in a charming 19th century hotel, an old style elevator is connected to a counterweight by a cable that passes over a rotating disk 2.50 m in diameter. the elevator is raised and lowered by turning the disk, and the cable does not slip on the rim of the disk but turns with it. at how many rpm must the disk turn to raise the elevator at 35.0 cm/s? to start the elevator moving, it must be accelerated at 18g. what must be the angular acceleration of the disk, in r a d / s 2 ? through what angle (in radians ) has the disk turned when it has raised the elevator 2.55 m between floors?

Answers

Answer 1

a) To raise the elevator at 35.0 cm/s, the disk must turn at approximately 0.044 rpm.

b) To accelerate the elevator at 18g, the angular acceleration of the disk must be approximately 141.4 rad/s^2.

c) The angle through which the disk has turned when it has raised the elevator 2.55 m between floors is approximately 2.04 radians.

To find the rpm of the disk required to raise the elevator at a speed of 35.0 cm/s, we can start by finding the speed at which the cable is moving over the disk. The circumference of the disk is

C = πd = π(2.50 m) = 7.85 m

The distance traveled by the cable in one revolution of the disk is equal to the circumference of the disk. Therefore, the speed of the cable is

v = C × rpm

To find the rpm required to raise the elevator at 35.0 cm/s, we can solve for rpm

35.0 cm/s = 0.35 m/s

0.35 m/s = 7.85 m × rpm

rpm = 0.35 m/s ÷ 7.85 m = 0.044 rpm

Therefore, the disk must turn at approximately 0.044 rpm to raise the elevator at a speed of 35.0 cm/s.

To accelerate the elevator at 18g, we need to find the force required:

F = ma = (18g)(m)

where m is the mass of the elevator. We can rearrange this equation to solve for m

m = F ÷ (18g)

To find the angular acceleration of the disk required to accelerate the elevator, we can use the equation

α = a ÷ r

where α is the angular acceleration, a is the linear acceleration, and r is the radius of the disk. The radius of the disk is half the diameter, or 1.25 m.

α = (18g) ÷ (1.25 m)

α ≈ 141.4 rad/s^2

Therefore, the angular acceleration of the disk must be approximately 141.4 rad/s^2 to accelerate the elevator at 18g.

To find the angle through which the disk has turned when it has raised the elevator 2.55 m between floors, we can use the equation

θ = s ÷ r

where θ is the angle in radians, s is the distance traveled by the cable, and r is the radius of the disk.

The distance traveled by the cable is equal to the difference in height between the floors, or 2.55 m.

θ = 2.55 m ÷ 1.25 m

θ ≈ 2.04 radians

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Related Questions

A wheel and axle is like a screw.

A- True
B- False

Answers

I don’t think this is true

Nuclei decay from a more stable form to a less stable form.Question 9 options:TrueFalse

Answers

ANSWER

False.

EXPLANATION

In radioactive decay (or nuclei decay), an unstable nucleus emits radiation into a nucleus that is table and has less energy and a lower mass.

Therefore, nuclei decay from a less stable form to a more stable form.

The answer is false.

A bowling ball has a mass of 50 kg and is traveling with a velocity of 18 m/s 4 points
down the lane. How much momentum does it have?

Answers

momentum= mass × velocity

p= 50×18

momentum= 900 kg m/s

what is one limitation of using a saltwater aquarium to model the ocean?
A. It can show only a small part of the actual ocean.
B. It can show how different ocean animals interact with each other.
C. It can show how certain plants grow in the ocean.
D. It can show how light affects ocean organisms.

Answers

Final answer:

Using a saltwater aquarium to model the ocean has limitations, such as showing only a small part of the actual ocean and being unable to replicate the vastness and complexity of the ocean ecosystem.

Explanation:

One limitation of using a saltwater aquarium to model the ocean is that it can only show a small part of the actual ocean. Since an aquarium is confined and limited in size, it cannot realistically replicate the vastness and complexity of the ocean ecosystem. For example, it may not have the space to accommodate large marine animals like whales or the turbulent currents that exist in the open ocean. Therefore, it is important to recognize that while a saltwater aquarium can provide some insights into the ocean, it cannot fully capture the dynamic nature and diverse interactions found within the entire ocean ecosystem.

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37. A baseball is pitched at a speed of 40 m/s. How long does it take the ball to travel 27
meters from the pitcher's mound to home plate?

Answers

Answer:

0.675

Explanation:

hope you get it right

Answer:

\(0.675\:\mathrm{s}\)

Explanation:

Displacement can be given as \(\Delta x=v_x\cdot t\)

Substituting given values, we have:

\(27=40t,\\t=\frac{27}{40}=\boxed{0.675\:\mathrm{s}}\)

A 1.5 kg ball is thrown at 10 m/s. What is the ball's momentum?

Answers

Answer:

\(\boxed {\boxed {\sf 15 \ kg*m/s}}\)

Explanation:

Momentum is the product of mass and velocity.

\(p=m*v\)

The mass of the ball is 1.5 kilograms and the velocity is 10 meters per second.

\(m= 1.5 \ kg \\v= 10 \ m/s\)

Substitute the values into the formula.

\(p= 1.5 \ kg* 10 \ m/s\)

Multiply.

\(p=15 \ kg*m/s\)

The momentum of the ball is 15 kilogram meters per second.

Answer:

15 kg m/s

Explanation:

\(p = mv \: = 1.5 \times 10 = 15 \: kgm {s}^{ - 1} \)

If a system is described by the following differential equation. dy(t) +ay(t) = Skx(t) dt The steady-state gain of the step response y(t) is 10 and the rise time is 4, what will be the value of "K" in

Answers

The differential equation is given as;

                                              dy(t) +ay(t) = Skx(t) dt

The step response of a system is defined as the output when the input of a system is a step function.

The value of K is 13.9.

The rise time is the time it takes for the output of a system to rise from 10% to 90% of the final value, in other words, the time it takes for the system to reach from 0.1 to 0.9 of its final value.

The steady-state gain of the step response y(t) is 10, and the rise time is 4.

The differential equation can be converted to the Laplace domain as;

                                            Y(s)[s+a] = Kx(s)/s..............(1)

where Y(s) and x(s) are the Laplace transforms of y(t) and x(t), respectively.

The step response in the Laplace domain is given by;

                                             Y(s) = Kx(s)/[s(s+a)]........................(2)

The rise time for a first-order system is given as;

                                              Tr=1.8/ζωn,

where ζ is the damping ratio, and ωn is the natural frequency of the system.

We know that the steady-state gain of the system is 10; therefore, the magnitude of the output in the Laplace domain at s = 0 is 10.

Thus, we can write;

                            lim_(s→0)⁡Y(s) = lim_(s→0)⁡Kx(s)/[s(s+a)]

                                                  = 10

Therefore;

                            lim_(s→0)⁡Kx(s)/[s(s+a)] = 10

                            lim_(s→0)⁡Kx(s) = lim_(s→0)⁡10s(s+a)

                            lim_(s→0)⁡Kx(s) = 10a

Therefore;

                            K = 10a

                           lim_(s→0)⁡x(s) = Ks/[s(s+a)]

Now substituting,

                               Tr = 4

                                and

                       gain K = 10;

                               a = 1/(ζTr)ωn

                                   = 1/TrK

                                    = 10a lim_(s→0)⁡x(s)

                                    = 10×1/(1.8/ζ4)

                                    = 10ζ/0.72=13.9

Therefore, the value of K is 13.9.

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If the boat goes from 30 km/h to 50 km/h over the next 4 h, what is its acceleration?
Please help me

Answers

Answer:

The acceleration is 5km/h

Explanation:

Given

Initial Velocity (u) = 30km/h

Final Velocity (v) = 50km/h

Time (t) = 4h

Required

Determine the acceleration

This question will be answered using the first equation of motion;

\(v = u + at\)

Substitute values for u, v and t

\(50 = 30 + a * 4\)

\(50 = 30 + 4a\)

Subtract 30 from both sides

\(50 - 30 = 30 - 30+ 4a\)

\(20 = 4a\)

Divide both sides by 4

\(\frac{20}{4} = \frac{4a}{4}\)

\(5 = a\)

\(a = 5\)

Hence;

The acceleration is 5km/h

Why does a small piece of steel rod sinks while a large steel oil tanker floats?

Plss help thanks! pls include EXPLANATION and EXAMPLES that I can proof to people that has no knowledge ​

Answers

Answer:

Too what i know its because of the air

Explanation:

The steel rod is more dense and doesnt have air whil'st the oil tanker is less dense with lots of air

You are on the steep edge of the Grand Canyon, which is miles deep. You fire an arrow at an 89-degree angle towards the canyon (nearly straight up, with no hope of reaching the other side) Describe the arrow's trajectory, in particular noting approximately when the arrow has the most deceleration, the most acceleration, and then why the shift begins to happen. Cover all major points in the trajectory from initial shot to final resting place. When is the arrow moving fastest?

Answers

Answer:

a. The arrow follows a parabolic path

b. As the arrow hits the ground,

Explanation:

a Describe the arrow's trajectory, in particular noting approximately when the arrow has the most deceleration, the most acceleration, and then why the shift begins to happen. Cover all major points in the trajectory from initial shot to final resting place.

This is because, the arrow is a projectile and its path follows a parabolic curve as it goes from initial shot to final resting place.

Its equation of motion is governed by y = ut - 1/2gt² where y = parabolic path, u = initial speed of arrow, t = time and g = acceleration due to gravity.

As the arrow rises, it undergoes the most deceleration. This is because as it rises, its speed decreases until it gets to the peak of its path, where its velocity is momentarily zero.  

Also, as the arrow drops, it undergoes the most acceleration. This is because as it drops from its peak, its speed increases until it gets to the bottom of its path, where its velocity is maximum and given by v = u' - gt where u' = velocity at peak = 0 m/s. So, v = 0 - gt = -gt.

b. When is the arrow moving fastest?

As the arrow hits the ground, its velocity is highest (maximum), so it is fastest at this point.

1. In 1638 the Italian scientist Galileo Galilei
and his assistant conducts an experiment to
measuring the speed of light. They settled down
in the hills, a few kilometers apart
the other. The assistant opened his headlight window
and, when Galileo observed his light, he opened
the window of his lantern.
a) The speed of light is 300,000 km/s.
The distance between the two hills is 3 km.
Choose the time you would mark in this
experiment and circle it.
10 seconds
1 second
1/1000 of a second
1/100,000 of a second
b) Can you tell this time with your eyes?
Explain your answer.
c) How far apart must the two observers be to distinguish the time of 1 second?

1. In 1638 the Italian scientist Galileo Galilei and his assistant conducts an experiment to measuring

Answers



a) The time that would be marked in this experiment would be 1/100,000 of a second.
b) No, it is not possible for the human eye to distinguish such a small amount of time.
c) To distinguish a time of 1 second, the two observers would need to be approximately 300,000 km apart. This is because the speed of light is approximately 300,000 km/s, so it would take light 1 second to travel that distance.

Why are Cepheid variable stars important to astronomers? How is the information they impart any more or less useful than using stellar parallax?

Answers

Cepheid variable stars are important to astronomers because their periods of variability are related to their absolute luminosity.

A Cepheid variable is a particular kind of variable star that pulses radially and undergoes changes in temperature and diameter. With a well defined, constant period and amplitude, its brightness varies. Cepheid variable stars are a unique class of variable star because they are hot, massive, and have a propensity to pulse radially. They also have a tendency to change in diameter and temperature.

An objective way to quantify the radiant power that a light-emitting device emits over time is luminosity. The total quantity of electromagnetic energy released by a star, galaxy, or other celestial object in a given amount of time is measured as luminosity in astronomy.

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The N-type and P-type doping levels of a silicon
P–N junction are ND = NA = 5 × 1016 cm−3.
Calculate the built-in voltage Vbi
(a) at room temperature
(b) at 700◦C (ni = 1.10 × 10^18 cm−3). Does a
negative value for Vbi mean anything?

Answers

The built-in voltage Vbi at 700◦C is -0.28 V, which means that the P-N junction is reverse-biased.

The built-in voltage Vbi of a P-N junction is given by:

\(Vbi = (kT/q) * ln(ND*NA/ni^2)\)

where k is Boltzmann's constant, T is the temperature in Kelvin, q is the electron charge, ND and NA are the N-type and P-type doping levels, and ni is the intrinsic carrier concentration.

(a) At room temperature (T = 300 K) and with ni = \(1.5 * 10^1^0 cm^3\) (for silicon), we have:

\(Vbi = (kT/q) * ln(ND*NA/ni^2)\)
\(= (1,38* 10^-^2^3 * 300 / 1.6 * 10^-^1^9) * ln (5 * 10^1^6 * 5 * 10^1^6 / (1.5 * 10^1^0)^2)\\= 0.71 V\)

Therefore, the built-in voltage Vbi at room temperature is 0.71 V.

(b) At 700◦C (T = 973 K) and with \(ni = 1.10 * 10^1^8 cm^3\), we have:

\(Vbi = (kT/q) * ln(ND*NA/ni^2)\)
\(= (1.38 * 10^-^2^3 * 973 / 1.6 * 10^-^1^9) * ln(5 * 10^1^6 * 5 * 10^1^6 / (1.10 * 10^1^8)^2)\\= -0.28 V\)

Therefore, the built-in voltage Vbi at 700◦C is -0.28 V, which means that the P-N junction is reverse-biased. A negative value for Vbi means that the majority carriers (electrons in the N-type and holes in the P-type) are attracted to the junction and will tend to flow away from it when an external voltage is applied in the forward direction.

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Which of the five criteria that define minerals explains why polymorphs are actually different minerals?​

Answers

It’s
Cender
Quarter
Coin
Feldr
And round

PLS HELP. ITS ONLY MULTIPLE CHOICE QUESTIONS AND ONE RESPONSE. thankyouuu, ill give u brainlest!

PLS HELP. ITS ONLY MULTIPLE CHOICE QUESTIONS AND ONE RESPONSE. thankyouuu, ill give u brainlest!

Answers

Answer:

1. C

2. B

5. C

B. The recoil is a result of conservation of momentum. The force of the ignition of the gunpowder that pushes the bullet forward will be balanced out by also pushing against the gun.

Newton's third law is displayed in each of these questions.

Answer:

1.) c

2.) b

3.) c

Explanation:

I actually had the same test and made a 90%

what does waining mean?

Answers

Answer:

(of the moon) have a progressively smaller part of its visible surface illuminated, so that it appears to decrease in size.

Explanation:

verb (used without object), waned, wan·ing.
to decrease in strength, intensity, etc.: Daylight waned, and night came on. Her enthusiasm for the cause is waning. to decline in power, importance, prosperity, etc.: Colonialism began to wane after World War II.

if the hanging mass were placed at the very end of the meter stick, where would the balance pint be located?

Answers

If the hanging mass were placed at the very end of the meter stick, the balance point would be located at the center of mass, which can be found using the formula and steps provided. The exact location of the balance point depends on the values of the hanging mass and the mass of the meter stick.

If the hanging mass were placed at the very end of the meter stick, the balance point would be located at the center of the mass of the system.

To determine the center of mass, follow these steps:

Step 1: Identify the masses and their locations. In this case, we have the hanging mass (m1) placed at the very end of the meter stick (L) and the mass of the meter stick itself (m2) with a uniform distribution.

Step 2: Calculate the center of mass of the meter stick. Since the meter stick's mass is uniformly distributed, its center of mass is at its midpoint (L/2).

Step 3: Use the formula for the center of mass of a system:
Center of mass = (m1 * x1 + m2 * x2) / (m1 + m2)

Step 4: Plug in the values:
Center of mass = (m1 * L + m2 * (L/2)) / (m1 + m2)

Step 5: Solve the equation to find the balance point.

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What is the effect of the types of interactions between molecules in solution on the viscosity Arrhenius activation energy in binary mixtures?

Answers

The types of interactions between molecules in solution have a significant effect on the viscosity Arrhenius activation energy in binary mixtures. The nature of the interaction can either increase or decrease the energy required for the reaction to occur, which in turn affects the viscosity of the mixture.

The viscosity Arrhenius activation energy in binary mixtures is influenced by the types of interactions that occur between molecules in solution. In a binary mixture, two different types of molecules are mixed, and the nature of the interaction between the two types of molecules determines the viscosity of the mixture.

The viscosity of a liquid is dependent on the intermolecular forces of attraction between molecules. Strong intermolecular forces result in a higher viscosity, while weak forces result in a lower viscosity. This is because stronger forces require more energy to be overcome when the molecules move past one another, resulting in a higher resistance to flow.

The Arrhenius activation energy is a measure of the energy required to initiate a chemical reaction. In binary mixtures, the type of interaction between the two types of molecules determines the activation energy. If the interaction is strong, a higher activation energy is required to initiate the reaction.

On the other hand, if the interaction is weak, a lower activation energy is required.

Thus, the types of interactions between molecules in solution have a significant effect on the viscosity Arrhenius activation energy in binary mixtures. The nature of the interaction can either increase or decrease the energy required for the reaction to occur, which in turn affects the viscosity of the mixture.

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The diagram shows a motion map for a train.

Three individual dots on the right of the diagram show that the train stopped for 3 seconds.

Which statement is supported by the motion map?

The train traveled south and then north.
The train moved at a velocity of 75 mph north.
The train had a greater velocity when it moved away from the origin.
The train stopped for 3 seconds.

Answers

The last option is correct i.e. the train stopped for 3 second.

The train's motion is depicted on the motion map. The train's path is indicated by the horizontal direction, its motion is indicated by the arrows (the length of an arrow indicates how far the train travels in one second), and each black dot represents one second in time. By taking into account this information, we can more accurately describe the train's motion, The train travels for three seconds away from the starting point.For three seconds, the train stopped (this corresponds to the 3 vertical dots)For two seconds, the train goes in the direction of the starting point.

Looking at the many choices, we can see that only the final choice is the train may be the right one.

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Answer:

The last option is correct i.e. the train stopped for 3 second.

Explanation:

Thirteen resistors are connected across points A and B as shown in the figure. If all the resistors are
accurate to 2 significant figures, what is the equivalent resistance between points A and B?

Thirteen resistors are connected across points A and B as shown in the figure. If all the resistors areaccurate

Answers

The equivalent resistance between points A and B in the diagram is 22 Ω

How do I determine the equivalent resistance?

We shall begin by obtaining the equivalent resistance in parallel (i,e the three 6 Ω resistor). Details below:

Resistor 1 (R₁) = 6 ΩResistor 2 (R₂) = 6 ΩResistor 3 (R₃) = 6 ΩEquivalent resistance (Rₜ) = ?

1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃

1/Rₜ = 1/6 + 1/6 + 1/6

1/Rₜ = 3/6

1/Rₜ = 1/2

Rₜ = 2 Ω

Finally, we shall determine the equivalent resistance between A and B (i.e series arrangement). Details below:

Resistor 1 (R₁) = Resistor 2 (R₂) = ... = Resistor (R₁₁) = 2 ΩEquivalent resistance (R) =?

R = R₁ + R₂ + R₃ + R₄ + R₅ + R₆ + R₇ + R₈ + R₉ + R₁₀ + R₁₁

R = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2

R = 22Ω

Thus, we can conclude that the equivalent resistance is 22 Ω

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Which statement about diffraction is correct?
O The amplitudes of two waves combine to appear as one big wave.
O Sound waves bend around the corners of various obstacles.
O The amplitudes of two waves combine to appear as a wave smaller than the individual waves.
O Sound waves can only travel in straight lines.

Answers

Answer:

Sound waves bend around the corners of various obstacles.

Explanation:

I took the test

exerts such a strong gravitational pull that no light escapes

Answers

Black holes are among the most extreme and fascinating objects in the universe, and their study has greatly advanced our understanding of gravity, the properties of matter, and the structure of the universe.

What is Gravitation?

Gravitation is the force of attraction between two masses in the universe. Every object in the universe that has mass exerts a gravitational force on every other object that has mass. The strength of the gravitational force depends on the mass of the objects and the distance between them. The greater the mass of an object, the stronger the gravitational force it exerts, and the closer two objects are, the stronger the gravitational force between them.

An object that exerts such a strong gravitational pull that no light can escape is called a black hole. Black holes are formed by the collapse of massive stars, in which the star's core collapses under the force of gravity to a point of zero volume and infinite density known as a singularity. The gravitational force of a black hole is so strong that even light, which has no mass, cannot escape its pull.

The boundary around a black hole beyond which nothing can escape is called the event horizon. Once something crosses the event horizon, it is inevitably pulled towards the singularity at the center of the black hole. The boundary of the event horizon is also known as the point of no return, beyond which escape is impossible.

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What are all the principles of Cell Theory. Group of answer choices Cell only form from living cells All cells have chromosomes All living things have cells All cells have a nucleus People only have cells Cells are the basic unit of life

Answers

Answer:

Cell theory is the scientific theory that states that all living things are composed of cells and that cells are the basic unit of life. The three principles of cell theory are the cell is the smallest unit of life, all cells come from preexisting cells, and cells are the basic unit of function in living things.

Explanation:

Please mark me brainliest

Which of these is the name for the force that acts against moving objects? A. Inertia b. Friction c. Acceleration d. Brakes

Answers

Answer:

B. Friction

Explanation:

Can someone explain how an avalanche occurs.

Answers

An avalanche occurs when a layer of snow collapses and slides downhill. This Is mainly caused either by a steep slope, snow cover, or a weak layer on the snow cover,and some sort of trigger.

Answer:

Explanation:

Thousands of avalanches occur in Canada each year. They happen in all regions of Canada, but are more frequent in the mountains of British Columbia, Yukon and Alberta. Avalanches can be triggered by wind, rain, warming temperatures, snow and earthquakes. They can also be triggered by skiers, snowmobiles, hikers, vibrations from machinery or construction.            Avalanche facts:

An avalanche occurs when a layer of snow collapses and slides downhill.

Avalanches are caused by four factors: a steep slope, snow cover, a weak layer in the snow cover and a trigger.

Roads and railway tracks may be rerouted to reduce risks.

Safe avalanches may be triggered in dangerous snow packs.

Avalanches can travel up to 90 km/h.

After one hour, only one in three victims buried in an avalanche is found alive. The most common causes of death are suffocation, wounds and hypothermia.

THe emf of a cell, E=3V which is balanced across l =100cm of a potentiometer wire. The cell is shunted by the resistance =30 ohm. The required balance length of shunt is 80cm. What's the value of current flowing through the shunt?

Answers

The value of the current flowing through the shunt is 0.08 A.

What's the value of current flowing through the shunt?

The value of the current flowing through the shunt is calculated by applying the following formula.

I = V/R

where;

V is the voltage through the shuntR is the resistance of the shunt

The voltage flowing through the shunt is calculated as;

V/V'  = L/L'

where;

V is the shunt voltageV' is the potential difference across potentiometerL is length of shuntL' is total length of wire

V/3 = 80/100

V = (3 x 80 ) / 100

V = 2.4 V

The current flowing through the shunt is calculated as;

I = 2.4 / 30

I = 0.08 A

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Your Cardiovascular system is made up of what three body parts?

Question 1 options:

Heart


Lungs


Blood vessels


Blood


Muscles

Answers

Answer:

heart, lungs, blood vessels

Explanation:

HELP PLEASE!!!

a= ?

v=

r=

HELP PLEASE!!!a= ?v=r=

Answers

Answer:

\(a=\frac{v^2}{r}\)

\(v=\sqrt{a*r}\)

\(r=\frac{v^2}{a}\)

Explanation:

This is the formula for centripetal acceleration in terms of the tangential velocity (v) and the radius of the circular motion (r).  The expression for the acceleration is already given, so simply type it as shown:

\(a=\frac{v^2}{r}\)

For the velocity (v) multiply by "r" both sides and then use the square root to solve for v:

\(a*r=v^2\\v=\sqrt{a*r}\)

For the radius multiply both sides by r and then divide both sides by the acceleration (a) in order to isolate r completely:

\(a*r=v^2\\r=\frac{v^2}{a}\)

(PLEASE HELP I'LL MARK BRAINLIEST) Breanna connected a wire coil to a lightbulb to demonstrate that a moving magnet can cause a current to flow in a wire. Then she moved a bar magnet first toward and then a way from the wire coil. However, she could not make the lightbulb up. Which factor could explain this outcome?

A. She moved the bar magnet toward the wire coil too quickly.

B. She did not connect the wire coil in the correct direction.

C. She moved the bar magnet below the wire coil instead of above the coil.

D. She did not move the bar magnet through the wire coil.

Answers

Answer:

D

Explanation:

just did the quiz :)

Two carts are free to slide along the frictionless track shown in figure below. Cart A of mass m1 = 8 kg is released from 12m. A cart B of mass m2 = 4 kg, initially at rest. The two carts combine together and move as one object. Calculate the height reached
by the two carts after collision.

Answers

The height reached by the two carts after collision is determined as 5.34 m.

Initial velocity of Cart A

Apply the principle of conservation of mechanical energy.

K.E = P.E

v = √2gh

v = √(2 x 9.8 x 12)

v = 15.34 m/s

Final velocity of the two carts after the collision

Apply the principle of conservation of linear momentum for inelastic collision.

m₁u₁ + m₂u₂ = v(m₁ + m₂)

8(15.34) + 4(0) = v(8 + 4)

122.72 = 12v

v = 10.23 m/s

Height reached by both carts

Apply the principle of conservation of mechanical energy.

P.E = K.E

mgh = ¹/₂mv²

h = v²/(2g)

h = (10.23²) / (2 x 9.8)

h = 5.34 m

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