A mass of 0.450 kg rotates at constant speed with a period of 1.45 s at a radius of R = 0.140 m . What is the rotation period for a mass of 0.550 kg at the same radius?

Answers

Answer 1

A mass of 0.450 kg rotates at constant speed with a period of 1.45 s at a radius of R = 0.140 m .The rotation period for a mass of 0.550 kg at the same radius of 0.140 m will also be 1.45 s.

This is because the period of rotation is independent of the mass and depends only on the radius and the centripetal force acting on the object.

Since the radius R is constant for both masses, we can use the equation for the moment of inertia to find the rotation period for the second mass:

I = \(mR^2\\\)

For the first mass: I1 = \((0.450 kg)(0.140 m)^2 = 0.00882 kg·m^2\)

For the second mass: \(I2 = (0.550 kg)(0.140 m)^2 = 0.01232 kg·m^2\)

The rotation period T is given by: T = 2π√(I/m)

where I/m is the angular acceleration.

For the first mass: \(T1 = 2π√(0.00882 kg·m^2/0.450 kg) = 1.34 s\)

For the second mass:\(T2 = 2π √(0.01232 kg·m^2/0.550 kg) = 1.49 s\)

Therefore, the rotation period for a mass of 0.550 kg at the same radius is approximately 1.49 seconds.

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Related Questions

Which of the following statements distinguishes Einstein from Newton and Aristotle?

Einstein had a background that was critical in modern labs where he could probe this mystery further.
Einstein devised theories using logic to extrapolate existing knowledge and predict results.
Einstein’s understanding of curved space-time helped him understand gravity better on Earth.
Einstein’s thought experiments, although superior, were not able to generate useful results quickly.

Answers

Einstein’s understanding of curved space-time helped him understand gravity better on Earth.

Who is Albert Einstein?

The man Albert Einstein was the person who first brought up the idea of relativity. The relativity theory drove home the assertion that there are no absolutes in the universe.

On the other hand, the works of Aristotle and Newton about gravity did not include this element of relativity. Though the work of Newton was highly empirical, the results did not incorporate the ideas of relativity.

Thus, what distinguishes Einstein from Newton and Aristotle is Einstein’s understanding of curved space-time helped him understand gravity better on Earth.

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Calculate the current when a charge of 475C
flows though a cell in 2.5 hours.

Answers

Answer = 0.05A

Using the equation Q=IT and rearranging it to find current to become I=Q/T, where:

Q = charge (Coulombs)
I = current (Amperes)
T = time (seconds)

Known values from the question:

Q = 475

T = 2.5 x 3600 (converting the 2.5 hours into seconds as this is the SI unit for time)

T = 9000

Substitute the known values into the equation:

I = Q/T

I = 475/9000

I = 0.05 (rounded to 1 s.f)

A bowling ball has a mass of 7. 2 kg and a weight of 70. 6 N. It moves down the bowling alley at 1 m/s and strikes a pin with a force of 15. 0 N. What is the force that the pin exerts on the bowling ball? 7. 2 N 15. 0 N 70. 6 N 85. 6 N.

Answers

The correct answer is option B

If a bowling ball has a mass of 7. 2 kg and a weight of 70. 6 N. It moves down the bowling alley at 1 m/s and strikes a pin with a force of 15. 0 N. The force that the pin exerts on the bowling ball is 15.0 N.

This is because the force of the ball hitting the pin (15.0 N) is equal and opposite to the force of the pin hitting the ball. The mass and weight of the bowling ball are not relevant to this calculation.

The force that the pin exerts on the bowling ball can be determined using Newton's third law of motion, which states that every action has an equal and opposite reaction. Since the bowling ball strikes the pin with a force of 15.0 N, the pin exerts an equal and opposite force on the bowling ball.

Therefore, the force that the pin exerts on the bowling ball is also 15.0 N. The mass and weight of the bowling ball (7.2 kg and 70.6 N, respectively) are not directly related to the force exerted by the pin on the ball.

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Which one of these is not a physical charge

A melting and ice cube
B crushing a can
C chopping wood
D metal resting

Answers

Answer:

the answer is D metal resting

Explanation:

I just think that because if you treasure can that's physical charge by dropping where you create a physical charge melting and Ice Cube might be 1 but I feel like metal resting is more likely

find the magnitude of the velocity v⃗ cr of the canoe relative to the river.

Answers

To find the magnitude of the velocity vector v⃗ cr of the canoe relative to the river, we need to consider the velocities of the canoe and the river separately and then subtract the vector of the river's velocity from the vector of the canoe's velocity.

Let's assume v⃗ c represents the velocity of the canoe and v⃗ r represents the velocity of the river.

The magnitude of the velocity vector v⃗ cr can be calculated using the Pythagorean theorem:

|v⃗ cr| = sqrt((v⃗ c)^2 + (v⃗ r)^2)

It's important to note that the magnitude of the velocity vector represents the speed or the magnitude of the velocity without considering its direction.

If you provide the magnitudes of v⃗ c and v⃗ r, I can help you calculate the magnitude of v⃗ cr.

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a horse accelerates a sled to the right. diagram all forces acting on the sled

The picture on the right is an example of what I'm looking for

a horse accelerates a sled to the right. diagram all forces acting on the sledThe picture on the right

Answers

When a horse accelerates a sled to the right. all forces acting on the sled:

Weight of the horse (downwards)Normal force on the horse (upwards)Force generated by the horse ( direction of motion).

What is free body diagram?

A free body diagram is a graphical representation used in physics and engineering to show the applied forces, moments, and consequent reactions on a body in a specific situation.

It shows a body or group of connected bodies along with all the applied forces, times, and reactions that the body experiences. The body could be compact or comprise several interior pieces.

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HELP ME Please!!!!!!
Select ALL that apply

HELP ME Please!!!!!!Select ALL that apply

Answers

Answer:

Increase the number of coils.

Explanation:

By increasing the number of coils we can increase the electromagnet.

Find the Parametric Equations for the Curve. The line passing through (2, 6) and (3, 9).

Answers

Parametric equations are commonly used in kinematics, where the trajectory of an object is represented by equations depending on time as the parameter.

What is Parametrics?

The application, a single parameter is often labeled t; however, parameters can represent other physical quantities (such as geometric variables) or can be selected arbitrarily for convenience.

Parameterizations are non-unique; more than one set of parametric equations can specify the same curve.

The same curve can be specified by more than one set of parametric equations because parameterizations are not unique.

Therefore, Parametric equations are commonly used in kinematics, where the trajectory of an object is represented by equations depending on time as the parameter.

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The frequency of phenotypes for a typical polygenic trait is most often illustrated as.

Answers

Answer:

a bell-shaped curve.

Explanation:

being able to detect the origin of a sound is called

Answers

Detailed explanation of sound localization:

1. Binaural Hearing: One of the primary mechanisms of sound localization is binaural hearing, which involves using both ears to perceive sound. Each ear receives sound waves at slightly different times and with slightly different intensities and frequencies, depending on the sound source's location relative to the listener.

2. Interaural Time Difference (ITD): The time difference between when a sound reaches one ear compared to the other ear provides information about the sound source's horizontal position. If a sound is coming from the right side, it will reach the right ear slightly before reaching the left ear. The brain processes this time delay to determine the direction of the sound source.

3. Interaural Level Difference (ILD): The intensity or volume of a sound can also differ between the ears due to the distance between the sound source and each ear. The brain analyzes these intensity differences to help determine the sound source's lateral position.

4. Head-Related Transfer Function (HRTF): The unique shape of our ears and the structure of our head create subtle modifications to the sound waves as they enter our ears. These modifications, known as the head-related transfer function, provide additional cues for sound localization. They help us perceive the elevation or vertical position of a sound source.

5. Auditory Processing: The brain integrates the inputs from both ears, along with other contextual cues, to accurately determine the direction and location of a sound source. It combines the information from ITD, ILD, and HRTF to create a spatial map of sound in our auditory perception.

Overall, sound localization is a remarkable ability that allows us to identify the direction and location of sounds in our environment. It relies on the complex interplay between our ears, brain processing, and contextual cues to provide us with a rich auditory experience and helps us navigate our surroundings and respond to auditory stimuli effectively.

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inner parts of the flattening cloud begin to fall freely inward, raining down on growing object at the center. gravitational potential energy of collapsing gas cloud is converted into heat and radiative energy.

Answers

These 2 statements are 2 steps of solar planet formation 1st statement is 3rd step 2nd statement is 4th step.

In the cosmos, there are a lot of planetary systems with solar planets around a host star, similar to our own. Because we refer to things that are connected to our star as "solar," our planetary system is sometimes known as "the solar system," after the Latin word for the Sun, "solis." The Sun, our star, and everything gravitationally connected to it, including the moons, planets, and dwarf planets like Pluto, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune, make up our solar system. Thousands of planetary systems orbiting other stars in the Milky Way have been found, in addition to our solar system. The Milky Way galaxy's outer spiral arm is where our solar system is situated. In our solar system, there is only the Sun.

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Solve Using the formula Formula v = d/t

What is the average speed of a car that travels 870 km in 14.5 h?

Answers

Solution:Distance = 870 KmTime = 14.5 hWe know, average speed = Total Distance ÷ Total TimeTherefore, the average speed of the car

= 870 Km ÷ 14.5 h

= 60 Km / h

So, the average speed of the car is 60 Km/h.Answer:

The average speed of a car that travels 870 Km in 14.5 h is 60 Km/h.

Hope it helps

ray4918 here to help..

HELP!! I'll give brainliest!
Which type of heat transfer causes a person sitting by the fire to feel warm?

absorption
conduction
convection
radiation

Answers

Radiation: Heat moves through space as energy waves. It is the type of heat one feels when sitting in front of a fireplace or around a campfire.

Answer:

Radiation

Explanation:

Heat is made by radiation

INSTRUCTIONS:

(1) Avoid using of and/or referring to any online sources!

(2) Write in your own words and sufficiently explain your reasoning based on your understanding of the astronomy concepts and thoughts presented in the chapter/textbook and related astronomy/astrophysics journals!

W.Q. 1: If photons of blue light have more energy than photons of red light, how can a beam of red light carry as much energy as a beam of blue light?

W.Q. 2: Name and explain at least two (2) advantages that reflecting telescopes have over refractors.

W.Q. 3: What is refraction and what causes it? Explain

NEXT PAGE!

W. Q. 4: Consider two optically perfect telescopes having different diameters but the same focal length. Is the image of a star larger or smaller in the focal plane of the larger telescope? Explain your answer!

W. Q. 5: Explain quantum efficiency and how it contributes to the detection of faint astronomical objects.

Answers

1) The number of photons in each beam is what determines the amount of energy each beam carries. A beam of red light contains more photons than a beam of blue light, but each photon in the blue beam carries more energy than each photon in the red beam. Therefore, the two beams can carry the same amount of energy despite having different energies per photon.

2) Reflecting telescopes have two advantages over refractors. They are cheaper to manufacture, and they do not suffer from chromatic aberration.

3) Refraction is the bending of light as it passes from one medium to another. Refraction occurs because light waves travel at different speeds through different materials. The amount of refraction depends on the angle at which the light passes through the medium.

4) The image of a star is larger in the focal plane of the larger telescope. This is because the larger telescope collects more light than the smaller telescope, which means that the image is brighter and has a higher signal-to-noise ratio.

5) Quantum efficiency is a measure of how efficiently a detector converts incoming photons into electrical signals. A higher quantum efficiency means that more of the incoming

photons are detected, which makes it easier to detect faint astronomical objects.

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1) The number of photons in each beam is what determines the amount of energy each beam carries.

2) Reflecting telescopes have two advantages over refractors.

3) Refraction is the bending of light as it passes from one medium to another.

4) The image of a star is larger in the focal plane of the larger telescope.

5) Quantum efficiency is a measure of how efficiently a detector converts incoming photons into electrical signals.

1) The number of photons in each beam is what determines the amount of energy each beam carries. A beam of red light contains more photons than a beam of blue light, but each photon in the blue beam carries more energy than each photon in the red beam. Therefore, the two beams can carry the same amount of energy despite having different energies per photon.

2) Reflecting telescopes have two advantages over refractors. They are cheaper to manufacture, and they do not suffer from chromatic aberration.

3) Refraction is the bending of light as it passes from one medium to another. Refraction occurs because light waves travel at different speeds through different materials. The amount of refraction depends on the angle at which the light passes through the medium.

4) The image of a star is larger in the focal plane of the larger telescope. This is because the larger telescope collects more light than the smaller telescope, which means that the image is brighter and has a higher signal-to-noise ratio.

5) Quantum efficiency is a measure of how efficiently a detector converts incoming photons into electrical signals. A higher quantum efficiency means that more of the incoming

photons are detected, which makes it easier to detect faint astronomical objects.

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what is the link between the observation that the universe is expanding and the big bang theory? choose one: a. all objects in the universe are moving away from earth, which means the big bang began with our solar system. b. the big bang theory refers to nuclear fission, where particles explode into more particles constantly and sporadically. these particles are emitted outward, expanding the universe. we call these explosions the big bang. c. the discovery of expansion provided the proof that the universe began as a large explosion known as the big bang. d. the discovery that all objects in the universe are spreading apart led to the idea that everything must have been together at some point and then began to expand. this idea is known as the big bang theory.

Answers

b. the big bang theory refers to nuclear fission, where particles explode into more particles constantly and sporadically. these particles are emitted outward, expanding the universe. we call these explosions the big bang is the link between the observation that the universe is expanding and the big bang theory

What is the idea that explains the universe's expansion?

The prevalent view, known as the isotropy hypothesis, contends that the cosmos is expanding not just in all directions, but also at the same rate.

The Doppler red-shift of light from distant stars and galaxies indicates that the universe is expanding (moving away from a central point). This enables Big Bang Theory, since following a "bang," all matter goes away from the place of origin.

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A microwave oven operates at 2.10GHz. What is the wavelength of the radiation produced by this appliance? Express the wavelength numerically in nanometers.

Answers

The wavelength of the radiation produced by a microwave oven operating at 2.10 GHz is approximately 14.3 centimeters, which is equivalent to 143 millimeters.

The wavelength of an electromagnetic wave can be calculated using the formula: wavelength = speed of light/frequency. In this case, the frequency is given as 2.10 GHz, which can be converted to hertz by multiplying by 10^9 (since 1 gigahertz = 10^9 hertz). So, the frequency becomes 2.10 × 10^9 Hz. The speed of light in a vacuum is approximately 3.00 × 10^8 meters per second. Using the formula mentioned earlier, we can calculate the wavelength as follows: wavelength = (3.00 × 10^8 m/s) / (2.10 × 10^9 Hz) Simplifying the equation, we find: wavelength ≈ 0.143 meters. To convert this to nanometers, we multiply by 10^9 since 1 meter is equal to 10^9 nanometers: wavelength ≈ 0.143 × 10^9 nanometers. These yields: wavelength ≈ 143 nanometers.

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you are standing on a scale in an elevator. suddenly you notice your weight increases. what do you conclude?

Answers

When standing on a scale in an elevator, if one notices an increase in their weight, it means that: the elevator is accelerating upwards.

This is due to the fact that the scale underfoot has to counter the upward acceleration of the elevator, which causes the weight measured on the scale to increase. The scale measures the normal force, which is the weight being exerted on the scale, which is equal to the mass of the individual multiplied by the gravitational acceleration on the surface of the earth.

This can be represented by the formula: W = mg,

where W is the weight, m is the mass of the object and g is the gravitational acceleration.

When the elevator is stationary or moving at a constant velocity, the gravitational acceleration is the same as the normal force and the weight of the individual remains constant. However, when the elevator begins to accelerate upwards, the normal force exerted by the scale must increase to counter the upward acceleration of the elevator.

This causes an increase in weight measured on the scale. Therefore, if one notices an increase in their weight while standing on a scale in an elevator, it indicates that the elevator is accelerating upwards.

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how to find standard deviation of probability distribution on ti-84

Answers

To find the standard deviation of a probability distribution on a TI-84 calculator, you can use the built-in statistical functions. Here are the steps:

Enter your data values into a list on your calculator. For example, if you have a probability distribution with values [x₁, x₂, x₃, ..., xn], you can enter them into a list, let's say L₁.

Press the "STAT" button on your calculator.

Use the right arrow key to select the "CALC" menu.

Choose "1-Var Stats" and press Enter.

Select the list that contains your data (L₁) and press Enter.

The calculator will display various statistics, including the standard deviation (denoted by the symbol σ). Look for the value of "σ" in the output. This represents the standard deviation of the probability distribution.

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what is measurement ?​

Answers

Answer:

Measurement is the assignment of a number to a characteristic of an object or event

Explanation:

Answer:

Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or event

. A car starts to move from rest has an acceleration of 3m/s².what will be the velocity and distance travelled by the car after 50sec.​

Answers

Sure! Here are the steps for calculating the velocity and distance traveled by the car after 50 seconds :

Step 1: Calculate the velocity using the equation:

\(v = u + at\)

where:

- \(v\) is the final velocity

- \(u\) is the initial velocity (0 m/s, as the car starts from rest)

- \(a\) is the acceleration (3 m/s²)

- \(t\) is the time (50 seconds)

Substituting the values into the equation:

\(v = 0 + (3 \, \text{m/s²}) \times (50 \, \text{s})\)

Step 2: Calculate the distance traveled using the equation:

\(s = ut + \frac{1}{2}at^2\)

where:

- \(s\) is the distance traveled

- \(u\) is the initial velocity (0 m/s)

- \(a\) is the acceleration (3 m/s²)

- \(t\) is the time (50 seconds)

Substituting the values into the equation:

\(s = 0 \times (50 \, \text{s}) + \frac{1}{2} \times (3 \, \text{m/s²}) \times (50 \, \text{s})^2\)

Now, let's simplify these equations:

\(v = 3 \times 50\)

\(s = \frac{1}{2} \times 3 \times 50^2\)

Calculating the results:

\(v = 150\) m/s

\(s = 3750\) meters

Therefore, after 50 seconds, the car will have a velocity of 150 m/s and would have traveled a distance of 3750 meters.

Learning Goal: To understand that centripetal acceleration is the acceleration that causes motion in a circle. Acceleration is the time derivative of velocity. Because velocity is a vector, it can change in two ways: the length (magnitude) can change and/or the direction can change. The latter type of change has a special name, the centripetal acceleration. In this problem we consider a mass moving in a circle of radius R with angular velocity ω, r⃗ (t)=R[cos(ωt)i^+sin(ωt)j^] =Rcos(ωt)i^+Rsin(ωt)j^. The main point of the problem is to compute the acceleration using geometric arguments. (Figure 1) Part A What is the velocity of the mass at a time t? You can work this out geometrically with the help of the hints, or by differentiating the expression for r⃗ (t) given in the introduction. (Figure 2) Express this velocity in terms of R, ω, t, and the unit vectors i^ and j^. V⃗ (t) = Part Assume that the mass has been moving along its circular path for some time. You start timing its motion with a stopwatch when it crosses the positive x axis, an instant that corresponds to t=0. [Notice that when t=0, r⃗ (t=0)=Ri^. ] For the remainder of this problem, assume that the time t is measured from the moment you start timing the motion. Then the time − t refers to the moment a time t before you start your stopwatch. Part B What is the velocity of the mass at a time − t? Express this velocity in terms of R, ω, t, and the unit vectors i^ and j^. V⃗ (−t) = SubmitMy AnswersGive Up Part C What is the average acceleration of the mass during the time interval from − t to t? (Figure 3) Express this acceleration in terms of R, ω, t, and the unit vectors i^ and j^.

Answers

Part A :The position of the particle in vector form is given by\(r⃗ (t)=R[cos(ωt)i^+sin(ωt)j^]\)where R is the radius of the circle and ω is the angular velocity.The velocity of the particle is given by taking the derivative of the position vector with respect to time.

Taking derivative with respect to time on both side we get \(v⃗ (t)=d/dt R[cos(ωt)i^+sin(ωt)j^]= R[-in(ωt)ωi^+cos(ωt)ωj^]=ωR[-sin(ωt)i^+cos(ωt)j^]v⃗ (t)=ωR[-sin(ωt)i^+cos(ωt)j^]\)Thus the velocity of the mass at a time t is given by \(v⃗ (t)=ωR[-sin(ωt)i^+cos(ωt)j^]\).

Part B :

We have to find the velocity at time -t. The velocity of the particle is given by taking the derivative of the position vector with respect to time. Thus the velocity of the mass at a time -t is given by \(v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^]\)

\(v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^]\)Part C :

The average acceleration of the particle can be computed using the formulaa = \(Δv/Δt\)The velocity at time t is given by\(v⃗ (t) = ωR[-sin(ωt)i^+cos(ωt)j^]\)

The velocity at time -t is given by \(v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^]\)

\(v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^]\)The change in velocity over the interval from -t to t is therefore

\(Δv = v(t) - v(-t) = 2ωR[sin(ωt)i^ + cos(ωt)j^]\)

The time interval over which this change occurs is\(Δt = 2t\)Thus the average acceleration of the particle is given by a = \(Δv/Δt = ω^2R[sin(ωt)i^ + cos(ωt)j^]/t\)

\(a = Δv/Δt = ω^2R[sin(ωt)i^ + cos(ωt)j^]/t\)

The acceleration can be expressed in terms of R, ω, t, and the unit vectors \(i^ and j^\) as \(a = ω^2R[sin(ωt)i^ + cos(ωt)j^]/t\).

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Rooms are fitted with ventilators to let the air move around. The phenomenon involved is:
a. conduction
b. Convection
c. radiation
d. condensation

Answers

Answer:

B. Convection

Explanation:

Convection is the process in which heat is transferred from one point to another by the actual movement of the material particles from a region of high temperature to a region of low temperature.

Answer is convection

What ocean features occur along areas of volcanic activity in the ocean floor and release high pressure, extremely hot water and chemicals?
Trenches
Mid-ocean ridges
Hydrothermal vents
Continental shelfs

Answers

Answer:

Hydrothermal vents

Explanation:

A hydrothermal vent is found along with areas of volcanic activity in the ocean floor which discharges geothermally heated water. Tectonic plates in such areas move apart at spreading centers and hotspots to form hydrothermal vent.

A hydrothermal vent ejects hot and often toxic, fluids and gases into the surrounding seawater when seawater meets magma.

Hence, the correct answer is "Hydrothermal vents".

Select the arrangement of electromagnetic radiation which starts with the lowest wavelength and increases greatest wavelength. Multiple Choice radio, ultraviolet, infrared, gamma rays gamma rays, ultraviolet, infrared, radio radio, infrared, ultraviolet, gamma rays gamma rays, infrared, radio, ultraviolet gamma rays, radio, ultraviolet, infrared

Answers

Answer:

gamma rays, ultraviolet, infrared, radio

Explanation:

Because on the Electromagnetic spectrum wavelength increases from the gamma end to radio end and frequency decrease in that order

Answer:

radio → infrared → ultraviolet → gamma

Explanation: yeaaahhh its c

ejbsjca bdsj dbcsc j ecsabkfskbj jcbaskjbb

Answers

Sorry but I can't help you cuz the words you use makes no sens if you are going to ask a question pls do and dont joke around about it thank you very much and have a great day! ^^

In a tug-of-war, one team pulls with a force of 150 Newtons.
How much force must the other team pull with if the tug-of-war rope is to be in a state of equilibrium?
A. O Newtons
B. 50 Newtons
C. 75 Newtons
D. 150 Newtons
E.
300 Newtons

Answers

Number D cause that is the same amount as what it is asking if you get what means

Which method determines the relative age of Earth's sedimentary layers based on their organization?

Answers

Answer:

Relative age-dating involves comparing a rock layer or rock structure with other near-by layers or structures. Using the principles of superposition and cross-cutting relationships, and structures such as unconformities, one can determine the order of geological events.

A 40 N block is resting on a rough inclined plane. The static friction between the block and the plane is ____ N.​

Answers

The static friction between the block and the plane is \(40(\mu_s) \ N\).

The given parameters:

Weight of the block, W = 40 N

The normal reaction on the rough surface due to weight of the block is calculated as follows;

\(F_n = 40 \ N\)

The static friction between the block and the plane is calculated as follows;

\(F_s = \mu_s F_n\)

where;

\(\mu_s\) is coefficient of static friction

Thus, the static friction between the block and the plane is \(40(\mu_s) \ N\).

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A balloon drifts 140 m toward the west in 45 s; then the wind suddenly changes and the balloon flies 90 m toward the east in the next 25 s. a. What distance did it travel during the first 45 s? b. What distance did it travel during the next 25 s? c. What total distance did it travel? d. What was its average speed during the first 45 s? e. What was its average speed during the next 25 s? f. What was its average speed for the entire trip? g. What was its displacement during the first 45 s? h. What was its displacement during the next 25 s? i. What was its total displacement?

Answers

Answer:

Explanation:

Given

1 ) 140 m west in 45 s .

2 ) 90 m east in 25 s .

a )

distance travelled in first 45 s = 140 m

b ) distance travelled in next 25 s = 90 m

c ) Total distance travelled = 140 m + 90 m

= 230 m

d ) average speed in first 45 s

= distance in 45 s  45

= 140 / 45 = 3.11 m /s

e ) average speed in next 25 s

distance in 25 s / 25

= 90 / 25 = 3.6 m /s

f ) average in entire trip

=  total distance / total time

= (140 + 90) / ( 25 + 45 )

= 3.28 m /s

g )

displacement in first 45 s = 140 m towards west

h )

displacement in next 25 s = 90 m towards east

i )

total displacement = 140 - 90

= 50 m towards west .

A sphere is filled with air. If the volume of the sphere is increasing at a rate of 569 cubic inches per minute

Answers

Then the rate of change in the sphere's surface area is Square inches per minute: 1138.

Computation of the sphere's surface area

Let V be the volume of the sphere, and A be its surface area.

We know that V = (4/3)πr³ and A = 4πr², where r is the radius of the sphere.

Differentiating V with respect to time, we get:

dV/dt = 4πr² dr/dt

Substituting the given value of dV/dt = 569, we get:

4πr² dr/dt = 569

dr/dt = 569/(4πr²)

Differentiating A with respect to time, we get:

dA/dt = 8πr dr/dt

Substituting the value of dr/dt from the above equation, we get:

dA/dt = 8πr (569/(4πr²))

dA/dt = 1138π square inches per minute

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