement and divide it by the time taken. The girl's displacement is the straight-line distance from her starting point to her ending point, which is a distance of 2r = 20.0 m because she has traveled exactly half way around the circular track. Therefore, the magnitude of her average velocity is:

magnitude of average velocity = displacement / time = 20.0 m / 15.0 s ≈ 1.33 m/s

Note that the magnitude of the girl's average velocity is less than her average speed because her average velocity takes into account the direction of her motion, while her average speed does not.

The correct expression for the natural frequency of oscillation of a stick of length (l) oscillating around one end is given by :[tex]\sqrt{g/l}[/tex].

The correct answer is option A.

To derive this expression, let's go through the calculation:

The restoring force acting on the stick is provided by the gravitational force, which is proportional to the displacement of the stick. The gravitational force is given by F = mg, where m is the mass of the stick and g is the acceleration due to gravity.

For a stick oscillating around one end, the effective length of the pendulum is l. The torque acting on the stick is given by τ = Iα, where I is the moment of inertia of the stick about the pivot point and α is the angular acceleration.

For small angular displacements, we can use the approximation α = θ'', where θ'' is the second derivative of the angular displacement with respect to time.

Using the torque equation, we have Iθ'' = mglθ, where θ represents the angular displacement.

Dividing both sides of the equation by θ and rearranging, we get θ'' + (g/l)θ = 0, which is a differential equation for simple harmonic motion.

The solution to this differential equation is of the form θ = A sin(ωt), where A is the amplitude and ω is the angular frequency.

Comparing this solution to the differential equation, we find that ω² = g/l.

The natural frequency of oscillation is given by f = ω/(2π), so substituting the value of ω, we have f = [tex]\sqrt{(g/l)/(2}[/tex]π).

Therefore, the correct expression for the natural frequency of oscillation is [tex]\sqrt{g/l}[/tex] which corresponds to option A.

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Answer:

Explanation:

The correct shutter speed for f/2.8 is 1/15 sec.

The aperture and shutter speed are two of the three factors that determine the exposure of a photograph. The third factor is the ISO sensitivity of the camera.

The aperture is a hole in the lens that allows light to pass through. The smaller the aperture, the less light that passes through. The shutter speed is the amount of time that the shutter is open, allowing light to hit the sensor.

In this case, we are changing the aperture from f/5.6 to f/2.8. This means that we are letting in twice as much light. To compensate for this, we need to halve the shutter speed.

So, the correct shutter speed for f/2.8 is 1/60 * 1/2 = 1/15 sec.

Here is the formula for calculating the correct shutter speed when changing the aperture:

shutter_speed_2 = shutter_speed_1 * aperture_1 / aperture_2

The moment of inertia of the object about the dash line is 2.1316 kg·[tex]m^2[/tex].

To calculate the moment of inertia of an object about a given axis, we need to know the mass of the object and its distribution of mass around the axis.

Given that the mass of the object is 4 kg and the distance from the axis of rotation (dash line) is 73 cm, we can calculate the moment of inertia using the formula:

Moment of inertia (I) = m * [tex]r^2[/tex]

Where m is the mass of the object and r is the perpendicular distance from the axis of rotation to the mass element.

Converting the distance from centimeters to meters:

r = 73 cm = 0.73 m

Substituting the values into the formula:

I = 4 kg * (0.73 [tex]m^2[/tex]

Calculating:

I = 4 kg * 0.5329[tex]m^2[/tex]

Simplifying:

I = 2.1316 kg·[tex]m^2[/tex]

Therefore, the moment of inertia of the object about the dash line is approximately 2.1316 kg·.[tex]m^2[/tex]

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Answer:

It is incredibly difficult to sustain fusion reaction.

Explanation:

Answer:

electric charges

dielectric substance

metal plates

Charge

electric charges

Charge

other charge

potential difference between them

Farad or F

Answer:

Capacitors are devices that store (electrical)energy. They usually consist of an insulating material inserted between two conductive plates. When a voltage is applied across the plates, electric charge builds up on the plates. The ratio of charge on one plate to the voltage across the plates is called the capacitance. The SI unit for capacitance is the farad (F).

Additional Information:

A capacitor is an electronic device that stores electrical energy. It consists of two conductive plates separated by an insulating material called a dielectric. When a voltage is applied across the plates, one plate accumulates a positive charge while the other plate accumulates an equal and opposite negative charge. This charge separation creates an electric field between the plates.

The capacitance of a capacitor, denoted by the symbol "C," determines its ability to store charge. It is defined as the ratio of the magnitude of charge stored on one plate (Q) to the potential difference (V) across the plates: C = Q/V. The unit of capacitance is the farad, F.

Capacitors store electrical energy in the electric field created between the plates. The amount of energy stored in a capacitor is given by the equations:

[tex]U=\dfrac{1}{2}QV= \dfrac{1}{2}CV^2=\dfrac{Q^2}{2C}[/tex]

Where:

Answer:

[tex]s_{avg}= \dfrac{2 \pi}{3} \approx 2.09 \ m/s[/tex]

[tex]v_{avg}=\frac{4}{3} \approx 1.33 \ m/s[/tex]

Explanation:

To find the girl's average speed and average velocity, we can use the following formulas:

[tex]s_{avg}= \dfrac{\pi r}{t} \\\\ \\v_{avg}= \dfrac{2r}{t}\\\\\\ \hrule[/tex]

(A) - Finding the average speed.

[tex]\Longrightarrow s_{avg}= \dfrac{\pi(10.0)}{15.0}\\\\\\\therefore \boxed{s_{avg}= \dfrac{2 \pi}{3} \approx 2.09 \ m/s}[/tex]

(B) - Finding the average velocity.

[tex]\Longrightarrow v_{avg}= \dfrac{2(10.0)}{15.0}\\\\\\\therefore \boxed{v_{avg}=\frac{4}{3} \approx 1.33 \ m/s }[/tex]

Thus, the problem is solved.

Answer:

Explanation:

The three physical characteristics of a sound stimulus and their corresponding perceptual characteristics are as follows:

1. Frequency: Frequency refers to the number of vibrations or cycles per second that occur in a sound wave. It is measured in hertz (Hz). Frequency gives rise to the perception of pitch. Pitch is the subjective perception of how high or low a sound is. Higher frequencies are perceived as higher pitches, while lower frequencies are perceived as lower pitches. For example, a sound wave with a higher frequency would be perceived as a higher-pitched sound, like a whistle, whereas a sound wave with a lower frequency would be perceived as a lower-pitched sound, like a deep bass note.

2. Amplitude: Amplitude is the magnitude or intensity of a sound wave and is usually measured in decibels (dB). It represents the amount of energy carried by the sound wave. Amplitude gives rise to the perception of loudness. Loudness is the subjective perception of the strength or intensity of a sound. Greater amplitudes are perceived as louder sounds, while smaller amplitudes are perceived as quieter sounds. For instance, a sound wave with a higher amplitude would be perceived as a louder sound, like a thunderclap, whereas a sound wave with a lower amplitude would be perceived as a softer sound, like a whisper.

3. Timbre: Timbre refers to the quality or tone color of a sound. It is the characteristic that allows us to distinguish between sounds with the same pitch and loudness. Timbre is influenced by the complex combination of different frequencies, amplitudes, and waveforms present in a sound wave. It gives rise to the perception of the unique "sound signature" of an instrument or voice. For example, a guitar and a piano playing the same note at the same loudness would still sound different due to their distinct timbres. Timbre enables us to identify and differentiate between various musical instruments and voices.

In summary, frequency determines the pitch perception of a sound, amplitude influences the perception of loudness, and timbre defines the unique quality or tone color of a sound. These physical characteristics directly relate to the corresponding perceptual characteristics, providing us with a rich and diverse soundscape in our auditory experience.

The independent variable in this experiment is the act of turning the bulb on and off, while the dependent variable is the behavior of the earthworm in response to changes in light. The scientist can analyze the data collected to determine the impact of light on the earthworm's behavior.

In the experiment where a scientist is turning a bulb on and off to check the behavior of an earthworm, the independent variable is the manipulation performed by the scientist, which is the act of turning the bulb on and off.

The independent variable is the variable that the scientist deliberately changes or controls in order to observe its effect on the dependent variable. In this case, the scientist is interested in investigating how the earthworm responds to changes in light. By turning the bulb on and off, the scientist is manipulating the presence or absence of light in the environment of the earthworm.

The behavior of the earthworm, which is the dependent variable, will be observed and measured in response to the changes in light. The scientist may record various behaviors such as movement, burrowing, or changes in activity level exhibited by the earthworm when the light is turned on and off.

By systematically controlling the independent variable (turning the bulb on and off) and observing the dependent variable (behavior of the earthworm), the scientist can analyze the relationship between light exposure and the earthworm's behavior. This allows for drawing conclusions about how the earthworm responds to light stimuli.

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The initial height H of the boy can be determined by adding the height of the slide h and the horizontal distance d the boy travels after leaving the track: H = h + d.

To determine the initial height H of the boy in terms of h and d, we can use the principle of conservation of energy. The total mechanical energy of the system remains constant throughout the motion.

At the top of the slide, the boy has gravitational potential energy given by mgh, where m is the mass of the boy, g is the acceleration due to gravity, and h is the height of the slide above the ground.

As the boy slides down the slide, there is no friction or other dissipative forces, so there is no change in mechanical energy. At the bottom of the track, the gravitational potential energy is converted entirely into kinetic energy.

Therefore, we can equate the initial potential energy to the final kinetic energy:

mgh = 1/2 m[tex]v^{2}[/tex],

where v is the horizontal velocity of the boy when he leaves the track.

Since the boy leaves the track horizontally, the vertical component of his velocity is zero. Therefore, we can use the relationship between horizontal distance d and horizontal velocity v:

d = vt.

Solving these equations, we can express the initial height H in terms of h and d:

H = h + d.

So the initial height H of the boy can be determined by adding the height of the slide h and the horizontal distance d the boy travels after leaving the track.G

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A form of energy released from the nucleus, the core of atoms, made up of protons and neutrons.

Explanation:

You are given   J    and   kg   and want    J/kg

so

8.2 x 10^7 J / 38.6 kg =~ 2.12 x10^6  J/kg

Answer:

The answer is approximately 350.4J to 1d.p

Explanation:

W=F×S

F=F cosø

W=Fcosø×S

W=71.5cos27×5.5

W=63.7×5.5

W=350.35J

W≈350.4J

Explanation:

You have to 'balance' the vertical and horizontal forces with an equal but opposite third force .....

vertical   :     100 sin60 + 200 sin (120)  = 259.8 N

Horizontal  100 cos 60 + 200 cos 120 = -50 N

Magnitude = sqrt ( 259.8^2 + (-50)^2) = 264.57 N

The vertical and horizontal components will be opposite the ones found above :

       angle = arc tan  -259.8 / (50) = 280.9 degrees

Answer:

50 Hz

Explanation:

Frequency is oscillations per second.

50/1 = 50

Answer: So, just as the blood enters the blocked portion of the vessel, its speed is approximately 7.31 times its initial speed v0

Explanation: The flow rate of a fluid is given by the equation Q = A * v, where Q is the flow rate, A is the cross-sectional area of the vessel, and v is the speed of the fluid. Since the blood is incompressible, its flow rate must remain constant. Therefore, if the cross-sectional area of the vessel decreases, the speed of the blood must increase to maintain a constant flow rate.

The cross-sectional area of a cylinder is given by the equation A = πr^2, where r is the radius of the cylinder. If the diameter of the vessel decreases by 63.0%, then its radius decreases by 63.0% as well. Therefore, the new radius of the vessel is r_new = r_old * (1 - 0.63) = 0.37 * r_old.

Substituting this into the equation for the cross-sectional area, we get:

A_new = π * (0.37 * r_old)^2

A_new = (0.37^2) * π * r_old^2

A_new = 0.1369 * A_old

Since the flow rate must remain constant, we have:

Q = A_old * v0 = A_new * v_new

Substituting in the values for A_old and A_new, we get:

v_new = (A_old / A_new) * v0

v_new = (1 / 0.1369) * v0

v_new ≈ 7.31 * v0

So, just as the blood enters the blocked portion of the vessel, its speed is approximately 7.31 times its initial speed v0.

The volumetric flow rate of the oil is 2.37 m³/s.

In order to calculate the volumetric flow rate of the oil, we need to use the formula for volumetric flow rate.Q = vA Where,Q = volumetric flow rate v = velocity of fluid A = cross-sectional area of the pipe

First, we need to calculate the cross-sectional area of the pipe. Since the thickness of the pipe is not given, we will use an approximate value for the inner diameter of the pipe, which is equal to the nominal diameter minus twice the wall thickness.

This is given by:Di = N.D. - 2e

For Schedule 80 pipes, the wall thickness is given by:

e = 0.0153D - 0.0153

For N.D. = 450 mm,

e = 0.0153(450) - 0.0153= 6.885 mm

= 0.006885 m.

Hence,Di = 0.45 - 2(0.006885)= 0.43623 m

Now, we can calculate the cross-sectional area of the pipe:

A = π/4 D²

= π/4 (0.43623)²

= 0.15015 m²

Finally, we can calculate the volumetric flow rate using the formula:

Q = vA

Q= 15.8 × 0.15015

Q= 2.37207 m³/s≈ 2.37 m³/s (to two decimal places).

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Mass over density is a mathematical expression that represents the ratio of mass to density. It is calculated by dividing the mass of an object or substance by its density. Mathematically, it can be represented as:

The equation relating mass (m) and density (ρ) is given by:

m = ρ * V

where:

m is the mass of the object or substance,

ρ is the density of the object or substance, and

V is the volume of the object or substance.

This equation states that the mass of an object is equal to the product of its density and volume. It shows that mass is directly proportional to density and volume.

A particle in a 3 dimensional space (x, y, z axes) that cannot move in the y direction has 2 degrees of freedom. It can still move freely along the x and z axes.

Degrees of freedom refer to the number of independent displacements (or motions) that a particle can make. Since this particle cannot move along the y axis, it only has 2 independent motions it can make:

Displacement along the x axis

Displacement along the z axis

So it has 2 degrees of freedom, one for each independent motion (displacement along x and z).

In general, for an n-dimensional space where m dimensions have constrained or fixed movement, the degrees of freedom will be:

Degrees of freedom = n - m

In this case:

n = 3 (since it's a 3D space - x, y and z axes)

m = 1 (y dimension has constrained movement)

Therefore:

Degrees of freedom = 3 - 1 = 2

So the final answer is that the particle has 2 degrees of freedom.

Given:A 1-ton object at 1AU from the sun will experience a gravitational force of 6N. Newton’s Law of Universal Gravitation states that the force of gravitational attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Mathematically,F ∝ (M1M2/d²)Where,F = Force of gravitational attraction between two objectsM1 = Mass of object 1M2 = Mass of object 2d = Distance between the centers of mass of two objects.Given,Mass of the first object, M1 = 1 tonMass of the second object, M2 = 220 tons Distance of the first object from the sun, d1 = 1 AU

Distance of the second object from the sun, d2 = 2 AUForce experienced by the first object, F1 = 6 NWe can use the formula to calculate the force experienced by the second object.

F1/F2 = (M1/M2) * (d2/d1)²F2 = F1 * (M2/M1) * (d1/d2)²

Putting the values,M1 = 1 ton

M2 = 220 tons

d1 = 1 AUd2 = 2 AUF1 = 6 N

Thus,F2 = 6 N * (220 tons/1 ton) * (1 AU/2 AU)²

F2 = 6 N * 220 * (1/4)

F2 = 330 NAnswer:

Therefore, the 220-ton object would experience a gravitational force of 330 N at a distance of 2 AU from the sun

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We can calculate the time taken by the compass to hit the ground by using kinematic equations of motion. The motion of the compass is a free-fall motion since it is only under the influence of gravity. When the compass is dropped, it is initially at rest.

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[tex]{\underline{\tt{Answer 1}}}[/tex]

For a fixed pulley alone, the resistance force is equal to the effort force, and the mechanical advantage is 1. When a movable pulley is added to the fixed pulley, the resistance force is reduced by half, the effort force is reduced, but the distance the effort force must be applied over is doubled. The mechanical advantage for a fixed and movable pulley is 2, and the slope of the line for each pulley represents the mechanical advantage.

[tex]{\underline{\tt{Answer 2}}}[/tex]

The work output for the pulleys is equal to the weight of the object multiplied by the distance it was lifted. The work input is equal to the force applied to the rope multiplied by the distance it was pulled. Since the weight of the object and the force applied to the rope are equal, the work output is equal to the work input. However, the pulleys allow the force to be applied over a greater distance, which means that less force is required to lift the object, but the force must be applied over a longer distance.

[tex]{\underline{\tt{Answer 3}}}[/tex]

Pulleys allow the effort force to be reduced while increasing the effort distance, and they allow the resistance force to be reduced while increasing the resistance distance. The advantages of using pulleys include the ability to lift heavy objects with less effort, the ability to change the direction of the force, and the ability to increase the distance that the force can be applied over.

If a third movable pulley were added to the pulley system, the mechanical advantage would be increased. Specifically, the mechanical advantage would be equal to 3, since the resistance force would be divided by three and the effort force would be equal to one-third of the resistance force.

Answer:

The relationship between the resistance force and the effort force for the fixed pulley alone is that they are equal in magnitude.

Explanation:

The relationship between the resistance force and the effort force for the fixed pulley alone is that they are equal in magnitude. In other words, the effort force needed to lift a certain weight is the same as the weight itself. However, when a movable pulley is added to the fixed pulley, the resistance force is halved compared to the effort force. This means that the effort force required to lift a certain weight is only half of the weight itself. The mechanical advantage of a pulley system can be determined by the slope of the line on a force vs. distance graph. The steeper the slope, the greater the mechanical advantage. In this case, the mechanical advantage is higher for the system with the movable pulley compared to the fixed pulley alone, as the slope is steeper for the former.

The work output relates to the work input for the pulleys based on the principle of work conservation. In an ideal scenario with no energy losses, the work input should be equal to the work output. However, due to friction and other factors, there might be some energy losses in the pulley system, resulting in a slightly lower work output compared to the work input.

Pulleys provide a mechanical advantage by reducing the amount of effort force required to lift a heavy object. As more pulleys are added, the mechanical advantage increases further. With respect to changes in effort force and effort distance compared to resistance force and resistance distance, pulleys allow for a trade-off between the two. By applying a smaller effort force over a longer distance, a greater resistance force can be overcome over a shorter distance. This is advantageous as it enables the lifting of heavy loads with less effort. Adding a third movable pulley would further increase the mechanical advantage, making it easier to lift heavier objects with even less effort force.