A(n) 0.95-kg bucket is tied to a rope of negligible mass that is wrapped around a pole mounted horizontally on frictionless bearings. The cylindrical pole has a diameter of 0.340 m and a mass of 2.60 kg. When the bucket is released from rest, how long will it take to fall to the bottom of the 20.0 m well?

Final velocity  [tex]V_{f}[/tex]  of the car will be  2 meters per second

Horizontal force exerted on the car will be = 200 newtons

It is given that mass= 2500 kg

Total energy =5000 j

Car distance = 25 m

So the change in KE [tex]=\dfrac{1}{2} mv_{f} ^{2} -\dfrac{1}{2} mv_{i} ^{2}[/tex]

                                   [tex]=\dfrac{1}{2} mv_{f} ^{2}[/tex]       Since [tex]V_{ i} =0[/tex]

                                   [tex]=\dfrac{1}{2} \times2500\times v_{f} ^{2}[/tex]

                           [tex]5000=\dfrac{1}{2} \times2500\times v_{f} ^{2}[/tex]

                                [tex]V_{f} =2 \dfrac{m}{s}[/tex]

Now the Total change in energy = Work done

                                       [tex]=F\times d[/tex]

                               [tex]5000= F\times 25[/tex]

                                   [tex]F= 200 N[/tex]

Hence

Final velocity  [tex]V_{f}[/tex]  of the car will be  2 meters per second

Horizontal force exerted on the car will be = 200 newtons

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Final answer:

The wavelength of the ultrasound is approximately 0.01482 meters.

Explanation:

The wavelength of ultrasound can be calculated using the formula:

λ = v/f

Where:

λ is the wavelength

v is the speed of sound in the medium

f is the frequency of the ultrasound

In this case, the frequency of the ultrasound is 100 kHz, which can be converted to 100,000 Hz. The speed of sound in water at 20°C is approximately 1482 m/s. Substituting these values into the formula, we get:

λ = 1482 m/s / 100,000 Hz

λ ≈ 0.01482 m

The wavelength of the ultrasound is approximately 0.01482 meters.

Answer:

Maximum height will be 85 meter

Explanation:

given that height of an object is function of time and it is given as

[tex]h(t) = -4.9 t^2 + 20t + 65[/tex]

here we can write it as

[tex]h(t) - 65 = 20 t + \frac{1}{2}(-9.8) t^2[/tex]

now we can compare it with the kinematics equation

[tex]y(t) - y_o = v_i t + \frac{1}{2}at^2[/tex]

now if we compare the two equations then we will have

initial height of object = 65 m

initial velocity of projection = 20 m/s

acceleration = - 9.8 m/s/s

now for the maximum height at which its final speed will become zero is given as

[tex]v_f^2 - v_i^2 = 2a(h - h_o)[/tex]

[tex]0 - 20^2 = 2(-9.8)(h - 65)[/tex]

[tex]-400 = -19.6(h - 65)[/tex]

[tex]h = 85.4 m[/tex]

So maximum height in meter in nearest integer will be 85 m

The angle between two equal forces depends on the resultant force when these two are added. It's 0 degrees if their sum is 2F (same direction), 90 degrees if their sum is sqrt of 2F (perpendicular), and 180 degrees if their sum is zero (opposite directions).

The angle between the two forces with the same magnitude F depends on the resultant force when the two forces are added vectorially.

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The electric field components at points on the x-axis are determined concerning a positive charge Q uniformly distributed along the y-axis and a negative charge -q on the x-axis. The x-component is caused only by -q and the y-component is determined by integrating the electric field due to Q over y=0 to y=a.

The electric field created by a point negative charge -q on the positive x-axis and a positive charge Q spread evenly along the positive y-axis is the subject of the problem set. The x-component and y-component for the E-field need to be determined.

Given the distribution of positive charge Q along the y-axis between y=0 and y=a, the electric field at any point y on the y-axis due to this distribution is E1 = kQ/y²

where 'k' is Coulomb's constant. The electric field E2 on the x-axis for the negative charge -q is equal to -kq/x² at any distance x from it. The total x-component, being only due to the negative charge, is -kq/x². The y-component, due to the positive charge, will be integrated over the limit y=0 to y=a, ∫kQ/y² dy from 0 to a.

This integral gives the total y-component of the electric field.

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The train car's stopping time on a 3.73-degree incline at a speed of 3.25 m/s can be found using kinematic equations in physics after calculating the component of gravitational acceleration along the incline.

To determine how long it takes for the last car of a train to come to rest when traveling up a 3.73 degrees incline at 3.25 m/s, we can use kinematics, a subdivision of mechanics in physics. The force pulling the train car back down the incline is due to gravity, which creates an acceleration opposite to the movement of the car.

First, find the acceleration due to gravity along the incline using the equation a = g * sin(θ), where g is the acceleration due to gravity (9.81 m/s²) and θ is the incline angle. In this case, a = 9.81 m/s² * sin(3.73 degrees).

Then, we can calculate the time it takes for the train car to come to rest using the kinematic equation v = u + at, where v is the final velocity (0 m/s), u is the initial velocity (3.25 m/s), a is the acceleration found previously, and t is the time. Rearrange to find t: t = -u/a.

Completing these calculations gives us the time the train car will take to come to rest momentarily.

Answer:

The time is 4.692 sec.

Explanation:

Given that,

Height [tex]h = 2.80t^3[/tex]

Time t = 1.55 s

We know that,

The rate of change of height is the velocity.

So, the velocity is at t = 1.55 s

[tex]\dfrac{dh}{dt}= v = 3\times2.80\times(1.55)^2[/tex]

[tex]v=20.181\ m/s[/tex]

The velocity is upward with respect to the ground

We need to calculate the distance above the releasing point

Using equation of motion

[tex]v^2=u^2-2gs[/tex]

Put the value into the formula

[tex]s=\dfrac{v^2}{2g}[/tex]

[tex]s=\dfrac{20.181^2}{2\times9.8}[/tex]

[tex]s=20.77\ m[/tex]

The height of the  helicopter releases a small mailbag

[tex]h=2.80\times(1.55)^3[/tex]

[tex]h = 10.43\ m[/tex]

We need to calculate the time

Using equation of motion

[tex]s=ut-\dfrac{1}{2}gt^2+h[/tex]

Put the value into the formula

[tex]0=20.77\times t-\dfrac{1}{2}\times9.8\times t^2+10.43[/tex]

[tex]t=-0.454,4.692[/tex]

On neglecting negative value of time

Hence, The time is 4.692 sec.

By definition, the mechanical advantage is the relationship that exists between the output force or load lifted and the value of the force applied.

Thus, using the definition, we have that the mechanical advantage is given by:

[tex] MA = \frac{100}{100}

MA = 1
[/tex]

Therefore, the mechanical advantage of lifting the box by using a pulley is equal to 1.

Answer:

The mechanical advantage in this situation is:

Equal to 1

The best answer would be, Newton's first law of motion.

Simple machines are not variations of two basic machines; there are actually six types of simple machines: levers, pulleys, screws, inclined planes, wedges, and wheels and axles.

False. Simple machines are not variations of two basic machines. In fact, there are six types of simple machines: levers, pulleys, screws, inclined planes, wedges, and wheels and axles.

Answer:

Gallons per minute, because the independent quantity is volume of water in gallons and dependent quantity is time in minutes.

Explanation:

As we know that gallons is the unit of volume which is used in US to measure volume of gas as well as liquids while time is measured in minutes.

Now we know that if we need to find the volume flow rate then in that case the measurement is done to find the amount of fluid flow per unit of time

so here since volume flow is an independent variable which do not depends on any other parameter while time is a dependent variable here which is given as

[tex]flow \: rate = \frac{dV}{dt}[/tex]

so correct answer will be

Gallons per minute, because the independent quantity is volume of water in gallons and dependent quantity is time in minutes.

The maximum height that the football would reach which is the vertical component of it's velocity at the highest point of it's trajectory is 10m.

Velocity is the directional speed of a moving object as an indication of its rate of change in position. It is observed from a specific frame of reference and measured by a specific time standard.

As, the boy kicks the football at an angle, the ball will follow a parabolic projectile path due to the effect of gravitational force. The velocity of the ball would be equal to zero at its maximum height.

We can derive the following equation from the equations for projectile motion:

Maximum height = velocity × sin Θ

Maximum height = 20 m / s × sin 30°

                             = 20× 1/2

                              =10m

Therefore, the maximum height that the ball would reach would be 10 m.

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The smallest change in energy levels corresponds to the longest wavelength of emitted radiation. Based on the options, the electron moving from 2 to 1 would result in the longest wavelength.

The energy-level change which emits electromagnetic radiation with the longest wavelength would be the smallest change in energy levels. According to the Planck-Einstein relation, the energy of a photon is inversely proportional to the wavelength. Thus, less energy transition implies longer wavelengths. Referring to the available options, an electron moving from 2 to 1 (option d) represents the smallest energy change and therefore emits radiation with the longest wavelength.

The energy-level change that emits electromagnetic radiation with the longest wavelength is when an electron moves from energy level 6 to energy level 1. This is because the energy difference between the highest and lowest energy levels is the greatest, resulting in the emission of photons with longer wavelengths.

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The CORRECT answer is:

Cooler, denser crust sinks into the mantle

I know this because I am an online student, this was a question on my quiz which I got wrong. One I submitted the quiz, it gave me the correct answers to anything I get wrong.

You're welcome.

Final answer:

The equilibrant force is equal in magnitude but opposite in direction to the net force. It is introduced to achieve equilibrium, cancelling out the net force and resulting in no acceleration.

Explanation:

The equilibrant is a force that is equal in magnitude but opposite in direction to the net force acting upon a point or object. When forces are perfectly balanced, the net force is 0 N, and the object remains in a state of equilibrium. In contrast, when there is a resultant force, the object will experience acceleration in the direction of the net force. However, by introducing an equilibrant force, we can return the system to equilibrium, effectively cancelling out this acceleration.

For instance, if two unequal forces act on an object in opposite directions, the net force would be the difference between those two forces, in the direction of the larger force. To achieve equilibrium, an equilibrant force must be introduced with the same magnitude as this net force but directed oppositely. If both forces act in the same direction, then the net force is the sum of the two forces, and an equilibrant, to balance the system, would again need to be of the same size but act in the opposite direction.

Answer:

The juice contains sugars, plant pigments, and other chemicals dissolved in water. This is a solution.  The pieces of orange pulp will rise to the top or settle to the bottom of the juice if it is allowed to sit.  The pieces of pulp mixed with the juice form a suspension.

Explanation:

Final answer:

The orange juice can be considered a combination of a suspension and a solution because it contains both suspended particles of orange pulp and dissolved species, such as juice molecules and ions.

Explanation:

The orange juice can be considered a combination of a suspension and a solution because it contains both suspended particles of orange pulp and dissolved species, such as juice molecules and ions.

The orange pulp in the juice is an example of a suspension, which is a heterogeneous mixture composed of relatively large particles that are visible. The pulp particles are suspended in the juice and can settle out over time.

On the other hand, the juice itself is a solution, which is a homogeneous mixture where no settling occurs. The dissolved juice molecules and ions are evenly distributed in the liquid, giving it a transparent appearance.

Refrigeration compressors turn gases into high-pressure and -temperature gases, are also used to maintain a low boiling point.

In a four stroke engine, the intake stroke pulls in air mixed with fuel as the piston expands, then the compression stroke rapidly compresses this mixture in a nearly adiabatic process with the valves closed, causing the fuel-air mixture's temperature to rise.

The intake and compression strokes are the first two phases of the four-stroke cycle in an internal combustion gasoline engine, often explained in terms of the Otto cycle. During the intake stroke, air is mixed with fuel in the combustion chamber as the piston expands. This causes an increase in the volume of the cylinder and draws in a mixture of gasoline and air.

In the second phase, the compression stroke, the air-fuel mixture is rapidly compressed in a nearly adiabatic process. The piston rises, with the valves closed, causing the temperature of the mixture to rise. Work is done on the gas during this stage as the piston compresses it from the expanded volume to a smaller volume. This prepares the mixture for ignition, which will occur in the succeeding phases of the four-stroke cycle. These processes convert chemical potential energy in the fuel into thermal energy and eventually into work, as part of the cyclical operation of the engine.

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Answer:

[tex]5.52 \cdot 10^2[/tex] Hz

Explanation:

For a wave, the relationship between velocity, wavelength and frequency is given by the wave equation:

[tex]v=f\lambda[/tex]

where

v is the velocity

f is the frequency

[tex]\lambda[/tex] is the wavelength

For the sound wave in this problem, we have:

v = 331 m/s

[tex]\lambda=0.6 m[/tex]

Solving the equation for f, we find the frequency:

[tex]f=\frac{v}{\lambda}=\frac{331}{0.6}=5.52\cdot 10^2 Hz[/tex]